Physics and Biology of Brachytherapy - Perez & Brady's Principles and Practice of Radiation Oncology (Perez and Bradys Principles and Practice of Radiation Oncology), 6 Ed.

Perez & Brady's Principles and Practice of Radiation Oncology (Perez and Bradys Principles and Practice of Radiation Oncology), 6 Ed.

Chapter 22. Physics and Biology of Brachytherapy

Jeffrey F. Williamson, X. Allen Li, and David J. Brenner

Brachytherapy (BT) (brachy is Greek for “short distance”) consists of placing sealed radioactive sources very close to or in contact with the target tissue. Because the absorbed dose falls off rapidly with increasing distance from the sources, high doses may be delivered safely to a localized target region over a short time. This chapter reviews the properties and applications of commonly used sealed radionuclides and sources; the basic biologic principles governing clinical response to BT; methods of dose calculation and source-strength specification; and principles of implant design and dose specification for interstitial and intracavitary BT.

BASIC TERMINOLOGY

Implantation techniques may be classified in terms of surgical approach to the target volume (interstitial, intracavitary, transluminal, or mold techniques); the means of controlling the dose delivered (temporary or permanent implants); the source loading technology (preloaded, manually afterloaded, or remotely afterloaded); and the dose rate (low, medium, or high).

Intracavitary insertion consists of positioning applicators (bearing the radioactive sources) into a body cavity in close proximity to the target tissue. Intracavitary BT is used most widely for treatment of localized gynecologic malignancies. All intracavitary implants are temporary implants; they are left in the patient for a specified time to deliver the prescribed dose. With a few exceptions, during temporary implantation, the patient must be confined to a controlled, if not shielded, area in the hospital to manage the radiation safety hazard posed by the large ambient exposure rates around the implant.

Interstitial brachytherapy consists of surgically implanting small radioactive sources directly into the target tissues. A permanent interstitial implant remains in place indefinitely and is not removable; the initial source strength is chosen so that the prescribed dose is fully delivered only when the implanted radioactivity has decayed to a negligible level.

Surface-dose applications (sometimes called plesiocurie therapy or mold therapy) consist of an applicator containing an array of radioactive sources, usually designed to deliver a uniform dose distribution, that is placed on the skin or mucosal surface immediately adjacent to the target tissue.

Transluminal brachytherapy consists of inserting a single line source into a body lumen to treat its surface and adjacent tissues.

Until the early 1960s, radioactive sources (needles for interstitial therapy or preloaded applicators for intracavitary therapy) were implanted directly into the patient. Radiation exposure to the brachytherapist and operating room staff was reduced significantly with the advent of afterloading technology.¹^,² Manual afterloading consists of implanting nonradioactive tubes or intracavitary applicators into the patient. Following transport of the patient to his or her room, sources are manipulated into the applicators by means of forceps and other handheld tools. Exposure to staff responsible for source loading and the care of BT patients can be greatly reduced or eliminated by use of a remote afterloading system, which consists of a pneumatically driven or motor-driven source transport system for robotically transferring radioactive material between a shielded safe and each treatment applicator.

According to Report No. 38 of the International Commission on Radiation Units and Measurements (ICRU),³ low–dose-rate (LDR) implants deliver doses at the rate of 40 to 200 cGy/hour (0.4 to 2 Gy/hour), requiring treatment times of 24 to 144 hours, during which the patient is confined to an inpatient treatment room. At the other extreme, high–dose-rate (HDR) BT uses dose rates in excess of 0.2 Gy/minute (12 Gy/hour). In fact, modern HDR remote afterloaders deliver instantaneous dose rates as high as 0.12 Gy/second (430 Gy/hour) at a distance of 1 cm, resulting in treatment times of a few minutes. Such treatments must be delivered in heavily shielded vaults using remote afterloading devices, but allow fractionated BT to be delivered on an outpatient basis. Medium dose-rate delivery, defined as the 2- to 12-Gy/hour range, rarely is used. Although not recognized by ICRU Report No. 38, the ultra-low–dose-rate range (0.01 to 0.3 Gy/hour) is of great importance; it is the dose-rate domain used in permanent implants with ¹²⁵I and ¹⁰³Pd seeds.

TABLE 22.1 PHYSICAL PROPERTIES AND USES OF BRACHYTHERAPY RADIONUCLIDES

PROPERTIES OF BRACHYTHERAPY SOURCES AND RADIONUCLIDES

The clinical utility of any radionuclide depends on physical properties such as half-life, radiation output per unit activity, specific activity (Ci/g), and photon energy. In addition, the methods of producing the radionuclide and its physical or chemical form strongly influence cost-effectiveness, safety, and toxicity. Detailed properties of BT radionuclides are listed in Table 22.1.

Photon Spectrum and Dosimetric Characteristics of Brachytherapy Sources

The dose delivered with a BT procedure depends on the individual source strengths, source arrangement, and implant duration, tissue composition, as well as the dosimetric characteristics of the implanted sources. These dosimetric characteristics are described by specifying the distribution of dose rates per unit strength about the source, often in terms of an “away-and-along” table⁴ in Cartesian coordinates or in terms of the Task Group 43 protocol⁵ described later in this chapter. The single-source dose distribution is of central importance to treatment planning because commercial computer planning systems estimate dose distribution from the spatial coordinates of the implanted sources using the principle of superposition. The source-superposition algorithm estimates the contribution of each source, given its tip-and-end coordinates and the single-source dose-rate array, to each point of interest. These contribution estimates are summed to estimate the total dose rate at each point. Often, total dose rates are calculated over a two-dimensional (2D) grid of points and are represented as isodose-rate curves.

For conventional BT, for which the therapeutically relevant distance range is 3 to 20 mm, only photons (γ-rays or characteristic x-rays) with energies in excess of 15 keV (kiloelectron volts) contribute to the therapeutic effect. In general, four factors influence the single-source dose distribution for photon-emitting sources: (a) distance (inverse-square law), (b) absorption and scattering in the source core and encapsulation, (c) photon attenuation, and (d) scattering in the surrounding medium (Fig. 22.1). Encapsulation prevents radioactive material from leaking out of the source and absorbs nonpenetrating radiation (β-rays, α-rays, and low-energy photons), which would otherwise give rise to high surface doses while contributing nothing to the therapeutic effect.

FIGURE 22.1. Typical cylindrical brachytherapy source, consisting of an active core (inner cylinder within which radioactivity is uniformly distributed) and the surrounding encapsulation (usually stainless steel or titanium for modern sources). The four principal factors influencing the relative dose distribution include (1) distance, (2) attenuation and scattering in source structure, (3) attenuation by surrounding medium, and (4) accumulation of scattering in surrounding medium.

FIGURE 22.2. An isotropic point source of activity, A. To illustrate the derivation of inverse-square law, the source is surrounded by vacuum and placed at the center of two concentric spherical surfaces of radii r₁ and r₂. By definition, an isotropic point source has no extension and radiates photons with equal likelihood in all directions in straight-line paths.

Each voxel of radioactive core material shown in Figure 22.1 can be assumed to be an isotropic point source (Fig. 22.2). Because of the straight-line emission of photons with equal likelihood in all directions, photon intensity or fluence, (r), at any point is proportional to the inverse square of its distance, r:

assuming that attenuation and scattering can be neglected.

As a result of this purely geometric effect, the absorbed doses D(r₁) and D(r₂) at the two distances r₁ and r₂ (Fig. 22.2) are related by:

This fundamental law applies exactly to each point of the radioactive core of the source shown in Figure 22.1 assuming that there is no attenuation and scattering of photons by the surrounding medium. However, Eq. (2) will not accurately describe the “collective” dose fall-off arising from the combined action of the point sources distributed throughout the core, unless both r₁ and r₂ are large relative to the active source dimensions. Of the four factors influencing the dose distribution (Fig. 22.1), inverse-square law is by far the most important. For a pure isotropic point source, dose will decrease by a factor of 100 between the distances of 0.5 and 5 cm. The influence of the remaining factors over the same distance range rarely exceeds a factor of 2 or 3. Consequently, most of the clinical characteristics of implants (e.g., the heterogeneous dose distribution within the target tissue and rapid fall-off of dose outside the implanted volume) can be accounted for by applying inverse-square law to each pointlike element of radioactivity within the implant. Control of intersource spacing and positioning relative to the target and dose-limiting tissues is the most challenging issue in delivering BT.

Although inverse-square law dominates the dose distribution, the surrounding medium and the source structure do significantly affect the dose distribution (Fig. 22.1). The source core and surrounding capsule reduce dose at the point of interest through absorption and scattering of primary photons. Primary photons contributing dose to points located near the longitudinal source axis (cylindrical axis of the source or axis of rotation) must traverse longer path lengths of capsule and core material and therefore experience more attenuation than photons contributing dose to equidistant points on the transverse source axis (plane perpendicular to the longitudinal source axis that bisects its active core). At a fixed distance from the source center, the dose near the longitudinal axis is usually smaller than on the transverse axis. This phenomenon is known as oblique filtration and is the main cause of dose anisotropy(variation of dose as a function of polar angle at each fixed distance relative to the source center) characteristic of extended BT sources. Because BT sources are cylindrically symmetric, the dose distribution will be equatorially isotropic (constancy of dose as a function of azimuthal angle for each fixed polar angle and distance).

The tissue-equivalent medium surrounding the source affects the dose distribution in two important and competing ways (factors (3) and (4) of Fig. 22.1). At each point of interest, the intervening medium reduces the dose distribution by attenuating primary photons (deflecting them from their straight-line trajectories). At the same time, photons are being emitted in all directions from the source and interacting with the medium by means of Compton scattering and photoelectric absorption. Thus, each volume element of tissue is effectively radiating scattered photons in all directions, many of which contribute to dose at the point of interest. This mechanism, known as scattered-photon buildup, enhances the dose. The overall influence of the surrounding medium is the combined effect of these two competing processes: photon attenuation and scattered-photon buildup. In contrast to external-beam therapy, in which the scattering volume is limited to a narrow cone, scattered photons dominate BT dose distributions at distances >2 cm. Photon scattering is the main source of complexity in BT dose measurement and algorithm development.

Figure 22.3 demonstrates that the relative dose versus distance from the source is nearly independent of its photon energy so long as the average photon energy is >200 keV. In this energy range, dose deviates from inverse-square law by <5% over the 1- to 5-cm distance range. All of the “radium substitute” isotopes, including ¹³⁷Cs, ¹⁹²Ir, and ¹⁹⁸Au, fall into this energy range. This behavior, which greatly simplifies BT dosimetry, is the result of equilibrium between primary photon attenuation and buildup of scattered photons. Only for low-energy sources (e.g., ¹⁰³Pd and ¹²⁵I) does the depth-dose curve significantly deviate from inverse-square law. Because photon absorption rather than Compton scattering dominates energy deposition below 40 keV, scatter buildup is unable to compensate for loss of dose resulting from attenuation.

For radium-substitute radionuclides, Figure 22.4A,B shows that the absolute dose rate (cGy/hour to fat or water tissue per mgRaEq or unit air-kerma strength [S_K]) and the relative dose distribution are nearly independent of both energy and composition of the surrounding medium above 100 keV. Compton scattering, which dominates photon absorption and scattering above 100 keV, depends mainly on electron density (electrons/g) of the medium, which is nearly constant for all biologic materials. Below this energy range, absolute and relative dose distributions vary significantly with energy and composition (atomic number) of the surrounding medium. Implanting an ¹²⁵I seed in fat medium (effective atomic number of Z_eff = 6) will deliver about half the absorbed dose at 1 cm, compared to the expected dose in water (Z_eff= 7.5). This is because energy absorption per unit mass from photo-effect interactions is proportional to the cube of the atomic number (Z_eff³) of the medium. Despite the significant impact of tissue composition heterogeneities on low-energy seed BT dose delivery, current treatment planning and dose measurement practices assume that patients are composed of uniform homogeneous water media.

FIGURE 22.3. A: Variation of dose as a function of distance for point sources of ⁶⁰Co, ²²⁶Ra, ¹³⁷Cs, ¹⁹⁸Au, ¹⁹²Ir, and ¹²⁵I. The results are normalized to 100% at 1-cm distances. The function (1/r²) is plotted for comparison. B: Relative dose (normalized to 1.0 at 1 mm) versus distance for various cylindric sources (0.65 mm diameter and 5 mm long) over the 1- to 5-mm distance range. (From Amols HI, Zaider M, Weinberger J, et al. Dosimetric considerations for catheter-based beta and gamma emitters in the therapy of neointimal hyperplasia in human coronary arteries. Int J Radiat Oncol Biol Phys1996;36:913–921, with permission from Elsevier.)

Figure 22.4B demonstrates that the inverse-square law actually underestimates relative dose at 5 cm by as much as a factor of 2 in the 60- to 100-keV energy range. In this narrow energy range, called the intermediate low-energy range, photoelectric effect is negligible, whereas Compton scattering transfers most of the colliding primary photon energy to the scattered photon rather than to the Compton electron. As a result of this imbalance between energy absorption and photon scattering, buildup of scattered photons overcompensates for loss of dose as a result of primary photon attenuation out to distances of 4 to 6 cm.

Above the 100-keV threshold, the photon-energy spectrum is much less important to optimizing BT dose-rate distributions than in external-beam therapy. Because artificial BT radionuclides in this energy range (⁶⁰Co, ¹³⁷Cs, ¹⁹²Ir, ¹⁹⁸Au) have dose-rate distributions nearly identical to those of ²²⁶Ra in the 1- to 5-cm distance range, they are referred to as radium substitutes.

Figure 22.4C demonstrates that although photon energy is a relatively unimportant determinant of tissue dosimetry, it significantly influences the cost, weight, and thickness of shielding required to protect critical anatomic structures in the patient and personnel involved in patient care. The half-value layer (HVL) in lead varies from 0.5 mm for a 100-keV source to 12 mm for ⁶⁰Co BT sources. Thus, for classical radium-equivalent BT, a radionuclide with a mean energy of about 100 to 200 keV is optimal. The major benefit of ¹²⁵I and ¹⁰³Pd BT sources is the ability to provide complete protection by thin lead foils (0.1 to 0.2 mm), greatly reducing exposure to physicians during the implant procedure and allowing permanent-implant patients to be released from medical confinement without posing a radiation safety hazard to the general public. Recently, interest has been expressed in using radionuclides in the intermediate low-energy range (60 to 120 keV).^6,⁷^–⁸ Tissue dose distributions are still approximately radium equivalent in this energy range, and thin layers of lead provide significant sparing of dose-limiting normal tissues near the implanted volume.

FIGURE 22.4. Variation of dosimetric properties of monoenergetic point sources as a function of photon energy. The location (in terms of average energy) of commonly used radionuclides is indicated by the labeled vertical arrows. A: Absolute dose rate per unit source strength in fat and water media at 1-cm distance. Source strength is specified in terms of output in air. B: Dose at 5 cm as a fraction of dose at 1 cm in fat and water media. The effect of inverse-square law, (1/5)² = 0.04, is shown for comparison as a heavy black line. C: Half-value layer in lead, the thickness (mm) in lead required to reduce primary dose by a factor of 2.

Sources for Low–Dose-Rate Intracavitary Brachytherapy

Since the 1930s, sources for classical LDR intracavitary BT have taken the form of “tubes” having a physical length of 2 to 2.5 cm and an external diameter of about 3 mm. For treatment systems influenced by the Manchester⁹ and M.D. Anderson¹⁰ treatment techniques, active lengths of 1.3 to 1.5 cm are typical. Radionuclides for intracavitary applications should have a half-life long enough to support a 5- to 10-year working life without large variations in prescription dose rate so that the high cost of these reusable sources can be amortized over a large number of patient treatments. The average photon energy should be at least 60 to 100 keV, as the dose fall-off for lower-energy sources (e.g., ¹²⁵I) is too rapid to adequately treat the target volume periphery (2 to 5 cm from the applicator center) without overtreating the mucosal surfaces in contact with the applicator system.

Radium 226 Sources

Radium 226, a naturally occurring radionuclide, was the first radionuclide isolated, intensively investigated, and used in clinical BT. The unit of activity, the curie (Ci), originally was defined as the rate of disintegration within 1 g of ²²⁶Ra. Radium 226 has a complex decay scheme, consisting of a cascade of transformations from one daughter product to another, ending with a stable isotope of lead, Pb. Radium decays to gaseous ²²²Rn with a half-life of 1,626 years. Approximately 75 γ-rays are emitted by radium and its decay products, ranging in energy from about 0.05 to 2.4 MeV, giving an average energy of about 0.8 MeV. The maximum β-ray energy is about 3.26 MeV. The exposure-weighted average energy of ²²⁶Ra is 1.25 MeV when its photon spectrum is filtered by 0.5 mm of platinum. Nearly all ²²⁶Ra BT sources are filtered by at least 0.5 mm Pt, which reduces the surface dose contributed by β particles to a negligible level.

Clinical ²²⁶Ra sources consisted of discrete cells of radium salt (radium sulfate plus filler) placed in needles or tubes with platinum walls of thickness of 0.5 and 1.0 mm, respectively. Intracavitary radium tubes were usually 22 mm long, containing 5 to 30 mg of radium (S_K = 30 to 200 μGy · m² · h⁻¹), with active lengths of 15 mm. For interstitial BT, the full-, half-, and quarter-intensity needles popularized by the Manchester LDR implant system typically contain 0.66 mg, 0.33 mg, or 0.165 mg of radium per centimeter of active length, respectively.

The clinical use of radium has disappeared and is now only of historic interest. The potential for damaged sources to leak radioactive salts or emit radon gas (²²²Rn) is the major reason for its decline, as well as the exposure hazard to interstitial BT practitioners.¹¹ Another factor is the high cost of extracting radium from pitchblende ore in comparison with the cost of radium-substitute sources. Finally, the safe disposal of spent ²²⁶Ra sources is a significant financial liability. However, because of its many years of therapeutic use, several widely used quantities for source-strength specification and prescription of intracavitary treatment are derived from the early experience with ²²⁶Ra.

Cesium 137 Sources

Cesium 137, a fission byproduct, is a popular radium substitute because of its 30-year half-life. Its single γ-ray (0.66 MeV) is less penetrating (HVL_Pb = 0.65 cm) than the γ-rays from radium (HVL_Pb = 1.4 cm) or ⁶⁰Co (HVL_Pb = 1.1 cm). Because ¹³⁷Cs decays to solid barium 137, ¹³⁷Cs sources have virtually replaced ²²⁶Ra intracavitary tubes in LDR gynecologic applications.

Cesium 137 BT sources were introduced in the early 1960s.¹²^,¹³ Recently marketed sources (e.g., the Amersham model CDCS-J tube [Amersham, UK] and 3M model 6500 intracavitary tube [St. Paul, MN]) consist of radioactive cesium distributed within an insoluble glass or ceramic matrix,⁴ which produces far less radiochemical hazard from ruptured sources than does the radon gas or cesium salts. These sources are encapsulated in stainless-steel sheaths with wall thicknesses of 0.5 to 1.0 mm, active lengths of 13.5 to 15 mm, diameters of 2.6 to 3.1 mm, and total lengths of about 20 mm. Figure 22.5 shows that cesium and radium sources produce nearly identical transverse-axis dose-rate distributions when their active lengths and source strengths are the same. However, the ²²⁶Ra tube isodose curves exhibit significant retraction along the longitudinal source axis as a result of oblique filtration of ²²⁶Ra γ-rays through the dense (ρ = 21 g ⋅ cm^-³) 1-mm-thick platinum capsule. In contrast, lightly filtered ¹³⁷Cs tubes produce nearly elliptical isodose curves. Consequently, vaginal applicator systems containing modern ¹³⁷Cs sources with their axes positioned perpendicular to the coronal patient plane (e.g., the Fletcher colpostat) always will give rise to higher bladder and rectal doses than when loaded with ²²⁶Ra tubes.¹⁴

Many other ¹³⁷Cs source designs have been used over the last 20 years including spherical steel-encapsulated ¹³⁷Cs pellets for the Selectron-composable source-train remote afterloader.¹⁵ For preoperative treatment of endometrial cancer¹⁶ or definitive treatment of medically inoperable endometrial cancer, afterloading sources with nominal strengths of 72 μGy · m² · h⁻¹, external diameters of about 1.2 mm, and lengths of 12 mm attached to the end of long metal stems (Heyman-Simon sources) were widely used up to the present time. However, all of these ¹³⁷Cs source configurations have disappeared from the market, reflecting the widespread conversion of LDR intracavitary BT to HDR techniques. As of this writing, only intracavitary tubes are commercially available from two manufacturers: Isotope Product Laboratories (Valencia, CA)¹⁷ and Bebig-IBt (Berlin, Germany).¹⁸

Experimental Intracavitary Brachytherapy Radionuclides

Californium 252 is a unique radionuclide that decays by α-emission with a half-life of 2.65 years and emits neutrons by spontaneous fission with average energies of 2.1 to 2.3 MeV. Depending on the distance from the source, one-half to two-thirds of the total dose is the result of the neutron component. Assuming a relative biologic effectiveness (RBE) of 6 for the neutron component, approximately 90% of the biologically effective dose derives from the neutron component. The radiobiologic rationale for using ²⁵²Cf, especially in treating bulky gynecologic malignancies, is that the high linear energy transfer (LET) neutron component more effectively depopulates the tumor’s radioresistant hypoxic core, thereby improving local control, while the rapid dose fall-off maintains an acceptable level of late complications.¹⁹ Californium 252 sources require carefully designed radiation protection and source handling procedures to reduce radiation exposure hazards to an acceptable level, due to the high neutron quality factor of 10 to 20 that is assumed by radiation protection standards.²⁰ Afterloading tube sources, suitable for use in LDR intracavitary BT, are fabricated at Oak Ridge National Laboratories (Oak Ridge, TN).²¹

Ytterbium 169⁷ and americium 241⁶ are examples of so-called intermediate low-energy photon emitters, giving rise to 60-keV and 100-keV photons, respectively. The emitted photon energy is low enough that relatively thin lead foils can be used to shield personnel and dose-limiting tissues in the patient but high enough that the resultant dose distributions in tissue remain approximately radium equivalent.²² Because relatively thin lead sheets can be used to shield critical structures (e.g., 0.4-mm-thick lead for 50% dose reduction from ¹⁶⁹Yb), customized rectal and bladder shielding can be more easily fabricated. Ytterbium 169 seeds⁷ (100-keV mean energy, 32-day half-life) have been investigated as a possible substitute for ¹⁹²Ir in interstitial implants²³ and for intracavitary treatment. In addition, ¹⁶⁹Yb has an extremely high specific activity. An HDR ¹⁶⁹Yb source and an associated single-stepping source remote afterloading system has recently been approved for sale.⁸

FIGURE 22.5. Comparison of isodose curves for a modern steel-clad ¹³⁷Cs source (left) containing radioactive ceramic pellets¹⁴ and a ²²⁶Ra tube (right) consisting of a RaSO₄ core encapsulated in 1-mm-thick Pt. Both sources have an air-kerma strength of 72 μGy · m² · h⁻¹ (10 mgRaEq).

Sources for Low–Dose-Rate Temporary Interstitial Brachytherapy

The main additional requirement for radionuclides used in temporary interstitial BT is a specific activity sufficient to support fabrication of miniaturized sources (<2 mm external diameter) so as to minimize trauma to the implanted tissues. Current interstitial implantation techniques favor disposable sources containing short-lived radionuclides that support afterloading and customization of active length.

Nonafterloading (“Preloaded”) Sources: Radium and Cesium Needles

Radium 226 needles were the mainstay of interstitial BT until about 1970. These sources had external diameters of 1.5 to 2 mm, active lengths ranging from 3 mm to 4.5 cm, and Pt-Ir alloy encapsulation ranging from 0.5 to 0.65 mm in thickness. Because needle implantation can result in large exposures to the radiation oncologist’s fingers, as well as whole-body exposure to operating room and implant imaging staff, interstitial implantation of ²²⁶Ra nor ¹³⁷Cs needles has been abandoned.

Afterloading Interstitial Sources: ¹⁹²Ir Ribbons and Wires

Temporary interstitial BT experienced a renaissance in the 1960s because of the introduction of ¹⁹²Ir.¹¹ This useful radionuclide is produced by bombarding nonradioactive ¹⁹¹Ir (available in relatively pure form) with thermal neutrons in a nuclear reactor. ¹⁹¹Ir has an extremely large neutron-capture cross-section, and produces no significant contaminant radioisotopes. Because of these properties, very high specific activities can be achieved. Miniaturized interstitial sources can be fabricated relatively cheaply. The use of ¹⁹²Ir in BT was pioneered by Ulrich Henschke,²⁴ who developed a family of widely used afterloading techniques, and by Pierquin and Dutreix,²⁵ who developed the ¹⁹²Ir-based Paris interstitial system in the early 1960s.

Iridium 192 has a 73.8-day half-life and a complex decay scheme, dominated by β decay to ¹⁹²Pt, but also including some electron capture and β+ decay. Its photon spectrum includes characteristic x-rays and γ-rays ranging from 63 keV to 1.4 MeV and has an exposure-weighted average energy of 397 keV. Compared with higher-energy ¹³⁷Cs, the thicknesses of lead and concrete shielding can be reduced by 33% and 20%, respectively.²⁶ More important advantages of ¹⁹²Ir sources are compatibility with afterloading techniques, technical flexibility, and patient comfort.

In the United States, ¹⁹²Ir is available in the form of seeds, 0.5 mm in diameter and 3 mm long, for LDR BT (Fig. 22.6). Iridium seeds, encapsulated in a 0.8-mm-diameter nylon ribbon and spaced at 1-cm or 0.5-cm center-to-center intervals, are available in strengths of 1 to 150 μGy · m² · h⁻¹ (0.1 to 20 mgRaEq). In Europe, ¹⁹²Ir is used in the form of a wire (0.3-mm or 0.6-mm outer diameter) consisting of an iridium-platinum radioactive core encased in a 0.1-mm sheath of platinum. In addition to eliminating radiation exposure hazards in the operating room, ¹⁹²Ir ribbons and wires can be trimmed to the appropriate active length for each catheter. Generally, ¹⁹²Ir ribbons or wires are used only for one to three patient procedures and then returned to the vendor for disposal.

Low-Energy Sources for Temporary Interstitial Brachytherapy

High-intensity ¹²⁵I sources²⁷ have been proposed for temporary interstitial implantation at classical dose rates. High-intensity model 6711 or 3631 A/M ¹²⁵I seeds now are used routinely as temporary interstitial sources for episcleral plaque treatment of intraocular choroidal melanoma.²⁸ By placing a 0.5-mm-thick gold shield over the episcleral plaque, tissues posterior to the eye are shielded, and radiation directed toward the tumor is partially collimated.²⁹ A disadvantage of high-intensity ¹²⁵I seed therapy is its high cost relative to ¹⁹²Ir seeds.

FIGURE 22.6. A: Construction and dimensions (in mm) of the two types of commercially available ¹⁹²Ir seeds. (A from Williamson JF. The accuracy of the line and point dose approximation in Ir-192 dosimetry. Int J Radiat Oncol Biol Phys 1986;12:409, with permission from Elsevier.) B: The 0.8-mm external diameter nylon carrier or ribbon in which the seeds are “encapsulated.” (B from Anderson LL, Nath R, Weaver KA, et al. Interstitial brachytherapy: physical, biological and clinical considerations. New York: Raven, 1990.)

Sources for Permanent Interstitial Brachytherapy

There are two basic approaches to permanent implantation. Classical LDR permanent BT originally used ²²²Rn seeds, and more recently ¹⁹⁸Au seeds, both of which have half-lives of a few days. To manage the radiation hazard as a result of the high-energy γ-rays emitted by these sources, the patient must be confined to the hospital until the source strength decays to a safe level (two to three half-lives or about 10 days). The contemporary approach to permanent implantation, ultra-low–dose-rate (ULDR) BT, uses longer-lived but low-energy photon emitters (e.g., ¹⁰³Pd and ¹²⁵I). The patient’s tissues or a thin lead foil are sufficient to reduce ambient exposure rates to negligible levels, eliminating the need to hospitalize patients solely for radiation protection. During the implant procedure, low-energy photon sources markedly reduce radiation exposure to operating room personnel and to the radiation oncologist’s hands.

Mathematics of Radioactive Decay

The phenomenon of exponential decay results in a reciprocal relationship between dose rate achieved and radionuclide half-life. The total activity, A(t), present in the implant after an interval of time t has elapsed after source insertion is given by Figure 22.7:

where A(0) is the activity at the time of insertion, ln2 is the natural logarithm of 2 (equal to 0.693), and T_1/2 is the half-life of the radionuclide. The quantity ln 2/T_1/2, represented by the symbol λ, is called the decay constant. Eq. (3) is applicable to any measure of source strength (S_K, equivalent mass of radium, etc.). Because dose rate, (t) at time t is proportional to activity, that is, , we can write:

where (0) is the dose rate at the time of source insertion. The total dose, D(T), accumulated over time interval T after source insertion is the shaded area under the curve of Figure 22.7 and can be obtained by integrating Eq. (4):

The product T_a = 1.443T_1/2 is called the average life of the radionuclide and is the time required for all radioactive atoms to decay, assuming the rate of decay remains fixed at its initial value, A(0). Eq. (5) should be used to calculate the total dose delivered by any implant when the treatment time, T, is more than 5% of the half-life. For shorter treatment times (<4 days for ¹⁹²Ir or <3 days for ¹²⁵I), the approximate expression

is accurate within 2% and may be used.

For permanent implants, the total dose administered to the patient, D_tot, resulting from complete decay of the implant can be obtained from Eq. (5):

This equation demonstrates that initial dose rate and radionuclide half-life are in reciprocal relationship with one another: the longer the half-life, the lower the dose rate will be. Typical total dose rates and total doses are given in Table 22.2 for commonly used permanent implant sources. These sources fall into two categories: short-lived radium-substitute sources with initial dose rates within the classical LDR range and longer-lived low-energy sources with dose rates below the classical range (ULDR).

TABLE 22.2 TOTAL DOSE AND INITIAL DOSE RATES FOR PERMANENTLY IMPLANTED RADIONUCLIDES

Classical Low–Dose-Rate Permanent Implant Sources: ¹⁹⁸Au

Seeds consisting of ²²²R gas encapsulated in thin-walled gold tubes³⁰ were used for permanent implantation for many years. Institutions³¹ that are still practicing classical LDR permanent interstitial BT use a reactor-produced radionuclide, ¹⁹⁸Au, which emits monoenergetic 412-keV γ-rays and has a half-life of 2.7 days. Its decay product is a nontoxic solid, thereby eliminating the contamination hazards associated with production and use of ²²²Rn. ¹⁹⁸Au seed implantation is not widely practiced because of exposure hazards to operating room personnel (especially the brachytherapist), the need to confine the patient to the hospital for radiation protection reasons, and the logistic problems associated with maintaining an appropriate inventory of such short-lived sources.

Ultra-Low–Dose-Rate and Energy Permanent Implant Sources: ¹²⁵I and ¹⁰³Pd

The introduction of electron-capture decay radionuclides, which have moderately long half-lives (10 to 60 days) and emit cascades of low energy (20 to 40 keV) characteristic x-rays and γ-rays, reignited interest in permanent BT. The first practical K-capture source, the titanium-encapsulated ¹²⁵Iodine seed (half life: 59.6 days, mean energy: 28 keV), was developed by Donald C. Lawrence³² in the early 1960s and its clinical applications first investigated in the late 1960s by Basil Hilaris and his colleagues³³^–³⁵ at Memorial Sloan-Kettering Hospital. Iodine 125 is produced by neutron activation in a specially equipped reactor designed to minimize activation of the contaminant radioisotope, ¹²⁶I. It produces a single 35-keV γ-ray. The captured K-shell electron produces a cascade of 27- to 32-keV characteristic x-rays. In addition, 93% of the γ-rays are internally converted, producing a second characteristic x-ray cascade. Thus, ¹²⁵I is an “x-ray emitter” because 95% of the useful primary photons are characteristic x-rays of atomic rather than nuclear origin.

Other important electron-capture radionuclides are ¹⁰³Pd (¹⁰³Palladium, 17-day half-life and 22-keV mean energy), commercially realized in 1987, and ¹³¹Cs (¹³¹Cesium, 9.6-day half-life and 29-keV mean energy), which was initially proposed by Henschke and Lawrence³⁶ but has only recently become available commercially.³⁷ The low-energy photons emitted by these sources dramatically reduce external exposure hazards: an 8-cm thickness of tissue reduces exposure 10-fold. Thin (0.2 mm) lead foils also produce almost complete shielding. Thus, there is usually no need to confine patients to the hospital solely for radiation safety reasons. As a result of the rapidly increasing popularity of transperineal ultrasound (TRUS)-guided permanent implant³⁸^,³⁹ for definitive treatment of low- and intermediate-risk prostate cancer,⁴⁰^,⁴¹ approximately 25 different models of ¹²⁵I and ¹⁰³Pd sources have been introduced to the market since 1999 (see the American Association of Physicists in Medicine [AAPM] revised Task Group [TG] 43 Report⁵^,⁴² and the Joint AAPM/Radiological Physics Center [RPC] Source Registry⁴³ for a review of many of the available sources). Most of these interstitial seeds are encapsulated in thin (0.05- to 0.10-mm thick) titanium tubing (see Wang and Hertel⁴⁴ for an exception) with external dimensions of approximately 0.8 × 4.5 mm (Fig. 22.8). The widely used Model 6711 seed,⁴⁵ the only ¹²⁵I source available from 1983 to 1998, contains a 3-mm-long silver rod on which radioactive iodine is absorbed and is available in strengths of 0.5 to 7 μGy · m² · h⁻¹ (0.5 to 5 mCi) (Fig. 22.8A, top). The silver rod is radio-opaque, so that the seeds can be visualized on orthogonal or stereoshift radiographs. Figure 22.8A (center) illustrates the more recent I-Seed ¹²⁵I source⁴⁶ product, which consists of radioactive iodine distributed in a low-density cylindrical annulus that fits over a gold rod used for radiographic localization.

¹⁰³Pd decays by K-electron capture and emits characteristic x-rays of 21 keV. It has all of the radiation protection advantages of ¹²⁵I along with a significantly shorter half-life of 17 days. With this source, an implant can deliver 112 Gy (90% of prescribed dose) in approximately 8 weeks at an initial peripheral dose rate of 21 cGy/hour. The Model 200 seed (Fig. 22.8A bottom) was the only commercially available ¹⁰³Pd seed from 1988 to 1999. The radioactive palladium is distributed within a thin Pd metal coating of the two graphite pellets, which are encapsulated in Ti tubing of the same dimensions as ¹²⁵I seeds. Currently, there are at least four different ¹⁰³Pd seed models commercially available. The biologic rationale for using shorter-lived ¹⁰³Pd and ¹³¹Cs interstitial sources is discussed later in the Biology section of this chapter.

Low-energy seed implantation poses a number of challenges. Their dose distributions are not radium equivalent (Fig. 22.8B), falling off more rapidly with distance. Dose estimation is inherently more complex, depending significantly on photon energy and composition of the surrounding medium (Fig. 22.4),⁴⁷^,⁴⁸ and is exquisitely sensitive to the internal seed geometry.⁴⁹^,⁵⁰ Because of shifts in calibration standards, large uncertainties in dose measurement, and questionable applicability of the classical dose calculation model, ¹²⁵I and ¹⁰³Pd dosimetry has been uncertain and variable over most of the clinical life of these products.¹¹ For example, between 1975 and 1999, the ¹²⁵I dose-rate constant was revised downward, in several steps, by nearly 50%.¹¹ Only with the development and validation of more sophisticated experimental and computation dosimetry techniques in the past 10 to 15 years can we claim to know low-energy seed dose-rate distributions with an uncertainty of 3% to 7%.⁵¹ Because of the low dose rates used, low-energy seed implantation is effectively a different therapeutic modality than classical LDR BT. In addition, 20- to 30-keV photons have a significantly higher LET spectrum, which results in an RBE for ¹²⁵I of 1.3 to 1.5 in in vitro systems compared with unity for radium-substitute photon spectra.⁵²^,⁵³ Thus, classical LDR clinical experience cannot be used to guide therapeutic decision making for ¹²⁵I permanent implantation. Despite these limitations, low-energy source permanent implantation has been demonstrated to be a highly effective and convenient treatment for prostate cancer.⁴⁰^,⁵⁴

FIGURE 22.7. Illustration of exponential decay of source strength and dose rate. The area of the shaded region is the total dose administered to the patient over treatment time, T.

FIGURE 22.8. A: Design characteristics of the GE Healthcare (formerly Amersham and 3M) Model 6711 ¹²⁵I seed⁵⁰ (top), the Bebig IsoSeed (formerly Symmetra) Model I25.S06 ¹²⁵I seed⁴⁵ (center), and the Theragenics Model 200 ¹⁰³Pd seed⁴⁹ (bottom). B: Isodose curves for a ¹⁹⁸Au seed (left half) and Model 6711 ¹²⁵I seed (right half) both with air-kerma strengths of 72 μGy · m ² · h⁻¹ (equivalent to 35 mCi of ¹⁹⁸Au and 57 mCi of ¹²⁵I).

Sources for High–Dose-Rate Brachytherapy

In contrast to inpatient-based LDR BT, HDR BT uses high-intensity sources to deliver discrete fractions ranging from 3 to 10 Gy in an outpatient setting. As described in more detail elsewhere in this text, a remote afterloading device must be used. A radionuclide with high specific activity (activity per unit mass; Ci/g) is needed so that treatment dose rates of at least 12 Gy/hour can be achieved without sacrificing the level of miniaturization needed to support intracavitary and interstitial BT. A source no larger than 1 mm diameter by 4 mm long with an exposure rate of at least 1 R/second at 1 cm is required.

The upper limit on specific activity of any substance, achieved when 100% of its atoms are radioactive, is a fundamental property that depends on its number of atoms per gram:

TABLE 22.3 SPECIFIC ACTIVITIES AND MAXIMUM EXPOSURE RATES ACHIEVABLE FOR DIFFERENT RADIONUCLIDES

For radionuclides produced by neutron activation, competition with radioactive decay precludes activating 100% of the target atoms. The theoretically achievable maximum Ci/g (Table 22.3) depends on the neutron capture cross-section of the target and the neutron flux in the reactor.⁵⁵ The extent to which this limit can be reached in practice depends on isotopic purity of the target, limits on reactor activation time, and the time required for shorter-lived contaminant radioisotopes to decay to an acceptable level. Finally, the exposure rate achieved by a small source (e.g., a 1 × 4-mm cylinder as shown in Table 22.3) depends on the chemical form (i.e., relative mass of nonradioactive atoms) of the source, its density, exposure-rate constant of the radionuclide, and photon self-absorption.

Table 22.3 shows that ²²⁶Ra cannot support HDR BT and that ¹³⁷Cs is, at best, a marginal choice. Cobalt 60 (5.26-year half-life and γ-rays of 1.17 and 1.33 MeV) has been widely used as an intracavitary HDR source in the form of small spherical pellets. Based solely on specific activity considerations, ¹⁹²Ir is the optimal choice for HDR BT and is the most widely used radionuclide for this application. Sources with external diameters as small as 0.6 mm are now available for use in single-stepping source remote afterloading devices. In contrast to ⁶⁰Co, the lower-energy ¹⁹²Ir photons are shielded effectively by the scatter and leakage barriers present in most existing ⁶⁰Co teletherapy and linear accelerator vaults. Because of their short half-lives, ¹⁹²Ir HDR sources usually are replaced at quarterly intervals. Because of the relative ease with which its low-energy photons can be shielded, a ¹⁶⁹Yb source for HDR intraoperative and intravascular BT has been developed.⁸

BRACHYTHERAPY DOSIMETRY AND SOURCE-STRENGTH SPECIFICATION

Two eras of BT dosimetry can be distinguished. The classical era (1940–1980) encompassed the maturation of the classical BT systems, the transition from ²²⁶Ra to artificial radionuclide sources, and the rise of modern BT. It began with the successful application of Bragg-Gray cavity theory⁵⁶ to the calibration of ²²⁶Ra and other high-energy sources in terms of exposure,⁵⁷ which allowed BT to be quantified using the same system of units and quantities as the orthovoltage external-beam therapy of the day. Classical or semiempirical dose computation models are based on the dose distribution about an idealized point source. Dose rates around needle and tube sources were calculated by integrating the basic point source model over their extended radioactivity distributions. Because of the technical difficulties in measuring absorbed dose in the presence of steep dose gradients, BT treatment planning relied largely on calculated rather than measured dose distributions.

The modern or quantitative era of BT dosimetry began in the 1980s and continues to the present. Quantitative dosimetry relies on measurement of source-specific dose distributions by means of small thermoluminescent dosimeters (TLDs) or silicon diode dosimeters.⁵⁸ Alternatively, radiation transport calculations in the form of three-dimensional (3D) Monte Carlo simulations are accepted as an accurate and reliable source of clinically useful dosimetry data.⁵⁸ These technical developments were motivated by concerns that semiempirical dose calculation algorithms were not valid in the low-energy regimen of ¹²⁵I and ¹⁰³Pd sources. To clinically utilize dose measurements and Monte Carlo calculations, and empirical dose calculation formalism, the TG-43 protocol⁵ was developed. Both the classical and quantitative dosimetry methods are based on the principle that BT source strength should be specified in terms of radiation output in free space.

Source-Strength Specification Quantities and Units

Brachytherapy calibration is an unnecessarily confusing topic due to the multitude of quantities that have been used to specify source strength throughout its history. Many of the historically obsolete but still widely used quantities (e.g., apparent activity and mgRaEq) were defined in terms of ²²⁶Ra properties, the only BT radionuclide intensively studied until about 1940. Such quantities obscure the experimental origin of calibration measurements by describing output measurements in activity units. Finally, the BT literature has added to the lack of conceptual clarity by obscuring the important distinction between quantities and units. A quantity is a property of nature that is directly or indirectly measurable (e.g., kerma, equivalent mass of radium, length, time), whereas a unit is a selected sample of a quantity to which the magnitude unity (1.0) is assigned (e.g., gray, mgRaEq, meter, second). A quantity such as absorbed dose can have many units (e.g., rad, cGy, Gy, J/kg).

Regardless of the units and quantity chosen to describe a calibration, all photon-emitting sealed BT sources are calibrated in terms of output (kerma rate, dose rate, or exposure rate) in air at a specific reference point on the transverse bisector of the source. Much like superficial x-ray beam calibration, a calibrated ion chamber (Fig. 22.9) is used to measure the BT source output in a free-air geometry in which the source and chamber are suspended in air in a large room.

Air-Kerma Strength

In North America, photon-emitting source strength is specified in terms of air-kerma strength, denoted by S_K, a practice that was introduced by the AAPM in 1987.⁵⁹ The AAPM⁵ currently defines S_K as the air-kerma rate, at distance d, in vacuo and due to photons of energy greater than δ, multiplied by the square of this distance, d²:

The distance d is the distance from the source center to the point of air-kerma rate specification (usually but not necessarily the point of measurement), which must be in the transverse plane of the source (the plane normal to the long axis of the source, which bisects its radioactivity distribution). S_K is independent of specification distance so long as d is large relative to the maximum linear dimension of the radioactivity distribution. is usually inferred from transverse-plane air-kerma rate measurements performed in a free-air geometry (see Fig. 22.9) at distances large in relation to the maximum linear dimensions of the detector and source, typically on the order of 1 meter. The in vacuo qualifier (equivalent in meaning to “in free space”) means that must be specified as if the source and small mass of air, producing ionization at distance d, were immersed in a vacuum. Air-kerma rate measurements must be corrected for photon attenuation and scattering by the surrounding air as well as for scattering from nearby objects. The energy cutoff, δ, is intended to exclude low-energy contaminant photons (e.g., characteristic x-rays originating in the outer layers of steel or titanium source cladding⁶⁰) that increase without contributing significantly to dose at distances >0.1 cm in tissue. The value of δ is typically 5 keV for a low-energy photon-emitting BT source. The unit of air kerma strength is μGy · m² · h⁻¹ and is often denoted in the literature by the symbol “U,” where 1 U = 1 cGy · cm² · h⁻¹ = 1 μGy · m² · h⁻¹.

Air-kerma strength is numerically (but not dimensionally) equal to the quantity reference air-kerma rate, _ref, a very similar quantity defined by the ICRU^3,⁶¹ and used outside North America. _ref is defined as the air-kerma rate in free space at a reference distance, l (taken to be 1 m), on the transverse axis; it has units of μGy · h⁻¹ at 1 m. Thus, _ref and S_K are identical.

The U.S. National Institute of Standards and Technology (NIST) maintains primary S_K standards for commercially available ¹³⁷Cs sources,⁶² LDR ¹⁹²Ir seeds,⁶³ and all ¹⁰³Pd, ¹³¹Cs, and ¹²⁵I seeds.⁶⁴ A primary standard is an instrument against which all other S_K measurement devices, called secondary or tertiary standards, must be intercompared. Such instruments are designed to permit inference of air-kerma values from the measured charge and instrument design using first principles. For ¹³⁷Cs and ¹⁹²Ir sources, the S_K standard is based on transverse-axis air-kerma measurements using spherical ion chambers with carbon walls—the same instruments used to maintain the ⁶⁰Co teletherapy air-kerma standard. For low-energy interstitial seeds, a special free-air chamber,⁶⁴ called the wide-angle free-air chamber (WAFAC), is used. Brachytherapy sources calibrated directly by the NIST standard or one of the AAPM-Accredited Dosimetry and Calibration Laboratories (ADCLs) are said to have directly NIST traceable calibrations. Sources that are calibrated against sources or ion chambers, which themselves have directly traceable NIST calibrations, are said to have indirectly NIST-traceable calibrations. For a more detailed description of air-kerma–based standards, measurement techniques, and traceability requirements, the reader is referred to a recent review by DeWerd.⁶⁵ The AAPM⁶⁶ recommends that individual clinics using BT sources maintain instrumentation able to make indirectly traceable calibration measurements for verification of vendor-supplied calibrations.

Kerma (kinetic energy released in the medium), K_x, is the ratio δE_tr/δm, where δE_tr is the total kinetic energy transferred to charged particles by photon interactions with atoms in small mass, δm, of medium x.⁶⁷ For photons, δE_trincludes the initial kinetic energies of any secondary charged particles (e.g., Compton electrons, photoelectrons, and positrons) liberated by Compton, photoelectric, and pair production interactions. Kerma is defined only for indirectly ionizing radiations (e.g., photons and neutrons) and quantifies the transfer of energy from these radiation fields to matter. It takes the same units (cGy and Gy) as the related quantity absorbed dose. Although kerma can be specified in any medium x, usually air medium (x = air) is assumed for radiation metrology. K_air replaces the obsolete quantity exposure and is closely related to absorbed dose, D: the ratio, δE_ab/δm, where δE_ab is the energy imparted to δm by the radiation field. Because the secondary electrons released by photon collisions may travel a significant distance before depositing their energy and may convert some of their kinetic energy to Bremsstrahlung radiation, D_air and K_air are not necessarily equal. When kerma remains relatively constant over the range of the secondary electrons, a special condition, secondary charged particle equilibrium (CPE), exists.⁵⁵^,⁶⁸ When the CPE is obtained, the rates of energy absorption and energy transfer are approximately equal, so that kerma closely approximates absorbed dose:

where X represents the quantity exposure. The quantity (W/e) is the average energy imparted to air per ion pair created and is a constant, independent of photon energy: (W/e) = 33.97 eV/ion pair = 33.97 J/C = 0.876 cGy/R.⁶⁹ The factor g is the fraction of kinetic energy transferred to the medium converted back to radiant energy (photons) by the Bremsstrahlung process; g is <0.001 at BT energies and usually is ignored, further simplifying Eq. (10). Virtually all BT dose calculation algorithms and dosimetric analyses assume that CPE is obtained and that dose, D, can be well approximated by kerma, K, everywhere. Although generally valid, CPE can be expected to break down in the presence of steep dose gradients near sources,⁷⁰ near metal–tissue interfaces,⁷¹ and within the active elements of thin, bounded detectors.⁷²

Activity

To define the obsolete quantities for describing source output, the quantity activity, A, must be introduced. It is defined as the rate of nuclear disintegration or transformation within a radioactive source. The contemporary unit of activity is the becquerel (1 Bq = 1 disintegration/second). We will freely use the more traditional but obsolete unit, the curie (1 Ci = 3.7 × 10¹⁰ disintegrations/s = 3.7 × 10¹⁰ Bq). A more convenient multiple of the curie, the millicurie, is defined as 1 mCi = 10⁻³ Ci = 3.7 × 10⁷ disintegrations/second. Each disintegration represents the spontaneous transformation of an atom from one nuclear state to another. For most BT radioisotopes, such transformations of nuclear state give rise to photons in the form of unconverted γ-rays, annihilation photons, characteristic x-rays, and Bremsstrahlung photons. Activity is measured by counting the number of photons, β particles, or other particles emitted by an unencapsulated point source of the radionuclide by means of scintillation or proportional counters, from which its activity is inferred.⁷³ For sealed BT sources, A refers to activity contained inside the sealed source.

Activity, as defined in this strict sense, is no longer used in BT dosimetry. However, activity continues to serve as the basis for treatment specification and dosimetry of unsealed radiopharmaceuticals used for diagnosis and therapy. NIST maintains contained activity standards for a wide variety of radionuclides in aqueous solution.⁷⁴

Relationship Between Activity and Exposure Rate

The activity, A, of radioactive nuclide-emitting photons and the exposure rate in free space, , (in R/hour) at distance r (in centimeters) due to photons of energy greater than δ, are related by a fundamental quantity, the exposure rate constant, (Γ_d)_X, defined as follows⁶⁷:

(Γ_d)_X has units of R cm² mCi⁻¹ h⁻¹ and is equal to the exposure rate in R/hour at 1 cm from a 1-mCi point source. It describes the rate at which air is ionized as a result of the emission of photons resulting from radioactive decay. The energy cutoff δ eliminates low-energy Bremsstrahlung and characteristic x-rays from consideration that are always absorbed within any practical source. The precise value of δdepends on the application; it usually is assumed to be about 10 keV. Because (Γ_d)_X is defined in terms of an isotropic point source and exposure rates are corrected for air attenuation and scattering, inverse-square law applies exactly. Thus, (Γ_d)_X is independent of the distance r used in Eq. (11).

(Γ_d)_X depends only on the number and energy of the photons emitted per disintegration. Suppose there are N different photons emitted per disintegration with energies E₁, E₂,… E_N in units of MeV. Each time an atom decays, suppose P_i photons of energy E_i are emitted where i = 1,… , N. The list {E_i,P_i}^N_i=1 is the photon spectrum of the radionuclide. If the spectrum is known, then (γδ)_x can be calculated by:

where is the mass energy absorption coefficient (in units of cm²/g) for air at energy E_i. A detailed derivation of this fundamental relationship is given in a recently published review²² and in a previous edition of this chapter.⁷⁵ The exposure-rate constant has been replaced by the air-kerma rate constant, , by the ICRU.⁶⁷ (γδ)_x is a fundamental property of the radionuclide’s unencapsulated photon spectrum, applies only to an ideal point source, and neglects many significant properties of real sources such as self-absorption, filtration, and extension.⁶⁷

²²⁶Ra is an exception to this practice. First, radium source strength is specified by the quantity—mass of ²²⁶Ra contained inside the source—denoted by M_Ra. M_Ra excludes the nonradioactive core components as well as radioactive decay products. Historically, M_Ra was introduced and widely used before the more general activity standards were available. Indeed, the unit curie originally was defined as the number of disintegrations produced by 1 g of ²²⁶Ra. M_Ra standards were prepared by carefully weighing pure ²²⁶Ra samples in an analytic balance. The first M_Ra standard was prepared by Marie Curie in 1913 and the currently used NIST standard was prepared by Hönigschmidt in 1934. To calibrate a user’s source in M_Ra, its radiation output is compared with that of the NIST radium standard by means of an ion chamber. NIST no longer offers an M_Ra calibration service. In contrast to the other radionuclides, exposure-rate constant of ²²⁶Ra—denoted by the special symbol (Γ_d)_Ra,t in this chapter—is tabulated as a function of its effective capsule thickness, t, in millimeters of platinum. (Γ_d)_Ra,t is normalized to the mass of radium contained in the source and has units of R cm² mg⁻¹ h⁻¹.

Obsolete Quantities for Specifying Source Output

Because of the close association of early BT with ²²⁶Ra, it is not surprising that the measured output of BT sources continues to be expressed as multiples of the output of a 1-mg radium needle. This quantity, equivalent mass of radium (M_eq), was introduced when artificial radioisotopes, such as ⁶⁰Co and ¹³⁷Cs, were developed as radium replacements. It allowed old implant and radium needle dosimetry tables, which gave dose per milligram-hour (mg-h) of ²²⁶Ra, to be used without modification for these new sources. M_eq is that mass of²²⁶Ra filtered by 0.5 mm Pt that has the same S_K as that of the given source.Because M_eq is simply a statement of S_K relative to that of a hypothetic radium needle, the given source being quantified need not contain ²²⁶Ra, be encapsulated in Pt, or have a wall thickness of 0.5 mm. Because K_air = X · (W/e) and (Γ_d)_Ra,0.5 = _{8.25 R} · _cm² · _mg^–1 · _h^–1 for ²²⁶Ra filtered by 0.5 mm Pt,⁷⁶S_K and M_eq are related by:

where (W/e) = 33.97 eV/ion pair. M_eq continues to be widely used to specify strength of intracavitary and interstitial BT radium-substitute sources such as ¹³⁷Cs and ¹⁹²Ir.

Similar to the philosophy of M_eq, apparent activity, A_app, is a statement of source output relative to that of a hypothetic unfiltered point source. A_app is the activity of a hypothetic unfiltered point source that has the same S_K as that of the given source:

Apparent activity in units of mCi continues to be widely used for specifying strength for permanent interstitial implants (e.g., ¹²⁵I and ¹⁰³Pd sources). In contrast to M_eq, which is based on the universally accepted (Γd)_Ra,0.5 value of 8.25 R · cm² · mCi^-1 · h^-1, no consensus as to (Γd)_X values for the other radionuclides exists. Often different vendors will assume different (Γd)_X values for the same radionuclide. Thus, A_app is an inherently ambiguous means of describing source strength. In an effort to reduce low-energy dose calculation errors associated with this ambiguity, the AAPM⁵ recommends that the (Γδ)_Xvalues of 1.476 and 1.45 R · cm² · mCi^–1 · h^–1 for ¹⁰³Pd and ¹²⁵I sources, respectively, be used universally for specification of A_app. Nearly all scientific societies involved in BT^3,⁶⁶^,⁷⁷ recommend that M_eq and A_app be abandoned in favor of S_K for source ordering, dose calculation, and implant prescription.

Milligram-Hours and Integrated Reference Air-Kerma

In gynecologic intracavitary therapy, the quantities M_Ra and M_eq are used both to describe source loadings and to prescribe individual treatments. For prescribing therapy, these quantities, in units of milligrams of ²²⁶Ra or mgRaEq, are integrated over treatment time yielding the so-called quantities mg-h and mgRaEq-h. As the product of total source strength and treatment time, mg-h and mgRaEq-h represent the total exposure or air-kerma accumulated at a distance of 1 m from the implant, under the assumptions that the implant is a point source and that tissue attenuation is negligible. The ICRU³ recommends that mg-h be abandoned as a prescription or reporting quantity in favor of quantities defined in terms of air-kerma. The American Brachytherapy Society (ABS) has proposed the quantity integrated reference air-kerma (IRAK), K_ref:

where S_K,i and t_i are the air-kerma strength and treatment time in hours, respectively, of the ith source. Thus, 1 unit of IRAK = 1 cGy · cm² = 1 μGy · m² = 1 U-h. A numerically identical quantity, total reference air kerma (TRAK), with units of μGy at 1 m, has been recommended by the ICRU.³ IRAK and TRAK are related to mg-h and mgRaEq-h:

Intracavitary treatment systems¹⁰ historically based on ²²⁶Ra tubes (1-mm Pt encapsulation) typically use mg-h, whereas systems based on ¹³⁷Cs or other radium substitutes prescribe therapy in units of mgRaEq-h. Because of the difference in platinum filtration assumed by these two milligram-based quantities, numerically identical prescriptions can deliver quantities of IRAK that differ by 7%. Use of IRAK as an integrated output reporting quantity eliminates this 7% ambiguity that has confused comparison of different implant systems since the appearance of radium-substitute sources for BT.

Classical Dose Calculation Formalism: Isotropic Point Source

Consider an unencapsulated point source with an air-kerma strength of S_K, illustrated in Figure 22.10. Because this source has no extension, there is no attenuation of the emitted radiation by the source itself. Isotropy (Fig. 22.2) implies that photons are emitted with equal likelihood in all directions and travel in straight lines. In contrast, actual BT sources are encapsulated, have finite dimensions, and usually are cylindrically rather than spherically symmetric. The dose rate, (r) (cGy/hour), at distance r (cm) in the water-equivalent medium surrounding the source is given by:

The inverse-square law term corrects for the difference in dose specification distance, r, and the 1-cm reference point assumed by the units of air-kerma strength. The quantity is the ratio of mass-energy absorption coefficients in medium to that in air averaged over the photon spectrum in free space. This correction, equal to _med/_air in free space, is a consequence of the fundamental relationship between particle fluence and dose.²²^,⁷⁵ It corrects for the efficiency with which the medium extracts energy from the emitted photons compared with air. For all radionuclides emitting photons with energies >200 keV, including all radium substitutes, has the value 1.11 in water medium.

The last term of Eq. (17)—the kerma-to-dose conversion factor, T(r)—describes the net influence of primary photon attenuation and buildup of scattered photons in the surrounding medium. Sometimes this factor is termed the effective attenuation factor or the scatter-buildup factor.

Figure 22.11 shows T(r) for several radium-substitute radionuclides as well as for a few low-energy radionuclides. For ²²⁶Ra-equivalent radionuclides, T(r) deviates <5% from unity (1.00) out to distances, r, of 5 cm. Numerous tabulations of T(r) are available in the literature; those of Meisberger et al.,⁷⁸ Berger,⁷⁹ and Van Kleffens and Star⁸⁰ are among the best known. Most of these data are derived from theoretic photon transport calculations. The classical semiempirical model assumes that T(r) is a function only of the radionuclide photon spectrum and that a single dataset (e.g., for ¹⁹²Ir) can be used for all ¹⁹²Ir sources regardless of their construction.

By solving Eqs. (13) and (14) for S_K and substituting the results into Eq. (18), one can derive equations relating the dose rate at distance r to equivalent mass of radium and apparent activity for the same unfiltered point source:

FIGURE 22.9. A: Illustration of a free-air geometry for measuring brachytherapy source strength in terms of a radiation output quantity such as air kerma. In practice, the source and cavity chamber are suspended in air in a large room and separated by a 20-cm to 100-cm distance (which must be large in relation to the detector and source dimensions). The measured air kerma must be corrected for photon scattering from walls, floor, and ceiling and for photon scattering and attenuation by the intervening air. B: Definition of air-kerma strength. For an actual source, the air-kerma rate must be measured at a distance, d, which is large in relation to the source dimensions.

FIGURE 22.10. Unencapsulated point source of strength S_K immersed in an unbounded water-equivalent medium.

FIGURE 22.11. Photon attenuation and scatter factors, T(r), for a number of radium-equivalent radionuclides, as presented in the classic paper of Meisberger et al.,¹⁹² and for several low-energy radionuclides. Meisberger et al. fit their data to a third-degree polynomial T(r) = A + B · r + C · r ² + D · r ³, which is widely used to represent T(r) in modern treatment-planning systems.

where f_med is the dose-to-exposure conversion factor given by:

For all ²²⁶Ra substitutes (radionuclides with photon energies of more than 200 keV), f_med has the value 0.974 cGy · R⁻¹ for water and 0.966 cGy · R⁻¹ for muscle medium.⁵⁵

Eqs. (17) and (19) give the dose rate, _med(r), for a point source surrounded by an arbitrary medium that has been specified in terms of equivalent mass of radium, apparent activity, and S_K. Assuming that the same exposure rate constants, (Γd)_Ra,0.5 and (Γd)_X, were used to evaluate absorbed dose as were used to convert the measured air-kerma strength to M_eq and A_app via Eqs. (13) and (14), all three equations should give numerically identical dose rates. This demonstrates that γδ is, in fact, a “dummy” constant that plays no physical role in the dosimetry of output-calibrated sealed sources because any arbitrary, but consistently used, value will yield identical dose-rate distributions. These unit conversions may not be performed by the same individual. For example, the vendor calibrates ¹²⁵I sources by intercomparing them with the NIST S_K standards. The vendor calculates A_app from the measured S_K by Eq. (14) using an assumed (Γd)_X value and records the result on the source’s calibration certificate. The hospital physicist, in calculating dose rates by Eq. (19), also must use an assumed (Γd)_X value. If the physicist fails to use the same value as the vendor, significant dose calculation errors may result. Use of S_K for clinical source-strength specification eliminates these dummy constants, thereby eliminating errors resulting from inconsistent conventional choices.

Modeling of Source Anisotropy: The Anisotropy Factor

Despite its simplicity, the classical isotropic point-source model, Eq. (17), accurately predicts the transverse-axis dose-rate distributions of most actual radium-substitute sources. Simply by using an output quantity to calibrate the source, rather than contained activity, A, the influence of its internal structure (filtration and self-absorption) has been implicitly accounted for. Had true activity, A, instead of A_appbeen used in Eq. (19b), then the expression for (Γd)_X (Eq. 12) would require correction for attenuation and scattering in the radioactive core and surrounding encapsulation. Any uncertainties in {E_i,P_i}^N_i=1(which are large for many radionuclides) and filtration corrections would directly degrade dose calculation accuracy. In addition, fundamental activity measurements are technically difficult for the high-intensity sources used in BT. For this reason, contained activity does not play a role in photon BT dosimetry. In contrast, Eq. (17) infers dose rate from a quantity measured outside the source, which is not influenced significantly by knowledge of the unfiltered photon spectrum. The required quantities, and T(r), are ratios and are therefore insensitive to errors in the assumed spectrum.

Practically all BT sources are cylindrical, giving rise to anisotropic dose distributions. In addition, some sources, especially those used in intracavitary BT, have active lengths that are comparable to typical calculation distances. Thus, the dose rate, (r,θ), around a BT source depends both on distance, r, and polar angle, θ (Fig. 22.8B). (r,θ) may deviate significantly from the transverse-axis dose rate, (r,p/2), predicted by Eq. (17), especially near the long axis of the seed.

In the case of implants consisting of many randomly oriented seeds with active lengths less than the minimum distance of interest, Eq. (17) will accurately represent the multiple-seed dose distribution if an average correction for single-seed dose anisotropy is applied.⁸¹ This correction factor, which the TG-43 protocol refers to as the “1-D anisotropy function,” φ_an(r), is defined by averaging the dose at each fixed distance r with respect to solid angle :

Often a distance-independent average value of φ_an(r), called the anisotropy constant, φ_an, is used. Incorporating this average correction into Eq. (17) leads to:

For radium-substitute sources, was often evaluated by measuring relative photon fluence in air at relatively large distances (30 to 100 cm) using a NaI or GeLi scintillation detector.⁴⁵^,⁸²

Eq. (22) implies that source strength should be increased by a constant fraction ranging from 2% (¹⁹²Ir seeds) to 10% (¹⁰³Pd seeds) to correct for polar anisotropy effects. Lindsay et al.⁸³ compared prostate implant 3D dose distributions derived from the isotropic point-source model, (r), to those derived from the full 2D single-source dose calculation model, (r,θ). Based on voxel-by-voxel comparisons, they found that the isotropic point-source model introduced errors exceeding 10% of the D₉₀ (see section on dose specification) in 8% and 33% of the target volume for the Model 6711 ¹²⁵I and Model 200 ¹⁰³Pd sources. Corbett et al.⁸⁴ found that large local dose-distribution differences, including 2D anisotropy effects, did not alter the dose–volume histogram (DVH): neither the V₁₀₀ nor the margin between D₁₀₀ and the prostate boundary were altered significantly. For volume implants consisting of parallel arrays of ¹⁹²Ir seeds, a similar finding has been reported.⁸¹

Dose Calculation for Extended Sources: The Sievert Integral Model

Dose distributions around larger sources, such as intracavitary tubes and interstitial needles, are calculated by partitioning the extended source into a set of point sources to which corrections for distance, oblique filtration, attenuation, and scattering are applied separately. By summing these point-source contributions, the dose at point P can be estimated. This class of algorithms, first described by Rolf Sievert in 1921,⁸⁵ is known as the Sievert integral algorithm, or more generally, the one-dimensional (1D) pathlength model.²²^,⁸⁶

Assume that the source illustrated in Figure 22.12 has an air-kerma strength, S_K, and contained activity, A. The classical Sievert model approximates the cylindrical active core by a line of radioactivity positioned along its axis. The axial length of the core is called the active length, L. Oblique filtration is modeled by assuming that the capsule reduces dose by exponential attenuation using an effective filtration coefficient, μ′. The dose rate δ(x,y) at point (x,y) from the incremental source δL located at angle Γ is:

where (Γd)_X is the exposure-rate constant of the unfiltered source material. Because S_K = A · (W/e) · (Γd)_X · e^–m^,t , Eq. (23) becomes:

FIGURE 22.12. A typical encapsulated line source, illustrating calculation of dose rate at point P at (x,y) relative to the source center by the Sievert integral method. The active length and radial encapsulation thickness are denoted by L and t, respectively. The distances x and y are referred to as “distance away” and “distance along,” respectively, in the literature.

FIGURE 22.13. Error in the isotropic point source model relative to the line source model [Eq. (26)] as a function of transverse-axis distance expressed in multiples of active length.

By summing over all these incremental sources (i.e., integrating with respect to θ′) and transforming to polar coordinates, we obtain the Sievert integral:

The extra eμ^′t term outside the integral is needed to avoid global “double correction” for filtration.

Variants of Eq. (25) applicable to the regions near the source capsule ends are available. Numerous improvements to the basic model have been introduced over the years,⁸⁷^,⁸⁸ including modeling of photon absorption by the source core, extension to noncylindrical sources, generalization to radioactivity distributed over a volume,⁴ extension to low-energy sources,⁸⁶ and treatment of applicator shielding and attenuation.⁸⁹^,⁹⁰

The Sievert algorithm is widely used to model 2D dose distributions around ¹³⁷Cs tubes and needles for clinical treatment planning. Both experimental⁹¹^,⁹² and Monte Carlo studies⁴^,⁹³ have demonstrated that the Sievert model accurately predicts dose-rate distributions in this energy range. When the filtration coefficient μ′ is approximated⁹⁴ by the linear energy absorption coefficient μ_en (0.023 mm⁻¹ for steel-clad ¹³⁷Cs sources), maximum errors are no larger than 5% to 8% and are much smaller (<3%) near the transverse axis. Published dose-rate distributions derived from the Sievert model, tabulated in terms of distances away and along, are available for several types of ¹³⁷Cs sources⁴^,⁹³ and ²²⁶Ra sources.⁹⁵ Williamson⁸⁶ showed that the classical Sievert integral gives rise to large errors (20% to 37% maximum error, 7% to 16% average error) when applied to lower-energy sources of ¹⁹²Ir, ¹⁶⁹Yb, and ¹²⁵I. Although accuracy can be improved by modifying the basic model,⁸⁶ classical semiempirical models should be used cautiously at photon energies below ¹³⁷Cs. Tabulated dose-rate distributions derived from direct measurement or Monte Carlo simulation are preferable for these sources.

If the encapsulation thickness is set to zero (t = 0) in Eq. (25), the Sievert integral reduces to a simple closed-form analytic expression:

where δθ is the angle, in radians, subtended by the active length, L, with respect to the point of interest (Fig. 22.12). When the interest point lies on the transverse axis (y = 0), then Dθ = 2 · tan⁻¹ (L/2x), where tan⁻¹ denotes the inverse tangent or arctan function in units of radians rather than degrees (180 degrees = π radians). This approximation is extremely useful as a manual calculation aid and is highly accurate near the transverse axis of lightly encapsulated ¹³⁷Cs sources.

Figure 22.13 shows that as the distance becomes large in relation to active length, L, Eq. (26) reduces to the point-source formula. For distances less than L (1.5 cm for intracavitary tubes), use of Eq. (17) will yield errors of at least 10%. For distances >1.5L (2 to 2.5 cm for gynecologic tubes), the point-source approximation is accurate within 5%.

Modern Quantitative Dosimetry

In contrast to classical dose calculation models, which assume that the parameters T(r) and depend only on the radionuclide used, quantitative dosimetry methods assume that dosimetry parameters are source-geometry specific and should be measured or calculated specifically for each type of source (i.e., commercially released source model). Classical approaches to BT dosimetry began to break down with the introduction of ¹²⁵I interstitial seeds in the early 1970s, as this 30-keV x-ray emitter clearly fell outside the scope of validated analytic models.¹¹ Although ¹²⁵I dose distributions derived from semiempirical models were published⁹⁶ and widely used, it was recognized⁴⁵that internal seed structure could modulate the emitted photon spectrum and have significantly alter the absorbed dose distribution. The growing use of ¹²⁵I and the introduction of a primary exposure standard in 1985⁹⁷ motivated investigation of more quantitative dosimetry methods. For a more detailed review of ¹²⁵I dosimetry history, the reader is referred to Appendix C of the original TG-43 report.⁹⁸ Currently, both experimental methods and sophisticated computational dosimetry approaches are routinely used to derive such source-specific parameters. Both the classical and quantitative dosimetry approaches are based on the NIST air-kerma strength standards.

Experimental Brachytherapy Dosimetry

Clinical acceptance of measured dose rates in BT is a relatively recent phenomenon, beginning in the mid-1980s. Historically, this is due not only to the difficulties and labor intensity attending such measurements, but also to a consensus that dose measurement was so difficult and intrinsically inaccurate that even simplistic theoretic models were more reliable. Brachytherapy dose measurement does indeed place severe demands on detectors because the dose distributions are characterized by large dose gradients, a large range of dose rates, and relatively low photon energies. The most severe measurement artifact is the exquisite sensitivity of detector response to positioning errors; measurement of dose near a point source with 2% accuracy requires that the source-to-detector distance be specified with accuracy of 20, 50, 100, and 200 μm, respectively, at distances of 2, 5, 10, and 20 mm.

Commonly used dose detectors include thermoluminescent detectors (TLDs), small ion chambers, diode detectors, and silver-halide radiographic film. Radiochromic film⁹⁹ and plastic scintillator detectors¹⁰⁰^,¹⁰¹ show promise as planar dose measurement systems. Three-dimensional dose measurement technologies under investigation include liquid scintillation cocktails¹⁰² with dose distributions reconstructed by optical emission tomography and polymer gel dosimetry¹⁰³^,¹⁰⁴ using magnetic resonance imaging (MRI) to quantify the detector signal. One consideration in selecting a detector for BT dosimetry is minimizing energy-response artifacts, which arise from compositional differences between water and the detector and can result in variation of detector reading/unit dose in medium as the photon spectrum changes with position. Silicon diodes are useful detectors for measuring relative dose distributions around ultra-low-energy sources (e.g., ¹⁰³Pd and ¹²⁵I) because diode sensitivity is nearly independent of measurement point location,¹⁰⁵^,¹⁰⁶ but they are not recommended for higher-energy BT sources, as variations in sensitivity with position in the phantom as large as 15% for ¹³⁷Cs and 75% for ¹⁹²Ir have been reported.¹⁰⁷

Among the established dosimetric techniques, LiF TLD dosimetry is considered to offer the best compromise between sensitivity, small size, and freedom from energy-response artifacts⁵⁸ and is currently considered to be standard of practice.⁵ The acceptance of TLD dosimetry owes much to a 3-year (1987–1989) multi-institutional contract to perform a definitive review of low-energy seed dosimetry that was funded by the National Cancer Institute. The three institutions, collectively called the Interstitial Collaborative Working Group (ICWG), consisted of Memorial Sloan-Kettering, Yale, and University of California, San Francisco (UCSF), led by principal investigators Lowell Anderson, Ravinder Nath, and Keith Weaver, respectively.¹⁰⁸ Using TLD-100 thermoluminescent chips and powder capsules, embedded in machined solid-water phantoms, the ICWG developed procedures, including TLD dose calibration and energy-response correction, for making quantitative estimates of absolute dose rates in water. Each of the three ICWG investigator groups independently measured transverse-axis dose distributions for the ¹²⁵I and ¹⁹²Ir then available to validate their TLD measurement methodology.¹⁰⁸ This was followed by more complete 2D dose distributions about ¹²⁵I, ¹⁹²Ir, and ¹⁰³Pd BT sources then available.¹⁰⁵^,¹⁰⁹^,¹¹⁰ The results showed good agreement among the different measurements and, overall, substantial differences between measured and classically computed dose rates for ¹²⁵I seeds (when normalized to the 194 Loftus air-kerma strength standard,⁹⁷ S_K,N85, then available), but good agreement between the classical and experimental approaches for ¹⁹²Ir. With careful correction for TLD linearity, perturbation of the photon field by the detectors, and relative energy response, absolute dose rate (cGy/hour in tissue per unit S_K) can be measured with a total uncertainty of 7% to 9% in the 1- to 5-cm distance range.⁵^,⁵⁸

Measured dose-rate distributions using TLD detectors are available for many common BT sources, including nearly all commercially available ¹²⁵I and ¹⁰³Pd sources (see the revised TG-43 Report⁵ and a recent review article⁵⁸ for more comprehensive discussions); many ¹⁹²Ir sources for LDR, HDR, and pulsed dose rate (PDR) applications; and for many investigational sources. For radium-substitute sources, the measurements are in close agreement with the classical semiempirical models: isotropic point source and Sievert integral models.⁴^,²²^,⁸⁶ For ¹²⁵I sources normalized to the S_K,N85 standard, measured dose rates were found to be 10% to 20% lower than those predicted by Eq. (17).⁵^,¹¹¹ Better agreement²² is observed between classical models and measurements when calibrations traceable to the 1999 WAFAC standard (S_K,N99)⁶⁴ are used. However, classical models such as the Sievert integral are not recommended for the low-energy source regimen as they poorly predict low-energy source anisotropy⁸⁶ and do not take into account modulation of the dose distribution by internal source geometry.

Computational Dosimetry Methods: Monte Carlo Photon Transport Simulation

Concurrently with the development of TLD dosimetry in the 1990s, other investigators were investigating the use of Monte Carlo photon-transport techniques as tools for quantitative evaluation of single-source dose distributions. Based on an accurate and detailed mathematical model of the internal structure of the source, photon histories can be generated and then evaluated to assess absorbed dose. Monte Carlo techniques are now accepted as a reliable and probably the most accurate source of BT dosimetry data.⁵^,⁵⁸ As illustrated in Figure 22.14, this theoretical method uses a digital computer to randomly select a small number (10⁵ to 10⁷) of photon trajectories or “histories.” A geometric model indicating the location of all media boundaries and photon sources must be available. By using probability distributions derived from total and differential cross-sections, a photon is randomly constructed by following each photon from birth through successive scattering events and, eventually, to absorption or escape from the system. At each decision point, random sampling is used to decide the fate of the photon. The process of randomly constructing photon trajectories is equivalent to selecting photon histories from the set of all those possible by random sampling. To statistically estimate the dose rate at a specified point, the dose contributed by each simulated collision is estimated and then averaged over all collisions. Monte Carlo simulation techniques are reviewed in more detail elsewhere.⁵⁸ Because particle histories can be accurately and efficiently constructed even in the presence of complex 3D geometries, approximation-free but statistically inexact solutions, derived from first principles, are possible for a wide range of geometrically complex but clinically relevant BT problems.

The dosimetric accuracy of Monte Carlo simulation has been confirmed across the entire energy spectrum from ¹²⁵I to ¹³⁷Cs. Agreement between Monte Carlo and TLD measurement ranges from 2% to 6%, both in homogeneous medium and in the presence of tissue and applicator heterogeneities.⁷^,⁴⁸^,¹⁰⁷^,¹¹²^,¹¹³ In contrast to experimental methods, Monte Carlo accuracy is not limited by dosimeter artifacts such as energy response and volume averaging. Because the geometric model can be specified exactly, detector positioning error is not an issue in Monte Carlo. Recent analyses⁵^,⁵¹^,⁵⁸ have shown that the uncertainty (including all known systematic and random error sources) of Monte Carlo absolute dose-rate estimates on the transverse axis of ¹²⁵I seeds is 2.5% to 5% over the 1- to 5-cm distance range. Unlike dose measurements, Monte Carlo dose calculations cannot account for unsuspected deviations from the design specifications of the problem (e.g., a contaminant radionuclide in the source or an error in measuring its source strength).

Currently, the most important role of Monte Carlo simulation is calculation of reference-quality transverse-axis dose-rate distributions and anisotropy functions for low- and medium-energy BT sources. For low-energy interstitial seeds for routine clinical use, both experimental and Monte Carlo–based published dosimetry studies in peer-reviewed journal are required for developing AAPM-approved consensus datasets or posting the interstitial seed product on the Joint AAPM/RPC Source Registry.⁵^,¹¹⁴ Monte Carlo simulation is a useful alternative to dose measurement in many other applications such as characterizing the effects of applicator shielding materials⁷^,¹⁰⁷ and tissue heterogeneities⁴⁸ on BT dose distributions; validating heuristic dose calculation algorithms;¹¹⁵ and optimizing new source and applicator designs.¹¹⁶

Because Monte Carlo simulation statistical precision increases with the square root of computing time, the long computing time (several hours or even days) characteristic of general purpose codes has limited Monte Carlo–based treatment planning¹¹⁷ to the experimental setting. However, due to advances in hardware and use of sophisticated variance reduction techniques,¹¹⁸ this logistic barrier has been effectively overcome. At least one group¹¹⁹ has reported single-processor calculation times on the order of a minute for clinical prostate seed implants. Even faster specialized BT codes have been introduced, including a fast correlated sampling code¹²⁰ and a planning code derived from EGSnrc.¹²¹ Other groups have investigated deterministic transport solutions, mainly discrete ordinates codes¹²² (also called “grid-based Boltzmann solvers” or GBBSs by some investigators) for more efficient but quantitatively accurate dose calculation for clinical treatments. Recently, Varian Medical Systems (Palo Alto, CA) has introduced a dose calculation engine based on the discrete ordinates method in its BrachyVision HDR planning system,¹²³ the first commercially available BT dose calculation engine based on a rigorous radiation transport simulation. Unlike current TG-43 clinical dose computations, Monte Carlo or deterministic transport solutions can account for the perturbing effect of multiple implanted sources on the single-source dose distributions, deviations in tissue composition from the assumed water medium, and the influence of applicator shielding and attenuation. These phenomena have been shown to introduce dose estimation as large as a factor of two. For more information on model-based dose calculation and its potential clinical impact, the reader is referred to a recent review by Rivard et al.¹²⁴

FIGURE 22.14. A: Two-dimensional representation of a typical photon history. The heavy solid lines illustrate the origin of the primary photon (randomly selected from the assumed distribution of radioactivity), and each successive collision, which is randomly selected from the competing collision mechanisms (photo-effect, Compton scattering, and coherent scattering), is based on their relative probabilities. The dashed lines illustrate the problem of estimation (i.e., calculating the probable contribution of each simulated collision to the point of interest). B: Functional diagram of a Monte Carlo code illustrating the required input data. Cross-section data include total attenuation coefficients, total cross-sections for each collision process, and differential cross-sections, which are used to randomly sample the distance between successive collisions, the interaction mechanism at each collision, and the angle and energy of the scattered photon leaving each collision, respectively. Sequences of random numbers are obtained from a “random number generator,” a computer program designed to generate a pseudorandom sequence of numbers uniformly distributed between 0 and 1.

AAPM Task Group 43 Report: A Table-Based Dose Calculation Formalism

An important milestone in modern BT dosimetry is the publication of the original AAPM Task Group 43 Report in 1995⁹⁸ and a substantially revised and expanded version in 2004.⁵ The TG-43 approach consists of using measured and Monte Carlo–generated dose-rate distributions directly for clinical dose calculation aided by a standard table-lookup formalism. The revised TG-43 report and a more recent supplement⁴² include the following:

1. A recommended dose calculation formalism for representing 2D and 1D dose distributions around interstitial sources specifically designed to use a sparse matrix of Monte Carlo or measured dose rates as its input.

2. A critically reviewed set of 2D dose distribution data for 16 ¹²⁵I ¹⁰³Pd seed models that satisfy the AAPM dosimetric prerequisites¹¹⁴ as of July 2003. For each of these source types, a consensus dose distribution in TG-43 formalism format is recommended based on “merging” published Monte Carlo and experimental dosimetry datasets that met the standards laid out in Section V of the report.

3. A history of air-kerma strength primary standards,⁶⁴^,⁹⁷ which summarizes previous AAPM guidance,¹²⁵^,¹²⁶ including the impact of calibration shifts on the delivered-to-prescribed dose ratio.

4. Methodologic recommendations for obtaining TG-43 dosimetry parameters from TLD measurements or Monte Carlo simulations, including uncertainty analyses.

5. Guidance on clinical implementation of TG-43 report recommendations.

The TG-43 report recommends that treatment-planning software vendors accept the TG-43 formalism as the basis of dose calculation or at least for data entry, allowing users to easily input the new data into their systems. With the introduction of the new WAFAC-based air-kerma strength standard by NIST and the growing number of low-energy interstitial BT sources commercially available, the radiotherapy community has embraced the TG-43 dose calculation formalism, described later, as well as many AAPM recommendations associated with TG-43 implementation. Most important among these are the AAPM dosimetric prerequisites for routine non-institutional review board–approved BT procedures.¹¹⁴ Only low-energy sources with NIST-traceable S_K calibrations supported by annual intercomparisons among NIST, the ADCLs, and the vendor¹²⁷ and two independent Monte Carlo and experimental dosimetry studies published in the peer-reviewed literature will be posted on the AAPM/RPC website⁴³ or included in future TG-43 supplements. A similar dosimetry validation process is under development for higher-energy sources.¹²⁸

Because changes in calibration standards and dosimetry parameters also alter prescribed-to-delivered dose ratios, radiation oncologists must embrace new dosimetry systems and source-strength standards that can have important implications for selection of prescribed dose, interpreting published outcome studies, and consistently reproducing their clinical experience through time. AAPM reports provide detailed discussions and recommendations on managing these changes. For example, in ¹²⁵I monotherapy for prostate cancer, the pre–TG-43 prescribed dose of 160 Gy is equivalent to 145 Gy using the TG-43 dosimetry parameters.¹²⁵ Managing the up to 10% variations in prescribed-to-administered dose ratios due to the complex dosimetric history of ¹⁰³Pd monotherapy is reviewed in a 2005 AAPM report.¹²⁶

FIGURE 22.15. Illustration of Task Group Report 43 formalism for calculation of absorbed dose rate, (r,θ), at (r,θ), in a polar coordinate system centered about the source active core.

TABLE 22.4 DOSE-RATE CONSTANTS FOR SELECTED INTERSTITIAL SEEDS

General Formalism for the Two-Dimensional Case

For a cylindrically symmetric source of strength S_K (Fig. 22.15), dose rate, (r,θ), at the point (r,θ) is calculated in the TG-43 formalism as follows:

where r denotes the distance (in cm) from the center of the active source to the point of interest, θ denotes the polar angle specifying the point of interest relative to the source longitudinal axis, r₀ denotes the reference distance (specified to be 1 cm), and θ₀ is the reference angle (90 degrees or π/2 radians) that defines the source transverse plane. For ¹²⁵I and ¹⁰³Pd sources, AAPM guidance¹²⁵^,¹²⁶ uses the symbols S_K,N99 to designate the 1999 WAFAC-based NIST standard⁶⁴ and S_K,N85 to designate the previous standard introduced by Loftus⁹⁷ in 1985. The other symbols in Eq. (27) denote the following quantities:

G_L(r,θ) is the line-source geometry function in units of cm⁻².

λ is the dose-rate constant of the source type in units of cGy ⋅ h⁻¹ ⋅ U⁻¹.

F(r,θ) is the dimensionless 2D anisotropy function that takes the value unity for θ₀ at all r.

g(r) is the dimensionless radial dose function that takes the value unity at r = r₀.

The dose-rate constant in liquid-water medium is defined by:

where (r₀,θ₀) is the measured dose rate at the reference point. λ includes the effects of source geometry, spatial distribution of radioactivity, encapsulation, self-filtration in the source, and attenuation and scattering of photons in the surrounding medium. It also depends on the standardization measurements to which the S_K calibration of the source is traceable. For radium-substitute point sources, . During the era (1984–1999) of the S_K,N85standard, Table 22.4 shows that the classical point-source model overestimated absolute doses by as much as 15% for ¹²⁵I sources relative to TLD measurements and Monte Carlo calculations. In 1999, the S_K,N85 standard was replaced by the WAFAC (S_K,N99), which required an upward adjustment of these values, bringing the classical and quantitative values closer together. The old and new dose calculations are in close agreement for ¹⁹²Ir and other radium substitutes. This table shows that for both ¹⁰³Pd and ¹²⁵I sources, average agreement between TLD and Monte Carlo is about 5%, well within the total uncertainty of these comparisons.⁵⁸

The purpose of the geometry function, G_X(r,θ) (where the subscript x denotes point or line source), is to improve the accuracy with which dose rates can be estimated by interpolation from data tabulated at discrete points. Physically, G_X(r,θ) neglects scattering and attenuation and provides an effective inverse-square law correction based on an approximate model of the spatial radioactivity distribution within the source. Because the geometry function is used only to interpolate between tabulated dose-rate values at defined points, highly simplistic approximations yield sufficient accuracy for treatment planning.⁵ To improve the accuracy of linear interpolation near the source, the AAPM protocol requires use of (r,θ) for 2D calculations and prefers G_L(r,θ) over G_P(r,θ) for 1D calculations. For small cylindrical seeds, G_X(r,θ) is approximated by a line source.

where δβ = θ₂ – θ₁ is the angle (in radians) subtended by the active source with respect to the point (r,θ). For sources where the radioactivity is distributed over or within a right-cylindrical volume or annulus, L can be taken as the length of this cylinder. For sources containing uniformly spaced multiple radioactive components, L should be taken as the effective length, L_eff, given by L_eff = δS × (N), where N represents the number of discrete pellets contained in the source with a nominal pellet center-to-center spacing, δS.

The 2D anisotropy function F(r,θ) gives the angular variation of dose about the source at each distance as a result of self-filtration, oblique filtration of primary photons through the encapsulating material, and photon attenuation and scattering in the surrounding medium.

where the dose rates, (r,θ), are obtained by measurement or Monte Carlo simulation. The line-source geometry function is used to suppress the influence of inverse-square law on the angular dose distribution at short distances. Thus, F(r,θ) needs be tabulated only at a few distances, r, to facilitate accurate interpolation at all distances. Examples of anisotropy functions for various interstitial sources are illustrated in Figure 22.16 and Table 22.6.

The radial dose function, g_X(r), accounts for the fall-off of dose along the transverse axis as a result of attenuation and scattering in the medium, capsule filtration, and self-absorption.

g_X(r) is normalized to unity at 1 cm distance and is illustrated by Table 22.5. For 2D dose calculations, TG-43 recommends that X = L.

FIGURE 22.16. Examples of anisotropy functions evaluated for three different interstitial sources by the author’s group. A: Theragenics Model 200 “light seed” ¹⁰³Pd source.⁴⁹ B: DRAXIMAGE Model LS-1 ¹²⁵I seed.³⁴² C: Nucletron MicroSelectron Model V2 high–dose-rate ¹⁹²Ir source.³⁴⁷

TABLE 22.5 LINE-SOURCE RADIAL DOSE FUNCTIONS FOR VARIOUS ¹²⁵I Seed Sources^a

TABLE 22.6 EXAMPLE OF A TABULATED 2D ANISOTROPY FUNCTION, F(R,θ) TABLE, ALONG WITH ITS ASSOCIATED 1D ANISOTROPY FUNCTION, φ_AN(R), VALUES FOR A THERAGENICS I-SEED (MODEL I25.S06) ¹²⁵I Source

One-Dimensional Isotropic Source Approximation

Most commercial treatment-planning systems used for permanent implant dose computation support only 1D isotropic point-source calculations. Thus, the TG-43 formalism includes a 1D equation analogous to the classical isotropic point-source model, Eq. (22).

where φ_an(r) is the 1D anisotropy function defined by Eq. (21) and illustrated by Table 22.6.

INTERSTITIAL IMPLANTATION

The traditional implant systems (Manchester, Quimby, and Paris) that arose early in the 20th century were developed to guide the radiation oncologist in arranging and positioning radium needles within the surgically identified target volume. In contrast, the most frequently practiced implant procedure today, transperineal permanent implants of the prostate, uses image guidance to position the sources. In place of nomograms and classical system lookup tables, 3D computerized planning is used to prescribe dose and to optimize the implant geometry. However, even the most sophisticated commercially available dwell-weight optimization software used with single-stepping source remote afterloaders (see Chapters 23 and 24) requires the operator to specify the source and needle locations. To guide source positioning, we continue to rely on the classical systems of BT and their later variants.

Classical Systems for Interstitial Brachytherapy with Radium-Substitute Sources

The Manchester and Quimby systems were developed before the advent of computer-aided dosimetry in implant therapy, whereas the Paris system is based on multiplanar isodose distributions. All interstitial implant systems consist of the following components:

1. Distribution rules: Given a target volume, the distribution rules determine how to distribute the radioactive sources and applicators in and around the target volume.

2. Dose specification and implant optimization criteria: At the heart of each system is a dose specification criterion (i.e., a definition of prescribed dose). In the Manchester system, for example, the prescribed dose is the modal dose in the volume bounded by the peripheral sources. The distribution rules and dose specification criterion together often reflect a compromise between mutually exclusive goals such as dose homogeneity, normal tissue sparing, number of catheters implanted, dosimetric margins around the target, and presence of high-dose regions outside the target.

3. Dose calculation aids: These devices are used to estimate the source strengths required to achieve the prescribed dose rate as defined by the system for source arrangements satisfying its distribution rules. Older systems (Manchester and Quimby) use tables that give dose delivered per mgRaEq-h as a function of treatment volume or area. The more recent Paris system makes extensive use of computerized treatment planning to relate absorbed dose to source strength and treatment time.

The Manchester System

The Manchester system was developed by Ralston Paterson (radiation oncologist) and Herbert Parker (physicist) in the 1930s^129–132 and often is called the Paterson-Parker (P-P) system. The P-P system remains relevant to today’s practice patterns: its distribution rules, anticipating the “peripheral loading technique,” were designed to maximize dose homogeneity inside the implanted volume for volume implants and in the treatment plane (plane parallel to the needles at the treatment distance) for mold or planar implants (Fig. 22.17). Its volume and area lookup tables remain useful as QA tools for optimized HDR volume implants.

The P-P system rules preferentially concentrate radioactivity in the rind or periphery of the implant, compensating for the dose fall-off characteristic of a uniform-density implant, thereby improving dose uniformity. After deriving the optimal fraction of radioactivity to be implanted in the rind and core (4:2 ratio) using a radioactive fluid model, Parker coalesced the continuous radioactivity distribution into several concentric cylindrical surfaces and then further discretized these surfaces into individual needles. A more detailed discussion of the mathematical derivation of the Manchester system is given by Anderson and Presser.¹³³ Table 22.7 lists the rules of the Manchester system, and Table 22.8 lists the stated dose per mgRaEq-h and unit IRAK as a function-treated area or volume.

The P-P rules are designed to yield target area or volume dose distribution that deviates by no more than ± 10% of the stated dose, excluding cold spots in the corners and local hotspots at distances <5 mm from the source centers. For planar implants, the target or treatment surface (Fig. 22.17) is that area bounded by the peripheral needles, which is parallel to and 5 mm from the needle plane. For volume implants, the target volume is that region bounded by the peripheral sources. The distribution rules assume that both planar and volume implants will be crossed at both ends by needles placed orthogonal to the predominant direction of insertion and at the level of the belt needle active tips. Fixed 1-cm needle spacing is recommended, with full-intensity sources placed on the periphery of planar implants and partial-strength needles used as central needles. For volume implants, these two groups of sources are called “belt” and “core” sources, respectively. The stated or prescribed dose is the modal dose in the target region and is approximately 10% higher than the minimum peripheral dose (minimum dose to the implanted volume or area) and 10% below the effective maximum dose.

In effect, single-plane interstitial implants with crossed ends treat a 1-cm-thick target volume with an area equal to that bounded by the peripheral sources. Thicker target volumes (>1 cm) must be treated by using two parallel planes of needles placed on the target volume boundaries (double-plane implant), with source strength arranged according to the single-plane rules. The mgRaEq-h is calculated from the 0.5-cm single-plane table, multiplied by the appropriate two-plane separation factor, and divided between the two planes. The dose actually is delivered to the inner plane 0.5 cm from each needle plane, resulting in midplane cold spots ranging from 10% to 30% for separations of 1.5 to 2.5 cm. Target volumes thicker than 2.5 cm must be treated by the volume implant system.

FIGURE 22.17. Relationship between target volume or area and peripheral needles (solid color active regions) and central needles (hatched active regions). Notice that peripheral needles always are placed on the boundary of the target region. A: A planar implant designed to treat a target area. B: A volume implant designed to treat a cylindrical target volume. The peripheral needles distributed on the cylindrical surface of the target are called belt needles, whereas those at right angles are called end or crossing needles. Because the inferior of these implants are uncrossed, the target volumes effectively treated are 7.5%–10% shorter than the active length of the belt or peripheral needles.

TABLE 22.7 MANCHESTER SYSTEM RULES

TABLE 22.8 MANCHESTER IMPLANT TABLES

Volume implants can treat cylindrical, spherical, or cubic target volumes in which needles or seeds are arranged on concentric cylinders, concentric spheres, or parallel planes, using a 1-cm needle-to-needle spacing when possible. The target region is the volume encompassed by the peripheral sources. Regardless of implant size, 75% of the source strength should be placed in the rind and 25% in the core, with more specific rules for cylinder implants.

To apply the P-P system, the relationship between target volume, implanted volume (region enclosed by peripheral sources), and treated volume (region receiving 90% of the stated dose) must be appreciated for crossed and uncrossed end cases. The treated volume may be larger than the target volume but always should contain the latter. When both ends are crossed, the active length (AL) required and target length (TL) are identical. For volume implants, AL should be at least 7.5% longer than TL for each uncrossed end. For planar implants, the required AL can be calculated as follows:

Conversely, given AL, the length of the treated volume always can be calculated by solving the appropriate Eq. (33) for TL. The area and volume used for looking up dose per mg Ra Eq-h from Table 22.8should be calculated using the treated length. For example, for a single-plane implant with two uncrossed ends, width W and needles of active length AL, the area, A, used for table lookup is given by A = W × AL × 0.81.

To apply P-P tables to modern implants using ¹⁹²Ir wires or ribbons, several corrections must be applied. The 1938 P-P tables assumed a γ value of 8.4, ignored attenuation and scattering, neglected oblique filtration, and specified treatment in terms of exposure rather than absorbed dose. For ²²⁶Ra needles, an average correction of 0.90⁹⁵ was applied to the original P-P tables to estimate absorbed dose. Modifying these corrections for ¹³⁷Cs needles and ¹⁹²Ir seeds and adding an additional factor of 10% to convert from stated (modal target dose) to minimum target volume dose, we obtain the following equivalencies:

Using the 0.90 cGy/P-P R conversion factor, Stovall and Shalek⁹⁵ found excellent agreement between computer calculations and the P-P tables for a variety of planar and cylindrical implants following the Manchester distribution rules. For single-plane implants, 90% of the stated dose in cGy covers 94% to 99% of the target area. For cubic arrays of seeds using fixed 1-cm spacing, agreement between the tables and computer calculations is excellent for larger treatment volumes (>100 cm³⁾¹³⁴^,¹³⁵ but exhibits errors ranging from 10% to 40% for smaller arrays. These discrepancies probably result from deviations from the 4:2 activity ratio and use of a dose specification criterion incompatible with the Manchester system.

The classical implant systems are based on ¹⁹²Ir wires or interstitial needles, consisting of continuous distributions of radioactivity (i.e., line sources) with well-defined active lengths. To apply the classical systems to modern interstitial sources consisting of discrete seeds, the dosimetric equivalence between ribbons of discrete seed sources and line sources must be appreciated (Fig. 22.18). A ribbon consisting of N seeds with center-to-center separations, S, has a dose distribution that closely approximates that of a continuous line source of length, AL, and strength (S_K)_line:⁸¹^,¹³⁶

This equivalence tends to break down at distances less than S/2: the cylindrical isodose curves break up into ellipsoidal shapes centered about each seed. In addition, the ribbon isodose curves undulate significantly at distances comparable with or less than the gap, S, between adjacent seeds, although on average the equivalence remains accurate.

Because the P-P system uses 1-cm interneedle spacing, the fraction of sources in the core (versus periphery) increases as volume increases. Thus, using uniform-strength ¹⁹²Ir ribbons and fixed spacing results in underloading the core for very small implants and overloading the core for very large implants, relative to the P-P distribution rules. In the latter case, the gap between minimum peripheral dose and central maximum dose widens. An alternative to the differential loading method is to vary the ribbon spacing with implant size, using smaller (<1 cm) spacing for very small implants and larger spacing (up to a limit of 1.5 cm) for larger implants, so that the relative number of central ribbons complies approximately with the P-P rules, allowing uniform seed strengths to be used. Two examples of this strategy are given in the next section.

To use the Manchester tables for verification of computerized dose calculations requires a method for objectively identifying the computer-generated isodose surface that corresponds to the minimum peripheral dose rate predicted by the Manchester system. For volume implants, mean central dose (MCD), a quantity proposed by the ICRU report on dose specification in interstitial BT, is useful⁶¹ (Fig. 22.19). In the authors’ experience, the maximum dose (110% of stated dose) of the Manchester system is closely approximated by MCD. Minimum peripheral dose and stated dose are given by 80% and 89%, respectively, of MCD. For planar implants, the minimum dose/MCD ratio varies from 55% to 70%, depending on catheter spacing, and is of limited value.

FIGURE 22.18. Relationship between a linear array of equally spaced discrete seeds and its dosimetrically equivalent line source. Both sources are assumed to have the same total strength. Common errors in defining this equivalence are illustrated.

Manchester Volume Implant Example

A 5-cm-high by 5-cm-diameter cylindrical target volume is to be treated using ¹⁹²Ir ribbons with seed-to-seed and intercatheter spacings of 1 cm and 1.3 cm, respectively (Fig. 22.20). The followings describe steps to calculate (a) the minimum ribbon length needed, (b) the required ribbon arrangement, and (c) the strength/seed needed to deliver 45 cGy/hour to the P-P minimum dose specification volume.

a. There are two approaches: treating the ribbons as needles with uncrossed ends or treating the proximal and distal seeds of each ribbon as crossing sources. In the uncrossed end approach, Eq. (33) implies that

Eq. (35) implies that N = 6 seeds/ribbon are required.

In the crossed-end approach, the first and last seeds must be placed at the target volume surfaces, again requiring 6 seeds/ribbon.

b. To satisfy the 1.3-cm ribbon-spacing requirement, 12 ribbons must be placed on the cylindrical target boundary, six ribbons must be placed on an inner cylindrical surface, and there should be one central ribbon. Treating the ends as uncrossed and assuming that the ribbons have uniform strengths, the belt-to-core ratio is 0.63:0.37, which is close to the P-P 4:2 ratio. Again, assuming all seeds have the same strength, Figure 22.20 shows that the required crossed-end ratios are also closely approximated. This illustrates that ribbon spacing can be manipulated to adhere to the P-P distribution rules with uniform strength sources.

FIGURE 22.19. A: Calculation of mean central dose (MCD) as the arithmetic mean of the doses at mid-distance between each pair of adjacent sources for single-plane implants and the mean of the local minimum doses between each group of three adjacent sources in a multiple-plane implant. All local minimum doses are specified in the “central transverse” plane, which is normal to and bisects the source axes. B: Practical specification of MCD for a computer plan.

FIGURE 22.20. A: Cylindric volume implant, example (C), using uniform strength ¹⁹²Ir ribbons spaced at 1.3-cm intervals. Central transverse (B) and coronal (C) isodose curves are plotted normalized to the mean central dose (MCD) = 58.9 cGy/hour = 100%: 115% (68 cGy/hour), 100% (59 cGy/hour), 90% (53 cGy/hour), 80% (47 cGy/hour), 60% (35 cGy/hour), 40% (24 cGy/hour), 20% (12 cGy/hour). Note that 80% of MCD, 47 cGy/hour, agrees closely with the minimum peripheral dose rate of 45 cGy/hour predicted by the Paterson-Parker tables.

c. Assuming the uncrossed end point of view:

Hence:

Differential Loading:

Uniform Loading:

TABLE 22.9 PARIS SYSTEM CHARACTERISTICS

The Quimby System

The Quimby system was developed by Edith Quimby et al.¹³⁷^–¹³⁹ at New York Memorial Hospital from 1920 to 1940. Unlike the Manchester system, equal linear intensity (mgRaEq/cm) needles are distributed uniformly (fixed spacing) in each implant. Like the Manchester system, the associated Quimby tables give the mgRaEq-h needed to deliver a stated exposure of 1,000 R as a function of target volume or area.

The so-called planar implant tables were intended for surface molds; none of the early Memorial publications suggest that it was used for single-plane interstitial implants. In part because Quimby’s stated dose is the maximum dose in the treatment plane, Quimby planar implants deliver 30% to 40% less radiation (IRAK) per unit stated dose than an equivalent Manchester implant delivers. Rules for distributing radium needles (relationship to target-area boundaries, crossed ends, spacing, etc.) are not clearly described. Volume implant needle arrangements are similar to their Manchester counterparts; both systems recommend crossed ends and placing peripheral needles on or beyond the target volume boundaries. However, Quimby allows the needle spacing to vary with implant size and specifies dose as the absolute minimum to the target volume. The physical and mathematical origins of the widely cited Quimby volume implant table are obscure; the tables published in the 1951 edition of Physical Foundations of Radiology¹³⁸ deliver 25% to 90% more mgRaEq-h per unit dose than P-P volume implants of similar size. Because they are evenly spaced, uniform-strength sources approximate the Manchester distribution rules for medium-size volumes, and these differences are likely a result of differences in the definition of “minimum dose” used by the two systems. Although vague on the subject, Quimby appears to specify minimum dose at a point located 3 to 5 mm from the peripheral needles (and therefore outside the target volume) near their active tips.¹³⁹ This corresponds to a treatment volume (volume encompassed by prescription isodose surface) that is 6 to 10 mm larger in diameter than the implanted volume (used for table lookup) in each linear dimension. The Quimby planar and volume dose specification criteria are clearly inconsistent, and a detailed derivation of the associated tables is lacking. For these reasons, we do not recommend Quimby tables for clinical use.

The Paris System

The Paris system was developed in the early 1960s by Pierquin, Chassagne, Dutreix, and Marinello¹⁴⁰^,¹⁴¹ and was motivated by the ¹⁹²Ir afterloading techniques developed by Henschke. Outside the United States, the Paris system is widely used for definitive BT of localized lesions in the head and neck, breast, and many other sites. An up-to-date summary of the system has been published by Gillin and Mourtada.¹⁴²

The starting point of the Paris system is the definition of the target volume, which is described in terms of thickness T, length L, and width W. The system provides rules for constructing implants, which, if followed, guarantee that the target volume is completely covered by the prescription isodose surface (Table 22.9). The prescription dose level, called the “reference dose,” is a fixed percentage (85%) of the basal dose (see Fig. 22.21), which closely resembles the more general concept of mean central dose in Figure 22.19. ¹⁹²Ir wire sources are arranged in parallel rectilinear arrays with their centers located in the central plane, which is perpendicular to the sources. Adjacent sources must be equidistant from one another, resulting in single-plane implants with equal spacing and double-plane implants with groups of adjacent sources arranged in equilateral triangles or squares in the central plane (see Fig. 22.21). The linear density (μGy · m² · h⁻¹/cm) must be uniform and the same for all sources. Interneedle spacing scales with the thickness, T, of the target volume. The number of sources is determined largely by the relative shape of the target volume cross-sectional area, W × T. In contrast, the Manchester system uses fixed spacing and increases the number of sources as the cross-sectional area of the target volume increases.

Table 22.9 shows that the location of the peripheral sources relative to the treated volume (region encompassed by the reference isodose-rate surface, as shown in Fig. 22.22) differs from the Manchester system, which implants to the boundary of the treated tissue. In the transverse plane, the peripheral sources lie 2 to 4 mm (the lateral margin distance, M) inside the treatment surface, whereas longitudinally the AL extends 15% to 20% beyond the distal and proximal margins of the target volume. In practice, the margin, M, is treated as a safety margin, and the peripheral needles are implanted along the margins of the clinical target volume (CTV). The maximum thickness, T, of a target volume treatable in the Paris system is about 2.5 cm. An example of a double-plane implant arranged in squares is shown in Figure 22.23.

To apply the Paris system, the target thickness T must be known, which defines the spacing and determines whether single-plane or double-plane geometry is required. The number of sources and selection of a square or triangular arrangement are defined by the relative cross-sectional shape of the target volume in the central plane perpendicular to the sources. Finally, the active length is calculated. The source tip and end coordinates are reconstructed from orthogonal radiographs and the dose distribution and basal dose are calculated by computer for the actual implant geometry realized in the patient, not the idealized implant of clinical intention. This approach differs from the classical Manchester method, which bases dose prescription on the P-P table and, in general, ignores deviations of the actual implant geometry from the ideal. The Paris system addresses only single- and double-plane implants; large-volume implants for treating pelvic masses and brain tumors were not part of the original system. Extensions of Paris system principles to large-volume implants are discussed by Leung¹⁴³ and Gillin et al.¹⁴⁴

FIGURE 22.21. The three central plane configurations allowed by the Paris system: (A) single-plane implant, (B) double-plane implant using the pattern of squares, and (C) double-plane implant using the pattern of equilateral triangles. The calculation of basal dose rate at a point equidistant from each group of adjacent sources is illustrated for each configuration. (From Gillin MT, Albano KS, Erickson B. Classical systems II for planar and volume temporary interstitial implants: the Paris and other systems. In: Williamson JF, Thomadsen BR, Nath R, eds. Brachytherapy physics. Madison, WI: Medical Physics Publishing, 1995:232–343, with permission.)

FIGURE 22.22. Relationship of the reference isodose, source locations, and target volume dimensions for each of the basic implant configurations allowed by the Paris system. The concept of safety margin (lateral margin, M) is illustrated. (From Pierquin B, Wilson JF, Chassange D. Modern brachytherapy.New York: Masson, 1987, with permission.)

Dose Specification in Interstitial Brachytherapy

Many of the differences between the Manchester, Paris, and Quimby systems can be attributed to fundamental differences in dose specification. Because of the high-dose gradients near the peripheral sources or the target volume boundary, reproducible specification of dose and evaluation of implant quality are difficult. Conversely, small differences in dose specification criteria can lead to large differences in treatment time or in the geometric relationship between implanted and treated volume. The term dose specification means objective identification of a spatial volume or location for evaluating absorbed dose for the purposes of prescription (defining the dose that the radiation oncologist intends to deliver), for describing the quantity of radiation actually delivered to the patient, or for reporting. The “specified dose” sometimes is called “reference dose.” The dose that an implant actually delivers to the patient, based on postinsertion treatment planning, may differ significantly from the dose prescribed for a variety of reasons. For example, anatomic or technical constraints may preclude accurate positioning of sources at their intended locations, resulting in a partial geometric miss or underdose of the specified volume. Dose specification for reporting purposes usually refers to efforts to develop reproducible and system-independent specification schemes to promote comparison of different implantation systems so as to minimize patient-to-patient and operator-to-operator variability in level of treatment delivered. The ability to objectively compare different interstitial implant plans as to target volume coverage, normal tissue sparing, and dose homogeneity depends on dose specification. Several divergent and rather abstract approaches to dose specification have been developed and promoted by various national and international advisory groups; no single approach to dose specification has been widely accepted within the BT community.

FIGURE 22.23. A: Isodose curves of a Paris system double-plane implant arranged “in squares” to treat a 2.5-cm × 4-cm × 5-cm target volume (heavy lines). The separation and active lengths of the ¹⁹²Ir wires are 1.6 cm and 7.3 cm, respectively. A linear strength of 6 μGy · m² · h⁻¹/cm gives reference (100%) and basal (117%) dose rates of 60 cGy/hour and 70.6 cGy/hour, respectively. B: Comparison of dose–volume histograms (DVHs) calculated separately for the 2.5-cm × 4-cm × 5-cm target volume and the tissue outside the target for the Paris implant shown and a Manchester implant consisting of three planes, 15 ¹⁹²Ir ribbons with six seeds each, and 1.25-cm spacing between planes and ribbons. Each graph shows volume of tissue (in multiples of volume of the target) receiving at least the specified dose (in multiples of prescribed dose). For the Paris and Manchester implants, respectively, prescribed dose is the calculated reference dose and minimum target dose predicted by the Paterson-Parker volume table. In both systems, the prescription isodose surface covers about 90% of the target. Surprisingly, both normal tissue sparing and dose homogeneity in the target are slightly better for the Paris implant.

Minimum Dose to an Anatomically Defined Target Volume

The minimum dose to the anatomically defined target volume harboring malignant cells is conceptually attractive because it is based on the intuitively satisfying premise that local tumor control will be determined by the minimum dose received by tumor cells. The ABS¹⁴⁵ recommends that minimum dose should be identified as accurately as possible by the best means available and should be used for dose prescription, evaluation, and reporting. In practice, minimum target dose specification is difficult to implement clinically for many implants. In the prostate BT literature,¹⁴⁶ minimum target dose usually is called “minimum peripheral dose,” or mPD, when used for implant preplanning prescription and D₁₀₀ (see discussion on dose–volume histograms) when used for postimplant dose evaluation. When imaging studies showing the target volume in relation to the sources are not available, the ABS recommends approximate target localization by means of intraoperatively placed surgical clips, orthogonal planar imaging, or measurements relative to peripheral sources. A clear disadvantage of minimum dose specification is that the target volume surface lies within the zone of largest dose gradient. This can result in large patient-to-patient fluctuations in the central-to-specified dose ratio because of small variations in the peripheral source locations relative to the apparent target boundary or uncertainties in delineating the target volume. As discussed in the Permanent Implantation section later, reviews of CT-based prostate implant dose evaluations show that absolute minimum delivered doses (D₁₀₀) relative to the prescribed dose show large patient-to-patient variabilities and average 30% to 60%.¹⁴⁷^,¹⁴⁸ The minimum dose covering at least 99% (or 95%) of the target volume has been found to be much less sensitive to small changes in the peripheral seed locations or uncertainties in the target volume surface location.

Minimum Implant Dose Relative to Sources

Traditional treatment planning uses planar radiographs for 3D reconstruction of radioactive source positions, yielding accurate dose estimates relative to the sources but not relative to an anatomic target volume.¹⁴⁹ Thus, it is natural to prescribe treatment to a point or surface that has a fixed relationship to the peripheral sources. The minimum implant dose, or MID, is the minimum dose received by the so-called target volume defined relative to the implanted volume, the smallest regular geometric shape circumscribing the peripheral sources. Often this specification volume is taken to be that volume that is 2 to 5 mm larger in each linear dimension relative to the implanted volume, as in the Paris and Quimby systems. With the exception of image-guided prostate implants, MID is perhaps the most widely used specification approach and is the basis of the classical systems and the U.S. practice of selecting prescription isodose surfaces from 2D isodose curve plots. However, MID yields information about tumor coverage only to the extent that the radiation oncologist has implanted peripheral sources at known distances from the anatomic target volume boundaries. In addition, MID lies in the zone of maximum dose gradient and can be difficult to evaluate objectively for an implant of irregular shape, again leading to large patient-to-patient variations and variations in the central-to-prescribed dose ratio. The Paris and Manchester systems eliminate the possibility of subjective isodose selection by rigidly specifying dose rate by means of basal dose rate and implant tables, respectively.

Mean Central Dose

The ICRU report on dose specification in interstitial BT⁶¹ emphasizes reporting mean central dose (MCD; see Fig. 22.19), although it recommends reporting the prescribed dose, the peripheral dose (minimum target dose), and a description of dose uniformity as well. MCD specifies dose in the low-gradient regions located between adjacent source locations in the central plane of the implant. Thus, MCD is relatively free of the variability inherent in minimum peripheral or target dose specification. It is a generalization of the Paris system basal dose. As a reporting parameter, MCD can be reproducibly estimated from 2D central transverse-plane isodoses and should be very useful for comparing implants performed using different clinical systems. However, for systems other than the Paris and Manchester systems (which rigidly specify how sources are to be arranged relative to the target volume), MCD does not have a known relationship to minimum peripheral or target dose. Thus, its value as a prescription parameter is limited.

Three-Dimensional Dose–Volume Histogram Representations

DVHs are 1D plots that describe the distribution of tissue volumes, V, irradiated by the implant with respect to dose, D. DVHs can be presented in either differential, δV(D)/δD, or cumulative, V(D), forms. DVH computation involves calculating dose over a fine 3D grid extending at least 2 cm beyond the peripheral seeds, dividing the dose axis into small bins of width δD, and then counting the number of voxels falling into each dose interval. The cumulative DVH gives the volume of tissue, V(D), receiving a dose of at least D.

DVHs can be evaluated for specific anatomic regions (e.g., target and normal tissue as illustrated by Fig. 22.23) or can be evaluated for tissue irradiated by the implant without regard to anatomic boundaries. For bounded volumes, V(D) is flat below the minimum dose received by the structure. When evaluated over unbounded space, V(D) steeply increases with decreasing dose and asymptotically approaches the central point-source DVH, V_point() = (4π/3) · [S_K · λ/]^3/2. The use of DVHs has enriched discussions of dose specification by focusing attention on describing the 3D dose distribution rather than on single parameters. However, in the absence of target volume and normal tissue geometry, DVHs in themselves do not solve the dose specification problem.

Because 3D anatomic models were often lacking until recently, several figures of merit (FOMs) derived from DVHs have been proposed that do not require an anatomically defined target volume. Such FOMs may be useful for ranking the quality of competing implant geometries in terms of uniformity and normal-tissue sparing or for optimally selecting a specification dose rate for a given implant geometry. An important contribution is the “natural” DVH introduced by Anderson.¹⁵⁰^,¹⁵¹ The natural DVH is a plot δV(u)/δu where u = D^−3/2. The natural DVH plots as a horizontal line for a central point source. It suppresses r⁻² effects, which dominate the conventional V(D) plot, making its detailed implant geometry–specific structure more evident. Low and Williamson¹⁵² introduced an alternative modified DVH, R_p(D) = V_impl(D)/V_point(D). Both of these modified DVHs show a sharply defined peak centered about MCD, the width and height of which quantify the volume of tissue receiving an approximately uniform dose. Other useful quality measures include the uniformity index¹⁵³ and the dose nonuniformity ratio (DNR).¹⁵⁴ The DNR, usually plotted as a function of reference dose, D_r, is defined as the ratio of volume receiving a specified multiple of D_r (usually 1.25 or 1.5) to that receiving at least D_r.

Target volume–dependent DVH quality indices were introduced by Saw and Suntharalingam.¹⁵⁵ For single- and double-plane implants designed to cover specified cubic target volumes, respectively, they defined three indices as a function of reference dose D_r. The coverage index, CI(D_r), is that fraction of the target tissue receiving a dose ≥D_r. The homogeneity index, HI(D_r), is the fraction of target volume receiving doses between D_r and 1.5 D_r. The external volume index, EI(D_r), is the volume of tissue outside the target volume, expressed in multiples of the target volume, receiving dose rates ≥D_r. When these indices are plotted (Fig. 22.24), the tradeoffs among these clinical end points are evident. If a prescription dose rate is selected to maximize dose homogeneity (i.e., maximize HI), then 85% to 95% coverage of the target must be accepted. To minimize irradiation of tissue outside the target, both target coverage and dose homogeneity must be compromised. Low and Williamson¹⁵² suggested ranking competing implant geometries by specifying the HI achieved for the maximum reference dose level that yields a CI of unity. Zwicker and Schmidt-Ullrich¹⁵⁶ have applied this general approach to the problem of identifying optimal interplane separations in double-plane implants.

For TRUS-guided prostate implantation, DVH metrics such as D₁₀₀, D₉₉, and D₉₀, denoting the minimum doses administered to the highest dose volumes covering 100%, 99%, and 90% of the contoured CTV or PTV (planned target volume), respectively, have become widely accepted as reporting parameters.¹⁵⁷ Volumetric indices, such as the V₁₅₀, V₁₀₀, and V₉₀, which denote the fraction of the CTV or PTV receiving at least 150%, 100%, and 90%, respectively, of the prescribed dose, are recommended to assess dose homogeneity and to assess adequacy with which the prescription has been fulfilled.

FIGURE 22.24. Plot of coverage index (CI), external index (EI), and homogeneity index (HI) as a function of reference dose rate for double-plane implant consisting of five ¹⁹²Ir ribbons with seven 1-mCi seeds in each plane and a 6-cm × 6-cm × 2.5-cm target volume. Ribbon and plane spacings of 1.5 cm were used. (From Saw CB, Suntharalingam N. Reference dose rates for single and double plane ¹⁹²Ir implants. Med Phys 1988;15:391, with permission.)

FIGURE 22.25. Comparison of reference dose rate per unit air-kerma strength versus volume of the target volume for Manchester volume implants and ¹⁰³Pd and ¹²⁵I permanent prostate implants. The inset gives the exponents and proportionality constants needed to describe these relationships in terms of a simple power-law equation [Eq. (36)]. The data in the figure are from Yu,¹⁵⁹ Memorial,¹⁵⁸ and Manchester.¹²⁹

Permanent Implantation

In contrast to temporary implantation, in which treatment time is varied to control the total dose delivered, the dose delivered by a permanent implant is determined by the initial geometric arrangement of sources and S_K per source: once the patient is implanted, neither the total dose delivered nor the relative distribution can be modified easily. Up through the mid-1980s, manual planning and dose calculation tools were used widely to estimate the number and density of sources needed to deliver the prescribed dose or to intraoperatively correct for deviations between the planned and actual source locations. For radium-substitute sources (e.g., ¹⁹⁸Au), the Manchester, Laughlin,¹³⁴ or Shalek¹³⁵ tables and associated distribution rules have been used for this purpose.

Manual planning aids for radium-equivalent sources cannot be applied to low-energy seed (¹²⁵I and ¹⁰³Pd) implants because of the importance of tissue attenuation in this energy range. The influence of photon energy on the relationship between dose rate, , and implanted volume, V, is illustrated by Figure 22.25. Parker¹²⁹ recognized that this relationship can be described accurately by a power-law formula, of the form

In fact, the original Manchester table (Table 22.8), converted to modern units and quantities, can be derived from Eq. (36) by setting α = 3.49 and β = 2/3. Although ¹⁰³Pd and ¹²⁵I volume implants also can be described by the power-law formula, they have somewhat larger exponents, β, demonstrating that dose rate falls off faster with increasing volume than for radium-substitute sources.¹⁵⁸^,¹⁵⁹ The proportionality constants, α, are substantially lower, indicating that low-energy seed implants require higher source strengths to achieve a stated dose rate. The author-to-author variations in α values for the same radionuclide are due, in part, to differences in dose specification and implant construction. Anderson’s¹⁵⁸ analysis, based on the pre-TRUS era Memorial nomogram, assumes that dose is specified in terms of matched peripheral dose (MPD) and that all seeds are implanted 2 to 5 mm inside the target (prostate) boundary, whereas Yu¹⁵⁹ assumes that peripheral seeds are implanted on or outside the boundary and that minimum target dose is specified. Manual planning tools¹⁵⁹^–¹⁶² are available for a variety of implant types, characterized by different underlying single-source dose-rate distributions, seed arrangements, dose specification criteria, and absolute prescribed doses, yielding estimated seed strengths that differ significantly from one another. Before using one of these methods for quality assurance checks or preplanning, readers should assess carefully its consistency with dose calculation and planning methods used in their clinical practices.

The best-known manual planning tool for permanent ¹²⁵I implantation is the Memorial dimension averaging method.¹⁵⁸^,¹⁶³ The associated nomogram was used for manual intraoperative planning of implants delivered by directly implanting seeds into the surgically exposed prostate. After surgical exposure of the target volume (prostate), the three orthogonal dimensions of target volume are measured, and the arithmetic mean of these measurements, or average diameter, d_a, in units of centimeter, is calculated. Next, the total apparent activity, A_app (in mCi units), to be implanted is calculated as follows:

By means of a nomogram consisting of several juxtaposed logarithmic scales, the total number of seeds needed is estimated graphically given the strength per seed. Other nomogram scales were used to estimate the spacing between needles given the seed spacing along each needle track. The seeds are to be implanted inside the target volume boundary, such that peripheral needle-to-target boundary distance is <50% of the interneedle spacing. Anderson et al.¹⁵⁸ have extended the dimension-averaging nomogram to ¹⁰³Pd and reviewed the underlying assumptions of this method.

Eq. (37) is designed to deliver an MPD of 160 Gy over the life of the implant when d_a is more than 3 cm.¹⁵⁸ MPD is defined as the dose level whose corresponding 3D isodose surface encompasses a volume, V_E, equal to that of an ellipsoid having the same orthogonal dimensions as the originally measured target volume (V_E = pd_xd_yd_z/6). For a given implant, MPD is derived from the corresponding cumulative DVH, V(D), according to V_E = V(MPD). By design, the Memorial nomogram delivers significantly higher MPDs to target volumes with average dimensions <3 cm. Prescribed doses of 160 Gy delivered in the 1985–1999 era correspond to doses of 144 Gy when corrected for implementation of the WAFAC primary standard and Task Group 43 dosimetry parameters.¹²⁶ The MPD overestimates minimum target dose (mPD) because the prostate gland is rarely ellipsoidal and has small protrusions that may extend outside the MPD isodose surface. Likewise, small deviations of the peripheral seeds from their planned locations can alter dramatically the shape of the MPD isodose surface. One study¹⁶⁴ found that, on average, MPD was twice the D₉₉ level (the dose ensuring 99% target coverage on postoperative CT imaging) and that only 69% to 89% of the target volume received a dose equal to or greater than MPD.

Modern Developments in Interstitial Brachytherapy

Computerized Treatment Planning

Three modern developments in BT planning and delivery technology have significantly influenced implant design and utilization of classical system rules: (a) computer isodose calculations, (b) dwell-weight optimization of single-stepping source remotely afterloaded implants, and (c) utilization of 3D imaging to define target volumes and to guide applicator insertion.

Computer isodose calculations for interstitial implants were introduced in the early 1960s¹¹ and, along with software for reconstructing implant geometry from radiographs, have been routinely available for about 35 years. In contrast to the older classical systems, which are based on idealized geometries, computer-assisted planning capability permits evaluation of the dose distribution for the implant geometry actually realized in the patient. Thus, the brachytherapist can compensate for deviations between the actual and intended implant geometries through selection of the prescription isodose or by modifying the catheter loadings or locations. In principle, dose calculation capability permits preprocedure customization of catheter spacings, loadings, and locations relative to the target boundary as an alternative to classical system distribution rules. Because manual forward planning is so time intensive, only a small number alternative plans can be compared in practice. However, use of computer dose calculation to design implants and to specify dose has displaced the tables and implant rules of classical systems in many U.S. centers. Khan¹⁶⁵ calls this approach the “computer system” and points out that, in fact, it does assume simple guidelines for distributing the sources. These include 1-cm intercatheter spacing, uniform loading, and implanting to the boundary of the tumor. Dose specification usually is based on the concept of MID, described earlier. Thus, even in the era of computerized dose calculation, distribution rules derived from one of the historical implant systems still have relevance.

Dwell-Weight Optimization

A major development of the last two decades is a pronounced shift from LDR manual afterloading techniques to HDR BT. Single-stepping HDR source remote afterloading (see Chapter 24 for a detailed treatment) allows the treatment time (dwell time) to be individually specified at each treatment (dwell) position in the catheter. This permits use of dwell-weight optimization as a tool for improving dose uniformity and target coverage within implants. In contrast to the classical systems, which assume that ribbons and needs are of uniform linear density, dwell-weight optimization supports far more elaborate nonuniform source-strength distributions than those envisioned by the Manchester system rules. The published experience, confined largely to Paris-like double-plane breast implants, demonstrates that geometric optimization¹⁶⁶ preferentially increases the dwell times at dwell positions near the catheter ends. The most striking finding is that optimization allows the active-to-target length (AL/TL) ratio to be reduced from 1.33–1.5 to 1.1–1.25.¹⁶⁷^–¹⁶⁹ In the transverse plane, target coverage remains unchanged, whereas dose homogeneity is improved modestly, depending on the figure of merit used to quantify this effect. When dose-point optimization (specifying dose constraints at dose calculation points throughout the treatment volume) is used, acceptable dose homogeneity results with even smaller AL/TL ratios, even when all peripheral dwell positions are placed inside the target volume (AL/TL = 1.0)¹⁵²^,¹⁷⁰ for idealized volume implants and clinical volume implants.¹⁶⁸These early efforts did not address the practical problem of how to distribute dose-constraint points in clinical volume implants with irregular catheter spacings and how to select dwell positions to be activated in each catheter. Although dwell-weight optimization has the potential to reduce AL/TL ratios to near unity without sacrificing target coverage or dose homogeneity, the brachytherapist must rely on clinical experience or one of the classical systems to determine the catheter arrangement and locations relative to the target volume boundaries.

Image-Guided Brachytherapy and Image-Based Dose Reconstruction

The use of 3D imaging to preplan implants or intraoperatively guide catheter or seed insertion is growing rapidly. The most widely practiced form of image-guided BT is use of intraoperative TRUS to guide transperineal insertion of needles used to implant the prostate gland with low-energy seeds.³⁸^,³⁹ However, image-guided implant methodologies have been developed for HDR multicatheter interstitial¹⁷¹ and balloon-applicator intracavitary¹⁷² implants for accelerated partial breast irradiation following lumpectomy as well as HDR interstitial implantation for prostate cancer.¹⁷³ All of these approaches require delineation of the target volume and critical structure surfaces from 3D imaging studies. Then catheter or needle trajectories and, ultimately, seed or dwell position locations can be selected to improve target volume coverage while minimizing unnecessary dose to critical structures. The issues involved in utilizing image-guided and -based BT in HDR interstitial brachytherapy, including treatment planning, selection of imaging modality, and impact on clinical workflow, are covered in detail elsewhere.¹⁷⁴

As practiced by most brachytherapists, image-guided, intraoperatively planned implants continue to rely on the operator’s judgment for selecting source locations. These decisions are guided by a “loading approach,” or set of guidelines that specify margins, seed locations relative to the target boundary, spacings, and approximate periphery-to-core loading ratios.¹⁷⁵^,¹⁷⁶ Dose calculations and DVH quality indices often are used to guide manual source position adjustments to improve target volume coverage, improve dose homogeneity, and select source strengths (or dwell times) and the prescription isodose.

An important advance upon standard dose-point optimization is anatomy-based optimization in which constraints and treatment goals are defined in terms of doses to CTV or normal tissues contoured from 3D imaging studies rather than surfaces defined relative to dwell positions. The simulated annealing HDR dwell-time optimization technique developed by Lessard and Pouliot¹⁷⁷ illustrates the general features of the various optimization approaches¹⁷⁸^–¹⁸¹ that have been brought to bear on this problem (see Ezzell’s¹⁸² review for a highly readable introduction to BT optimization techniques). An objective or cost function mathematically measures the compliance of each candidate 3D dose distribution with the treatment goals and constraints specified by the physician. It consists of the sum of individual penalty factors, one for dose or dose-volume constraint for a specified structure, e.g., CTV, urethra, rectum, etc. Lower values imply greater success in meeting the specified treatment goals. The optimizer tries to find the set of dwell weights that minimizes the objective function. The inverse-planning technique of Lessard and Pouliot¹⁷⁷reduces CTV dose heterogeneity (V₁₅₀ of 29% vs. 50%) and urethral doses in clinical prostate implants compared to geometric optimization¹⁸³ and solves the problem of selecting active dwell positions and locations for dose-constraint points faced by the older dose-point optimization algorithms. While anatomy-based inverse planning does not optimize catheter trajectories, its proponents¹⁸⁴ argue that it reduces the dependence of implant quality on the number and accurate positioning of the catheters relative to the CTV boundary. If true, inverse planning could reduce the dependence of implant quality on operator skill and reduce the need to follow system-based needle insertion rules.

In summary, computerized dose calculation, dwell-weight optimization, and image-guided BT have made anatomy-based dose specification and higher quality implants a reality in some clinical settings. However, innovations still require users to conceptually plan implants in terms of specified source and needle distribution patterns, implant-target volume margins, and loading ratios. Specific rules borrowed from the classical systems (e.g., AL/TL ratios) may require significant modification when adapted to these modern technologies.

Permanent Implant Developments

The most important advance in permanent implantation in the last two decades is the rise of image-based and -guided techniques in prostate BT, currently its only widely practiced indication. The transperineal approach using intraoperative TRUS^38,¹⁸⁵ typically consists¹⁷⁴ of (a) acquiring a preplanning TRUS examination or “volume” study 2 to 3 weeks before the scheduled implant, (b) inserting the needles using interactive real-time TRUS imaging, (c) followed by CT-based postprocedure planning 0 to 30 days after the procedure. During preplanning, the PTV often is defined as the contoured prostate gland plus a discretionary margin. Most brachytherapists practice some form of peripheral loading to improve uniformity and reduce dose to the urethra. For example, the modified uniform loading as defined by Butler¹⁷⁵ distributes about 75% of the source activity in the periphery and emphasizes insertion of peripheral needles on or near the PTV boundary. Typically, needle locations and seed strengths are manipulated to achieve a prescribed minimum target dose (mPD or D_100%) of 145 Gy for ¹²⁵I monotherapy. For ¹⁰³Pd monotherapy, the ABS¹⁸⁶ recommends retaining the prescribed dose of 125 Gy (compared to 115 Gy used before 2000) following implementation of the NIST S_K,N99 standard and recently revised TG-43 parameters, based on the AAPM’s most recent analysis¹²⁶ of ¹⁰³Pd prescribed-to-administered dose ratios due to changes in calibration standards and dosimetry practice.

Dose specification, for recording and reporting doses actually administered by a permanent implant, is based on postimplant dose evaluation.¹⁴⁶ Following the implant procedure, a CT exam is obtained; the prostate gland, rectum, and bladder are contoured; and the seed locations are identified from the transverse images. The choice of dose specification parameter for this purpose has been the subject of intense investigation. Based on analysis of both idealized and actual implants, Yu et al.¹⁵⁹ found that the postinsertion D₁₀₀ was very sensitive to small random displacements of the seeds from their intended positions, which resulted in underdoses of 15% or more to small volumes in the target periphery. However, they found that the mPD of the idealized implant (no seed displacement) covered at least 90% of the target (i.e., D₉₀ ≥ mPD and V₁₀₀ ≥ 90%), even in the face of 6-mm seed displacements. Subsequent retrospective studies of patient implants (e.g., Merrick et al.¹⁴⁷) have confirmed these findings. Two groups¹⁸⁷^,¹⁸⁸ found a correlation between prostate-specific antigen (PSA) relapse-free survival at 4 years and D₉₀. In particular, Potters et al.¹⁸⁷ found a D₉₀ dose-response cutoff of 90% of the prescribed dose but could find no statistically significant cutoffs for D₁₀₀ and V₁₀₀.

An important contemporary development is “intraoperative planning,”¹⁷⁴^,¹⁸⁹ in which TRUS-based planning (and postimplant dose evaluation as well, in some implementations) is performed during the procedure itself rather than on a volume study acquired weeks before. Intraoperative planning eliminates uncertainties from differences in planning and treatment anatomy due to probe positioning errors or impact of hormone ablation or external-beam therapy. An extension of intraoperative planning is dose-guided implantation¹⁷⁴^,¹⁹⁰ or “dynamic dose planning,”¹⁹¹ in which intraoperative planning is repeated one or more times during the implantation procedure, thereby allowing optimized insertion of needles yet to be implanted to overcome errors in previously inserted sources.

INTRACAVITARY BRACHYTHERAPY

In contrast to the comparatively uniform dose distributions of interstitial BT, the unidirectional source arrangements used in gynecologic intracavitary BT give rise to dose distributions that fall off rapidly with distance from the applicator surface, producing large dose gradients across the target volume. Such large dose gradients make target volume–based dose specification difficult and give this treatment modality a highly empirical character. Numerous parameters have been used to prescribe, constrain, or report intracavitary therapy applications, including mg-h, mgRaEq-h, reference point doses (points A and B), bladder and rectal reference point doses, vaginal surface dose, treatment time, and the ICRU Report No. 38³ 60-Gy reference volume. This section will emphasize the physical relationships among these parameters and their dependence on applicator characteristics. Systems for treating carcinoma of the cervix, the most intensively studied form of intracavitary therapy, will be reviewed. Our focus will be further restricted to applicator geometries and treatment systems (e.g., Fletcher and Washington University/Mallinckrodt systems) derived from the Manchester system. This limited focus is justified by the fact that Manchester- or Fletcher-style applicators continue to be the dominant choice across the world for both HDR and LDR treatments.

The Manchester Family of Intracavitary Therapy Systems

The Manchester system, developed in 1938 by Tod and Meredith,⁹ has heavily influenced intracavitary treatment practice patterns throughout the world, especially in North America. The widely used Fletcher-Suit applicator system, the Fletcher loadings, and the point A and B reference points are all derived from the Manchester system. This system was the first to use applicators and loadings designed to satisfy specific dosimetric constraints.⁹^,¹⁹² It was the first system to use a radiation field quantity, exposure at point A, rather than mg-h, to specify treatment.

The Classical Manchester System

The original Manchester applicator system consisted of a rubber intrauterine tandem and two vaginal “ovoids,” whose ellipsoidal shape was designed to conform to the isodose curves arising from ²²⁶Ra tubes placed along their long axes. The applicators were designed for use with ²²⁶Ra tubes 2.2 cm long with 1-mm platinum filtration and an active length between 1 and 1.5 cm. The small, medium, and large ovoid minimum diameters were 2, 2.5, and 3 cm, respectively, and are the same as Fletcher’s small, medium, and large colpostats.¹⁹³ The preloaded ovoids contained no shielding and relied on extensive anterior and posterior packing to spare bladder and rectal tissue.

The reference point A (Fig. 22.26) originally was defined as the point “2 cm lateral to the center of the uterine canal and 2 cm from the mucous membrane of the lateral fornix in the plane of the uterus.”⁹ This seemingly arbitrary definition reflected the system developers’ view that “radiation necrosis is not the result of direct effects of radiation on the bladder and rectum, but high dose effects in the area in medial edge of the broad ligament where the uterine vessels cross the ureter.”¹⁹⁴ They believed the radiation tolerance of this area, termed the paracervical triangle, to be the limiting factor in the treatment of cervical cancer and used point A exposure to represent its average dose. In current practice, point A dose is used to approximate the average or minimum dose to the tumor. Point B, defined to be 5 cm from the patient’s midline at the same level as point A, was intended to quantify the dose delivered to the obturator lymph nodes.

The Manchester ovoid dimensions and applicator loadings were designed to ensure that the point A dose rate, about 0.52 Gy/hour in modern units, remained constant for all allowed applicator loadings and combinations. The design also ensured that the vaginal loading contribution to point A was limited to 40% of the total dose. Small, medium, and large ovoids were loaded with 17.5, 20, and 22.5 mg of radium, respectively, to compensate for the greater source-to-point A treatment distances with the larger ovoids. Medium (4 cm long) and long (6 cm) tandems were loaded, os to fundus, with source trains consisting of 10- and 15-mg sources and 10-, 10-, and 15-mg sources, respectively, whereas the short tandem (used for cervical stump cancer) was loaded with a single 20-mg radium tube. With the exception of the short tandem, these loadings satisfied the dosimetric constraints within 2%. The point B dose, determined largely by inverse-square law, is approximately 9 Gy for every 4,000 mg-h administered.

Without external-beam treatment to the whole pelvis, a total point A exposure of 8,000 R (72.8 Gy) in 140 hours split between two applications was prescribed.¹⁹² Because the point A dose rate is constant whether the application contains 60 mg of ²²⁶Ra (small ovoids, medium tandem) or 80 mg (large ovoids, long tandem), delivery of a fixed point A dose amounts to using time, not milligram-hours, as the factor that terminates the treatment. In contrast to the Paris and Stockholm systems, which prescribed a fixed number of milligram-hours, equivalent Manchester treatment regimens can deliver from 8,400 to 11,200 mg-h—a variation of 33%.

FIGURE 22.26. Definition of points A and B in an ideal application (left) and a distorted application (right), which is displaced to the left of the patient’s midline, and a uterus, which is tilted toward the right. Note that point A is carried with the uterus, whereas points B and P are defined to be 5 and 6 cm, respectively, to the right and left of patient midline. Point P is used by the Mallinckrodt Institute of Radiology System to specify minimum dose to the pelvic lymph nodes. (Adapted from Meredith WJ. Dosage for cancer of cervix uteri. In: Meredith WJ, eds. Radium dosage: The Manchester System, 2nd ed. Edinburgh: E & S Livingston, 1967:42–50.)

As the size of an intracavitary application (i.e., colpostat diameter and tandem length) increases, the penetration or “lateral throw-off” of the dose distribution increases. As colpostat diameter increases from 2 to 3 cm, the vaginal surface dose decreases by 35% relative to the dose 2 cm from the applicator surface; this is simply a consequence of increasing the source-to-surface distance. Similarly, increasing the tandem length increases the point B contribution relative to the uterine cavity surface dose; the radioactivity near the ends of the long tandem contributes little to the surface dose (because of inverse-square law), whereas each tandem segment makes roughly equal contributions to points remote from the applicator. These physical principles underlie the practice of using the largest colpostats and longest tandem that the patient’s anatomy can accommodate.¹⁰^,¹⁹²

FIGURE 22.27. A: Fletcher-Suit applicator system. From left to right are tandem insert loaded with dummy sources, colpostat source holders, vaginal cylinder sleeves, three curvatures of intrauterine tandems, cervical collars, Delclos mini-colpostats, and round-handled Fletcher-Suit colpostats with small and medium caps. The tubelike instrument in the left foreground is a cervical localization seed implanter. (A from Fletcher GH, Hamberger AD. Squamous cell carcinoma of the uterine cervix: treatment techniques according to size of the cervical lesion and extension. In: Fletcher GD, eds. Textbook of radiotherapy, 3rd ed. Philadelphia: Lea & Febiger, 1980:732–772, with permission.) B: Three orthogonal views of the 3M Fletcher-Suit Delclos colpostat, consisting of a stainless steel body. The removable parts of the tungsten alloy shield, which allow conversion of the applicator to a shielded Delclos mini-colpostat, are inset into a nylon cap (not shown) with an outer diameter of 2 cm. Shown are isodose curves (C) in the coronal plane 10 mm from the posterior face of the applicator and (D) in the transverse plane of the colpostat for a 72 μGy × m ² × h^{−1 137}Cs tube. (B–D from Williamson JF. Dose calculations about shielded gynecological colpostats. Int J Radiat Oncol Biol Phys 1990;19:167–178, with permission from Elsevier.)

Modern Fletcher-Suit Applicator Systems

The Fletcher applicator system (Fig. 22.27A) adhered to the basic Manchester design while incorporating many improvements including internal shielding. These shields are located on the medial aspects of the anterior and posterior colpostat faces (Fig. 22.27B) and consist of 180-degree and 150-degree disk-shaped 3- to 5-mm-thick tungsten sectors to shield the rectum and bladder, respectively.¹⁹³ The cylindrical colpostat body has a diameter of 2 cm that can be increased to 2.5 and 3 cm by use of small and large slip-on plastic caps, thereby retaining the Manchester ovoid dimensions. Afterloading capability was added to the Fletcher applicator by Suit et al.² The Fletcher loadings—15, 20, and 25 mg for small, medium, and large colpostats, respectively—are similar to those of the Manchester system, whereas tandem loadings are identical to their Manchester counterparts. Because of the similarity of Fletcher loadings (55 to 85 mg) to the Manchester loadings, point A dose rates are nearly independent of applicator dimensions.

The shielded Fletcher colpostat was designed to reduce dose to the bladder trigone and the anterior rectal wall without decreasing irradiation to the uterosacral and broad ligaments, thereby reducing the need for the extensive vaginal packing characteristic of Manchester insertions.¹⁹³ For a single colpostat (Fig. 22.27B–D), the maximum dose reduction varies from 40% to 50%.¹⁴^,¹⁹⁵^,¹⁹⁶ When the effects of the intrauterine tandem and the contralateral colpostat are included, applicator shielding reduces midline rectal and bladder doses by 21% to 34% relative to conventional treatment-planning calculations, which ignore shielding and include only the effects of source encapsulation.¹⁹⁷ CT-based dose evaluation studies reveal that colpostat shielding modestly reduces rectal doses, reducing the rectal D_2% by 2% to 11%¹⁹⁸ and the D_2mL by 10%.¹⁹⁹ Modern versions of the shielded Fletcher colpostat for LDR BT include the LDR 3M Fletcher-Suit-Delclos (FSD)¹⁴ and reproductions of the round-handled Fletcher-Suit¹⁹⁵ colpostats. For HDR BT, the Fletcher-Williamson²⁰⁰ applicator duplicates the original Fletcher shielding configuration. Weeks and Montana²⁰¹ have designed a CT-compatible version with afterloadable shields and an aluminum body having the same dimensions as the FSD applicator.

FIGURE 22.28. Mallinckrodt Institute of Radiology/Washington University (WU) applicator loadings used with Fletcher-Suit applicators for treatment of cervix carcinoma. Because the WU system uses Model 6500 3M ¹³⁷Cs tubes, equivalent mass of radium is used to specify loadings and mgRaEq-h, rather than mg-h, to prescribe intracavitary therapy. The point A dose rates assume the classical Manchester definition and average colpostat separations and tandem-colpostat alignments.

FIGURE 22.29. Radiographic definition of classical point A (2 cm above the cephalic-most aspect of the colpostat in the tilted coronal plane) and the revised point A (2 cm above the cervical collar top or center). Because the distance from the caudal-most intrauterine source tip to the colpostat center (tandem-to-colpostat displacement) varies from patient to patient, the vaginal contribution to revised point A is highly variable. The revised definition was suggested by Tod and Meredith in their 1953 article.¹⁹² (From Potish RA, Gerbi BJ. Role of point A in the era of computerized dosimetry. Radiology1986;158:827–831, with permission.)

Dose Specification in Intracavitary Brachytherapy

Point A Dose and Milligram-Hours

Two quantities are used widely to prescribe intracavitary BT: mg-h (or its modern equivalent, IRAK) is used in practices influenced by the M.D. Anderson Cancer Center system,¹⁰^,²⁰²^,²⁰³ whereas some form of the Manchester point A dose specification is used by most other practitioners. Efforts to unify these two prescription practices by identifying a linear relationship between the two quantities are misguided²⁰⁴ from the perspective of the Manchester system. The Manchester-like loadings specified by the Washington University/Mallinckrodt Institute of Radiology (WU) clearly show (Fig. 22.28) that despite a twofold variation in source strength loaded into the smallest versus the largest applicator system, the point A dose rate varies by only 15%. To deliver a fixed point A dose of 65 Gy with WU loadings, a constant total treatment time of approximately 100 hours is needed, resulting in delivery of mgRaEq-h ranging from 5,200 to 10,000 in any sample of patients characterized by a range of applicator sizes. Conversely, for fixed mgRaEq-h, prescription would result in a nearly twofold variation in total treatment time and point A dose.

The proportionality of point A dose and treatment time applies only to the classical (Manchester) definition of point A. Many radiation oncologists use a revised definition of point A (Fig. 22.29) that references its location to the cervical os (tandem collar, proximal aspect of the most caudal tandem source, or a gold seed implanted in the cervix) rather than to the lateral fornix. This practice obscures the relationship between point A and milligram-hour prescription philosophies. Potish and Gerbi’s²⁰⁴ study of 90 Fletcher applications demonstrates that the revised point A dose rates vary widely from patient to patient and are, on average, significantly higher than the classical Manchester value. Because point A is fixed to the tandem and the vertical tandem-to-colpostat displacement varies with each patient, the vaginal contribution to point A is highly variable. In contrast, classically defined point A dose rates are tightly grouped, are independent of the loading, and are in close agreement with the Tod-Meredith value. The vaginal contribution to classical point A is fixed by definition, whereas the intrauterine contribution is insensitive to colpostat-to-tandem displacement because of the parallel tandem isodose curves. Thus, the revised point A definition does not have the physical significance of the classical quantity. Use of revised point A dose to prescribe therapy for “free-floating” tandem and colpostat insertions may introduce large patient-to-patient fluctuations in treatment times because of small, clinically insignificant variations in implant geometry.

The previous discussion is applicable only to the Fletcher applicator system with relative loadings approximating those of the Manchester system. As the intrauterine-to-vaginal loading ratio (1:1 for the Manchester system) increases, and the maximum width of the pear-shaped reference isodoses falls and the rectal dose increases,²⁰⁵ appreciation of how loading influences isodose shape and normal-tissue doses is especially important in HDR BT as dwell-weight optimization invites deviation from classical loading rules. Using judiciously placed dose points to control the relative dimensions of the point A isodose surface, Mai et al.²⁰⁶ were able to increase tapering near the cephalad aspect of the tandem, reduce the vaginal surface dose, and modestly reduce the rectal dose with only slight loss of the maximum width of the pear-shaped isodose. These considerations suggest that dose-point–driven optimization of the dwell-weight distribution should be accompanied by a geometric analysis of the point A isodose surface (see ICRU Report 38 discussion later in this chapter) so that changes to target coverage can be assessed at least approximately.

Other applicators in current use include the HDR tandem and ring applicator²⁰⁷ and the LDR Henschke applicator.¹ The latter consists of hemispheric colpostats rigidly attached to the tandem with the vaginal source axes parallel to the intrauterine sources rather than transverse as in the Fletcher system. Henschke colpostats with internal shielding²⁰⁸ are available. Delclos et al.¹⁹⁵ note that the Fletcher and Henschke applicators system do not yield equivalent dose distributions, especially with respect to normal tissue sparing. The vaginal ring applicator consists of a circular guide tube (usually 34 mm outer diameter) with its plane fixed rigidly normal to the tandem. It is placed up against the cervix and vaginal fornices with a donut-shaped cap attached, which increases the distance between the vaginal mucosa and the circular array of dwell positions (of which only the lateral dwell positions are activated) to 7 mm (compared to 10 to 15 mm for the Fletcher colpostat). Thus, the fraction of source strength loaded into the ring must be reduced to avoid overdosing the vaginal mucosa.²⁰⁶^,²⁰⁹ Although rectal and vaginal vault doses relative to the point A dose similar to that of the Fletcher system can be achieved through careful optimization, the lateral coverage (i.e., maximum coronal width of the point A isodose) is reduced.²⁰⁶ Care must be taken in positioning the applicator system to avoid underdosing the gross tumor volume. Applicator geometry and loading practices should be changed only after extensive comparative evaluation of the old and new dose distributions to avoid dose distribution changes that would invalidate the evaluated clinical experience on which the brachytherapist’s knowledge of dose response rests. Finally, for applicator systems that deviate from the classical Manchester geometry or relative loading rules, one cannot assume that point A dose is proportional to treatment time over all allowed variations of applicator sizes and loadings.

FIGURE 22.30. Geometry for measuring of the three orthogonal dimensions of the pear-shaped International Commission on Radiation Units and Measurements (ICRU) reference isodose surface (broken line) in a typical treatment of cervix carcinoma using one rod-shaped uterine applicator and two vaginal applicators. Plane a is the “oblique” frontal plane that contains the intrauterine device. The oblique frontal plane is obtained by rotation of the frontal plane around a transverse axis. Plane b is the “oblique” sagittal plane that contains the intrauterine device. The oblique sagittal plane is obtained by rotation of the sagittal plane around the AP axis. The height (d_h) and the width (d_w) of the reference volume are measured in plane a as the maximal sizes parallel and perpendicular to the uterine applicator, respectively. The thickness (d_t) of the reference volume is measured in plane b as the maximal size perpendicular to the uterine applicator. (From ICRU. Dose and volume specification for reporting intracavitary therapy in gynecology: report 38. International Commission of Radiation Units and Measurements, 1985, with permission.)

Volumetric Specification of Intracavitary Treatment: ICRU Report No. 38 Recommendations

The ICRU³ introduced the concept of reference volume enclosed by the reference isodose surface for reporting and comparing intracavitary treatments performed in different centers regardless of the applicator system, insertion technique, and method of treatment prescription used. Specifically, ICRU Report No. 38 recommended that the reference volume be taken as the 60-Gy isodose surface, resulting from the addition of dose contributions from any external-beam whole-pelvis irradiation and all intracavitary insertions. The ICRU proposed that this pear-shaped reference volume (Fig. 22.30) be described in terms of its three orthogonal maximal dimensions: height (d_h), width (d_w), and thickness (d_t), measured in the oblique coronal and sagittal planes containing the intrauterine sources. Figure 22.31 illustrates the bladder and rectal reference points recommended by the ICRU.

In contrast to point A dose and mgRaEq-h, the ICRU proposal is only a means of describing or reporting treatment. No guidance is given as to how to prescribe treatment, use these measurements to evaluate implant quality, or correlate reference volume dimensions with clinical outcome. The 60-Gy dose-level choice appears to have been motivated by the preoperative radiotherapy regimen popular within the French school of radiotherapy at the time.²¹⁰Descriptions of institution-specific treatment techniques for early stage cervical cancer patients include rules for evaluating the 60-Gy reference volume dimensions and offsets relative to the applicator system for the allowed combinations of applicator dimensions and loadings.²¹⁰ Within North America, Potish et al.,²¹¹^,²¹² and later Eisbruch et al.,²¹³ found that the individual ICRU reference volume dimensions and various geometric characteristics of Fletcher implants (e.g., colpostat separation and vertical and horizontal displacement of the tandem from the colpostat centers) were moderately well correlated. Other investigators²¹⁴^–²¹⁶ have proposed using the product of ICRU dimensions, V_ICRU = d_t × d_w × d_h, to estimate the relative volume contained within the reference isodose surface. Esche et al.²¹⁵ found that V_ICRU was directly proportional to mg-h, whereas Nath et al.²¹⁶ pointed out that V_ICRUincreased steeply with increasing whole-pelvis dose. In a retrospective clinical study,²¹⁴ grade 3 rectal complications were correlated with high d_t × d_w × d_h product, and severe bladder complications were associated with the combination of high bladder doses and large V_ICRU on a 2D scattergram. The rationale for studying the product of ICRU reference volume dimensions is the well-established correlation between the volume of tissue irradiated by external irradiation and clinical outcome.²¹⁷ In contrast to ICRU Report 38,³ which defines reference isodose surface dimensions for a single fixed dose level, these studies treat ICRU reference volume dimensions as functions of total dose or intracavitary dose.

The ICRU reference volume concept appropriately emphasizes that volume of tissue irradiated, as well as dose, is an important predictor of clinical response to intracavitary irradiation. Wilkinson and Ramachandran²¹⁸ and Eisbruch et al.²¹³ used DVHs to study the correlation between volume enclosed by intracavitary isodose surfaces and other prescription parameters. The latter analyzed the volumetric characteristics of 204 intracavitary insertions in 128 patients with carcinoma of the cervix and demonstrated that intracavitary implants delivering the same mgRaEq-h have nearly identical DVHs over the dose range of clinical interest despite significant differences in geometry and loadings (Fig. 22.32). They also showed that the volume, V(D,M), enclosed by isodose surfaces can be estimated accurately from a modified power-law model requiring knowledge of only the intracavitary dose in cGy (D) and mgRaEq-h (M):

The volume predicted by this simple model is accurate within ± 10% in 95% of the implants when M/D is more than 0.8, which corresponds to an intracavitary dose of 100 Gy for 8,000 mgRaEq-h of intracavitary therapy. In addition, the ratio of ICRU dimension product to the true volume given by DVH analysis, d_t × d_w × d_hV(D,M), varied widely from patient to patient and differed systematically from one implant type to another.

The consequences of Eq. (38) can be summarized as follows:

1. Volumetrically, an intracavitary implant behaves like a central point source: V(D,M) ∝ (MD)^3/2 .

2. Describing an implant in terms of volume contained within its isodose curves carries no more information content than a statement of mgRaEq-h or total reference air kerma.

3. The volume of tissue irradiated to a specified dose is closely related to total exposure given by the implant in terms of mgRaEq-h, TRAK, or IRAK.

Consequence (2) suggests that the correlation between clinical outcome, in terms of tumor control and complications and isodose surface volume, should be no better or worse than the correlation between clinical outcome and mgRaEq-h for a fixed external pelvis dose. Consequence (3) suggests a new and fundamental physical interpretation of mgRaEq-h or its derivative, total reference air kerma. Prescribing intracavitary BT by mgRaEq-h is equivalent to treating until each specified isodose surface achieves a fixed volume independent of the underlying implant geometry. Use of mgRaEq-h to constrain intracavitary treatment therefore limits the volume of tissue irradiated to high doses. This observation may help explain the clinical utility of mgRaEq-h as a dose specification parameter. Finally, the individual reference isodose dimensions, which are more strongly influenced by implant geometry than their product, clearly convey additional information about the spatial extension of the reference isodose surface in their respective planes and cannot be reduced to a statement of total exposure from the implant and may have additional prognostic significance.

Practical Systems for Intracavitary Prescription and Reporting

For Manchester-like loadings and applicators, if treatment were to be prescribed as a fixed number of mgRaEq-h or IRAK without regard to the diameter and length of the applicators, the treatment times and total point A doses would differ by the ratio of total source strengths in the applications. Small applications would have unacceptably high point A and vaginal vault surface doses and excessively long treatment times. In contrast, large applications treated to a fixed mgRaEq-h prescription would underdose these reference points. In contrast, the ICRU reference volume for fixed levels of whole pelvic irradiation and mgRaEq-h would be independent of the loading because the mgRaEq-h is constant. Conversely, when the point A dose is held constant, the mgRaEq-h needed to deliver these doses will vary significantly, introducing corresponding variations in the volume of the ICRU reference isodose.

TABLE 22.10 SIMPLIFIED FLETCHER SYSTEM PRESCRIPTIONS

Clearly, no IRAK-based system would endorse such a naive approach. Actual mgRaEq-h–based systems use a combination of parameters. Physically, mgRaEq-h or IRAK controls the volume of tissue treated to high doses, and parameters such as time, colpostat surface dose, and point A are used to control doses at points near the applicator to ensure that surface tolerance is not exceeded and that the tumor is not undertreated. For each applicator combination and choice of external-beam dose, a compromise between volume of tissue treated and dose delivered near the applicator must be reached. For example, the Fletcher system¹⁰^,²¹² specifies both a maximum treatment time and maximum milligram-hour constraint for each combination of external-beam and intracavitary therapy (Table 22.10). Whichever constraint is reached first terminates the application. Small applications tend to be terminated by the maximum time constraint, which limits the milligram-hour and prevents tissues near the applicator from exceeding tolerance doses, whereas larger applications are terminated by the milligram-hour constraint, ensuring adequate dose to the tumor. Although the historical Fletcher system does not use point A dose either for prescription or reporting, the total point A dose is constant within 12% for allowed tandem and colpostat loadings within each treatment scheme (A–E) of Table 22.10. The reader should note that the Fletcher system is a complex, highly individualized treatment system that resists formulation in terms of a few rules. Table 22.10 is a highly condensed and simplified summary derived from the literature, not from observation of current M.D. Anderson Cancer Center practice patterns.

The Washington University/Mallinckrodt Institute of Radiology (WU) system for prescribing intracavitary therapy illustrates another empirical approach for ensuring adequate dose delivery to the tumor while limiting the volume of tissue treated to high doses. Like the Fletcher system, intracavitary BT prescriptions are stated in mgRaEq-h. Historically, the WU system used Manchester-like applicators and loadings preloaded with ²²⁶Ra or ⁶⁰Co tubes, until the late 1950s when the Ter-Pogossian applicator was introduced. The system changed with the introduction of high-energy x-ray external-beam therapy in 1958, the adoption of the Fletcher-Suit applicator in 1965, and the acquisition of ¹³⁷Cs tubes in 1971.²⁰³ Because of the long association of the WU system with artificial radionuclides, equivalent mass of radium rather than mass of radium is used to specify source strength; hence, 1 mgRaEq-h in the WU system is equivalent to 1.07 mg-h in the Fletcher system, which, in turn, is equivalent to an IRAK of 0.00723 mGy m².

Manchester-like applicator loadings (Fig. 22.28) currently are used for LDR applications, yielding an approximately constant point A dose rate of 65 cGy/hour. For HDR applications, the dwell weights are selected to duplicate the relative Manchester loadings and the IRAK per insertion is reduced to reflect the increased radiobiologic effectiveness of the HDR fractionation schedule relative to the LDR regimen. Classically defined point A doses are calculated for reporting purposes for all patients, although this quantity plays no role in prescribing therapy. Dose to the pelvic lymph nodes is calculated at point P, located 2 cm superior to the lateral fornix and 6 cm lateral to the patient’s midline. Bladder and rectal reference points (Fig. 22.31) are defined according to ICRU Report No. 38.³ The prescribed doses for the external-beam and intracavitary (delivered in two LDR insertions) components of treatment are listed in Table 22.11 as a function of extent and stage of disease. The mgRaEq-h prescription is divided equally between the vaginal and uterine components and is delivered exactly as prescribed only in the case of the standard 80-mgRaEq application (2-cm diameter colpostats and long tandem, loaded 20-10-10). For nonstandard loadings using mini-colpostats, the vaginal and intrauterine IRAK prescriptions are modified independently. When Delclos minicolpostats are used, vaginal IRAK is constrained by the vaginal vault surface dose limit, which for LDR is 150 Gy (including whole-pelvic dose and the dose from the ipsilateral colpostat but excluding dose from the tandem and contralateral colpostat.). For medium and large colpostats, the vaginal mgRaEq-h is increased by 16% and 28%, respectively, to compensate for their larger source-to-surface distances. When medium and short tandem loadings are used, the target IRAK prescription is modified by the ratio of the actual loading to the standard loading (80 mgRaEq-h).

Table 22.12 illustrates detailed application of the WU system to three applicator configurations for prescription schema C, listing total doses for point A, point P, and the vaginal mucosa along with the volumes of tissue enclosed by point A and ICRU 60-Gy reference isodose surfaces. The mgRaEq-h actually delivered by equivalent implants varies by a factor of 1.62, leading to a reference volume variation of 2.08. However, compared to fixed point A prescription 65 Gy, which would allow administered mgRaEq-h to vary by a factor of 2.31, the variation of irradiated volume is somewhat limited. These rules represent an empirically developed compromise between limiting volume of tissue treated and maintaining a tumoricidal dose contribution to the colpostat surface and to point A.

Table 22.11 shows that as tumor size increases and therapeutic emphasis shifts from intracavitary insertions to external-beam therapy, the point A dose increases, from 58 Gy for small IB lesions (schema A) to 94 Gy for stage IV lesions (schema E). The mgRaEq-h actually administered within a given treatment group may deviate from the target mgRaEq-h prescriptions by as much as –30% to +40% for very small and large insertions, respectively. Despite reliance on the mgRaEq-h prescription philosophy, treatment times are approximately constant and total point A doses are nearly independent of applicator size, the defining features of the Manchester system.

TABLE 22.11 WASHINGTON UNIVERSITY PRESCRIPTIONS FOR CARCINOMA OF THE CERVIX

TABLE 22.12 WASHINGTON UNIVERSITY SCHEMA C: 8,000 MG-H, 20 GY WHOLE PELVIS, AND 30 GY SPLIT PELVIS

Summary Principles: Intracavitary Brachytherapy Dose Specification

The most widely used intracavitary BT systems in North America are based on Manchester-type loadings and applicators, in which the point A dose rate is approximately constant and independent of loading, leading to a linear relationship between point A dose and time, not mgRaEq-h. Practical mgRaEq-h systems use various dose specification parameters to constrain and guide treatment and are far more Manchester-like than the “strict” milligram-hour philosophy would suggest. These parameters have the following roles: (a) IRAK limits volume of tissue treated to a high dose, (b) point A dose ensures that tumor periphery receives adequate dose, (c) vaginal surface dose ensures that dose to mucosal surfaces in contact with the applicator system remains within tolerance, and (d) treatment time ensures indirect control of point A dose.

Although the traditional treatment specification quantities have clear physical meanings and interrelationships, these concepts can be applied to patient treatment only within a clinical system supported by a base of evaluated clinical experience. In current practice, implant placement is guided by direct visualization and palpation, and treatment prescription is guided by the radiation oncologist’s knowledge of treatment outcome averaged over groups of uniformly treated patients with similar tumor size and location and medical condition. This implies that the implant system must be applied as a whole: mixing dose specification methods, insertion techniques, and normal-tissue dose-response relationships from different clinical systems is a dangerous practice that can lead to suboptimal or indeterminate clinical outcomes. For example, use of the WU-recommended rectal tolerance dose (75 to 80 Gy) to guide prescription in a system using higher whole-pelvic doses will not guarantee an acceptable level of complications. Second, because classical dose specification quantities incompletely describe the dose distribution, a radiation oncologist must be trained in all details of an intracavitary system to duplicate the results of its developers. Finally, for the clinical physicist, consistency of current dosimetric practice with past clinical experience may be more important than absolute dose computation accuracy or compliance with a practice standard external to the treatment system.

Image-Guided Intracavitary Brachytherapy

Classical intracavitary BT, with its empirically based rules, prescription practices, and feedback derived from patient follow-up to shape and position intracavitary dose distributions, demonstrates that even massive cervical cancers are potentially curable with concomitant chemoradiation therapy. In an effort to improve clinical outcomes in locally advanced cervical cancer and to reduce the incidence of local failure and late normal-tissue toxicity, many groups are investigating anatomy-based dose specification using 3D x-ray CT or magnetic resonance imaging (MRI) studies acquired with the applicator system in place. Early studies²¹⁹^–²²¹ consistently demonstrated that conventional orthogonal film-based reference points overestimate minimum doses to the cervix and underestimate maximum doses to critical structures by factors of 1.5 to 2.3 with large patient-to-patient variations. Because MRI has been shown to be far superior to CT for distinguishing tumor from normal cervical stroma²²² and for delineating surrounding critical structures, advisory groups²²³^,²²⁴ recommend using T2-weighted MRI studies acquired prior to initiating treatment and after each intracavitary insertion for BT planning and dose reconstruction. One such group, the gynecologic GEC-ESTRO Working Group, has proposed a widely accepted target volume nomenclature (high-risk, intermediate-risk, and low-risk CTVs)²²³ and specific DVH parameters²²⁵ for assessing the correlation between clinical outcome and the delivered dose distribution.

Early reports of image-based conformal therapy in locally advanced cervical cancer are promising. For example, use of intensity-modulated radiation therapy (IMRT) to replace traditional whole- and split-pelvis fields²²⁶^,²²⁷suggests that grade 3/4 late toxicity is significantly reduced relative to historical controls without increasing local recurrence. The most extensively reported experience with MRI-based intracavitary BT planning (156 patients at Medical University of Vienna) achieved excellent 3-year local control rates of 86% to 100% (FIGO Ib to IIIb) with grade 2/4 late toxicities of 4% or less.²²⁸ A robust dose-response relationship between high-risk CTV (HRCTV) D₉₀and D₁₀₀ for large tumors²²⁹ was demonstrated as well as a correlation between bladder and rectal DVH parameters (e.g., D_2mL) and major late complications.²³⁰ Challenges to image-guided intracavitary therapy include substantial soft-tissue displacement and deformation due to applicator insertion and removal, tumor regression, and bladder and rectal filling variations (all ignored by clinical experiences cited earlier), making it difficult to meaningfully evaluate cumulative dose distributions. An important area of research is application of deformable image registration to account explicitly for the temporal sequence of deforming 3D anatomies needed to accurately characterize a multiple insertion course of intracavitary and external-beam therapy.²³¹ Using dose summation over weekly magnetic resonance image sets that had been contoured and nonrigidly registered, Lim et al.²³² demonstrated that 5-mm PTV expansion of the intermediate-risk CTV surface for the IMRT component of treatment was adequate for most patients, although large variations between planned and cumulative normal-tissue doses were observed for some patients. As IMRT is used to create more conformal external-beam dose distributions and to address peripheral HRCTV underdoses by the intracavitary treatment components, the need to accurately account for local tissue deformation will become more acute.²³³

THE RADIOBIOLOGY OF BRACHYTHERAPY

The development of high-strength remote-afterloading stepping sources and low-energy permanently implantable sources has resulted in clinical utilization of dose rates and dose-time-fractionation patterns that can differ radically from conventional LDR BT protocols. A clear understanding of the principles governing selection of dose-time-fractionation protocols in BT or combined external-beam radiation therapy (EBRT-BT) has become an essential clinical tool.

The highly conformal dose distribution characteristic of BT sources significantly reduces the exposed volume, and often, the maximum dose in adjacent normal tissues, compared to EBRT.²³³^,²³⁴ As well as diminishing late-responding normal-tissue complications, such dose sparing keeps early-responding normal tissue sequelae to acceptable levels, making the short treatment times commonly used in temporary-implant BT tolerable. This is in contrast to EBRT, where the risk of early-responding tissue sequelae requires treatment times to be prolonged for up to about 8 weeks, potentially reducing tumor control through repopulation. The short overall treatment times used in temporary implants are likely to contribute significantly to clinical efficacy and social-economical benefits for those tumor sites (e.g., cervix, head and neck, and lung) where long overall treatment time is associated with reduced local control.

Biophysical Modeling of Brachytherapy

Based on improved understanding of the radiobiologic principles of BT, biophysical models have been developed for predicting responses to alternative temporal dose-delivery schemes. In the 1970s, before the differential response of early- and late-responding tissues was understood, the most widespread approach for designing alternative fractionation schemes was the nominal standard dose (NSD) equation,²³⁵ which was based on data from early-responding tissues only. By contrast, the currently used linear-quadratic (LQ) model unequivocally distinguishes between early and late responses and is based on mechanistic notions about how cells are killed by radiation. After several decades of investigation and use, the basic ideas and parameters in the LQ model have been well supported by clinical experience and outcome data.

The Linear-Quadratic Model and Its Mechanistic Basis

Central to the LQ approach is a biologic model of radiation action, which was spelled out in detail more than 50 years ago by Lea and Catcheside,²³⁶^,²³⁷ based on a mechanistic analysis of radiation-induced chromosome aberration induction. The application of the LQ formalism to radiation therapy has been reviewed by Thames and Hendry,²³⁸ Dale,²³⁹ Fowler,²⁴⁰ and many others. The LQ model assumes that radiotherapeutic response is primarily related to cell survival (or survival of groups of cells). Although not the sole determinant of biologic response, there is now a wealth of evidence that cell killing (i.e., loss of reproductive integrity) is the dominant determinant of radiotherapeutic response, both for early- and late-responding end points.²³⁸

In the most basic LQ approach, cellular survival, S, from dose D given in a single acute exposure or fraction, is written as:

The mechanistic interpretation of Eq. (39) is that cell killing results from the interaction of two elementary damaged species, most often DNA double-strand breaks (DSB), to produce species that cause cell lethality, such as dicentric chromosomal aberrations. The first term in Eq. (39), which is linear in dose, describes production of two DSBs by the same ionizing radiation quantum (usually a charged particle), while the second term, quadratic in dose, describes production of multiple DSBs by two independent quanta. If the radiation is delivered over a protracted period rather than delivered acutely, the two DSBs may be formed at different times. Therefore, it is possible that the first may be repaired before it has a chance to interact with the second. This will not affect the first term in Eq. (39), because the two DSBs are formed simultaneously from a single particle track, but DSB repair during a prolonged exposure will result in a reduction of the second, quadratic term in Eq. (39) by a factor denoted by “G”:²³⁶^,²³⁷

where, for acute exposures, G → 1, and for very long exposures, G → 0. In this context, “acute” and “long” are defined relative to the half-time (T_r) for DSB repair of sublethal damage. In general, G will depend on the detailed temporal distribution of dose delivery, as well as on T_r. For many simple cases, G can be calculated analytically. For example, for a permanent exponentially decaying implant, G can be approximated as λ/(μ + λ) where λ = ln 2/T_1/2 = 0.693/T_1/2 is the decay constant of the radionuclide, and μ (=0.693/T_r) is the sublethal damage repair rate. In the case of our two-DSB damage model, μ describes repair of single DSBs. Formulae for G for many other standard schemes also have been derived,²³⁷^,²⁴¹ as has a general formalism for any possible protraction scheme.²⁴²

The LQ formalism, described by Eqs. (39) and (40), is not simply a convenient formula for fitting cellular survival curves, but can be derived from a variety of underlying mechanistic models via first-order time-dependent perturbation theory when the dose or dose rate is not too high, a constraint that includes most clinically and experimentally relevant doses and dose rates.²⁴³ For example, the theory of dual radiation action²⁴⁴ is only one of several different approaches to describe radiobiologic damage mechanistically. The approach devised by Lea and Catcheside²³⁶^,²³⁷ deals instead with the kinetics of damage development. Typical kinetic models track the temporal evolution of lesions as a cell gradually repairs or misrepairs initial damage.²⁴⁵^–²⁴⁷ Many different molecular mechanisms have been studied kinetically, such as pairwise misrepair of DNA DSBs, direct one-hit induction of lethal lesions, and saturable repair pathways in which the repair enzyme system can be overloaded.

Practical Applications of the LQ Model

Eq. (40) can be used either to design “equivalent” dose protraction protocols (i.e., design a regimen with the same tumor response, or the same late complications, as a “tried and tested” regimen) or to predict absolute radiotherapeutic responses. We will discuss both approaches here, although we will argue that designing equivalent protraction schemes is a considerably more robust procedure.

In order to design a new dose protraction protocol (labeled “2”) that will have the same effect as a current protocol (labeled “1”), based on Eq. (40), we need to ensure the quantity (αD + GβD²) is equal for the two protocols; that is:

The quantity on either side of Eq. (41) is often called the biologically effective dose (BED),²⁴⁰ so generating a new “equivalent” regimen amounts to matching its BED to that of the old regimen.

By contrast, to use the LQ model to calculate absolute tumor control probabilities (TCPs) or normal-tissue complication probabilities (NTCPs), we need additional models relating cellular survival (S) with TCP or with NTCP. The simplest approach, the Poisson statistics TCP,²⁴⁸ equates TCP with the probability that after radiation treatment there are no remaining tumor stem cells capable of initiating tumor regrowth. Let us suppose that a dose, D, delivered in a given protraction pattern produces a stem-cell-survival probability, S. Let K be the initial number of potential stem cells in the tumor. Then, the probability that any given stem cell will be unable to initiate tumor regrowth is (1 – S). Thus, the TCP for the irradiated tumor is simply (1 – S)^K, which, for small values of S, can be approximated as:

Thus, if cell survival, S, is described by Eq. (40), then

Eq. (43) may also be used to calculate NTCP, except that now the parameter K does not refer to the number of tumor cells that need to be sterilized, but rather to the number of groups of cells in the normal tissue (“tissue-rescuing units”),²⁴⁹ whose destruction would result in the late complication.

A challenge faced by Poisson TCP models and similar approaches is their exquisite sensitivity to the parameter values assumed, particularly the K parameter. In contrast, using the LQ model to compare competing protraction regimens [Eq. (41) and its extensions described later] makes no assumptions about the relationship between surviving fraction and clinical outcome, therefore making them much less sensitive to the LQ parameter values.²⁵⁰

To improve the clinical utility of TCP or NTCP models, extensive efforts have been made to fit these models to clinical data, yielding tumor/tissue-specific model parameters, for example, for head and neck tumors,²⁵¹^,²⁵² breast tumors,²⁵³^,²⁵⁴ prostate cancer,²⁵⁵^,²⁵⁶ brain tumors,²⁵⁷ rectal cancer,²⁵⁸ and liver cancer.²⁵⁹

FIGURE 22.31. Reference points for bladder and rectal brachytherapy doses proposed by International Commission on Radiation Units and Measurements (ICRU) Report 38.³

FIGURE 22.32. Dose–volume histograms for seven Washington University (WU) intracavitary insertions using 1.4-cm-active-length ¹³⁷Cs sources. The strength of each source was determined by the loading rules for WU schema C (20 Gy, whole pelvis plus 8,000 mgRaEq-h) and then was scaled down to 1,000 mgRaEq-h. Note that as the size of the insertion increases, the volume of tissue encompassed by the high-dose isosurfaces decreases. Point A doses ranged from 8.28 to 11.35 Gy.

FIGURE 22.33. Isoeffect curves showing the total dose to produce a given end point, plotted against dose per fraction, a surrogate, in this context, for dose rate. The triangles, joined by dashed lines, refer to a variety of different early-responding end points (of which tumor control is an example), whereas the squares, joined by solid lines, refer to a variety of different late-responding sequelae. Note the generally steeper slopes of the solid lines, suggesting that late-responding tissues are more sensitive than early-responding tissues to changes in the protraction of a given radiation dose. (Adapted from Withers HR, Taylor JMG, Maciejewski B. The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Radiol 1988;27:131–146.)

Use of the Linear-Quadratic Model in Brachytherapy

Quantifying the Rationale for Low–Dose-Rate Brachytherapy

It has long been known that lowering the dose rate generally reduces radiobiologic damage²⁶⁰ because of increased opportunity to repair sublethal damage.²³⁶^,²³⁷ It also has been clear since the pioneering work of Coutard²⁶¹ that fractionating or protracting a radiotherapeutic exposure improves the “therapeutic ratio” (ratio of tumor control to complications). However, the exact link between these observations was not clearly made until the 1980s by Withers et al.²⁶²^,²⁶³

To understand their insight, consider the isoeffect curves in Figure 22.33 representing “equivalent” schemes for either early- or late-responding end points as a function of treatment time. For higher dose rates, the dose reduction needed to match late effects is larger than the dose reduction needed to match tumor control. For any selected dose, increasing the dose rate will increase late effects much more than it will increase tumor control. Conversely, decreasing the dose rate will decrease late effects much more than it will decrease tumor control. Thus, the therapeutic ratio increases as the dose rate decreases.

These observations can be interpreted in terms of the α/β ratio²⁶² in the LQ Eq. (40). In terms of survival curves (Fig. 22.34), the α/β ratio essentially describes the degree of “curviness” of the acute survival curve. A small value of α/β means that the β (dose squared) term dominates cell killing at radiotherapeutic doses, resulting in a curvy survival curve (Fig. 22.34). A large value of α/β means the α (linear in dose) term dominates, resulting in a straighter semi-log survival curve. Now, as a first approximation, the dose-response relation for a fractionated (or LDR) regimen can be thought of as simply the result of multiple repeats of the initial part of the survival curve. It is clear that repeating the early part of a curvy survival curve many times will result in far more sparing than repeating the early part of a straighter survival curve.

Thus, late effects, which are very sensitive to changes in fractionation, are characterized by small values of α/β (a typical value is 3 Gy), and early effects (tumor control or early-responding normal sequelae) are characterized by large values of α/β, a typical value for most tumors being about 10 Gy. As clinical data from which α/β ratios can be derived have accumulated, the dichotomy between α/β ratios for early and late effects that has held up remarkably well. Consequently, when using the LQ model, it is essential to be clear about whether the calculation is designed to refer to early- or late-responding tissue, and to then use the appropriate α/β value. From Eq. (41), it is clear that use of different values of α/β will result in different predictions for the isoeffect dose.

FIGURE 22.34. Illustration of the differing effects of protraction on early- and late-responding tissues, as elucidated by Thames et al.²⁶²

Modeling the Effect of Treatment Time

For temporary implants or HDR, the effect of tumor cell repopulation is generally small, but this is not necessarily the case with longer permanent implants. By increasing the surviving fraction by a factor exp(γT), where T is the overall treatment time, Eq. (40) can be modified to take into account repopulation as a function of T.²⁶⁴ One can also take into account delay in the onset of accelerated repopulation, by replacing T with (T − T_D), where T_D is the delay after the beginning of the treatment before tumor-cell proliferation begins.²⁴⁰ With these two corrections, the surviving fraction becomes:

The parameter γ determines the speed of repopulation, and is given by γ = 0.693/T_P, where T_P is the effective doubling time of cells in the tumor. If we can ignore cell loss, T_P is the same as T_POT, which is the measurable²⁶⁵ in vitrodoubling time of the tumor cells.

If tumor repopulation is relevant, then, in order to design a new equivalent regimen, rather than matching the quantity (aD + G ⋅ bD²), we need to match (aD + G ⋅ bD² - g[T - T_D]), and Eqs. (41) or (43) can be modified correspondingly.

Redistribution and Reoxygenation

Radiobiologic response is dominated by the four Rs: repair, repopulation, redistribution, and reoxygenation.²⁶⁶ Eq. (40) describes repair, which is extended using Eq. (44) to include repopulation. The LQ model can be further extended to include the remaining two Rs²⁶⁷ by treating redistribution of cells among the phases of the cell cycle and reoxygenation as a single phenomenon, termed resensitization, which occurs when a radiation exposure preferentially kills the more radiosensitive cells in a diverse population, leaving a cell population with decreased average radiosensitivity. Subsequent biologically driven changes then tend to gradually restore the original population average radiosensitivity. The resultant LQR model uses two additional adjustable parameters—an overall resensitization rate τ_S (analogous to sublethal damage repair rate) and overall resensitization amplitude ½σ². The LQR model replaces the LQ Eq. (40) with:

The new term, , is the product of (representing the average of the dominant resensitization effects over the heterogeneous tumor) while the factor Gˆ models the influence of fractionation on resensitization. In fact, Gˆ has exactly the same form as the sublethal damage repair function, G, except that μ is replaced by τ_S. In contrast to repair, resensitization tends to increase radiosensitivity as the overall time increases. For example, tumor cells in a resistant part of the cell cycle at the beginning of the treatment, and thus that were spared preferentially, may move to a more sensitive part of the cell cycle as the treatment progresses. While mechanistically driven, LQR is sufficiently simple that it can be used for isoeffect calculations in radiation therapy and supporting reasonable fits to relevant experimental data.²⁶⁷

If reoxygenation or repopulation are relevant, then, in order to design a new equivalent regimen, we need to match the quantity , and Eqs. (41) or (43) can be modified correspondingly.

The Effects of Tumor Shrinkage

If the reference surface to which dose is prescribed diminishes in size as the tumor shrinks during the treatment, then the physical dose rate and total dose will increase as cells near the dose specification surface are closer to the implanted sources. This phenomenon has been described using the LQ formalism by Dale et al.²⁶⁸^,²⁶⁹ For permanent implants in tumors with long doubling times, tumor shrinkage may significantly enhance the clinical potential of longer-lived permanent implant radionuclides such as ¹²⁵I but would have much less effect for short-lived radionuclides such as ¹⁰³Pd or ¹³¹Cs or for rapidly growing tumors. In fact, this is one argument against the use of long-lived nuclides for permanent-implant BT, in that the outcome may depend on shrinkage parameters that we are not able to predict.

Nonuniform Dose Distributions

The LQ model and many other radiobiologic models assume that an implant dose delivery can be approximated by a single uniformly administered prescribed dose, an assumption that ignores the highly nonuniform dose distributions produced by BT. Suppose the dose distribution over an organ or tumor is described by a DVH {D_i,ν_i}^N_i=1, where ν_i is the fractional volume of dose bin D_i. If the structure is a tumor, the biologic effect of this inhomogeneous dose distribution can be quantified by computing the overall surviving fraction S for the entire tumor target:

where Eq. (40) has been used as an example. A more intuitive simple scalar metric for quantifying impact of such nonuniform dose is the equivalent uniform dose (EUD) concept proposed by Niemierko.²⁷⁰ It is defined as the uniform dose that, if delivered with the same dose protraction regimen as the nonuniform dose distribution of interest, yields the same radiobiologic effect. In terms of BED and equivalent dose in 2 Gy fractions (D_2Gy)s, EUD is given by:

showing that EUD computation requires knowing the absolute value of α. To extend the concept of EUD to normal tissues, Mohan et al.²⁷¹ and then Niemierko²⁷² proposed a phenomenologic formula referred to as the generalized EUD or gEUD:

where n_i is the fractional organ volume receiving a dose D_i and a is a tissue-specific parameter that describes the volume effect. For a → –∞, gEUD approaches the minimum dose; thus, negative values of aare used for tumors. For a→ +∞, gEUD approaches the maximum dose (serial organs). For a = 1, gEUD is equal to the arithmetic mean dose. For a = 0, gEUD is equal to the geometric mean dose. Unlike EUD, gEUD is a purely empirical model without a more mechanistic interpretation rooted in cell survival. However, the gEUD is often used as a plan comparison and optimization metric for EBRT and may be used for comparing different protraction schemes in BT because the same functional form can be applied to both target volumes and organs at risk (OARs) with a single parameter capturing (it is hoped) the dosimetric “essence” of the biologic response.

To compare different inhomogeneous dose distributions, TCP and NTCP can be computed by substituting Eq. (45) into the Poisson TCP model, Eq. (42), yielding

The second equation shows that inhomogeneous dose TCP, ({D_i,n_i}), is the product of exponentially scaled (by volume fraction, n_i) TCPs, each describing uniform tumor irradiation by dose bin D_i. The third equation shows that substituting EUD into the uniform dose TCP also reproduces TCP ({D_i,n_i}). Several authors²⁷³^,²⁷⁴ have extended this approach also to account for nonuniform distributions of target cells within the tumor and intertumoral radiosensitivity (α) variations over a patient population. Similar approaches have been proposed for NTCP models²⁷⁵ based on the survival of functional subunits (FSUs). Many organs are best modeled by FSUs organized with a parallel architecture such that a complication results only when a sufficiently large number of FSUs are inactivated,²⁷⁶ although serial architectures such as the spine can also be modeled.²⁷³

The Relative Effectiveness of Different Radioisotopes Used in Brachytherapy

As discussed earlier in this chapter, the mean photon energies of currently used BT radionuclides range from 398 keV (¹⁹²Ir) down to 21 keV (¹⁰³Pd). It is well established that biologic effectiveness varies with photon energy, as a result of different patterns of energy deposition produced by the different photon spectra.²⁷⁷^,²⁷⁸ It is possible, however, to estimate the RBE of these different isotopes directly from the energy deposition patterns—the subject matter of microdosimetry.²⁷⁹ In this approach, the response per unit dose at low dose rates (or low doses), R_i, to a particular radiation, i, can be written as²⁸⁰:

where y is the stochastic quantity, lineal energy,²⁷⁹ defined as the energy deposited by a single photon track, divided by the average path length in the cellular target, and d_i(y) is the dose-weighted probability that a photon will deposit lineal energy y in the target volume of interest. The quantity d_i(y) often is referred to as the microdosimetric single-event spectrum. It can be measured using a low-pressure proportional counter or calculated.²⁷⁹ The quantity w(y) describes the response of an individual cellular target to a lineal energy deposition, y. For sparsely ionizing radiations (e.g., photons and electrons), it is reasonable to assume that w(y) is proportional to y.²⁷⁹ Thus, at low dose rates:

where d_i(y) is the dose-averaged lineal energy. Based on this approach, RBE values have been estimated from measured or calculated microdosimetric spectra.²⁷⁸^,²⁸¹ For example, Wuu et al.²⁷⁸ report low–dose-rate RBE values relative to ⁶⁰Co of 1.3, 2.1, 2.1, and 2.3, respectively, for ¹⁹²Ir, ²⁴¹Am, ¹²⁵I, and ¹⁰³Pd. These values are comparable to those obtained experimentally. The approach outlined previously is applicable only to LDR BT, but it can be generalized to HDR regimens.²⁸⁰ Incorporating the low–dose-rate RBE into the LQ equations is surprisingly easy,²⁸² requiring a simple modification of Eq. (41):

The LQ Model for Permanent Implants

To use the LQ model to predict the total dose that a permanent implant needs to deliver to a repopulating tumor with an effective doubling time of T_p, we need to match the quantity (aD + G · bD² – γ[T − T_D]) [see Eq. (44)] to an appropriate reference regimen. However, as shown by Dale,²⁸³ the effective treatment time, T_eff, for a permanent implant is not infinite, but achieves a finite value when the dose rate becomes sufficiently low that the rate of cell kill equals the number of tumor cells created per unit time by repopulation, at which point the treatment is effectively over and any subsequent dose is wasted. This can be expressed by requiring that a(∂BED(T_eff)/∂t) = a₀e^–l^T_eff γ, assuming that G 1 at low dose rates and TD << T_eff. Thus:

where λ is the radioactive decay constant of the particular nuclide used and T_pot is the potential doubling time of the tumor. At this time, T_eff, the dose that has been delivered, is not the total dose, D, but rather a smaller effective dose, given by:

As an example, using reasonable parameters for prostate tumors, the effective dose for a 145-Gy ¹²⁵I permanent seed implant is actually 139 Gy, which is the value that would be used in LQ-based calculations.

The LQ model can be used to optimize the choice of radionuclide for a permanent implant.²⁸⁴^,²⁸⁵^–²⁸⁶ The most common sources in current use are ¹²⁵I and ¹⁰³Pd (with half-lives of 59 and 17 days, respectively), although ¹³¹Cs (half-life 10 days) is being increasingly considered.²⁸⁷ The optimal radionuclide for a given tumor depends on its growth rate, α/β ratio, radiosensitivity (α), and DSB repair rate. Generally speaking, short-lived radionuclides are more advantageous for treating fast-growing tumors, while longer-lived radionuclides are more optimal for slow-growing tumors. However, short-lived radionuclides can effectively treat in addition, are less sensitive to the tumor properties and LQ parameter values assumed than is the case for long-lived radionuclides.

HDR Intracavitary Brachytherapy for Cervical Cancer

There has been a trend in the past few years toward increased use of HDR BT in some tumor sites, driven largely by the economic and logistical benefits of outpatient-based fractionated HDR BT. While sometimes delivered in a single fraction, more often three to 12 HDR fractions are used. In some situations, such as palliative or intraoperative BT, the therapeutic ratio between tumor control and late sequelae is not a primary consideration; but, in general for curative intent treatments, increasing the dose rate is likely to decrease the therapeutic advantage between tumor control and late sequelae. However, there are two curative applications (intracavitary implants for cancer of the uterine cervix and implant therapy for prostate cancer) where, for differing reasons, HDR BT is as effective, or potentially even more effective, compared to LDR BT.

The radiobiologic principles involved in converting LDR to HDR intracavitary insertions are illustrated schematically in Figure 22.35, which shows typical dose-response relationships for early- and late-responding tissues. As we have discussed, the dose-response relations for late effects are significantly “curvier” (smaller α/β ratio) than for early-responding tissues such as tumors, which have larger α/βratios. Suppose that we want to replace an LDR treatment delivering dose D with an HDR treatment that gives identical tumor control. As illustrated in the left panel, we need to reduce the dose by a dose reduction factor, DRF (see left panel). From the right panel, however, it can be seen that this adjusted dose, DRF × D, will result in increased late effects compared to LDR. But now let us suppose that the LDR dose to OAR giving rise to the late effects is not the treatment dose D, but some lower dose (e.g., D/2). This is the case for cervical BT because the bladder and rectum are generally some significant distance from the cervical implant. From the right-hand panel in Figure 22.35, we see that if HDR preserves the LDR level of dose sparing (i.e., delivers dose DRF × D/2 to the OAR, where DRF matches tumor control), we will not get more late effects for HDR compared to LDR, but actually a similar late-effect probability because we are further up the survival curve. Indeed, if the rectal dose were an even smaller fraction of the treatment dose (say D/3, in Fig. 22.35), HDR would have even fewer late effects than the equivalent LDR regimen. In fact, if the cervical BT results in a dose to the bladder/rectum that is less than about three-fourths of the treatment dose, and then if the HDR dose is reduced to give equal tumor control compared with LDR, the HDR late effects should not be worse than the LDR late effects.²⁴²^,²⁸⁸

Of course, there is another related factor to consider, which is that the short treatment time characteristic of HDR allows packing and retraction of the sensitive organs, which typically results in a 20% further decrease in the rectal/bladder dose compared to that achievable with LDR.²⁸⁹ This gives an extra, physically based advantage to HDR, in addition to the biologic factors discussed here.

To summarize, radiobiologic considerations suggest that if the dose to the dose-limiting critical normal tissues (e.g., bladder and rectum) is less than about three-fourths of the prescribed dose, HDR BT (administered in five or more fractions to ensure adequate tumor reoxygenation) results in comparable (or fewer) late effects than LDR—for the same level of tumor control. These theoretical conclusions are supported by a number of clinical studies²⁹⁰^–²⁹⁶showing that HDR and LDR for cervical BT produce similar rates of local control and late complications.

As BT is often combined with pelvic EBRT,²⁹⁷ different time-dose patterns of EBRT and intracavitary BT should be taken into account to calculate the combined effects to tumor and OARs. For a given BT effective dose, BED_BT, the equivalent EBRT dose expressed in conventional fractionation of 2 Gy per day (EQD2) can be calculated as EQD2 = BED_BT/(1 + 2/(α/β)). Also, the dose from EBRT has to be recalculated if a fractionation schedule different from 2 Gy per day is to be used. EQD2 values from EBRT and BT may be summed assuming that the volumes and points of interest of BT receive the stated EBRT dose. This estimate serves as a worst-case assumption for OARs and is reasonable for the BT target volume, which usually receives a uniform EBRT dose. More realistic calculations must consider the highly nonuniform dose delivery of BT and IMRT, as described in the next section.

FIGURE 22.35. Illustration of the interplay between early and late effects for low–dose-rate (LDR) and high–dose-rate (HDR) brachytherapy for cervical cancer. DRF is the dose reduction factor that produces the same early effects (tumor control) for HDR as LDR. If D is the LDR giving rise to late effects, then reducing D by DRF for HDR will result in more late effects than at LDR. As the HDR dose to late-responding tissue is reduced by treatment planning, then reducing that dose by the factor DRF no longer produces worse late effects than at LDR.

Brachytherapy for Prostate Cancer

Optimized Dose Protraction for Prostate Cancer Brachytherapy

As discussed earlier, one of the main reasons for protracting any radiotherapeutic exposure is that protraction spares late responding normal tissues more than typical tumors; this strategy is supported by the generally lower α/β ratios found for late-responding normal tissues (3 Gy is typical) relative to tumors (10 Gy is typical). These different α/β ratios are thought to be due to the larger proportion of cycling cells in tumors compared with normal tissues. Because prostate tumors contain unusually small fractions of cycling cells,²⁶⁵ it has been hypothesized that they may have α/β ratios and responses to protraction more typical of late-responding normal tissues.²⁹⁸^,²⁹⁹ If so, much of the rationale for low dose rate, or highly fractionated regimens, would disappear.

A first estimate of α/β for prostate cancer was made in 1999²⁹⁸ by comparing results from EBRT with those from permanent seed ¹²⁵I BT. Consistent with the theoretical hypotheses (see earlier), the estimated value of α/β was 1.5 Gy (95% confidence interval [CI]: 0.8 to 2.2 Gy), indeed comparable to α/β values for late-responding normal tissues and much smaller than those for most tumors.

Since this first estimate of α/β for prostate, there have been more than 20 further estimates.²⁵⁶^,³⁰⁰^–³⁰⁵ These analyses have considered the impact of many potential biases and uncertainties, including the comparison of EBRT and permanent seed implant (which has much higher dose delivery uncertainties) outcomes; differences in dose inhomogeneity; RBE and overall time differences;³⁰⁶ patient selection bias; differences in outcome endpoints; and³⁰⁷ any or all of which could bias the α/β estimate. However, most of these analyses support the hypothesis that the α/β value for prostate cancer is indeed quite low, probably in the 1 to 4 Gy range, similar to those of most late-responding tissues. For example two studies each analyzed the results of more than 5,000 prostate cancer patients who received different external beam fractionation schedules, and derived estimated α/β values of 1.55 Gy³⁰⁸ and 1.4 Gy³⁰⁹respectively. A review of all the studies concluded that the results are all reasonably consistent, the mean of all estimated values being 2.7 Gy.³¹⁰

If the α/β value for prostate cancer is indeed similar to that for the surrounding late-responding normal tissue, HDR or hypofractionated external-beam therapy regimens could be employed to match conventional fractionated regimens with respect to tumor control and late sequelae while reducing early urinary sequelae³¹¹ and improving cost-effectiveness and patient convenience.

The arguments presented here really relate to the α/β value for prostate cancer in relation to the α/β value for the relevant late-responding normal tissue. Brenner³¹² reported an α/β value for Radiation Therapy Oncology Group (RTOG) grade 2 or higher late rectal toxicity of 5.4 ± 1.5 Gy based on an analysis of clinical data. Another recent analysis of RTOG 94-06 data suggested that the α/β value for grade 2 or higher late rectal toxicity was 4.8 Gy.³¹³These α/β values, which are larger than that of most late-responding tissues, are higher than recent estimates of prostate tumor α/β ratio. This suggests that HDR prostate BT, as well as being logistically convenient, might actually improve the therapeutic outcome of prostate cancer BT.

HDR (or hypofractionation) in a curative setting, even when the dose is appropriately lowered, is a prima facie unsettling idea. However, there is now a significant body of clinical evidence suggesting that these approaches do not lead to increased early or late sequelae after prostate radiotherapy, either for EBRT or for BT, providing further evidence to support the underlying radiobiologic rationale. For EBRT, in those hypofractionation studies that have reported on late sequelae, to date there is little indication of any unexpected late sequelae after median follow-up periods of 48 to 97 months.³¹⁴^–³¹⁷ Indeed, two completed phase III trials have reported similar therapeutic ratios with a suggestion of an advantage for hypofractionation.³¹⁸^,³¹⁹ HDR has been used in prostate BT both as a monotherapy³²⁰^,³²¹ and, more commonly, as a boost to external-beam radiotherapy.³²²^–³²⁵ In both cases, the results are promising with no evidence for excessive normal tissue complications. The American Brachytherapy Society has recently published consensus clinical and treatment planning guidance on HDR prostate brachytherapy.³²⁶

Comparing and Combining External-Beam Radiation Therapy with Brachytherapy for Prostate Cancer

BT (permanent-implant or HDR BT) is widely used in treatment of prostate cancer, either as sole therapy or as a boost in conjunction with EBRT. We can use the EUD formalism to compare the biologic effectiveness of various EBRT-BT combinations using the LQ model to account dose nonuniformity and dose-time fractionation effects at each voxel.³²⁷ For typical DVHs, {D_i,vi}, the surviving fraction for each modality is calculated by:

For EBRT and HDR BT treatment courses, delivering a total dose D = nd of n fractions, T_eff is the number of treatment fractions multiplied by 1.4 (five fractions per week). Assuming each EBRT fraction is delivered over a short time relative to the repair half-time, G = 1/n. However, for each HDR BT fraction, the delivery time T_f (assumed to be 15 minutes in analysis to follow) is typically comparable to the repair half-time for prostate tumor cells,³²⁷necessitating a more complex sublethal damage repair correction²⁵⁵^,³²⁸:

where μ and λ denote the sublethal damage repair rate and physical decay constant, respectively.

For permanent BT, the total dose D and effective treatment are given by Eqs. (53) and (52), respectively. The sublethal damage repair correction is given by²⁸³^,³²⁷:

where ₀ is the initial dose rate.

The overall surviving fraction S of a combined EBRT and BT regimen is given by:

where S_EBRT and S_BT are estimated from Eq. (54) using typical DVHs and T′ is the time interval between the two treatments (T′ = 0 if the treatments are overlapped with each other). TCP may be calculated using Eq. (42). To quantify the combined-modality surviving fraction S in terms of EUD, relative to a reference EBRT regimen consisting of 2-Gy daily fractions, we compute:

TABLE 22.13 COMPARING EBRT, BT, AND EBRT + BT BASED ON CALCULATED EUD AND TCP USING TWO SETS OF LQ PARAMETERS

TABLE 22.14 PRESCRIBED BRACHYTHERAPY DOSE NEEDED TO ACHIEVE STATED CUMULATIVE EUD WHEN COMBINED WITH EBRT DOSE OF 46 GY (2.0 GY × 23)

Table 22.13 illustrates the combined-modality EUD evaluation, along with corresponding TCPs, for the RT regimens commonly used for localized high-risk prostate cancer. The results show that the permanent seed BT alone offers high-risk prostate cancer control rates intermediate to EBRT alone delivering conventional (70.2 Gy) and escalated (81 Gy) prescribed doses. An interesting observation is that combined treatments of EBRT and permanent/HDR BT support higher EUDs and TCPs, and therefore should lead to more disease control than either EBRT or BT monotherapy.

Table 22.14 demonstrates how the combined-modality LQ-EUD analysis can be applied to design brachytherapy dose prescription schedules. The prescribed BT dose needed to achieve cumulative EUDs ranging from 68 to 110 Gy for an ¹²⁵I, ¹⁰³Pd, or fractionated HDR implant when combined with an EBRT dose of 46 Gy is tabulated using the LQ parameter set b from Table 22.13. To achieve TCPs of 90% to 100%, cumulative EUDs in the range of 80 to 100 Gy must be delivered. It is gratifying to note that at the upper end of this EUD range, the predicted BT doses of 112 Gy, 87 Gy, and 9.5 Gy × 3 for ¹²⁵I, ¹⁰³Pd, and HDR BT, respectively, are close to those used in current clinical practice. The currently practiced multimodality regimen treatment (initial EBRT + permanent/HDR BT boost) is predicted to support superior tumor control than current monotherapy protocols. Hypofractionation with either EBRT or HDR BT can also improve EUD and TCP with significantly lower prescription doses. These radiobiologic tools may be useful in analyzing treatment outcomes or in designing clinical trials to explore new treatment regimens. However, caution needs to be exercised in using these results to modify clinical decisions. One must consider the radiation effects (e.g., EUD) not only on prostate but also on OARs. In addition, the results are sensitive to the LQ parameters used. For example, to achieve a specified EUD, the required EBRT prescribed doses for a fraction size of 4.0 Gy will vary by 10% as in the α¤β ratio range of 1.5 to 3.1. Small uncertainties in the model parameters can lead to large EUD and TCP uncertainties if there are cold spots in the tumor and/or hot spots in normal tissue. For more detailed discussion of these issues, readers are referred to previous publications.³²⁷^,³²⁹^,³³⁰

Summary: Biophysical Outcome Models in Brachytherapy

This survey of biophysical models for predicting clinical outcomes from brachytherapy regimens shows that the basic linear-quadratic model is sufficiently supported by clinical experience to be used for developing equivalent fractionation regimens or for optimizing therapeutic ratios in many clinical settings. More sophisticated NTCP and TCP models, while not sufficiently robust for use in clinical planning, are able to semiquantitatively account for the LDR and HDR brachytherapy clinical outcomes in several sites in terms of underlying descriptive radiobiologic mechanisms.

CONCLUSIONS

This chapter has focused on several basic topics including the interplay between physical properties, single-source dosimetry, source-strength specification, classical interstitial and intracavitary brachytherapy systems and dose specification, and biologic effects and clinical utility of brachytherapy sources. Many topics usually covered in an introductory survey have been omitted. For a review of radiographic imaging and localization of brachytherapy sources, the reader is referred to more specialized recent reviews.¹⁴⁹^,³³¹ For discussions on quality assurance of manual and remote afterloading brachytherapy and treatment planning, the reader is referred to Chapters 23, 24, and 25of this text as well as a number of excellent reviews⁶⁶^,³³²^–³³⁵ including appropriate chapters from Brachytherapy Physics, 2nd edition.³³⁶ For a more systematic approach to brachytherapy quality management, including application of industrial engineering approaches, the textbook by Thomadsen³³⁷ and the proceedings of recent ASTRO Symposium on quality assurance for technologically advanced radiation therapy³³⁸ are recommended. For a discussion of brachytherapy licensing and regulatory issues, the review by Glasgow³³⁹ is suggested. For more detailed discussions on applications of radiobiological models to clinical brachytherapy, the reader is referred to the many sources cited by this review.

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