Residency · Residency · Radiation Oncology

Brachytherapy Physics: Dose Calculations, Source Characteristics, and TG-43

Introduction

Brachytherapy is a form of radiation therapy that involves placing sealed radioactive sources directly within or adjacent to the target tissue. This approach allows for the delivery of high radiation doses with a rapid dose fall-off, sparing surrounding healthy tissues. A thorough understanding of the physics underlying brachytherapy sources, the formalisms used for dose calculations, and quality assurance protocols is essential for safe and effective clinical practice. The AAPM Task Group 43 (TG-43) formalism serves as the standard framework for calculating brachytherapy doses.

Radioactive Source Characteristics

Common Brachytherapy Isotopes

Several isotopes are commonly used in brachytherapy, each with distinct physical properties suited to specific clinical applications. Iridium-192 (Ir-192) has a half-life of 73.8 days and emits photons with a mean energy of 380 keV; it is primarily used in high-dose-rate (HDR) and pulsed-dose-rate (PDR) treatments. Cesium-137 (Cs-137), with a much longer half-life of 30.2 years and a mean photon energy of 662 keV, was historically used in low-dose-rate (LDR) brachytherapy. Iodine-125 (I-125) and Palladium-103 (Pd-103) are low-energy sources with half-lives of 59.4 and 17.0 days, respectively, and mean energies of 28 keV and 21 keV; both are commonly employed in permanent LDR implants. Cobalt-60 (Co-60), with a half-life of 5.27 years and a mean energy of 1.25 MeV, is used in HDR cobalt units.

Source Construction

Brachytherapy sources consist of an active core containing the radioactive material, which is encapsulated within stainless steel or titanium. This encapsulation provides structural integrity and filters low-energy photons, thereby modifying the effective energy spectrum emitted by the source. Typical source dimensions for HDR sources are approximately 3 to 5 millimeters in length and less than 1 millimeter in diameter. The encapsulation plays a crucial role in shaping the radiation field and protecting the source from damage.

Source Strength Specification

The strength of brachytherapy sources is specified using the air kerma strength (SK), measured in units of U, where 1 U equals 1 cGy cm² per hour. Air kerma strength is defined as the product of the air kerma rate at a reference distance and the square of that distance, effectively normalizing the measurement to a standard geometry. Although apparent activity is sometimes used clinically, it is not recommended by the AAPM for dose calculations due to its variability. In European practice, the reference air kerma rate (RAKR) is also used. For TG-43 dose calculations, air kerma strength remains the standard input parameter.

TG-43 Dose Calculation Formalism

Overview

The TG-43 formalism, initially published in 1995 and updated in 2004 (TG-43U1) with additional supplements in 2007, provides a model-based approach to brachytherapy dose calculation. It relies on parameters derived from measurements and Monte Carlo simulations, assuming a water-equivalent medium without accounting for tissue heterogeneity. The dose rate at a point P defined by coordinates (r, θ) relative to the source is calculated using a standardized equation.

The TG-43 Equation

The dose rate at point P(r, θ) is given by the equation:

**D(r,θ) = SK Λ [G(r,θ)/G(r₀,θ₀)] g(r) F(r,θ)**

In this equation, SK represents the air kerma strength, and Λ (lambda) is the dose rate constant, which converts air kerma strength to dose rate in water at the reference point. G(r, θ) is the geometry function that accounts for the spatial distribution of radioactivity, normalized by its value at the reference point G(r₀, θ₀). The radial dose function g(r) accounts for photon absorption and scatter along the transverse axis, while the anisotropy function F(r, θ) describes angular variations in dose rate caused by source geometry and encapsulation.

Reference Point

The reference point for normalization is set at a distance r₀ of 1 cm and an angle θ₀ of 90 degrees, corresponding to the transverse axis of the source. All parameters in the TG-43 formalism are normalized to this reference point to standardize dose calculations.

TG-43 Parameters in Detail

Dose Rate Constant (Λ)

The dose rate constant, Λ, represents the dose rate delivered to water per unit air kerma strength at the reference point. It is specific to each source, depending on the isotope, encapsulation, and source geometry. Typical values include approximately 1.108 cGy/h/U for Ir-192 and 0.965 cGy/h/U for I-125. These constants are determined through a combination of Monte Carlo simulations and experimental measurements.

Geometry Function G(r,θ)

The geometry function models the spatial distribution of radiation from the source. For a point source approximation, it follows the inverse square law, expressed as G(r) = 1/r². However, clinical brachytherapy sources are better represented by a line source approximation, where G(r, θ) equals β divided by (L r sin θ), with β being the angle subtended by the active length of the source at point P. This line source model is standard for sources with a measurable active length.

Radial Dose Function g(r)

The radial dose function describes how the dose falls off along the transverse axis relative to the reference point. It accounts for photon absorption, scatter buildup, and changes in the energy spectrum with increasing distance from the source. This function is normalized to unity at 1 cm. Low-energy sources such as I-125 and Pd-103 exhibit a steeper fall-off in g(r) due to greater photon attenuation compared to higher-energy sources.

Anisotropy Function F(r,θ)

The anisotropy function characterizes the angular variation in dose rate at a given distance from the source. It is normalized to unity at θ = 90 degrees, corresponding to the transverse axis. Dose rates are typically reduced near the source tips (angles close to 0 or 180 degrees) because of self-filtration and encapsulation effects. This angular dependence is more pronounced for low-energy sources.

Limitations of TG-43

Water-Equivalent Assumption

A key limitation of the TG-43 formalism is its assumption that all tissues are water-equivalent in composition and density. This simplification ignores the presence of tissue heterogeneities such as bone, air cavities, and metal applicators. As a result, TG-43 tends to overestimate dose near air cavities and underestimate dose near high atomic number (high-Z) materials. These inaccuracies can be clinically significant in anatomical sites like the lung or bone interfaces.

Model-Based Dose Calculation Algorithms (MBDCA)

To address these limitations, the AAPM introduced TG-186 in 2012, which provides guidelines for moving beyond the TG-43 formalism. Model-based dose calculation algorithms (MBDCAs), such as Acuros BV and collapsed cone methods, incorporate tissue heterogeneity by utilizing CT-based tissue assignment and detailed source modeling. Although these advanced algorithms are not yet universally adopted, they represent the future direction of brachytherapy dosimetry.

Source Calibration and Quality Assurance

Calibration

Before clinical use, all brachytherapy sources must undergo independent calibration. The standard instrument for this purpose is the well-type ionization chamber, which provides measurements traceable to a primary standards laboratory such as the National Institute of Standards and Technology (NIST). The measured air kerma strength should agree within 3% of the vendor-stated value to ensure accuracy.

Quality Assurance

Quality assurance protocols include verification of source position using autoradiography, fluoroscopy, or imaging techniques, as well as verification of dwell time accuracy for HDR units. Emergency procedures must be in place for source retraction failures, particularly in HDR treatments. Regular checks of source transit time and positional accuracy are essential, along with an annual physicist survey and calibration in accordance with TG-56 guidelines.

HDR Unit Safety

Safety measures for HDR units include checking source retraction before each treatment, maintaining redundant radiation monitoring within the treatment room, and ensuring emergency source retraction tools are readily accessible. Additionally, door interlocks and treatment interrupt functions must be verified daily to maintain a safe treatment environment.

Key Clinical Pearls

The TG-43 formalism remains the standard for brachytherapy dose calculation, utilizing parameters such as air kerma strength, dose rate constant, geometry function, radial dose function, and anisotropy function. However, it assumes a water-equivalent medium and does not account for tissue heterogeneities, a limitation addressed by the TG-186 guidelines introducing model-based dose calculation algorithms. Air kerma strength is the preferred unit for specifying source strength, while apparent activity should be avoided for dose calculations. Independent source calibration using a well-type ionization chamber is mandatory prior to clinical use. Low-energy sources like I-125 and Pd-103 exhibit steeper dose fall-off and more pronounced anisotropy compared to higher-energy sources such as Ir-192.

References

1. Rivard MJ, Coursey BM, DeWerd LA, et al. Update of AAPM Task Group No. 43 Report: a revised AAPM protocol for brachytherapy dose calculations. Med Phys. 2004;31(3):633-674.
2. Beaulieu L, Carlsson Tedgren A, Carrier JF, et al. Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: current status and recommendations for clinical implementation. Med Phys. 2012;39(10):6208-6236.
3. Nath R, Anderson LL, Luxton G, et al. Dosimetry of interstitial brachytherapy sources: recommendations of the AAPM Radiation Therapy Committee Task Group No. 43. Med Phys. 1995;22(2):209-234.
4. DeWerd LA, Ibbott GS, Meigooni AS, et al. A dosimetric uncertainty analysis for photon-emitting brachytherapy sources: report of AAPM Task Group No. 138 and GEC-ESTRO. Med Phys. 2011;38(2):782-801.

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