Dose rate constant and energy spectrum of interstitial brachytherapy sources

In the past two years, several new manufacturers have begun to market low-energy interstitial brachytherapy seeds containing 125I and 103Pd. Parallel to this development, the National Institute of Standards and Technology (NIST) has implemented a modification to the air-kerma strength (S(K)) standard for 125I seeds and has also established an S(K) standard for 103Pd seeds. These events have generated a considerable number of investigations on the determination of the dose rate constants (inverted V) of interstitial brachytherapy seeds. The aim of this work is to study the general properties underlying the determination of dose rate constant and to develop a simple method for a quick and accurate estimation of dose rate constant. As the dose rate constant of clinical seeds is defined at a fixed reference point, we postulated that dose rate constant may be calculated by treating the seed as an effective point source when the seed's source strength is specified in S(K) and its source characteristics are specified by the photon energy spectrum measured in air at the reference point. Using a semi-analytic approach, an analytic expression for dose rate constant was derived for point sources with known photon energy spectra. This approach enabled a systematic study of dose rate constant as a function of energy. Using the measured energy spectra, the calculated dose rate constant for 125I model 6711 and 6702 seeds and for 192Ir seed agreed with the AAPM recommended values within +/-1%. For the 103Pd model 200 seed, the agreement was 5% with a recently measured value (within the +/-7% experimental uncertainty) and was within 1% with the Monte Carlo simulations. The analytic expression for dose rate constant proposed here can be evaluated using a programmable calculator or a simple spreadsheet and it provides an efficient method for checking the measured dose rate constant for any interstitial brachytherapy seed once the energy spectrum of the seed is known.