A Preliminary Study of a Deterministic Dose Calculation Method for Brachytherapy

Abstract

Dose calculations in brachytherapy, a form of cancer treatment in which ionising radiation is used to kill cancer cells, are commonly performed using the TG-43 formalism. In this approach, dosimetry is performed in a large water medium and subsequently superimposed onto the patient geometry. This simplification neglects patient-specific factors such as tissue heterogeneities, applicators materials, and finite patient dimensions, limiting its accuracy in clinical practice. With increasing computational capabilities, more advanced physics-based techniques, termed model based dose calculation algorithms (MBDCAs), are being developed that do not have these limitations.

In this work, a deterministic solver originally developed for external beam radiotherapy (EBRT) is adapted for brachytherapy dose calculations. Deterministic methods solve the Linear Boltzmann transport equation (LBTE), which governs radiation transport, through discretisation in space, angle, and energy. The required modifications for application in brachytherapy are discussed, and several limitations of the solver were identified. In particular, the use of a fixed voxel-grid is shown to be unsuitable for brachytherapy, where dose calculations for brachytherapy span a large backscatter volume (at least 5 cm beyond the region of interest) while also requiring a fine grid to resolve to resolve steep dose gradients near the source and to model the sub-millimetre features of brachytherapy sources.

A series of increasingly complex test cases was developed to evaluate the solver. We started with homogenous water mediums, and introduced heterogeneities and high-Z shielding materials later. The results were compared against Monte Carlo (MC) reference data. Overall, good agreement between was observed between the deterministic and MC method. For both low- and high-energy photon sources, larger deviations were observed within the source (dose underestimation), very close to the source (dose overestimation), and near the boundaries of heterogeneities (dose overestimations). For low-energy photon sources, dose was underestimated through the entire medium, primarily due to the increased importance of photon attenuation.

These findings demonstrate that the developed deterministic solver shows good potential for brachytherapy applications. However, the use of a fixed voxel grid currently limits its suitability for clinical applicability. The development of an adaptive mesh capability is therefore required to enable dose calculations for clinical cases.