A finite volume approach to dosimetric calculations in diffusing alpha-emitters radiation therapy.

Objective. In diffusing alpha-emitters radiation therapy ('Alpha DaRT'), the diffusion-leakage (DL) model is used to determine the spatial distributions of the emitters and the corresponding alpha dose, critical for a successful treatment. This work first introduces a finite volume (FV) approach to develop numerical schemes to simulate the DL model in one, two and three dimensions then presents how variations over realistic ranges of the DL model parameters related to desorption, diffusion and leakage processes affect the alpha dose distribution and the position of the clinically significant alpha particle10Gy isodose. This work also presents the effects of three modeling approximations: two source geometry approximations (solid cylinder instead of hollow, pixelized cross section instead of circular), and one dosimetric approximation (single-source dose superposition instead of multiple-sources direct dose calculation). Approach. The introduced FV approach was used to obtain spatial distributions of the emitters, from which the corresponding alpha dose distributions were calculated under the assumption of a local deposition of the alpha particles' energies. Variation ranges of the DL model parameters were based on previously published data. For each modeling approximation studied, the error and relative error on the alpha dose distribution were calculated and the displacement of the10Gy isodose was evaluated. Main results. Over realistic ranges, the desorption probabilities, diffusion lengths, and leakage probabilities affect the position of the alpha particle10Gy isodose by∼0.1mm,∼1.5mm and∼0.5mm, respectively. The three modeling approximations studied have a negligible effect on the alpha particle10Gy isodose position, with displacements⩽0.01mm. Significance. This work quantitatively evaluates the relative importance of different parameters and approximations in Alpha-DaRT alpha dose calculations based on their impact not only on the dose variation at a given distance from the source but also on the displacement of clinically significant isodoses.