Finite-element modeling of the alpha particle dose of realistic sources used in Diffusing Alpha-emitters Radiation Therapy

TL;DR

This paper develops a finite-element numerical scheme for modeling alpha particle dose distributions in Diffusing Alpha-emitters Radiation Therapy (DaRT), introducing new computational methods and approximations for accurate and efficient dose calculations.

Contribution

It presents a detailed finite-element approach for solving the DL model equations in DaRT, including simplified schemes for infinite sources, enhancing accuracy and computational efficiency.

Findings

Validated 2D numerical scheme against approximations

Provided guidelines on the applicability of simplified models

Enabled accurate temporal modeling from seconds to days

Abstract

Diffusing Alpha-emitters Radiation Therapy (DaRT) is a new method for treating solid tumors using alpha particles. Unlike conventional radiotherapy, where the physical models for dose calculations are known and routinely used, for DaRT a new framework, called the Diffusion-Leakage (DL) model, had to be developed. In this work we provide a detailed description of a finite-element numerical scheme for solving the time-dependent DL model equations for cylindrical DaRT sources (``seeds'') of finite diameter and length in two dimensions. Using a fully-implicit scheme and adaptive time step, this approach allows to accurately follow temporal transients ranging from seconds to days. In addition to the full two-dimensional calculation, we further provide a closed-form approximation and a simple one-dimensional scheme to solve the equations for infinitely-long cylindrical sources. These simpler solutions can be used both to validate the two-dimensional code and to enable efficient parameter scans to study the properties of DaRT seed lattices. We compare these approximations to the full 2D solution over the relevant parameter space, providing guidelines on their usability and limitations.