Monte Carlo Simulation of the Diffusion-Leakage Model In Alpha Dart: Methodological Pitfalls and Acceleration Shortcuts
Abstract
Purpose
In diffusing alpha-emitters radiation therapy (Alpha DaRT), the Diffusion-Leakage (DL) model is used to calculate the spread of radionuclides from unsealed sources implanted in a solid tumor. Various numerical methods for simulating the DL model have been published. The ones rigorously simulating each of the physical processes of the model are all grid-based deterministic methods, either finite difference (FD), finite element (FE) or finite volume (FV) methods. This work summarizes a stand-alone grid-free Monte Carlo (MC) method for simulating the DL model, identifies methodological pitfalls to avoid and specifies acceleration shortcuts that have been implemented.
Methods
Random sampling from well-known probability distributions (multinomial, uniform, exponential, normal, Maxwell-Boltzmann) was used to simulate physical processes involved in the DL model (radioactive decay, desorption, diffusion, leakage) and obtain radionuclides decay positions. The MC method validation was performed by calculating the probability density function (pdf) corresponding to decay positions of 212Pb radionuclides leaving a point source and comparing this pdf to its analytical counterpart. Two methodological pitfalls were identified, related to the simulation of diffusion and leakage processes respectively. Analytical pdfs corresponding to each pitfall were calculated, again for a point source, and compared to a reference analytical pdf.
Results
The relative difference between MC simulations and analytical results agrees with a fluctuation envelope corresponding to the natural stochasticity of the simulated processes. Pitfall #1 (diffusion) leads to an overestimation of the number of decays near and far from the source and an underestimation (up to 35%) at distances between 0.8 and 5.2 diffusion lengths from the source. Pitfall #2 (leakage) leads to an underestimation (up to 50%) of the number of decays near the source and an overestimation far from the source (> 2.4 diffusion lengths).
Conclusion
The method presented is the first MC method to rigorously simulate the DL model.