A finite element method for modeling diffusion of alpha-emitting particles in tissue

Area of Science:

• Medical Physics
• Computational Biology
• Radiotherapy Research

Background:

• Diffusing alpha-emitters Radiation Therapy (DaRT) utilizes interstitial ²²⁴Ra sources for solid tumor treatment.
• Alpha particles from decaying ²²⁴Ra and its daughters create a localized tumor kill region.
• The Diffusion-Leakage (D-L) model describes alpha-emitter transport in tumor tissue.

Purpose of the Study:

• To develop a flexible finite element method (FEM) for solving the D-L model.
• To validate existing numerical solutions (DART1D, DART2D) of the D-L model.
• To assess dose variations based on D-L model parameters.

Main Methods:

• A 2D FEM solution for the D-L model was developed using FEniCS.
• The variational formulation was solved on an unstructured triangular Lagrangian element mesh.
• Local dose calculations were validated against DART1D and DART2D results.

Main Results:

• The FEM solution showed <1% difference in the source midplane and <3% along the source axis compared to DART1D/DART2D.
• Discrepancies were larger in high-gradient areas with denser FEM meshes.
• Dose in the source midplane at 2 mm varied over a factor of 3 within experimental parameter ranges.

Conclusions:

• The 2D FEM model accurately reproduces DART1D/DART2D dose calculations under D-L model assumptions.
• Significant dose variation necessitates further studies to determine statistical distributions of model parameters.
• The FEM model is adaptable for dose calculations in diverse 2D geometries beyond the D-L model.