Modelling the transport of ionizing radiation using the finite element method

Area of Science:

• Medical Physics
• Computational Physics
• Numerical Analysis

Background:

• Accurate radiation therapy dose calculation is crucial for treatment planning.
• Solving coupled Boltzmann transport equations (BTEs) is necessary for precise dose calculations, but computationally intensive.
• Existing methods often simplify the BTEs or rely on approximations.

Purpose of the Study:

• To develop and validate a finite element method (FEM) approach for solving coupled Boltzmann transport equations (BTEs) in radiation therapy.
• To address the six-dimensional nature of the stationary BTEs.
• To provide an accurate and efficient alternative to traditional dose calculation methods.

Main Methods:

• Application of the finite element method (FEM) to solve the six-dimensional Boltzmann transport equations.
• Derivation of the variational formulation for the coupled photon-electron system.
• Simulation of photon and electron transport in two spatial dimensions using the FEM approach.
• Comparison of FEM results with established Monte Carlo calculations.

Main Results:

• The FEM approach successfully solves the coupled BTEs for photon and electron transport.
• The derived variational formulation ensures the existence and uniqueness of the solution.
• FEM simulations demonstrate good agreement with Monte Carlo calculations for absorbed dose distribution.
• The method effectively handles the complexities of particle transport in radiation therapy scenarios.

Conclusions:

• The finite element method (FEM) offers a viable and accurate approach for solving coupled Boltzmann transport equations in radiation therapy.
• This method provides a robust framework for precise dose calculations, potentially improving treatment planning.
• The FEM approach shows promise for enhancing the accuracy and efficiency of radiation dosimetry.