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An Energy-Adaptive Finite Element Angular Discretization Towards a Fast Deterministic Dose Calculation in Magnetic Fields

R Yang1,2, B Fallone1,2 , J St-Aubin3* , (1) Cross Cancer Institute, Edmonton, AB, (2) University of Alberta, Edmonton, AB, (3) University of Iowa, Iowa City, IA


(Tuesday, 7/31/2018) 4:30 PM - 6:00 PM

Room: Karl Dean Ballroom C

Purpose: To leverage flexibility of a finite element (FE) discretization in angle for an energy-adaptive strategy tailored to the solution anisotropy in a deterministic solution to the Linear Boltzmann Transport Equation (LBTE) with magnetic fields.

Methods: Angular fluence and scattering cross-section anisotropy were quantified across photon and electron Multigroup energies calculated in a heterogeneous phantom containing water, bone, and air with a 1.5T magnetic field parallel to a 6MV photon beam. Angular mesh coarsening was performed on both the number of elements (h-refinement), and the polynomial degree (p-refinement) for each energy group while maintaining a high degree of accuracy compared to the Monte Carlo code GEANT4 based on a 3D gamma analysis. Notably, our FE meshing strategy conformal to the unit sphere allowed for a greater degree of mesh refinement in the forward direction (0≤θ≤π/2) to optimally model forward peaked scattering.

Results: Forward peaked scattering at higher megavoltage energies was accurately modeled using 16 elements with quadratic basis functions in the forward direction, and 4 linear elements for backscatter. The angular mesh was relaxed at lower energies to 4 quadratic elements on both hemispheres. Gamma analysis on final dose distributions against GEANT4 confirmed high accuracy even in strong magnetic fields, with 99.98% (95.52%) of points passing a 2%/2mm (1%/1mm) criterion. This method provided a nearly 3 fold decrease in runtime for a problem with 52800 spatial elements on a non-parallelized Matlab code (1134s from 3125s using a uniform angular discretization of 32 quadratic elements). Moreover the solution was free from statistical uncertainty or ray-effect artifacts.

Conclusion: An energy-adaptive, forward peaked angular meshing strategy substantially reduced intrinsic computational complexity and overall runtime while preserving high accuracy, establishing a significant step towards a fast, accurate, deterministic dose calculation for MRIgRT.

Funding Support, Disclosures, and Conflict of Interest: This work was supported in part by Alberta Innovates Health Solutions. Dr. B G Fallone is CEO and Co-founder of MagnetTx Oncology Solutions.


Finite Element Analysis, Magnetic Fields, Anisotropy


TH- External beam- photons: dose computation engines- deterministic

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