Fitting Monte Carlo simulation results with an empirical model of megavoltage x-ray beams for rapid depth dose calculations in water

Abstract

Objective. 
The purpose of this study was to assess a method of accelerating Monte Carlo simulations for modeling depth-dose distributions from megavoltage x-ray beams by fitting them to an empirically-derived function.

Approach. 
Using Geant4, multiple simulations of a typical medical linear accelerator beam in water and in water with an air cavity were conducted with varying numbers of initial electrons. The resulting percent depth dose curves were compared to published data from actual linear accelerator measurements. Two methods were employed to reduce computation time for this modeling process. First, an empirical function derived from measurements at a particular linear accelerator energy, source- to-surface distance, and field size was used to directly fit the simulated data. Second, a linear regression was performed to predict the empirical function’s parameters for simulations with more initial electrons.

Main Results. 
Fitting simulated depth dose curves with the empirical function yielded significant improvements in either accuracy or computation time. When compared to published measurements, the maximum error for the largest simulation was 5.58%, which was reduced to 2.01% with the best fit of the function. Fitting the empirical function around the air cavity heterogeneity resulted in errors less than 2.5% at the interfaces. The linear regression prediction modestly improved the same simulation with a maximum error of 4.22%, while reducing the required computation time from 66.53 hours to 43.75 hours.

Significance. 
This study demonstrates the effective use of empirical functions to expedite Monte Carlo simulations for a range of applications from radiation protection to food sterilization. These results are particularly impactful in radiation therapy treatment planning, where time and accuracy are especially valuable. Employing these methods may improve patient outcomes by ensuring that dose delivery more accurately matches the prescription or by shortening the preparation time before treatment in Monte Carlo-based treatment planning systems.