Development of a stand‐alone precalculated Monte Carlo code to calculate the dose by alpha and beta emitters from the Ra‐224 decay chain
Authors: Hoseini‐Ghahfarokhi Mojtaba , Kamio Yuji , Mondor Julien , Jabbari Keyvan , Carrier Jean‐François 
Published: May 2023

Background

Recent developments in alpha and beta emitting radionuclide therapy highlight the importance of developing efficient methods for patient‐specific dosimetry. Traditional tabulated methods such as Medical Internal Radiation Dose (MIRD) estimate the dose at the organ level while more recent numerical methods based on Monte Carlo (MC) simulations are able to calculate dose at the voxel level. A precalculated MC (PMC) approach was developed in this work as an alternative to time‐consuming fully simulated MC. Once the spatial distribution of alpha and beta emitters is determined using imaging and/or numerical methods, the PMC code can be used to achieve an accurate voxelized 3D distribution of the deposited energy without relying on full MC calculations.

Purpose

To implement the PMC method to calculate energy deposited by alpha and beta particles emitted from the Ra‐224 decay chain.

Methods

The GEANT4 (version 10.7) MC toolkit was used to generate databases of precalculated tracks to be integrated in the PMC code as well as to benchmark its output. In this regard, energy spectra of alpha and beta particles emitted by the Ra‐224 decay chain were generated using GAMOS (version 6.2.0) and imported into GEANT4 macro files. Either alpha or beta emitting sources were defined at the center of a homogeneous phantom filled with various materials such as soft tissue, bone, and lung where particles were emitted either mono‐directionally (for database generation) or isotropically (for benchmarking). Two heterogeneous phantoms were used to demonstrate PMC code compatibility with boundary crossing events. Each precalculated database was generated step‐by‐step by storing particle track information from GEANT4 simulations followed by its integration in a PMC code developed in MATLAB. For a user‐defined number of histories, one of the tracks in a given database was selected randomly and rotated randomly to reflect an isotropic emission. Afterward, deposited energy was divided between voxels based on step length in each voxel using a ray‐tracing approach. The radial distribution of deposited energy was benchmarked against fully simulated MC calculations using GEANT4. The effect of the GEANT4 parameter StepMax on the accuracy and speed of the code was also investigated.

Results

In the case of alpha decay, primary alpha particles show the highest contribution (>99%) in deposited energy compared to their secondary particles. In most cases, protons act as the main secondary particles in the deposition of energy. However, for a lung phantom, using a range cutoff parameter of 10 µm on primary alpha particles yields a higher contribution of secondary electrons than protons. Differences between deposited energy calculated by PMC and fully simulated MC are within 2% for all alpha and beta emitters in homogeneous and heterogeneous phantoms. Additionally, statistical uncertainties are less than 1% for voxels with doses higher than 5% of the maximum dose. Moreover, optimization of the parameter StepMax is necessary to achieve the best tradeoff between code accuracy and speed.

Conclusions

The PMC code shows good performance for dose calculations deposited by alpha and beta emitters. As a stand‐alone algorithm, it is suitable to be integrated into clinical treatment planning systems.