A Dose Kernel Superposition Approach for 2D Lattice Dosimetry of Alpha Dart (224Ra) Sources
Abstract
Purpose
To achieve accurate dosimetric modeling of Alpha DaRT sources by accounting for the spatial superposition of dose contributions from multiple implanted sources arranged in a regular lattice geometry.
Methods
In this work, we implemented a two-dimensional dose superposition algorithm to model the dose from an array of Alpha DaRT sources using a single-source dose kernel derived from GEANT4 simulations. The radial dose distribution of a single source was represented by a kernel function, K(r). Assuming linear superposition, the total absorbed dose at any point was calculated as the sum of dose contributions from all sources, accounting for all emission components. Analysis of isodoses around a single ²²⁴Ra Alpha DaRT source was performed to determine the radial distance at which the absorbed alpha particle dose reaches a therapeutic level of 100 Gy-Eq. This radius corresponds to half of the lattice spacing in a hexagonal arrangement of sources. Based on this lattice spacing, dose distributions were subsequently calculated for a hexagonal lattice of sources using reference diffusion parameters.
Results
The resulting two-dimensional 100 Gy-Eq isodose represents a high-dose region with a radius of R100 = 2.2 mm and an optimal hexagonal lattice spacing of 4.4 mm. The resulting dose distribution for the hexagonal lattice illustrates the total equivalent dose contributions from all emission components (alpha particles, beta particles, recoil nuclei, IC electrons, and secondary gamma rays).
Conclusion
This superposition approach enables near real-time dose calculation of Alpha DaRT lattice geometries, making it practical for clinical use. This superposition approach enables near real-time dose calculation of Alpha DaRT lattice geometries, which is suitable in a clinical setting. This superposition model effectively captures the dose enhancement in inter-source regions provided by the longer range of beta and secondary gamma emissions.