Purpose: To perform Monte Carlo simulations of the decay chain of ²²⁴Ra used in Diffusing Alpha-emitters Radiotherapy (DaRT) for dosimetry applications. This will provide information on the absorbed dose, especially due to the alpha particles reaching distances of approximately 5 mm in tissue.
Methods: Geometry, material and physics of the decay chain of ²²⁴Ra in DaRT seeds were modeled in a Monte Carlo-based user code building on Geant4 simulation toolkit. Stainless-steel DaRT seeds with a density of 7.92 g/cm³, inner diameter of 0.4 mm, outer diameter of 0.7 mm, and a length of 10 mm, were implemented with ²²⁴Ra atoms fixed to their surface. The seed is placed inside a spherical water phantom with radius 10 cm. Geant4 package simulates the decay chain but does not the diffusion of ²²⁰Rn. As a first approach, the diffusion in this code was implemented according to a published analytical diffusion equation which sets a maximum diffusion length or limit for the ²²⁰Rn atoms diffusion. Taking this into consideration, the developed software, after decay of ²²⁴Ra, randomly samples a position for the diffusion of ²²⁰Rn from all possible positions that satisfy the limit condition. After diffusion of ²²⁴Ra, it continues to decay into another alpha-emitters radionuclide until it reaches a stable state with ²⁰⁸Pb.
Results: The results for this simulation display the positions of ²²⁴Ra along the seed surface, the emitted ²²⁰Rn and other decay products. The mean position at which ²²⁰Rn was emitted from ²²⁴Ra is approximately 0.13 mm around the seed.
Conclusion: The results indicate that implementation of appropriate diffusion equation inside a Monte Carlo particle transport code is possible. The developed software allows us to modify the distance where the daughter is emitted depending to the diffusion properties of its mother.
Funding Support, Disclosures, and Conflict of Interest: CONACyT-Regional Centro grant,TransMedTech grant (Canada First Research Excellence Fund) co-funded by Mitacs,the Jewish General Hospital Foundation,Alpha Tau Medical. The authors would also like to acknowledge funds from Canada Research Chairs Program (grant #252135). No conflict of interest except that the peer-reviewed grant is co-funded by the company Alpha Tau Medical.