Modeling of the Alpha DaRT coated source using GEANT4: Investigating nuclei effective desorption probabilities,...

In this study, we modeled the geometry of an Alpha diffusing alpha-emitters radiation therapy (DaRT) source using GEANT4. Four distributions of²²⁴Ra were considered to evaluate the desorption probabilities of daughter nuclei both with and without a coating layer of PDMS. By considering²²⁴Ra radioactive nuclei as a source, we evaluated the desorption probability of the daughter nuclei. We then adjusted the desorption probability values of²²⁰Rn to approximately 40% and 45%, consistent with values reported in the literature by either increasing the thickness of a thin cylindrical steel layer covering a thin²²⁴Ra layer (1.54 × 10^-4nm), or by adjusting theσvalue of a half-Gaussian distribution of²²⁴Ra. The resulting four source configurations correspond to steel layer thicknesses covering the²²⁴Ra layer of 1.00 nm and 2.04 nm, andσvalues of the half-Gaussian²²⁴Ra distributions of 1.35 nm and 2.59 nm resulting in²²⁰Rn desorption probabilities of 45% and 40%, respectively. For half-Gaussian distributions withσ= 1.35 nm, the calculated desorption probabilities from the source are as follows:²²⁰Rn (45.11%),²¹⁶Po (14.14%),²¹²Pb (7.64%),²⁰⁸Tl (1.51%), and²⁰⁸Pb (3.73%), all calculated with Monte Carlo statistical uncertainties less than 0.01%. Recoil effects led to the desorption of some atoms from the source, while others penetrated deeper into the steel layer. The corresponding average recoil penetration depths within the seed are as follows:²²⁰Rn (7.83 nm),²¹⁶Po (12.28 nm),²¹²Pb (16.36 nm),²⁰⁸Tl (19.42 nm), and²⁰⁸Pb (20.61 nm). Then, we developed a model to calculate nuclear decay from²²⁴Ra to²⁰⁸Pb, which accounts for desorption and leakage processes. Furthermore, the integrated activity of each radionuclide within the source and its vicinity was computed. The Alpha DaRT source models developed in this work provides valuable insights into the behavior of radionuclides in both bare and coated sources and can be integrated with diffusion and radiation transport processes to enable accurate simulations of dose distributions for all types of radiation emitted from nuclei embedded in the source and diffused nuclei for any leakage probability of²¹²Pb.