Alpha dose modeling in diffusing alpha-emitters radiation therapy. Part II: Lattice studies

Background: Diffusing alpha-emitters radiation therapy (“DaRT”) is a new method, presently in clinical trials, which allows treating solid tumors by alpha particles. DaRT relies on interstitial seeds carrying μCi-level ²²⁴Ra activity on their surface, which release a chain of short-lived alpha emitters that spread throughout the tumor volume primarily by diffusion. Alpha dose calculations in DaRT are based on describing the transport of alpha emitting atoms, requiring new modeling techniques. Purpose: A previous study introduced a simplified framework, the “diffusion–leakage (DL) model,” for DaRT alpha dose calculations, and employed it to a point source, as a basic building block of arbitrary configurations of line sources. The aim of this work, which is divided into two parts, is to extend the model to realistic seed geometries (in Part I), and to employ single-seed calculations to study the properties of DaRT seed lattices (Part II). Such calculations can serve as a pragmatic guide for treatment planning in future clinical trials. Methods: We employ the superposition of single-seed solutions, developed in Part I, to study the alpha dose in DaRT seed lattices and investigate the sensitivity of the required seed activity and spacing to changes in the DL model parameters and to seed placement errors. Results: We show that the rapid fall-off of the dose, which guarantees sparing healthy tissue already 2–3 mm away from the tumor, strongly favors a hexagonal, rather than square, seed placement pattern. Realistic variations in the seed manufacturing parameters (²²⁴Ra activity and emission rate of its daughters) are shown to have a negligible effect on the required lattice spacing. On the other hand, tumor parameters (i.e., diffusion lengths and ²¹²Pb leakage probability), as well as seed placement errors, have a significant effect. Conclusions: In most cases, hexagonal lattice spacing on the scale of ∼3.5–4.5 mm using seeds carrying a few μCi/cm ²²⁴Ra will enable overcoming realistic uncertainties in measured tumor environment parameters, as well as seed placement errors, and result in therapeutically relevant alpha dose levels.