Diffusing alpha-emitters radiation therapy: approximate modeling of the macroscopic alpha particle dose of a point source.

Diffusing alpha-emitters radiation therapy ('DaRT') is a new cancer-treatment modality, which enables treating solid tumors by alpha particles. The treatment utilizes implantable seeds embedded with a low activity of radium-224. Each seed continuously emits the short-lived alpha-emitting daughters of radium-224, which spread over several mm around it, creating a 'kill region' of high alpha-particle dose. DaRT is presently tested in clinical trials, starting with locally advanced and recurrent squamous cell carcinoma (SCC) of the skin and head and neck, with promising results with respect to both efficacy and safety. This work aims to provide a simple model which can serve as a zero-order approximation for DaRT dosimetry, allowing for calculating the macroscopic alpha particle dose of a point source, as a basis for more realistic source geometries. The model consists of diffusion equations for radon-220, lead-212 and bismuth-212, with the other short-lived daughters in local secular equilibrium. For simplicity, the medium is assumed to be homogeneous, isotropic and time-independent. Vascular effects are accounted for by effective diffusion and clearance terms. To leading order, the alpha particle dose can be described by simple analytic expressions, which shed light on the underlying physics. The calculations demonstrate that, for a reasonable choice of model parameters, therapeutic alpha-particle dose levels are obtained over a region measuring 4-7 mm in diameter for sources carrying a few [Formula: see text]Ci of radium-224. The model predictions served as the basis for treatment planning in the SCC clinical trial, where treatments employing DaRT seeds carrying 2 [Formula: see text]Ci of radium-224 and spaced 5 mm apart resulted in  ∼[Formula: see text] complete response of the treated tumors with no observed radiation-induced toxicity. The promising results of the SCC clinical trial indicate that in spite of its approximate nature, the simple diffusion-based dosimetry model provides a quantitative starting point for DaRT treatment planning.