Microdosimetry Aspects in Diffusing Alpha-emitters Radiation Therapy. Part I: Effect of Broad Nucleus Size Distributions

TL;DR

A microdosimetric model that links the macroscopic alpha dose, cell survival, and tumor control probability while explicitly accounting for broad distributions of spherical nucleus radii is presented, and it is shown that the width of the nucleus size distribution strongly influences the survival gap between radiosensitive and radioresistant populations.

Abstract

Diffusing alpha-emitters Radiation Therapy ("Alpha DaRT") is a new treatment modality focusing on the use of alpha particles against solid tumors. The introduction of Alpha DaRT in clinical settings calls for the development of detailed tumor dosimetry, which addresses biological responses such as cell survival and tumor control probabilities at the microscopic scale. In this study, we present a microdosimetric model that links the macroscopic alpha dose, cell survival, and tumor control probability while explicitly accounting for broad distributions of spherical nucleus radii. The model combines analytic expressions for nucleus-hit statistics by alpha particles with Monte Carlo-based specific-energy deposition to compute survival for cells whose nucleus radii are sampled from artificial and empirically derived distributions. The results indicate that introducing finite-width nucleus size distributions causes survival curves to depart from the exponential trend observed for uniform cell populations. We show that the width of the nucleus size distribution strongly influences the survival gap between radiosensitive and radioresistant populations, diminishing the influence of intrinsic radiosensitivity on cell survival. Tumor control probability is highly sensitive to the minimal nucleus size included in the size distribution, indicating that realistic lower thresholds are essential for credible predictions.Our findings highlight the importance of careful characterization of clonogenic nucleus sizes, with particular attention to the smallest nuclei represented in the data. Without addressing these small-nucleus contributions, tumor control probability may be substantially underestimated. Incorporating realistic nucleus size variability into microdosimetric calculations is a key step toward more accurate tumor control predictions for Alpha DaRT and other alpha-based treatment modalities.

Figures (10)

• Figure 1: Visualization of the simulated target. (Left) A spherical cell containing a nucleus crossed by an alpha particle track marked by a red arrow. (Right) Zoom-in view on the nucleus with the hit points marked by captions.
• Figure 2: Monte-Carlo calculation of the mean number of alpha-particle hits to the nucleus as a function of its radius, resulting from uniformly distributed alpha emitters: $^{220}$Rn (6.29 MeV), $^{216}$Po (6.78 MeV), $^{212}$Bi (6.05, 6.09 MeV) and $^{212}$Po (8.79 MeV), each for an absorbed dose of 10 Gy. Dotted lines represent the respective analytical calculation according to Equation (\ref{['eq:n_hit']}). The inset focuses on the region of small radii.
• Figure 3: Monte-Carlo calculation of the Single-hit Specific Energy Distribution (SSED) for $^{220}$Rn, $^{216}$Po, $^{212}$Bi, and $^{212}$Po, for a spherical nucleus with a radius of 2 $\mu$m (left) and 5 $\mu$m (right). The alpha-emitters are uniformly distributed inside and outside of the nucleus.
• Figure 4: Nucleus radius distribution data extracted from Poole et al. 2015, fitted using a Gamma distribution function with parameters $k$ = 4.047 and $\theta$ = 1.141 with no lower threshold on the nucleus radius.
• Figure 5: Laplace transforms $T_1(z_0;R_n,E_{\alpha})$ of the SSED for $^{220}$Rn, $^{216}$Po, $^{212}$Bi, and $^{212}$Po, for a range of nucleus radii, and two selected values of the radiosensitivity parameter: $z_0=0.5$ Gy (left) and $z_0=1$ Gy (right). The alpha-emitters are uniformly distributed inside and outside of the nucleus.