Microdosimetry aspects in diffusing alpha-emitters radiation therapy: I. Effect of broad nucleus size distributions

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. 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. Introducing finite-width nucleus size distributions including very small nuclei causes survival curves to depart from the exponential trend observed for uniform cell populations, especially at high therapeutic doses. 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. We provide an extensive discussion on the origins of very small nuclei, addressing both genuine biological phenomena and methodological factors arising from histological reconstruction. 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. Methodological and biological advances will enable more reliable treatment planning and potentially enhance the clinical utility of microdosimetric models.