On the shape of the radiation survival curve in tumor spheroids: The role of oxygen heterogeneity

BACKGROUND: The shape of cell survival curves at the tissue level remains an open question in radiobiology. While homogeneous cell populations (so-called single cells) typically exhibit an exponential decrease in survival with increasing dose, it is unclear whether this behavior persists in multicellular systems, where oxygen and nutrient gradients introduce additional complexity. PURPOSE: This study investigates how oxygen diffusion and consumption in tumor spheroids modify the aggregate radiation response and whether the resulting survival curves follow a purely exponential or a linear-quadratic (LQ) form on the logarithmic scale. METHODS: . Oxygen-dependent, location-specific cellular radiosensitivity was modeled via the oxygen enhancement ratio (OER), and the overall spheroid survival fraction was obtained by integrating survival over the viable spheroid volume, using both numerical calculation and a closed-form analytical approximation. RESULTS: Both the mechanistic oxygen-diffusion-based numerical survival model and the simplified approximation reproduced experimental survival data for WiDr spheroids of diameters 100-1200 µm reported by Buffa et al. and West et al. The predicted survival curves become progressively less steep as spheroid size increases, reflecting the larger hypoxic fraction. For large spheroids, both model and data exhibit a distinct upward curvature of the survival curve at high doses, deviating from both exponential and downward-bending LQ behavior. This effect arises from dose-dependent weighting of oxic and hypoxic cell subpopulations within the heterogeneous spheroid. CONCLUSIONS: The results support the hypothesis that oxygen heterogeneity fundamentally alters the apparent dose-response relationship in multicellular systems. The transition from single-cell to spheroid-level behavior introduces non-linear averaging effects that produce survival curves not captured by standard exponential or LQ models. These findings provide a mechanistic bridge between cellular radiobiology and tissue-scale dose-response modeling.