Fractal Diffusion–Reaction Framework for FLASH-UHDR Tissue Sparing

We present a tissue-dependent diffusion–reaction model to explain the differential sparing of normal tissues under FLASH ultra-high dose rate (UHDR) irradiation. Conventional models assume homogeneity and fail to capture the distinct responses of normal versus tumor tissues at extreme dose rates. Our framework proposes that tissue microstructure-specifically its fractal geometry-plays a critical role in governing molecular transport and reactive oxygen species (ROS) dynamics.

The model uses coupled reaction–diffusion equations on a random network to simulate ionization track evolution in fractal media. This approach reflects the porous, irregular nature of biological cells (normal and malignant), where ROS propagation is influenced by stochastic spatial fluctuations. Tissue sensitivity is defined by two geometric parameters: the fractal dimension (D), indicating structural complexity, and the track dimensionality (d), representing ROS symmetry-spherical for (d = 3), and cylindrical for (d = 2).

Our findings show a transition from collective to localized diffusion as tissue complexity increases. In near-homogeneous tissues (), diffusion is Gaussian, ionization tracks overlap, and recombination is enhanced-leading to higher sensitivity to the dose rate and radioprotection, characteristic of FLASH effects in normal tissues. In contrast, tumor-like tissues (D < d) exhibit subdiffusive, isolated transport, reducing recombination, less sensitivity to the dose rate, thereby diminishing the protective FLASH response.

This geometry-driven framework bridges physics and radiobiology, offering a robust explanation for tissue-specific radiation sensitivity. It emphasizes how structural disorder in tumors limits cooperative diffusion, whereas organized architectures in normal tissues enhance inter-track interactions and promote sparing.