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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.15478 |
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| _version_ | 1866908973195591680 |
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| author | Valizadeh, Neda Rahimi, Robabeh Abolfath, Ramin |
| author_facet | Valizadeh, Neda Rahimi, Robabeh Abolfath, Ramin |
| contents | {\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport in biological tissues. {\bf Methods}: We formulate a generalized diffusion--reaction model on fractal substrates to describe molecular transport in heterogeneous media. Tissue architecture is characterized by a fractal (Hausdorff) dimension \(D\), while scale-dependent transport inefficiency and memory effects are captured by a fractional parameter \(θ\). Analytical solutions for radially symmetric geometries are derived and compared with classical normal (Euclidean) diffusion and a Gaussian reference model under identical physical conditions. Transport behavior is quantified through transient probability distributions and steady-state spatial profiles. {\bf Results}: The model reveals systematic suppression of long-range transport and enhanced localization as tissue structural complexity increases. Increasing \(θ\) leads to subdiffusive dynamics, reduced effective diffusion lengths, and persistent non-Gaussian concentration profiles, even in the steady state. While increasing \(D\) alone enhances spatial accessibility, fractional dynamics dominate transport behavior when \(θ>0\), counteracting geometric connectivity. These effects produce a separation between regimes characterized by efficient inter-track overlap and rapid homogenization, and regimes marked by isolated, long-lived reactive domains. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_15478 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractal geometry-governed oxygen diffusion: Tumors vs. Normal Tissues Valizadeh, Neda Rahimi, Robabeh Abolfath, Ramin Medical Physics Disordered Systems and Neural Networks Pattern Formation and Solitons Biological Physics Computational Physics {\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport in biological tissues. {\bf Methods}: We formulate a generalized diffusion--reaction model on fractal substrates to describe molecular transport in heterogeneous media. Tissue architecture is characterized by a fractal (Hausdorff) dimension \(D\), while scale-dependent transport inefficiency and memory effects are captured by a fractional parameter \(θ\). Analytical solutions for radially symmetric geometries are derived and compared with classical normal (Euclidean) diffusion and a Gaussian reference model under identical physical conditions. Transport behavior is quantified through transient probability distributions and steady-state spatial profiles. {\bf Results}: The model reveals systematic suppression of long-range transport and enhanced localization as tissue structural complexity increases. Increasing \(θ\) leads to subdiffusive dynamics, reduced effective diffusion lengths, and persistent non-Gaussian concentration profiles, even in the steady state. While increasing \(D\) alone enhances spatial accessibility, fractional dynamics dominate transport behavior when \(θ>0\), counteracting geometric connectivity. These effects produce a separation between regimes characterized by efficient inter-track overlap and rapid homogenization, and regimes marked by isolated, long-lived reactive domains. |
| title | Fractal geometry-governed oxygen diffusion: Tumors vs. Normal Tissues |
| topic | Medical Physics Disordered Systems and Neural Networks Pattern Formation and Solitons Biological Physics Computational Physics |
| url | https://arxiv.org/abs/2604.15478 |