{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T07:47:47Z","timestamp":1791791267570,"version":"4.3.4"},"reference-count":51,"publisher":"IOP Publishing","issue":"19","license":[{"start":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T00:00:00Z","timestamp":1791763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T00:00:00Z","timestamp":1791763200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2026,10,14]]},"abstract":"Abstract<\/jats:title>\n \n Objective.<\/jats:italic>\n 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.\n Approach.<\/jats:italic>\n We formulate a generalized diffusion\u2013reaction model on fractal substrates to describe molecular transport in heterogeneous media. Tissue architecture is characterized by a fractal (Hausdorff) dimension\n \n \n \n <\/jats:tex-math>\n \n \n D<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , while scale-dependent transport inefficiency and memory effects are captured by a fractional parameter\n \n \n \n <\/jats:tex-math>\n \n \n \u03b8<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n . 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.\n Main results.<\/jats:italic>\n The model reveals systematic suppression of long-range transport and enhanced localization as tissue structural complexity increases. Increasing\n \n \n \n <\/jats:tex-math>\n \n \n \u03b8<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n leads to subdiffusive dynamics, reduced effective diffusion lengths, and persistent non-Gaussian concentration profiles, even in the steady state. While increasing\n \n \n \n <\/jats:tex-math>\n \n \n D<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n alone enhances spatial accessibility, fractional dynamics dominate transport behavior when\n \n \n \n <\/jats:tex-math>\n \n \n \u03b8<\/mml:mi>\n ><\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , 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.\n Conclusion.<\/jats:italic>\n Fractal geometry provides a unifying physical framework for understanding tissue-dependent transport and differential response under FLASH UHDR irradiation. Normal tissues, characterized by near-Euclidean geometry and weak anomalous effects, permit greater inter-track interaction and recombination, whereas tumor-like tissues with elevated structural complexity exhibit localized transport and reduced collective chemical reactivity. This proof-of-principle study establishes tissue architecture as a fundamental determinant of transport efficiency and offers a mechanistic basis for experimentally observed FLASH tissue sparing, motivating geometry-aware modeling of radiobiological response.\n Significance.<\/jats:italic>\n This work shifts the emphasis from purely chemical kinetics toward a geometry-governed description of oxygen and reactive oxygen species transport in cells and tissues.\n <\/jats:p>","DOI":"10.1088\/1361-6560\/aeabe7","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T22:53:34Z","timestamp":1790204014000},"page":"195038","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Fractal geometry-governed oxygen diffusion: tumors vs. normal tissues"],"prefix":"10.1088","volume":"71","author":[{"given":"Neda","family":"Valizadeh","sequence":"first","affiliation":[{"name":"University of Mohaghegh Ardabili"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7651-5479","authenticated-orcid":true,"given":"Robabeh","family":"Rahimi","sequence":"additional","affiliation":[{"name":"University of Maryland School of Medicine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5722-2526","authenticated-orcid":true,"given":"Ramin","family":"Abolfath","sequence":"additional","affiliation":[{"name":"Howard University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,10,12]]},"reference":[{"key":"pmbaeabe7bib1","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2023.1060910","type":"journal-article","article-title":"A stochastic reaction\u2013diffusion modeling investigation of FLASH ultra-high dose rate response in different tissues","volume":"11","author":"Abolfath","year":"2023","journal-title":"Front. 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