{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T22:27:25Z","timestamp":1773268045647,"version":"3.50.1"},"reference-count":75,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CBET\u20101301198"],"award-info":[{"award-number":["CBET\u20101301198"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["NIH NINDS 1R21NS099896"],"award-info":[{"award-number":["NIH NINDS 1R21NS099896"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Institute of Aging","award":["NIH NIA 1R56AG066634-01"],"award-info":[{"award-number":["NIH NIA 1R56AG066634-01"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation <jats:italic>in silico<\/jats:italic> using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with <jats:italic>in vivo<\/jats:italic> oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer\u2019s disease.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008584","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T18:32:14Z","timestamp":1611858734000},"page":"e1008584","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":29,"title":["Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7107-3050","authenticated-orcid":true,"given":"Grant","family":"Hartung","sequence":"first","affiliation":[]},{"given":"Shoale","family":"Badr","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7620-8404","authenticated-orcid":true,"given":"Mohammad","family":"Moeini","sequence":"additional","affiliation":[]},{"given":"Fr\u00e9d\u00e9ric","family":"Lesage","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9797-4722","authenticated-orcid":true,"given":"David","family":"Kleinfeld","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1491-4634","authenticated-orcid":true,"given":"Ali","family":"Alaraj","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2694-630X","authenticated-orcid":true,"given":"Andreas","family":"Linninger","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"issue":"1","key":"pcbi.1008584.ref001","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1111\/j.1749-6632.2009.05026.x","article-title":"Hypoxia and Neurodegeneration","volume":"1177","author":"C Peers","year":"2009","journal-title":"Ann N Y Acad Sci"},{"key":"pcbi.1008584.ref002","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1042\/bse0430153","article-title":"Hypoxia and Alzheimer\u2019s disease","volume":"43","author":"C Peers","year":"2007","journal-title":"Essays Biochem"},{"issue":"2","key":"pcbi.1008584.ref003","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.neurobiolaging.2008.03.022","article-title":"The effects of healthy aging on intracerebral blood vessels visualized by magnetic resonance angiography","volume":"31","author":"E Bullitt","year":"2010","journal-title":"Neurobiol Aging"},{"issue":"8","key":"pcbi.1008584.ref004","doi-asserted-by":"crossref","first-page":"1947","DOI":"10.1016\/j.neurobiolaging.2014.01.136","article-title":"Aging-related differences in cerebral capillary blood flow in anesthetized rats","volume":"35","author":"M Desjardins","year":"2014","journal-title":"Neurobiol Aging"},{"issue":"8","key":"pcbi.1008584.ref005","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1161\/ATVBAHA.111.227314","article-title":"Aging causes collateral rarefaction and increased severity of ischemic injury in multiple tissues","volume":"31","author":"JE Faber","year":"2011","journal-title":"Arterioscler Thromb Vasc Biol"},{"issue":"5","key":"pcbi.1008584.ref006","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1016\/j.neurobiolaging.2011.09.022","article-title":"Brain regional angiogenic potential at the neurovascular unit during normal aging","volume":"33","author":"N Murugesan","year":"2012","journal-title":"Neurobiol Aging"},{"issue":"1","key":"pcbi.1008584.ref007","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0197-4580(85)90070-3","article-title":"Aging in the rat medial nucleus of the trapezoid body. 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Griffeth","year":"2011","journal-title":"NeuroImage"},{"issue":"3","key":"pcbi.1008584.ref018","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1016\/j.neuroimage.2007.12.061","article-title":"A vascular anatomical network model of the spatio-temporal response to brain activation.","volume":"40","author":"DA Boas","year":"2008","journal-title":"NeuroImage"},{"issue":"4","key":"pcbi.1008584.ref019","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1002\/mrm.1910400405","article-title":"Quantification of intravascular and extravascular contributions to BOLD effects induced by alteration in oxygenation or intravascular contrast agents","volume":"40","author":"J Zhong","year":"1998","journal-title":"Magn Reson Med"},{"issue":"1","key":"pcbi.1008584.ref020","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1038\/s41598-017-19086-z","article-title":"Insights into cerebral haemodynamics and oxygenation utilising in vivo mural cell imaging and mathematical 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Hsu","year":"1989","journal-title":"Math Biosci"},{"issue":"1","key":"pcbi.1008584.ref033","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1137\/100813853","article-title":"Finite element approximation of elliptic problems with Dirac measure terms in weighted spaces: applications to one-and three-dimensional coupled problems","volume":"50","author":"C D\u2019Angelo","year":"2012","journal-title":"SIAM J Numer Anal"},{"issue":"8","key":"pcbi.1008584.ref034","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1142\/S0218202508003108","article-title":"On the coupling of 1d and 3d diffusion-reaction equations: application to tissue perfusion problems","volume":"18","author":"C D\u2019Angelo","year":"2008","journal-title":"Math Models Methods Appl Sci"},{"key":"pcbi.1008584.ref035","first-page":"1715","article-title":"Splitting method for elliptic equations with line sources","author":"IG Gjerde","year":"2019","journal-title":"Comput 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Possenti","year":"2019","journal-title":"Int J Numer Methods Biomed Eng"},{"key":"pcbi.1008584.ref043","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.mvr.2018.11.003","article-title":"Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system","volume":"122","author":"L Possenti","year":"2019","journal-title":"Microvasc Res"},{"key":"pcbi.1008584.ref044","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.jcp.2017.01.007","article-title":"A computational approach to modeling cellular-scale blood flow in complex geometry","volume":"334","author":"P Balogh","year":"2017","journal-title":"J Comput Phys"},{"issue":"12","key":"pcbi.1008584.ref045","doi-asserted-by":"crossref","first-page":"2815","DOI":"10.1016\/j.bpj.2017.10.020","article-title":"Direct Numerical Simulation of Cellular-Scale Blood Flow in 3D Microvascular Networks","volume":"113","author":"P Balogh","year":"2017","journal-title":"Biophys 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Ghaffari","year":"2017","journal-title":"Comput Biol Med"},{"issue":"7","key":"pcbi.1008584.ref049","doi-asserted-by":"crossref","DOI":"10.1002\/cnm.2987","article-title":"Quantification of near-wall hemodynamic risk factors in large-scale cerebral arterial trees","volume":"34","author":"M Ghaffari","year":"2018","journal-title":"Int J Numer Methods Biomed Eng"},{"key":"pcbi.1008584.ref050","first-page":"635","volume-title":"Computer Aided Chemical Engineering","author":"M Ghaffari","year":"2015"},{"issue":"7","key":"pcbi.1008584.ref051","article-title":"Voxelized model of interstitial transport in the rat spinal cord following direct infusion into white matter","volume":"131","author":"JH Kim","year":"2009","journal-title":"J Biomech Eng"},{"issue":"11","key":"pcbi.1008584.ref052","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1006549","article-title":"Simulations of blood as a suspension predicts a depth dependent hematocrit in the circulation throughout the cerebral 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