{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T20:38:09Z","timestamp":1767731889527,"version":"build-2238731810"},"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2008,8,15]],"date-time":"2008-08-15T00:00:00Z","timestamp":1218758400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1000152","type":"journal-article","created":{"date-parts":[[2008,8,14]],"date-time":"2008-08-14T17:48:26Z","timestamp":1218736106000},"page":"e1000152","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":48,"title":["A Novel Three-Phase Model of Brain Tissue Microstructure"],"prefix":"10.1371","volume":"4","author":[{"given":"Jana L.","family":"Gevertz","sequence":"first","affiliation":[]},{"given":"Salvatore","family":"Torquato","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2008,8,15]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1088\/0034-4885\/64\/7\/202","article-title":"Diffusion and related transport mechanisms in brain tissue.","volume":"64","author":"C Nicholson","year":"2001","journal-title":"Rep Prog Phys"},{"key":"ref2","first-page":"155","article-title":"Extracellular space diffusion and pathological states.","author":"E Sykov\u00e1","year":"2000"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.1115\/1.1483342","article-title":"Random Heterogeneous Materials: Microstructure and Macroscopic Properties","author":"S Torquato","year":"2002"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0166-2236(98)01261-2","article-title":"Extracellular space structure revealed by diffusion analysis.","volume":"21","author":"C Nicholson","year":"1998","journal-title":"Trends Neurosci"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"S5213","DOI":"10.1088\/0953-8984\/16\/44\/018","article-title":"Diffusion and tissue microstructure.","volume":"16","author":"PN Sen","year":"2004","journal-title":"J Phys Condens Matter"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1529\/biophysj.103.039495","article-title":"A model of the effective diffusion and tortuosity in the extracellular space of the brain.","volume":"87","author":"J Hrabe","year":"2004","journal-title":"Biophys J"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1016\/S0006-3495(93)81532-7","article-title":"Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue.","volume":"64","author":"AW El-Kareh","year":"1993","journal-title":"Biophys J"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"8306","DOI":"10.1073\/pnas.150338197","article-title":"Changes in brain cell shape create residual extracellular space volume and explain tortuosity behavior during osmotic challenge.","volume":"97","author":"KC Chen","year":"2000","journal-title":"Proc Natl Acad Sci U S A"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.jtbi.2004.03.003","article-title":"Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells.","volume":"229","author":"L Tao","year":"2004","journal-title":"J Theor Biol"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"2927","DOI":"10.1529\/biophysj.105.063016","article-title":"A model for diffusion in white matter in the brain.","volume":"89","author":"PN Sen","year":"2005","journal-title":"Biophys J"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.neuint.2003.11.011","article-title":"Contribution of dead-space microdomains to tortuosity of brain extracellular space.","volume":"45","author":"S Hrab\u011btov\u00e1","year":"2004","journal-title":"Neurochem Int"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1137\/S0036139997323942","article-title":"A lattice cellular automata model for ion diffusion in the brain-cell microenvironment and determination of tortuosity and volume fraction.","volume":"59","author":"L Dai","year":"2004","journal-title":"SIAM J Appl Math"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/j.jtbi.2004.12.009","article-title":"Cell cavities increase tortuosity in brain extracellular space.","volume":"234","author":"A Tao","year":"2005","journal-title":"J Theor Biol"},{"key":"ref14","first-page":"1035","article-title":"Encyclopedia of Biomaterials and Biomedical Engineering","author":"WC Broaddus","year":"2004"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"2064","DOI":"10.1103\/PhysRevLett.84.2064","article-title":"Is random close packing of spheres well defined?","volume":"84","author":"S Torquato","year":"2000","journal-title":"Phys Rev Lett"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"11849","DOI":"10.1021\/jp011960q","article-title":"Multiplicity of generation, selection, and classification procedures for jammed hard-particle packings.","volume":"105","author":"S Torquato","year":"2001","journal-title":"J Phys Chem B"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"8354","DOI":"10.1021\/jp0208687","article-title":"Controlling the short-range order and packing densities of many-particle systems.","volume":"106","author":"S Torquato","year":"2002","journal-title":"J Phys Chem B"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1080\/10586458.2006.10128964","article-title":"New conjectural lower bounds on the optimal density of sphere packings.","volume":"15","author":"S Torquato","year":"2000","journal-title":"Exp Math"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"10612","DOI":"10.1073\/pnas.0601389103","article-title":"Packing, tiling and covering with tetrahedra.","volume":"103","author":"JH Conway","year":"2006","journal-title":"Proc Natl Acad Sci U S A"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1002\/mrm.1910370115","article-title":"An analytical model of restricted diffusion in bovine optic nerve.","volume":"37","author":"GJ Stanisz","year":"1997","journal-title":"Magn Res Med"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1063\/1.102184","article-title":"Efficient simulation technique to compute effective properties of heterogeneous media.","volume":"55","author":"S Torquato","year":"1989","journal-title":"Appl Phys Lett"},{"key":"ref22","article-title":"Gray's Anatomy, 38th edition","author":"H Gray","year":"1995"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"5567","DOI":"10.1073\/pnas.0509425103","article-title":"In vivo diffusion analysis with quantum dots and dextrans predicts the width of brain extracellular space.","volume":"103","author":"RG Thorne","year":"2006","journal-title":"Proc Natl Acad Sci U S A"},{"key":"ref24","article-title":"Molecular Biology of the Cell, 4th edition","author":"B Alberts","year":"2002"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1063\/1.462184","article-title":"Diffusion of finite-sized Brownian particles in porous media.","volume":"96","author":"IC Kim","year":"1992","journal-title":"J Chem Phys"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"8975","DOI":"10.1073\/pnas.95.15.8975","article-title":"Geometric and viscous components of the tortuosity of the extracellular space in the brain.","volume":"95","author":"DA Rusakov","year":"1998","journal-title":"Proc Natl Acad Sci U S A"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/S0006-3495(89)82744-4","article-title":"Effect of cytoskeletal geometry on intracellular diffusion.","volume":"64","author":"J Blum","year":"1989","journal-title":"Biophys J"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0006-3495(01)76007-9","article-title":"Mechanisms of permeation and selectivity in calcium channels.","volume":"80","author":"B Corry","year":"2001","journal-title":"Biophys J"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"2927","DOI":"10.1103\/PhysRevLett.71.2927","article-title":"Link between the conductivity and elastic moduli of composite materials.","volume":"71","author":"LV Gibiansky","year":"1993","journal-title":"Phys Rev Lett"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/S0020-7403(97)00031-3","article-title":"Effective mechanical and transport properties of cellular solids.","volume":"40","author":"S Torquato","year":"1998","journal-title":"Int J Mech Sci"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"4989","DOI":"10.1063\/1.340445","article-title":"On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality.","volume":"63","author":"M Avellaneda","year":"1988","journal-title":"J Appl Phys"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"2644","DOI":"10.1103\/PhysRevLett.64.2644","article-title":"Relationship between permeability and diffusion-controlled trapping constant of porous media.","volume":"64","author":"S Torquato","year":"1990","journal-title":"Phys Rev Lett"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1063\/1.858194","article-title":"Rigorous link between fluid permeability, electrical eonductivity, and relaxation times for transport in porous media.","volume":"3","author":"M Avellaneda","year":"1991","journal-title":"Phys Fluids A"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/0021-9797(86)90320-6","article-title":"A new Monte Carlo approach to diffusion in constricted porous geometries.","volume":"109","author":"RA Siegel","year":"1986","journal-title":"J Colloid Interface Sci"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"3892","DOI":"10.1063\/1.346276","article-title":"Determination of the effective conductivity of heterogeneous media by Brownian motion simulation.","volume":"68","author":"IC Kim","year":"1990","journal-title":"J Appl Phys"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1063\/1.348708","article-title":"Effective conductivity of suspensions of hard spheres by Brownian motion simulation.","volume":"69","author":"IC Kim","year":"1991","journal-title":"J Appl Phys"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"2727","DOI":"10.1063\/1.351046","article-title":"Effective conductivity of suspensions of overlapping spheres.","volume":"71","author":"IC Kim","year":"1992","journal-title":"J Appl Phys"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1063\/1.354792","article-title":"Effective conductivity of composites containing spheroidal inclusions: comparison of simulations with theory.","volume":"74","author":"IC Kim","year":"1993","journal-title":"J Appl Phys"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1063\/1.369287","article-title":"Effective conductivity, dielectric constant, and diffusion coefficient of digitized composite media via first-passage-time equations.","volume":"85","author":"S Torquato","year":"1999","journal-title":"J Appl Phys"},{"key":"ref40","article-title":"Simulation, 4th edition","author":"S Ross","year":"2006"}],"updated-by":[{"DOI":"10.1371\/annotation\/c9faa83b-3c7b-4f38-8d74-1a4309403688","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2009,1,6]],"date-time":"2009-01-06T00:00:00Z","timestamp":1231200000000}}],"container-title":["PLoS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1000152","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T16:51:06Z","timestamp":1540313466000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1000152"}},"subtitle":[],"editor":[{"given":"Olaf","family":"Sporns","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2008,8,15]]},"references-count":40,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2008,8,15]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1000152","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8,15]]}}}