{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T17:05:53Z","timestamp":1763226353906,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,2,6]],"date-time":"2016-02-06T00:00:00Z","timestamp":1454716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In tissue engineering, porous biodegradable scaffolds are used as templates for regenerating required tissues. With the advances in computational tools, many modeling approaches have been considered. For example, fluid flow through porous medium can be modeled using the Brinkman equation where permeability of the porous medium has to be defined. In this review, we summarize various models recently reported for defining permeability and non-invasive pressure drop monitoring as a tool to validate dynamic changes in permeability. We also summarize some models used for scaffold degradation and integrating mass transport in the simulation.<\/jats:p>","DOI":"10.3390\/computation4010007","type":"journal-article","created":{"date-parts":[[2016,2,9]],"date-time":"2016-02-09T13:45:23Z","timestamp":1455025523000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Applications of Computational Modelling and Simulation of Porous Medium in Tissue Engineering"],"prefix":"10.3390","volume":"4","author":[{"given":"Carrie","family":"German","sequence":"first","affiliation":[{"name":"School of Chemical Engineering, Oklahoma State University, 212 Cordell North Stillwater, OK 74078, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7498-5760","authenticated-orcid":false,"given":"Sundararajan","family":"Madihally","sequence":"additional","affiliation":[{"name":"School of Chemical Engineering, Oklahoma State University, 212 Cordell North Stillwater, OK 74078, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1038\/nmat2441","article-title":"Complexity in biomaterials for tissue engineering","volume":"8","author":"Place","year":"2009","journal-title":"Nat. Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.pharmthera.2012.01.001","article-title":"A critical evaluation of in vitro cell culture models for high-throughput drug screening and toxicity","volume":"134","author":"Astashkina","year":"2012","journal-title":"Pharmacol. Ther."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1002\/jcp.24683","article-title":"3D cell culture systems: Advantages and applications","volume":"230","author":"Ravi","year":"2015","journal-title":"J. Cell. Physiol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Haycock, J.W. (2011). 3D Cell Culture, Humana Press.","DOI":"10.1007\/978-1-60761-984-0"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"17675","DOI":"10.1073\/pnas.0903716106","article-title":"Image-based multiscale modeling predicts tissue-level and network-level fiber reorganization in stretched cell-compacted collagen gels","volume":"106","author":"Sander","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_6","unstructured":"ElectrospinningCompany Why 3d Cell Culture?. Availabe online:http:\/\/www.electrospinning.co.uk\/why-3d-cell-culture\/."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pal, A., and Kleer, C.G. (2014). Three dimensional cultures: A tool to study normal acinar architecture vs. Malignant transformation of breast cells. J. Vis. Exp., 86.","DOI":"10.3791\/51311"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1089\/adt.2014.573","article-title":"Three-dimensional cell culture systems and their applications in drug discovery and cell-based biosensors","volume":"12","author":"Edmondson","year":"2014","journal-title":"Assay Drug Dev. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1038\/nrm3873","article-title":"Three-dimensional organotypic culture: Experimental models of mammalian biology and disease","volume":"15","author":"Shamir","year":"2014","journal-title":"Nat. Rev. Mol. Cell Biol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5610","DOI":"10.1016\/j.ijheatmasstransfer.2008.04.041","article-title":"Mass transfer model for drug delivery in tissue cells with reversible electroporation","volume":"51","author":"Granot","year":"2008","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.jbiosc.2012.03.010","article-title":"Application of computational fluid dynamics in tissue engineering","volume":"114","author":"Patrachari","year":"2012","journal-title":"J. Biosci. Bioeng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5131","DOI":"10.1016\/j.biomaterials.2010.03.013","article-title":"Oxygen mass transfer in a human tissue-engineered trachea","volume":"31","author":"Curcio","year":"2010","journal-title":"Biomaterials"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1002\/btpr.1547","article-title":"Dynamics of diffusivity and pressure drop in flow-through and parallel-flow bioreactors during tissue regeneration","volume":"28","author":"Podichetty","year":"2012","journal-title":"Biotechnol. Prog."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1002\/jor.1100170119","article-title":"Bioreactor cultivation conditions modulate the composition and mechanical properties of tissue-engineered cartilage","volume":"17","author":"Martin","year":"1999","journal-title":"J. Orthop. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.tibtech.2003.12.001","article-title":"The role of bioreactors in tissue engineering","volume":"22","author":"Martin","year":"2004","journal-title":"Trends Biotechnol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s11242-005-2720-3","article-title":"A criterion for non-darcy flow in porous media","volume":"63","author":"Zeng","year":"2006","journal-title":"Transp. Porous Media"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1007\/s10439-013-0815-5","article-title":"A survey of methods for the evaluation of tissue engineering scaffold permeability","volume":"41","author":"Pennella","year":"2013","journal-title":"Ann. Biomed. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1146\/annurev.bioeng.9.060906.151850","article-title":"Interstitial flow and its effects in soft tissues","volume":"9","author":"Swartz","year":"2007","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1007\/s10439-014-1009-5","article-title":"Modeling pressure drop using generalized scaffold characteristics in an axial-flow bioreactor for soft tissue regeneration","volume":"42","author":"Podichetty","year":"2014","journal-title":"Ann. Biomed. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1002\/jbm.b.33054","article-title":"Modeling of porous scaffold deformation induced by medium perfusion","volume":"102","author":"Podichetty","year":"2014","journal-title":"J. Biomed. Mater. Res. Part B Appl. Biomater."},{"key":"ref_21","first-page":"3","article-title":"The effect of pore size on permeability and cell attachment in collagen scaffolds for tissue engineering","volume":"15","author":"Harley","year":"2007","journal-title":"Technol. Health Care"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1089\/ten.teb.2012.0437","article-title":"Three-dimensional scaffolds for tissue engineering applications: Role of porosity and pore size","volume":"19","author":"Loh","year":"2013","journal-title":"Tissue Eng. Part B Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.jmbbm.2007.11.002","article-title":"Engineering functionally graded tissue engineering scaffolds","volume":"1","author":"Leong","year":"2008","journal-title":"J. Mech. Behav. Biomed. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1080\/16864360.2007.10738500","article-title":"Stochastic modeling of tissue engineering scaffolds with varying porosity levels","volume":"4","author":"Sogutlu","year":"2007","journal-title":"Computer-Aided Des. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2991","DOI":"10.1016\/j.cma.2006.09.023","article-title":"Computational design of tissue engineering scaffolds","volume":"196","author":"Hollister","year":"2007","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_26","first-page":"2055","article-title":"A mathematical approach to bone tissue engineering","volume":"367","author":"Doblare","year":"2009","journal-title":"Philos. Trans. R. Soc. A Math Phys. Eng. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"011001","DOI":"10.1115\/1.4002933","article-title":"Engineered tissue scaffolds with variational porous architecture","volume":"133","author":"Khoda","year":"2011","journal-title":"J. Biomech. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s10237-014-0599-z","article-title":"Multiscale fluid-structure interaction modelling to determine the mechanical stimulation of bone cells in a tissue engineered scaffold","volume":"14","author":"Zhao","year":"2015","journal-title":"Biomech. Modeling Mechanobiol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.actbio.2010.09.038","article-title":"Mathematical modeling of degradation for bulk-erosive polymers: Applications in tissue engineering scaffolds and drug delivery systems","volume":"7","author":"Chen","year":"2011","journal-title":"Acta Biomater."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.jmbbm.2015.08.030","article-title":"Modelling the degradation and elastic properties of poly(lactic-co-glycolic acid) films and regular open-cell tissue engineering scaffolds","volume":"54","author":"Shirazi","year":"2016","journal-title":"J. Mech. Behav. Biomed. Mate."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3393","DOI":"10.1016\/j.biomaterials.2008.04.042","article-title":"A phenomenological model for the degradation of biodegradable polymers","volume":"29","author":"Wang","year":"2008","journal-title":"Biomaterials"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s10237-013-0493-0","article-title":"Mathematical model of the role of degradation on matrix development in hydrogel scaffold","volume":"13","author":"Dhote","year":"2014","journal-title":"Biomech. Modeling Mechanobiol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"9","DOI":"10.4161\/cam.2.1.5884","article-title":"Cell colonization in degradable 3d porous matrices","volume":"2","author":"Lawrence","year":"2008","journal-title":"Cell Adh. Migr."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4963","DOI":"10.1016\/S0020-7683(98)00104-8","article-title":"A method for the determination of mechanical parameters in a porous elastically deformable medium : Applications to biological soft tissues","volume":"35","author":"Naili","year":"1998","journal-title":"Int. J. Solids Struct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1016\/j.jbiomech.2013.05.028","article-title":"Using regression models to determine the poroelastic properties of cartilage","volume":"46","author":"Chung","year":"2013","journal-title":"J. Biomech."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:18:58Z","timestamp":1760210338000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,6]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["computation4010007"],"URL":"https:\/\/doi.org\/10.3390\/computation4010007","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2016,2,6]]}}}