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Incorporating spatial dependence into a multicellular tumor spheroid growth model
dc.contributor.authorGarner, Allen L.en_US
dc.contributor.authorLau, Y. Y.en_US
dc.contributor.authorJackson, Trachette L.en_US
dc.contributor.authorUhler, Michael D.en_US
dc.contributor.authorJordan, David W.en_US
dc.contributor.authorGilgenbach, Ronald M.en_US
dc.date.accessioned2011-11-15T15:58:44Z
dc.date.available2011-11-15T15:58:44Z
dc.date.issued2005-12-15en_US
dc.identifier.citationGarner, Allen L.; Lau, Y. Y.; Jackson, Trachette L.; Uhler, Michael D.; Jordan, David W.; Gilgenbach, Ronald M. (2005). "Incorporating spatial dependence into a multicellular tumor spheroid growth model." Journal of Applied Physics 98(12): 124701-124701-8. <http://hdl.handle.net/2027.42/87333>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/87333
dc.description.abstractRecent models for organism and tumor growth yield simple scaling laws based on conservation of energy. Here, we extend such a model to include spatial dependence to model necrotic core formation. We adopt the allometric equation for tumor volume with a reaction-diffusion equation for nutrient concentration. In addition, we assume that the total metabolic energy and average cellular metabolic rate depend on nutrient concentration in a Michaelis-Menten-like manner. From experimental results, we relate the necrotic volume to nutrient consumption and estimate both the time and nutrient concentration at necrotic core formation. Based on experimental results, we demand that the necrotic core radius varies linearly with tumor radius after core formation and extend the equations for tumor volume and nutrient concentration to the postnecrotic core regime. In particular, we obtain excellent agreement with experimental data and the final steady-state viable rim thickness.en_US
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleIncorporating spatial dependence into a multicellular tumor spheroid growth modelen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumBioelectromagnetism Laboratory, Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.contributor.affiliationumDepartment of Mathematics, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.contributor.affiliationumBioelectromagnetism Laboratory, Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109 and Molecular and Behavioral Neuroscience Institute, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.contributor.affiliationumBioelectromagnetism Laboratory, Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/87333/2/124701_1.pdf
dc.identifier.doi10.1063/1.2146073en_US
dc.identifier.sourceJournal of Applied Physicsen_US
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dc.owningcollnamePhysics, Department of


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