A Distributed Parameter Liver Model of Benzene Transport and Metabolism in Humans and Mice - Developmental, Theoretical, and Numerical Considerations

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Title: A Distributed Parameter Liver Model of Benzene Transport and Metabolism in Humans and Mice - Developmental, Theoretical, and Numerical Considerations
Author: Gray, Scott Thomas
Advisors: Dr. Munindar P. Singh, Chair
Dr. R. Michael Young, Member
Dr. Mona Singh, Member
Abstract: In the Clean Air Act of 1970, the U. S. Congress names benzene ahazardous air pollutant and directs certain government agencies toregulate public exposure. Court battles over subsequent regulations haveled to the need for quantitative risk assessment techniques. Models forhuman exposure to various chemicals exist, but most current modelsassume the liver is well-mixed. This assumption does not recognize (mostsignificantly) the spatial distribution of enzymes involved in benzenemetabolism. The development of a distributed parameter liver model that accountsfor benzene transport and metabolism is presented. The mathematicalmodel consists of a parabolic system of nonlinear partial differentialequations and enables the modeling of convection, diffusion, andreaction within the liver. Unlike the commonly used well-mixed model,this distributed parameter model has the capacity to accommodate spatialvariations in enzyme distribution. The system of partial differential equations is formulated in a weak orvariational setting that provides natural means for the mathematical andnumerical analysis. In particular, general well-posedness results ofBanks and Musante for a class of abstract nonlinear parabolic systemsare applied to establish well-posedness for the benzene distributedliver model. Banks and Musante also presented theoretical results for ageneral least squares parameter estimation problem. They included aconvergence result for the Galerkin approximation scheme used in ournumerical simulations as a special case. Preliminary investigations on the qualitative behavior of thedistributed liver model have included simulations with orthograde andretrograde bloodflow through mouse liver tissue. Simulation of humanexposure with the partial differential equation and the existingordinary differential equation model are presented and compared. Finally, the dependence of the solution on model parameters is explored.
Date: 2001-12-03
Degree: PhD
Discipline: Applied Mathematics
URI: http://www.lib.ncsu.edu/resolver/1840.16/5616


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