Partial Differential Equation Constrained Optimization and its Applications to Parameter Estimation in Models of Nerve Dendrites

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dc.contributor.advisorBell, Jonathan
dc.contributor.authorWang, Dan
dc.contributor.departmentMathematics and Statistics
dc.contributor.programMathematics, Applied
dc.date.accessioned2015-10-14T03:11:45Z
dc.date.available2015-10-14T03:11:45Z
dc.date.issued2008-10-12
dc.description.abstractOne important application of the parameter identification method in neuroscience is to determine how voltage-dependent ion channels are spatially distributed through measurements of voltage along the dendrites. While in the past 50 years we have made tremendous strides experimentally to understand how neurons process information, there has also been a lot of supporting mathematical modeling work, initiated by the successful modeling work of Hodgkin and Huxley. As these models and experiments got more detailed, questions about the values of model parameters became more important, initiating parameter estimation investigations.In this study, we used optimization techniques to solve a parameter identification problem in mathematical modelling of neuronal processing of information at the cellular level, which is governed by a set of nonlinear partial differential equations. We first applied this method to a simplified neuron equation system, which we successfully identified spine density functions. The method is then extended to a more realistic model. We tested our method on cases where the densities to be estimated were either continuous functions with very steep gradients, or piecewise constant functions with large jumps. The method correctly identified the location and size of the jumps, and closely approximated the main features of the unknown density.We have successfully demonstrated the possibility and advantages of using a PDE-constrained optimization approach to recover the spatial distribution of dendritic spines from measurements. In particular, the method is very successful in identifying extreme densities with large jumps.
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dc.identifierdoi:10.13016/M2BW94
dc.identifier.other1250
dc.identifier.urihttp://hdl.handle.net/11603/1017
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department Collection
dc.rightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
dc.sourceOriginal File Name: umi-umbc-1250.pdf
dc.subjectmathematics (0405)
dc.subjectPDE
dc.subjectoptimization
dc.subjectinverse problem
dc.subjectparameter estimation
dc.subjectdendrite
dc.titlePartial Differential Equation Constrained Optimization and its Applications to Parameter Estimation in Models of Nerve Dendrites
dc.typeText
dcterms.accessRightsAccess limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.

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