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Inverse problems for blood perfusion identification

Trucu, Dumitru (2009) Inverse problems for blood perfusion identification. PhD thesis, University of Leeds.

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Abstract

In this thesis we investigate a sequence of important inverse problems associated with the bio-heat transient flow equation which models the heat transfer within the human body. Given the physical importance of the blood perfusion coefficient that appears in the bio-heat equation, attention is focused on the inverse problems concerning the accurate recovery of this information when exact and noisy measurements are considered in terms of the mass, flux, or temperature, which we sampled over the specific regions of the media under investigation. Five different cases are considered for the retrieval of the perfusion coefficient, namely when this parameter is assumed to be either constant, or dependent on time, space, temperature, or on both space and time. Theanalytica:l and numerical techniques that arc used to investigate the existence and uniqueness of the solution for this inverse coefficient identification are embedded in an extensive├║ computational approach for the retrieval of the perfusion coefficient. Boundary integral methods, for the constant and the time-dependent cases, or Crank-Nicolson-type global schemes or local methods based on solutions of the first-kind integral equations, in the space, temperature, or space and time cases, are used in conjunction either with Gaussian mollification or with Tikhonov regularization methods, which arc coupled with optimization techniques. Analytically, a number of uniqueness and existence criteria and structural results are formulated and proved.

Item Type: Thesis (PhD)
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds)
The University of Leeds > Faculty of Engineering (Leeds) > School of Chemical and Process Engineering (Leeds)
Other academic unit: Centre for Computational Fluid Dynamics, School of Process, Environmental and Materials Engineering
Identification Number/EthosID: uk.bl.ethos.505067
Depositing User: Ethos Import
Date Deposited: 22 Aug 2018 13:38
Last Modified: 22 Aug 2018 13:38
URI: http://etheses.whiterose.ac.uk/id/eprint/21104

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