Inverse Problems for Blood Perfusion Identification

Research output: Book/ReportBook

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.

The analytical and numerical techniques that are 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 are coupled with optimization techniques. Analytically, a number of uniqueness and existence criteria and structural results are formulated and proved.
Original languageEnglish
Place of PublicationUniversity of Leeds
PublisherPhD Thesis, University of Leeds
Number of pages234
Publication statusPublished - Jun 2009

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