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Multiscale Analysis for the Bio-Heat Transfer Equation

Please always quote using this URN: urn:nbn:de:0297-zib-7302
  • The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In [{\sl Deuflhard, Hochmuth 2002}] the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected. Moreover, asymptotic corrector results are derived.

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Metadaten
Author:Reinhard Hochmuth, Peter Deuflhard
Document Type:ZIB-Report
Tag:Robin boundary conditions; bio-heat equation; correctors; heat transfer; homogenization; hyperthermia
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B27 Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A20 Heat and mass transfer, heat flow
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
Date of first Publication:2003/04/15
Series (Serial Number):ZIB-Report (03-08)
ZIB-Reportnumber:03-08
Published in:Appeared in: Mathematical Models and Methods in Applied Sciences 14 (2004) 1621-1634
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