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.
Author: | Reinhard Hochmuth, Peter Deuflhard |
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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 |