Multiscale analysis for the bio-heat transfer equation - The nonisolated case

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The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In Ref. 8 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, which covers more biologically relevant geometries. Moreover, asymptotic corrector results are derived under weaker assumptions.
Original languageEnglish
JournalMathematical Models and Methods in Applied Sciences
Issue number11
Pages (from-to)1621-1634
Number of pages14
Publication statusPublished - 01.11.2004
Externally publishedYes

Bibliographical note

Funding Information:
The first author has been supported by a Konrad Zuse Fellowship. The second author gratefully acknowledges cooperation within the former SFB 273 “Hyperthermia: Scientific Methods and Clinical Applications”. This work was supported by the DFG Research Center “Mathematics for Key Technologies” in Berlin.

    Research areas

  • Mathematics - heat transfer, bi-heat transfer equation, hyperthermia, homogenization, robin boundary conditions