Multiscale analysis of thermoregulation in the human microvascular system

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The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the derivation of the Helmholtz term arising in the bio-heat transfer equation is not completely satisfactory. Here we use homogenization techniques to show that this term may be understood as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. An appropriate scaling of so-called heat transfer coefficients in Robin boundary conditions on tissue-blood boundaries is seen to play the crucial role. In view of a future application of our new mathematical model for treatment planning in hyperthermia, we derive asymptotic estimates for the first-order corrector.

Original languageEnglish
JournalMathematical Methods in the Applied Sciences
Issue number8
Pages (from-to)971-989
Number of pages19
Publication statusPublished - 25.05.2004
Externally publishedYes

    Research areas

  • Mathematics
  • Bio-heat equation, Correctors, Heat transfer, Homogenization, Hyperthermia, Robin boundary conditions