Multiscale analysis of thermoregulation in the human microvascular system

authored by: Peter Deuflhard, Reinhard Hochmuth
Abstract: 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.
Organisation(s): Faculty of Mathematics and Physics
External Organisation(s): Zuse Institute Berlin (ZIB)
University of Freiburg
Type: Article
Journal: Mathematical Methods in the Applied Sciences
Volume: 27
Pages: 971-989
No. of pages: 19
ISSN: 0170-4214
Publication date: 25.05.2004
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mathematics(all), Engineering(all)
Electronic version(s): https://doi.org/10.1002/mma.499 (Access: Unknown)