Multiscale analysis of thermoregulation in the human microvascular system

verfasst von

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.

Organisationseinheit(en)

Fakultät für Mathematik und Physik

Externe Organisation(en)

Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)
Albert-Ludwigs-Universität Freiburg

Typ

Artikel

Journal

Mathematical Methods in the Applied Sciences

Band

27

Seiten

971-989

Anzahl der Seiten

19

ISSN

0170-4214

Publikationsdatum

25.05.2004

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.), Ingenieurwesen (insg.)

Elektronische Version(en)

https://doi.org/10.1002/mma.499 (Zugang: Unbekannt)