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

authored by: Reinhard Hochmuth, Peter Deuflhard
Abstract: 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.
External Organisation(s): TU Bergakademie Freiberg - University of Resources
Zuse Institute Berlin (ZIB)
Type: Article
Journal: Mathematical Models and Methods in Applied Sciences
Volume: 14
Pages: 1621-1634
No. of pages: 14
ISSN: 0218-2025
Publication date: 11.2004
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Applied Mathematics
Electronic version(s): https://doi.org/10.1142/S0218202504003775 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{c7d089522c24427c9af2fec2bccb59dd,
title = "Multiscale analysis for the bio-heat transfer equation - The nonisolated case",
abstract = "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.",
keywords = "Bio-heat transfer equation, Heat transfer, Homogenization, Hyperthermia, Robin boundary conditions",
author = "Reinhard Hochmuth and Peter Deuflhard",
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.",
year = "2004",
month = nov,
doi = "10.1142/S0218202504003775",
language = "English",
volume = "14",
pages = "1621--1634",
journal = "Mathematical Models and Methods in Applied Sciences",
issn = "0218-2025",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "11",
}