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

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Multiscale analysis for the bio-heat transfer equation - The nonisolated case. / Hochmuth, Reinhard; Deuflhard, Peter.
In: Mathematical Models and Methods in Applied Sciences, Vol. 14, No. 11, 01.11.2004, p. 1621-1634.

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@article{20706d62f80d4f108452be08077bdb06,
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 = "Mathematics, heat transfer, bi-heat transfer equation, hyperthermia, homogenization, 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,
day = "1",
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",

}

RIS

TY - JOUR

T1 - Multiscale analysis for the bio-heat transfer equation - The nonisolated case

AU - Hochmuth, Reinhard

AU - Deuflhard, Peter

N1 - 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.

PY - 2004/11/1

Y1 - 2004/11/1

N2 - 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.

AB - 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.

KW - Mathematics

KW - heat transfer

KW - bi-heat transfer equation

KW - hyperthermia

KW - homogenization

KW - robin boundary conditions

UR - http://www.scopus.com/inward/record.url?scp=8744285686&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/017d1892-cc89-3940-9795-cb251a545c8f/

U2 - 10.1142/S0218202504003775

DO - 10.1142/S0218202504003775

M3 - Journal articles

VL - 14

SP - 1621

EP - 1634

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 11

ER -