Multiscale analysis of thermoregulation in the human microvascular system

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Multiscale analysis of thermoregulation in the human microvascular system. / Deuflhard, Peter; Hochmuth, Reinhard.
In: Mathematical Methods in the Applied Sciences, Vol. 27, No. 8, 25.05.2004, p. 971-989.

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@article{84a751663a7e4c7f885a08c466edb259,
title = "Multiscale analysis of thermoregulation in the human microvascular system",
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.",
keywords = "Mathematics, Bio-heat equation, Correctors, Heat transfer, Homogenization, Hyperthermia, Robin boundary conditions",
author = "Peter Deuflhard and Reinhard Hochmuth",
year = "2004",
month = may,
day = "25",
doi = "10.1002/mma.499",
language = "English",
volume = "27",
pages = "971--989",
journal = "Mathematical Methods in the Applied Sciences",
issn = "0170-4214",
publisher = "John Wiley & Sons Ltd.",
number = "8",

}

RIS

TY - JOUR

T1 - Multiscale analysis of thermoregulation in the human microvascular system

AU - Deuflhard, Peter

AU - Hochmuth, Reinhard

PY - 2004/5/25

Y1 - 2004/5/25

N2 - 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.

AB - 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.

KW - Mathematics

KW - Bio-heat equation

KW - Correctors

KW - Heat transfer

KW - Homogenization

KW - Hyperthermia

KW - Robin boundary conditions

UR - http://www.scopus.com/inward/record.url?scp=2442710613&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/92b50cb8-c488-3d1f-aa7a-f9944d10d80b/

U2 - 10.1002/mma.499

DO - 10.1002/mma.499

M3 - Journal articles

VL - 27

SP - 971

EP - 989

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 8

ER -

DOI