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, Jahrgang 14, Nr. 11, 01.11.2004, S. 1621-1634.Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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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 -