Multiscale analysis of thermoregulation in the human microvascular system
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In: Mathematical Methods in the Applied Sciences, Vol. 27, No. 8, 25.05.2004, p. 971-989.
Research output: Journal contributions › Journal articles › Research › peer-review
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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 -