Details
| Original language | English |
|---|---|
| Pages (from-to) | 971-989 |
| Number of pages | 19 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 27 |
| Issue number | 8 |
| Publication status | Published - 25 May 2004 |
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
- Bio-heat equation, Correctors, Heat transfer, Homogenization, Hyperthermia, Robin boundary conditions
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Engineering(all)
- General Engineering
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In: Mathematical Methods in the Applied Sciences, Vol. 27, No. 8, 25.05.2004, p. 971-989.
Research output: Contribution to journal › Article › Research › peer review
}
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 - 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
U2 - 10.1002/mma.499
DO - 10.1002/mma.499
M3 - Article
AN - SCOPUS:2442710613
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 -