Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 971-989 |
| Seitenumfang | 19 |
| Fachzeitschrift | Mathematical Methods in the Applied Sciences |
| Jahrgang | 27 |
| Ausgabenummer | 8 |
| Publikationsstatus | Veröffentlicht - 25 Mai 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.
ASJC Scopus Sachgebiete
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Mathematical Methods in the Applied Sciences, Jahrgang 27, Nr. 8, 25.05.2004, S. 971-989.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -