Details
| Original language | English |
|---|---|
| Pages (from-to) | 1311-1323 |
| Number of pages | 13 |
| Journal | International Journal of Phytoremediation |
| Volume | 87 |
| Issue number | 12 |
| Publication status | Published - Dec 2008 |
| Externally published | Yes |
Abstract
In [P. Deuflhard and R. Hochmuth, On the thermoregulation in the human microvascular system, Proc. Appl. Math. Mech. 3 (2003), pp. 378–379; P. Deuflhard and R. Hochmuth, Multiscale analysis of thermoregulation in the human microsvascular system, Math. Meth. Appl. Sci. 27 (2004), pp. 971–989; R. Hochmuth and P. Deuflhard, Multiscale analysis for the bio-heat transfer equation–the nonisolated case, Math. Models Methods Appl. Sci. 14(11) (2004), pp. 1621–1634], homogenization techniques are applied to derive an anisotropic variant of the bio-heat transfer equation as asymptotic result of boundary value problems providing a microscopic description for microvascular tissue. In view of a future application on treatment planning in hyperthermia, we investigate here the homogenization limit for a coupling model, which takes additionally into account the influence of convective heat transfer in medium-size blood vessels. This leads to second-order elliptic boundary value problems with non-local boundary conditions on parts of the boundary. Moreover, we present asymptotic estimates for first-order correctors.
Keywords
- Bio-heat equation, Correctors, Heat transfer, Homogenization, Hyperthermia, Non-local boundary conditions, Robin boundary conditions
ASJC Scopus subject areas
- Environmental Science(all)
- Environmental Chemistry
- Environmental Science(all)
- Pollution
- Agricultural and Biological Sciences(all)
- Plant Science
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In: International Journal of Phytoremediation, Vol. 87, No. 12, 12.2008, p. 1311-1323.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Homogenization for a non-local coupling model
AU - Hochmuth, R.
PY - 2008/12
Y1 - 2008/12
N2 - In [P. Deuflhard and R. Hochmuth, On the thermoregulation in the human microvascular system, Proc. Appl. Math. Mech. 3 (2003), pp. 378–379; P. Deuflhard and R. Hochmuth, Multiscale analysis of thermoregulation in the human microsvascular system, Math. Meth. Appl. Sci. 27 (2004), pp. 971–989; R. Hochmuth and P. Deuflhard, Multiscale analysis for the bio-heat transfer equation–the nonisolated case, Math. Models Methods Appl. Sci. 14(11) (2004), pp. 1621–1634], homogenization techniques are applied to derive an anisotropic variant of the bio-heat transfer equation as asymptotic result of boundary value problems providing a microscopic description for microvascular tissue. In view of a future application on treatment planning in hyperthermia, we investigate here the homogenization limit for a coupling model, which takes additionally into account the influence of convective heat transfer in medium-size blood vessels. This leads to second-order elliptic boundary value problems with non-local boundary conditions on parts of the boundary. Moreover, we present asymptotic estimates for first-order correctors.
AB - In [P. Deuflhard and R. Hochmuth, On the thermoregulation in the human microvascular system, Proc. Appl. Math. Mech. 3 (2003), pp. 378–379; P. Deuflhard and R. Hochmuth, Multiscale analysis of thermoregulation in the human microsvascular system, Math. Meth. Appl. Sci. 27 (2004), pp. 971–989; R. Hochmuth and P. Deuflhard, Multiscale analysis for the bio-heat transfer equation–the nonisolated case, Math. Models Methods Appl. Sci. 14(11) (2004), pp. 1621–1634], homogenization techniques are applied to derive an anisotropic variant of the bio-heat transfer equation as asymptotic result of boundary value problems providing a microscopic description for microvascular tissue. In view of a future application on treatment planning in hyperthermia, we investigate here the homogenization limit for a coupling model, which takes additionally into account the influence of convective heat transfer in medium-size blood vessels. This leads to second-order elliptic boundary value problems with non-local boundary conditions on parts of the boundary. Moreover, we present asymptotic estimates for first-order correctors.
KW - Bio-heat equation
KW - Correctors
KW - Heat transfer
KW - Homogenization
KW - Hyperthermia
KW - Non-local boundary conditions
KW - Robin boundary conditions
UR - http://www.scopus.com/inward/record.url?scp=85064779521&partnerID=8YFLogxK
U2 - 10.1080/00036810802555433
DO - 10.1080/00036810802555433
M3 - Article
AN - SCOPUS:85064779521
VL - 87
SP - 1311
EP - 1323
JO - International Journal of Phytoremediation
JF - International Journal of Phytoremediation
SN - 1522-6514
IS - 12
ER -