Homogenization for a non-local coupling model

Research output: Contribution to journalArticleResearchpeer review

Authors

External Research Organisations

  • University of Kassel
View graph of relations

Details

Original languageEnglish
Pages (from-to)1311-1323
Number of pages13
JournalInternational Journal of Phytoremediation
Volume87
Issue number12
Publication statusPublished - Dec 2008
Externally publishedYes

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

Cite this

Homogenization for a non-local coupling model. / Hochmuth, R.
In: International Journal of Phytoremediation, Vol. 87, No. 12, 12.2008, p. 1311-1323.

Research output: Contribution to journalArticleResearchpeer review

Download
@article{c86d911b0d624b288e3cef370f367c4a,
title = "Homogenization for a non-local coupling model",
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",
author = "R. Hochmuth",
year = "2008",
month = dec,
doi = "10.1080/00036810802555433",
language = "English",
volume = "87",
pages = "1311--1323",
journal = "International Journal of Phytoremediation",
issn = "1522-6514",
publisher = "Taylor and Francis Ltd.",
number = "12",

}

Download

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 -

By the same author(s)