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Multiscale analysis for the bio-heat transfer equation - The nonisolated case

Research output: Journal contributions › Journal articles › Research › peer-review

Standard

Multiscale analysis for the bio-heat transfer equation - The nonisolated case. / Hochmuth, Reinhard; Deuflhard, Peter.
In: Mathematical Models and Methods in Applied Sciences, Vol. 14, No. 11, 01.11.2004, p. 1621-1634.

Research output: Journal contributions › Journal articles › Research › peer-review

Harvard

Hochmuth, R & Deuflhard, P 2004, 'Multiscale analysis for the bio-heat transfer equation - The nonisolated case', Mathematical Models and Methods in Applied Sciences, vol. 14, no. 11, pp. 1621-1634. https://doi.org/10.1142/S0218202504003775

APA

Hochmuth, R., & Deuflhard, P. (2004). Multiscale analysis for the bio-heat transfer equation - The nonisolated case. Mathematical Models and Methods in Applied Sciences, 14(11), 1621-1634. https://doi.org/10.1142/S0218202504003775

Vancouver

Hochmuth R, Deuflhard P. Multiscale analysis for the bio-heat transfer equation - The nonisolated case. Mathematical Models and Methods in Applied Sciences. 2004 Nov 1;14(11):1621-1634. doi: 10.1142/S0218202504003775

Bibtex

@article{20706d62f80d4f108452be08077bdb06,
title = "Multiscale analysis for the bio-heat transfer equation - The nonisolated case",
abstract = "The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In Ref. 8 the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected, which covers more biologically relevant geometries. Moreover, asymptotic corrector results are derived under weaker assumptions.",
keywords = "Mathematics, heat transfer, bi-heat transfer equation, hyperthermia, homogenization, robin boundary conditions",
author = "Reinhard Hochmuth and Peter Deuflhard",
note = "Funding Information: The first author has been supported by a Konrad Zuse Fellowship. The second author gratefully acknowledges cooperation within the former SFB 273 “Hyperthermia: Scientific Methods and Clinical Applications”. This work was supported by the DFG Research Center “Mathematics for Key Technologies” in Berlin.",
year = "2004",
month = nov,
day = "1",
doi = "10.1142/S0218202504003775",
language = "English",
volume = "14",
pages = "1621--1634",
journal = "Mathematical Models and Methods in Applied Sciences",
issn = "0218-2025",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "11",

}

RIS

TY - JOUR

T1 - Multiscale analysis for the bio-heat transfer equation - The nonisolated case

AU - Hochmuth, Reinhard

AU - Deuflhard, Peter

N1 - Funding Information: The first author has been supported by a Konrad Zuse Fellowship. The second author gratefully acknowledges cooperation within the former SFB 273 “Hyperthermia: Scientific Methods and Clinical Applications”. This work was supported by the DFG Research Center “Mathematics for Key Technologies” in Berlin.

PY - 2004/11/1

Y1 - 2004/11/1

N2 - The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In Ref. 8 the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected, which covers more biologically relevant geometries. Moreover, asymptotic corrector results are derived under weaker assumptions.

AB - The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In Ref. 8 the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected, which covers more biologically relevant geometries. Moreover, asymptotic corrector results are derived under weaker assumptions.

KW - Mathematics

KW - heat transfer

KW - bi-heat transfer equation

KW - hyperthermia

KW - homogenization

KW - robin boundary conditions

UR - http://www.scopus.com/inward/record.url?scp=8744285686&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/017d1892-cc89-3940-9795-cb251a545c8f/

U2 - 10.1142/S0218202504003775

DO - 10.1142/S0218202504003775

M3 - Journal articles

VL - 14

SP - 1621

EP - 1634

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 11

ER -

Other publications by the same author(s)

Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings

Göller, R. (Editor), Biehler, R., Hochmuth, R. K. & Rück, H.-G., 2017, Kassel: Kompetenzentrum Hochschuldidaktik Mathematik - Universität Kassel. 509 p. (khdm-Report; vol. 2017, no. 05)

Research output: Books and anthologies › Conference proceedings › Research

Mathematik im Ingenieurwissenschaftsstudium – Ansätze zu einer fachbezogenen Kompetenzmodellierung

Hochmuth, R. K. & Schreiber, S., 2014, TeachING-LearnING.EU Tagungsband: movING Forward; Engineering Education from vision to mission. Tekkaya, A. E., Jeschke, S. & Petermann, M. (eds.). Technische Universität Dortmund, p. 68-76 9 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

Mit Werkzeugen Mathematik und Stochastik lernen

Wassong, T., Frischemeier, D., Fischer, P. R., Hochmuth, R. & Bender, P., 2014, Wiesbaden: Springer Spektrum. 497 p.

Research output: Books and anthologies › Book

Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen.

Liebendörfer, M., Hochmuth, R. K., Schreiber, S., Göller, R., Kolter, J., Biehler, R., Kortemeyer, J. & Ostsieker, L., 2014, Beiträge zum Mathematikunterricht 2014: Beiträge zur 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 10. bis 14. März 2014 in Koblenz. Roth, J. & Ames, J. (eds.). WTM - Verlag für wissenschaftliche Texte und Medien, Vol. 2. p. 739-742 4 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research

Blended-Learning Brückenkurs Mathematik für Wirtschaftswissenschaftler.

Goguadze, G. & Hochmuth, R., 25.11.2013, Mathematik im Übergang Schule / Hochschule und im ersten Studienjahr: Extended Abstracts zur 2. khdm-Arbeitstagung. Hoppenbrock, A., Schreiber, S., Göller, R., Biehler, R., Büchler, B., Hochmuth, R. & Rück, H.-G. (eds.). Universitätsbibliothek Kassel, Vol. khdm-Report 13-01. p. 63-64 2 p. (KHDM-Report; vol. 13, no. 01).

Research output: Contributions to collected editions/works › Other › Research

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