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Multiscale analysis of thermoregulation in the human microvascular system
Author(s) -
Deuflhard Peter,
Hochmuth Reinhard
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.499
Subject(s) - homogenization (climate) , heat transfer , mathematics , boundary value problem , heat equation , asymptotic analysis , scaling , term (time) , helmholtz equation , mathematical analysis , mechanics , physics , geometry , biodiversity , ecology , quantum mechanics , biology
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. Copyright © 2004 John Wiley & Sons, Ltd.