TY - GEN A1 - Hochmuth, Reinhard T1 - Homogenization for a Nonlocal Coupling Model N2 - In [7,8,12] 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 nonlocal boundary conditions on parts of the boundary. Moreover, we present asymptotic estimates for first order correctors. T3 - ZIB-Report - 04-50 KW - Homogenization KW - nonlocal boundary conditions KW - Robin boundary conditions KW - correctos KW - heat transfer KW - bio-heat equation KW - hyperthermia Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8251 ER - TY - GEN A1 - Hochmuth, Reinhard A1 - Deuflhard, Peter T1 - Multiscale Analysis for the Bio-Heat Transfer Equation N2 - The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In [{\sl Deuflhard, Hochmuth 2002}] 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. Moreover, asymptotic corrector results are derived. T3 - ZIB-Report - 03-08 KW - bio-heat equation KW - hyperthermia KW - homogenization KW - correctors KW - heat transfer KW - Robin boundary conditions Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7302 ER - TY - GEN A1 - Deuflhard, Peter A1 - Hochmuth, Reinhard T1 - Multiscale Analysis of Thermoregulation in the Human Microvascular System N2 - The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the deduction of the Helmholtz term in the bio-heat transfer equation is not co role. In view of a future numerical application of this new mathematical model to treatment planning in hyperthermia we derive asymptotic estimates for first and second order correctors. T3 - ZIB-Report - 02-31 KW - bio-heat equation KW - hyperthermia KW - homogenization Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6985 ER -