The matching of thermal fields surrounding countercurrent microvessels and the closure approximation in the Weinbaum-Jiji equation.
A second order perturbation theory is developed to show the difference between the average artery-vein temperature Tm and the local average tissue temperature theta. This theory demonstrates that the closure approximation in the Weinbaum-Jiji bioheat equation does not require that theta = Tm and that although the difference between these two temperatures is second order the magnitude of the countercurrent convection terms in the Weinbaum-Jiji equation can be of order unity. The theory also shows that to second order this new bioheat equation is the same as the simplified set of one-dimensional model equations used in Baish et al.
Weinbaum
S
S
Department of Mechanical Engineering, City College of the City University of New York, New York 10031.
Jiji
L M
LM
D001158:Arteries / Q000502:physiology*; D001833:Body Temperature Regulation / Q000502:physiology*; D008833:Microcirculation / Q000502:physiology; D008954:Models, Biological; D014680:Veins / Q000502:physiology*