Page 275 - Computational Modeling in Biomedical Engineering and Medical Physics

264 Computational Modeling in Biomedical Engineering and Medical Physics

The boundary conditions for the thermal problem are: metabolic temperature

(37 C) for arterial and venous artery inlets and convection heat transfer (@T/@n 5 0,
n 5 |n|n is the normal unit vector) for the arterial and venous outlets. On the outer
boundary, convective heat transfer with a specified heat transfer coefficient, h, is set.
The tumor is removed from the computational domain, its thermal contribution is
reflected by its surface (inner border), which is considered isothermal at 45 C. This

value is higher than the usual values encountered in situations alike (41 C 42 C), but

we chose to use this value to highlight the presence of the tumor from a thermal point
3
of view. The metabolic power rate is 1317 W/m (Morega et al., 2015b).
“Model A” refers to the homogenized model and “Model B” to the combined
bioheat (for capillaries) and general heat transfer model (for larger vessels). The two
flows are not connected here as they were connected previously when a porous
medium, Brinkman flow was used for the capillaries. The reason is to show off the
discrepancies between the two modes of heat transfer: the homogenization technique
(with perfusion, non-directional flow) and the convection heat flow (directional flow).
The boundary condition on the outer surface is convection, and it introduces an
average heat transfer coefficient, h. It is not known a priori, and some “natural” thermal
criterion has to be used to find a realistic estimation for it. The boundary here is imag-
inary, as the computational domain is “cut” from an organ (e.g., liver). Convection
and not conduction is required here because the surface of the ROI is, at any point,
in contact with some biological fluid. The reference temperature, under these circum-
stances, may not be that of the ambient, extracorporeal environment, for example,
T amb 5 18 C, which is common for thermographic investigations. Using this condi-

tion, inadequate for the body inside, may produce vasoconstriction in regions that are
not affected by some pathologic inflammatory process (De May et al., 2016).
The tumor is excluded from the computational domain, and its surface is an inte-
rior boundary. Here a Dirichlet condition is used, T tumor 5 45 C, as previously men-

tioned. The reason for this choice is to increase the thermal contrast with the
background.
As the ROI is homogenized in Model A, the temperature on the outer surface of
the ROI is, for reasons of symmetry, uniform, Fig. 8.9 (left). The tumor is evidenced
by the overall increase in the temperature of the outer boundary that remains, how-
ever, isothermal.
In Model B the temperature on the boundary departs from uniform due to the
blood vessel trees, Fig. 8.9 (right). Comparing the two models, the tumor thermal
“mapping” on the boundary of the ROI differs depending on the modeling assump-
tions. Moreover, it may be conjectured that in thermography too, the mapping of the
tumor as perceived by the camera is prone to the vascularization in between the heat
source and the body surface. Here, the temperature outside the ROI, the position,
size, and morphology of the tumor, and the structure of the blood vessel network are