Biomedical Engineering Reference
In-Depth Information
FIgure 23.7
Mesh network of the real geometrical human hand. (From Shao HW et al.,
Computer Methods
in Biomechanics and Biomedical Engineering
, 2012. With permission.)
slices, the regions with the minimum distance were connected to generate the hexahedral mesh. We
believe that the hexahedral mesh is beneficial for finite element method (FEM) to generate accept-
able results, and it requires less solver time than the other kinds of mesh. Hence, this method for
generating hexahedral mesh is more suitable for the finite element method solver and can be applied
to the mesh generation of other tissues. A mesh network of the hand that was generated for further
analysis is shown in Figure 23.7.
23.4.3 m
odelinG
B
lood
p
erfuSion
and
H
eat
t
ranSfer
in
B
ioloGical
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iSSueS
23.4.3.1 blood Perfusion modeling based on darcy's equation
Blood in the hand flows through arteries, capillaries, and veins in turn. In this work, blood flow
was divided into two parts: blood flow in large vessels (diameters > 1 mm) and blood perfusion in
microvessels. Blood flow in the large vessels was set as a time-dependent input in the numerical
model. Blood perfusion in microvessels was considered to be a fluid phase in porous media. Pennes
equation was numerically solved to describe the dynamic temperature distribution in the hand.
Because of the huge number of microvessels, modeling all of them would have been difficult and
unnecessary. An effective method to deal with this problem is to simplify the tissue with microves-
sels as porous media. The earliest model for fluid transport in porous media is considered to be
Darcy's law, which can be expressed as
µ
∇=−
P
(23.13)
Darcy
k
where µ is the viscosity of blood,
k
is the permeability of the porous media, and
V
Darcy
is the Darcy's
velocity. In the present study, blood perfusion in the tissue through the microvessels was considered
to occur through seepage in the porous media. For different parts of the human hand, the permeabil-
ity
k
varies with the density of the microvessels. In the analysis that is presented in Section 23.5, the
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