Biomedical Engineering Reference
In-Depth Information
where N is the apparent viscosity,
U
is the average velocity of the flow,
d
is the
diameter of the vessel, and
k
1
and
k
2
are empirical coefficients that depend on the
percentage of blood volume that is occupied by red blood cells, known as the
hematocrit (69). This description of the apparent viscosity can be used in lami-
nar flow correlations to predict blood flow behavior.
A single-vessel model for flow can be incorporated into a model for entire
vasculature networks. In the context of design of microvascular networks for
vascularized tissue engineering of vital organs, we (36) have developed a com-
putational algorithm for simulation of blood flow in the microvascular networks.
This algorithm takes into account the non-Newtonian blood rheology and its
particulate nature, both of which are important in modeling the microcirculation.
Pressure drop in each vessel is related to blood viscosity, which itself varies with
vessel cross-sectional surface area and hematocrit (volume fraction of red blood
cells).
In many cases, the distensibility of the vessel wall will also affect blood
flow through a vessel. As with non-Newtonian behavior, wall deformation be-
havior can be predicted for a single vessel (20), and the single-vessel model can
be incorporated into a network model. We have used such a model to model
flows in distensible vasculature networks (77).
There are other widely varying models for flow through biological net-
works. Some models examine features general to all vasculature, such as the
hypothesis that wall shear is constant throughout any biological vasculature sys-
tem (39). Others develop models for specific tissues (31). The lungs are of par-
ticular interest, as the structure of the lungs and the flow through them is very
different from other organs (20,44).
Modeling of network behavior requires understanding the structure of the
networks. For decades researchers have injected polymers into an organ to ob-
tain a cast of the vasculature, and taken measurements from these casts
(33,40,59,86) (Figure 16).
Recent developments in imaging have allowed researchers to develop
automated techniques for imaging of physiological flow networks (1) (Figure
17). These measurements of the vessel geometries and network connectivity can
be tabulated in forms convenient for use in modeling of flows through the net-
works (Figure 18).
2.3.5. Modeling of Molecular Transport in Tissue
The transport of molecules through tissue occurs in three ways. Molecules
are carried by the bulk flow of tissue in convective transport, the obvious exam-
ple being blood carrying nutrients throughout the body (compare also with Part
II, chapter 3, by Savage and West, this volume). Molecules are also transported
by diffusion, such as nutrients diffusing from the blood, through blood vessel
