Biomedical Engineering Reference
In-Depth Information
Fahraeus-Lindqvist effect occurs are also the vessels with the highest flow resist-
ance (i.e., the arterioles). If a Newtonian fluid of the same viscosity was substituted
for non-Newtonian blood, flow resistance would be much higher.
4.3.3 Infl uence Fluid Flow on Blood
Blood behaves as a Newtonian fluid only in regions of high shear rate (
100 s
−1
)
and, for flow in large arteries where the shear rate is well above 100 s
−1
, a value
of 3.5 cP is often used as an estimate for the viscosity of blood [Figure 4.5(b)]. In
smaller arteries and in the capillaries where the shear rate is very low, blood must
be treated as a non-Newtonian fluid. The non-Newtonian behavior is traceable to
the elastic red blood cells (RBCs). RBCs take up about half the volume of
whole
blood
, and have a significant influence on the flow. The specific gravity of whole
blood is 1.056 in which plasma is 1.026, and RBCs are 1.090. The mean hydro-
static pressure falls from a relatively high value of 100 mmHg in the largest arteries
to values of the order of 20 mmHg in the capillaries and even lower in the return
venous circulation. The parameter used for modeling purposes is the hematocrit
level, the volume fraction that RBCs occupy in a given volume of blood. The av-
erage hematocrit is 40-52% for men, and 35-47% for women. Average blood
volume in humans is about 5 liters, with 3 liters of plasma and 2 liters represent-
ing the volume of the blood cells, primarily the RBCs. When the RBCs are at rest,
they tend to aggregate and stack together in a space-efficient manner (region 1 in
Figure 4.6). In order for blood to flow freely, the size of these aggregates must be
reduced, which in turn provides some freedom of internal motion. The forces that
disaggregate the cells also produce elastic deformation and orientation of the cells,
causing elastic energy to be stored in the cellular microstructure of the blood (region
2 in Figure 4.6). As the flow proceeds, the sliding of the internal cellular structure
requires a continuous input of energy, which is dissipated through viscous friction
(region 3 in Figure 4.6). These effects make blood a viscoelastic fluid, exhibiting
both viscous and elastic properties (discussed in Chapter 5). In certain cases, RBCs
stack together in presence of serum proteins (particularly increased fibrinogen and
globulins) or other macromolecules. When four or more RBCs are arranged in a
linear pattern as a “stack of coins,” it is known as
rouleaux formation
. Such long
chains of RBCs sediment more readily. This is the mechanism for the sedimenta-
tion rate, which increases nonspecifically with inflammation and increased “acute
phase” serum proteins.
>
4.4 Conservation of Energy
4.4.1 Different Energy Forms
Energy is necessary to perform various activities including the functioning of the
heart and body movement. According to the conservation of energy principle, en-
ergy cannot be created or destroyed, but only transferred from one system to an-
other. In other words, the total energy of interacting bodies or particles in a system
remains constant. Some parts are gaining energy while others are losing energy
