Biomedical Engineering Reference
In-Depth Information
Fig. 2 Stress strain curve of
arteries illustrating the effects
of elastin and collagen. Curve
A represents a stiffer artery
then Curve B
stiffness. The mechanical behavior of the blood vessel can be described by the
strain energy function, which quantifies changes in blood vessel function due to
changes in structure with a hyper elastic nonlinear arterial model (Fig. 2 ).
Experimental stress strain data can be used to plot this curve using the pseudo-
elastic strain energy function:
q o W ¼ 1
2 ð a 1 E xx þ a 2 E yy þ 2a 4 E xx E yy Þ
where a 1 , a 2 , and a 4 are material constants with units of stress, E xx and E yy are the
circumferential and longitudinal moduli of the artery [ 24 ]. The medial portion of
the artery is responsible for most of the physical properties. Tension at low dis-
tending pressures or stresses is born by the elastin fibers while collagen fibers
remain folded. At higher pressures or stresses, the less extensible collagen fibers
bare the stress, thus invoking a higher stress on the vessel due to an increase in
strain, resulting in increased vessel stiffness.
The interactions between the large and small arteries have significant implications
on the transmission of the pulsatile pressure and flow through the arterial circulation.
Large pulmonary arteries dampen flow pulsations resulting from the intermittent
ventricular ejection; consequently, small arteries deliver semi-steady optimal blood
flow to the lungs. Interactions between the macro- and micro-circulations are based
on pulse pressure and flow wave transmissions [ 25 ]. Alterations in one part of the
system can affect the other. The microcirculation can influence the pulse pressures
in the macro circulation through increased vascular resistance [ 26 ]. In turn, the
compliance of the macro circulation regulates pulse pressures waves and influences
extension of pulsations into the microcirculation [ 27 ].
3 Vascular Resistance
The resistance arteries consist of small arteries which are less than 400 lmin
diameter [ 28 ]. An increase in pulmonary vascular resistance (PVR) is primarily
caused by a decrease in the lumen diameter of small arteries and arterioles.
As described by Poiseuille's law, resistance is inversely proportional to the fourth
 
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