136

Dynamics

of

the Vascular System

4.5.4

Nonlinear Aspects and Pressure-Dependent Arterial Compliance

Although the Navier-Stokes equation in its complete form has

recently been solved in closed form (Melbin and Noordergraaf,

there are other kinds of nonlinearities. Thus, depending on the particular

problem or application at hand, assumptions included in order to

eliminate some or all of the nonlinearities may still be valid to provide a

satisfactory solution. This is particularly true with regard to the use of

Fourier analysis in studying pressure and flow waveforms and the

derived input impedance analysis.

The general definition of arterial compliance is the ratio of an

incremental change in volume due to an incremental change in

distending pressure, i.e.

C

dV/dP

(4.5.63)

This is defined by the inverse of the slope of the pressure-volume (P-

V) curve, with pressure plotted on the ordinate and volume on the

abscissa (Fig.

Thus, compliance is the inverse of elastance.

Fig.

Arterial pressure-volume diagram, defining compliance as the slope

of

the

relation (C=dV/dP). It

clear that the slope changes with increasing pressure (dVJdP,

vs. dV2/dPl) and at higher pressures the volume change is smaller.

The pressure-volume curves of arteries have been found to be

curvilinear. The slope changes along the P-V curve, steeper at higher

pressures, signifying increased arterial stiffness or decreased compliance

and distensibility. In other words, arteries stiffen when pressurized. This

physiological phenomenon has been observed in many experiments.