the Vascular System
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.
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
Thus, compliance is the inverse of elastance.
Arterial pressure-volume diagram, defining compliance as the slope
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.