Quick, C. M., J. K-J. Li, D. A. O’Hara, and A. Noordergraaf
XII Congress, Cardiovascular System Dynamics Society, Baltimore, MD, 1996
J. Cardiovasc. Diag. Proc. 13: 297, 1996.
Modern hemodynamics arose out of two distinct competing schools of thought. In the English school, the arterial system was viewed as a distributed system for which pulse wave velocity was all-important. In the German school, the arterial system was described by the Windkessel, a lumped model for which compliance was critical.
The English were intensely interested in measuring and predicting pulse wave velocity, which was assumed to have a constant value, co. However, three problems arose. First, the numerous available methods to experimentally determine co yielded inconsistent values. Second, the numerous available equations that predicted co all grossly under-estimated the measured values. Third, co was shown to be sensitive to changes in heart rate and the peripheral vasculature.
The solution to the first problem came when Fourier analysis was applied to experimental data. It became clear that the measured pulse wave velocity could not be represented by a single number as had been assumed. Instead the “apparent pulse wave velocity,” capp, was a strong function of frequency. The solution to the second and third problems came from transmission line theory. It predicted that pulse wave reflections cause the capp to be much different from the phase velocity (the velocity without reflections). Furthermore, these pulse wave reflections were shown to be greatly affected by heart rate and the peripheral vasculature. co emerged as a special case of capp.
Recently, there has been much interest in determining systemic compliance, which is assumed to have a constant compliance, Cw, described by the Windkessel. However, three problems have arisen. First, the numerous methods to determine Cw yield inconsistent values. Second, Cw tends to overestimate the experimental values of total arterial compliance. Third, Cw is sensitive to heart rate and the peripheral vasculature. History, it seems, is repeating itself.
The solution to the first problem comes from treating systemic compliance as a complex function of frequency. This “apparent compliance,” Capp, can be derived from experimentally measured input impedance, Zin, and peripheral resistance, Rs.
Capp=dV/dP(w) =(Rs - Zin )/jwRsZin
Capp derived from the measured aortic input impedance of a dog is shown. Clearly, the measured systemic compliance cannot be represented by a single number as had been assumed. Instead the apparent compliance is a strong function of frequency.
The solution to the second and third problems can once again be supplied by transmission theory. This theory relates Zin to characteristic impedance, Zo, and the global reflection coefficient, G,via Zin=Zo (1+G)/(1- G). Inserting into the equation above:
Capp=[Rs (1-G) - Zo(1+ G)]/[jwRsZo(1+ G)]
The present theory predicts that pulse wave reflections cause Capp to be much different from the true arterial compliance. Furthermore, these pulse wave reflections are greatly affected by heart rate and peripheral vasculature. Cw emerges as a special case of Capp. With this historical perspective, the concept of apparent compliance should be as elucidating as the concept of apparent phase velocity has been.