Simple and accurate way for estimating total and segmental arterial compliance: The pulse pressure method

Abstract

We derived and tested a new, simple, and accurate method to estimate the compliance of the entire arterial tree and parts thereof. The method requires the measurements of pressure and flow and is based on fitting the pulse pressure (systolic minus diastolic pressure) predicted by the two-element windkessel model to the measured pulse pressure. We show that the two-element windkessel model accurately describes the modulus of the input impedance at low harmonics (0-4th) of the heart rate so that the gross features of the arterial pressure wave, including pulse pressure, are accounted for. The method was tested using a distributed nonlinear model of the human systemic arterial tree. Pressure and flow were calculated in the ascending aorta, thoracic aorta, common carotid, and iliac artery. In a linear version of the systemic model the estimated compliance was within 1% of the compliance at the first three locations. In the iliac artery an error of 7% was found. In a nonlinear version, we compared the estimates of compliance with the average compliance over the cardiac cycle and the compliance at the mean working pressure. At the first three locations we found the estimated and "actual" compliance to be within 12% of each other. In the iliac artery the error was larger. We also investigated an increase and decrease in heart rate, a decrease in wall elasticity and exercise conditions. In all cases the estimated total arterial compliance was within 10% of mean compliance. Thus, the errors result mainly from the nonlinearity of the arterial system. Segmental compliance can be obtained by subtraction of compliance determined at two locations.

Systolic Hypertension Mechanisms: Effect of Global and Local Proximal Aorta Stiffening on Pulse Pressure

“…17 Stergiopulos and Westerhof showed that, for a given ejection volume, PP can be completely and very precisely determined by only two arterial parameters: total arterial resistance, R, and total arterial compliance, C. The explanation is the PP is primarily determined by the low frequency components of the pulse (first 3 to 4 harmonics) and for these frequencies the 2-element Windkessel provides and very faithful description of the input impedance of the arterial system. 15 This seems to be a paradoxical finding, because the Windkessel model neglects wave phenomena, which apparently play an important role in shaping aortic pressure and augmenting systolic pressure in presence of stiffening. Yet the Windkessel model predict PP in a very precise manner and that in presence or absence of strong reflections, 17 however, falls short in describing detailed morphology and cannot take thoroughly into account changes in local stiffness.…”

“…1 The increase in PP, when compliance decreases, can be attributed to loss in Windkessel function. 1,[15][16][17] The Windkessel model, however, does not account for wave propagation phenomena, which also play an important role in the development of systolic hypertension following arterial stiffening. The prevailing theory is that aortic stiffening leads to an increase in wave speed and in the amplitude of the reflected wave.…”

Amplification of the Pressure Pulse in the Upper Limb in Healthy, Middle-Aged Men and Women

“…As independent variables, we included parameters with a correlation coefficient Ͼ0.15 in univariate analysis. In addition to basic clinical and morphological data, these parameters included carotid-femoral pulse wave velocity and total arterial compliance (PP method 18 ) as measures of arterial stiffness, the carotid augmentation index (AIx) and reflection magnitude (ratio of backward and forward pressure wave amplitudes) as measures of wave reflection, and systemic vascular resistance. We refer to Segers et al 17 for details on how these parameters were determined.…”

The arterial Windkessel

“…The pulse pressure method [59,62] is based on fitting the systolic and diastolic pressures, as predicted by the twoelement Windkessel with measured aortic flow as input, to the measured values of systolic and diastolic pressure. Although the two-element Windkessel does not produce correct wave shapes, its low frequency impedance is close to the actual impedance, while in three-element Windkessel (by assuming the characteristic impedance as a resistor) introduces errors at the low frequencies.…”

“…0 Hz) which equals R, is in the threeelement Windkessel R + Z c . The use of a resistor for characteristic impedance also causes errors in the low frequency range of the input impedance [59]. However, since characteristic impedance is, in the systemic circulation of all mammals, about 5-7% of peripheral resistance [72] the errors are small.…”