Role of total arterial compliance and peripheral resistance in the determination of systolic and diastolic aortic pressure

The goal of the study was to define the major arterial parameters that determine aortic systolic (Ps) and diastolic (Pd) pressure in the dog. Measured aortic flows were used as input to the two-element windkessel model of the arterial system, with peripheral resistance calculated as mean pressure over mean flow and total arterial compliance calculated from the decay time in diastole. The windkessel model yielded an aortic pressure wave from which we obtained the predicted systolic (Ps, wk) and diastolic (Pd, wk) pressure. These predicted pressures were compared with the measured systolic and diastolic pressures. The measurements and calculations were carried out in 7 dogs in control conditions, during aortic occlusion at four locations (the trifurcation, between trifurcation and diaphragm, the diaphragm and the proximal descending thoracic aorta) and during occlusion of both carotid arteries. Under all conditions studied the predicted systolic and diastolic pressure matched the experimental ones very well: Ps, wk = (1.000 +/- 0.0055) Ps with r = 0.958 and Pd, wk = (1.024 +/- 0.0035) Pd with r = 0.995. Linear regression for pulse pressure gave PPwk = (0.99 +/- 0.016) PP (r = 0.911). We found the accuracy of prediction equally good under control conditions and in presence of aortic or carotid artery occlusions. Multiple regression between pulse pressure and arterial resistance and total arterial compliance yielded a poor regression constant (r2 = 0.19) suggesting that the two arterial parameters alone cannot explain pulse pressure and that flow is an important determinant as well. We conclude that, for a given ejection pattern (aortic flow), two arterial parameters, total arterial resistance and total arterial compliance are sufficient to accurately describe systolic and diastolic aortic pressure.

Determinants of pulse pressure

Nikolaos Stergiopulos, Nico Westerhof

We have searched to define the major arterial parameters that determine aortic systolic (Ps) and diastolic (Pd) pressure in the dog. Measured aortic flows were used as input to the 2-element windkessel model of the arterial system, with peripheral resistance calculated as mean pressure divided by mean flow and total arterial compliance calculated from the decay time in diastole. The windkessel model yielded an aortic pressure wave from which we obtained the predicted systolic (Ps,wk) and diastolic (Pd,wk) pressures. These predicted pressures were compared with the measured systolic and diastolic pressures. The measurements and calculations were performed for 7 dogs under control conditions during aortic occlusion at 4 locations (the trifurcation, between the trifurcation and diaphragm, the diaphragm, and the proximal descending thoracic aorta) and during occlusion of both carotid arteries. Under all conditions studied, the predicted systolic and diastolic pressures matched the experimental ones very well: Ps,wk=(1.000+/-0.0055) Ps with r=0.958 and Pd,wk=(1.024+/-0.0035) Pd with r=0.995. Linear regression for pulse pressure (PP) resulted in PPwk=(0.99+/-0.016) PP with r=0.911. We found the accuracy of prediction equally good under control conditions and in the presence of aortic or carotid artery occlusion. Multiple regression between pulse pressure and arterial resistance and total arterial compliance yielded a poor regression constant (R2=0.19), suggesting that the 2 arterial parameters alone cannot explain pulse pressure and that flow is an important determinant as well. We conclude that for a given ejection pattern (aortic flow), 2 arterial parameters, total arterial resistance and total arterial compliance, are sufficient to accurately describe systolic and diastolic aortic pressure.

1998

Predicting systolic and diastolic aortic blood pressure and stroke volume in the intact sheep

Patrick Segers, Nikolaos Stergiopulos, Nico Westerhof

We developed a mathematical model describing the interaction between the heart and the arterial system. The model was constructed and tested on basis of invasive hemodynamic data in six sheep. Data from a first group of three animals (49 cardiac cycles) were used to assess a template time-varying elastance curve for the left ventricle, while the baseline steady-state data of a second group of three animals were used to assess reference cardiac and arterial parameters in sheep. The model is fully characterized by nine parameters, which were converted into 6 dimensionless numbers using the Buckingham pi theorem. The model was then used to generate LV pressure and volume and aortic pressure and flow for 86 conditions obtained by varying parameters 50 to 200% of their reference value. Systolic (SBP) and diastolic (DBP) blood pressure and stroke volume (SV) were determined from these model-generated curves and multiple linear regression analysis yielded the following expressions: SBP = Pisovolumic [0.638 - 0.0773 Emax C + 0.0507 RC/T] (r2 = 0.89); DBP = Pisovolumic [0.438-0.0712 Emax C + 0.0655RC/T] (r2 = 0.88) and SV = LVEDV [1.265-1.040 LVEDV/(LVEDV - Vd) + 0.125 Emax C-0.0777RC/T] (r2 = 0.93) with Pisovolumic = Emax (LVEDV - Vd), Emax and Vd being the slope and intercept of the end-systolic pressure-volume relation, R and C the total peripheral resistance and compliance, LVEDV the left ventricular end-diastolic volume, and T the cardiac cycle length. These expressions were validated using data from the second group of three animals obtained during vena cava occlusion at baseline and during administration of dobutamine (61 cycles). The correlation between measured and predicted values was 0.98, 0.97 and 0.92 for SBP, DBP and SV, respectively. Compared to the measured values, SBP and DBP were, on average, underestimated by 5 and 6mmHg, respectively, and SV overestimated by 1.4 ml. We conclude that the derived expressions for blood pressure and stroke volume remain valid in the intact sheep for various hemodynamic conditions, and, taking into account their dimensionless form, may hold in other species and in humans.

2001

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

Jean-Jacques Meister, Nikolaos Stergiopulos, Nico Westerhof

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.

1994

Predicting systolic and diastolic aortic blood pressure and stroke volume in the intact sheep

Patrick Segers, Nikolaos Stergiopulos, Nico Westerhof

2001