N. Westerhof

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

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.

Pulse wave reflection: can it explain the differences between systemic and pulmonary pressure and flow waves? A study in dogs.

We have studied the effect of changes in pulse wave reflection on the configurations of pressure and flow in systemic and pulmonary circulation. Electromagnetic flow transducers, atrial catheters, and pacing leads were implanted in 10 dogs. In four animals, the flow transducer was placed on the pulmonary artery, in another four on the ascending aorta, and in two additional dogs on both vessels. One week later, ascending aortic and/or pulmonary artery flow and pressure (catheter tip manometer) were measured under general anesthesia (Nembutal, 30 μg/kg, iv). When the pulmonary circulation was studied (six dogs), measurements were made before and during serotonin infusion (0.5–0.75 μg/min). When the systemic circulation was studied (six dogs), measurements were made before and during nitroprusside infusion (50–200 μg/min). To quantify the arterial load, we calculated pulmonary and systemic input impedances. To estimate the amount of reflection, we used a reflection index which we defined as the amplitude ratio of reflected and forward wave. Nitroprusside decreased total peripheral resistance, increased total arterial compliance, and decreased the reflection index; similarity between aortic pressure and flow wave shapes increased, and they looked more like their pulmonary counterparts. Serotonin increased pulmonary vascular resistance, decreased pulmonary arterial compliance, and increased the reflection index. Resemblance of pressure and flow waves decreased. The differences in wave shapes can thus be explained by the amount of reflection: the less reflection the more pressure and flow resemble each other.

Comparison of models used to calculate left ventricular wall force.

Myocardial wall force per area (=stress) is a major determinant of muscle function and oxygen consumption. It cannot be measured accurately but has to be derived from a mathematical model. Many models have been presented in the literature but a comparison between models has not been available. In this study angiographic data from the literature are used to calculate left ventricular wall force for normal and diseased hearts using a thin-walled spherical model, a thick-walled spherical model and six ellipsoidal models, and the results are compared. There appeared to be large differences between the stresses yielded by the models for the same cardiac geometry. The thick-walled sphere yields circumferential stresses that are approximately 25% lower than the stresses yielded by most of the ellipsoidal models. Of the ellipsoidal models the one suggested by Streeter el al. gives circumferential stresses that are 25% higher than those of the other ellipsoids. Similar differences are found for left ventricular wall stress in the longitudinal direction. However, all models correspond closely in the prediction of the deviation from normal stress in the various pathological states studied.Some of the models give information about the stress distribution over the thickness of the wall as well. We found substantial differences in this predicted stress distribution for models that employ similar assumptions. These differences plus the uncertainties with regard to the properties of the myocardial wall material, that change during the cardiac cycle, call for some scepticism concerning the calculated stress distribution over the wall. The ellipsoidal model suggested by Falsetti et al. is very simple and yields approximately the same mean wall stress values as the more complicated models that we studied. This model therefore appears to be the best choice.

Optimal power generation by the left ventricle. A study in the anesthetized open thorax cat.

We studied the interaction of the left ventricle and the systemic arterial bed in the open thorax cat. In the steady state, the ventricle can be characterized by the pump functiongraph (i.e., the relationship between mean left ventricular pressure and mean outflow). From this pump function graph, the apparent source resistance of the heart is found. Apparent source resistance is defined as the ratio of the difference between maximal and actual mean left ventricular pressure, and mean outflow. The arterial system can be characterized by the ratio of mean aortic pressure and mean flow (peripheral resistance). The pressure and flow at which the heart operates is defined as the working point. We have investigated whether the ventricle in the intact cat is working optimally, i.e., that it cannot increase work output further at the end-diastolic volume, contractile state, and prevailing heart rate. This condition is considered as ‘matching’ of ventricle and load. It could be shown that optimal power is transferred when the ratio of peripheral and apparent source resistance equals twice the ratio of mean aortic and mean left ventricular pressure (the matching principle). In four cats, we observed that mean aortic and mean left ventricular pressures are proportionally related. Mean external power (the time intergral of the product of pressure and flow divided by cycle length) and steady power (the product of mean pressure and mean flow) were found to be proportional as well. These proportionalities allow for the calculation of peripheral resistance and mean external power from the pump function graph. Pump function graphs were determined in three groups: control (n = 9), atrial pacing (n = 8), and halothane (n = 5). We compared the ratio of peripheral and source resistance at the working point and at the point of optimal work output (expressed in steady ventricular power). It could be shown that, in all investigated groups, the power optimum and the working point coincide. It was concluded that circulatory control in the intact anesthetized cat keeps the ventricle at optimal work output under the conditions studied.

Pulmonary endarterectomy normalizes interventricular dyssynchrony and right ventricular systolic wall stress

BackgroundInterventricular mechanical dyssynchrony is a characteristic of pulmonary hypertension. We studied the role of right ventricular (RV) wall stress in the recovery of interventricular dyssynchrony, after pulmonary endarterectomy (PEA) in chronic thromboembolic pulmonary hypertension (CTEPH).MethodsIn 13 consecutive patients with CTEPH, before and 6 months after pulmonary endarterectomy, cardiovascular magnetic resonance myocardial tagging was applied. For the left ventricular (LV) and RV free walls, the time to peak (Tpeak) of circumferential shortening (strain) was calculated. Pulmonary Artery Pressure (PAP) was measured by right heart catheterization within 48 hours of PEA. Then the RV free wall systolic wall stress was calculated by the Laplace law.ResultsAfter PEA, the left to right free wall delay (L-R delay) in Tpeak strain decreased from 97 ± 49 ms to -4 ± 51 ms (P < 0.001), which was not different from normal reference values of -35 ± 10 ms (P = 0.18). The RV wall stress decreased significantly from 15.2 ± 6.4 kPa to 5.7 ± 3.4 kPa (P < 0.001), which was not different from normal reference values of 5.3 ± 1.39 kPa (P = 0.78). The reduction of L-R delay in Tpeak was more strongly associated with the reduction in RV wall stress (r = 0.69,P = 0.007) than with the reduction in systolic PAP (r = 0.53, P = 0.07). The reduction of L-R delay in Tpeak was not associated with estimates of the reduction in RV radius (r = 0.37,P = 0.21) or increase in RV systolic wall thickness (r = 0.19,P = 0.53).ConclusionAfter PEA for CTEPH, the RV and LV peak strains are resynchronized. The reduction in systolic RV wall stress plays a key role in this resynchronization.

INTERACTION OF HEART AND ARTERIAL SYSTEM

AbstractWe have studied the interrelation of left ventricle and arterial system in the anesthetized open-thorax cat. The ventricle was characterized by its pump function graph, relating mean ventricular pressure (

Endothelium Function Is Protected by Albumin and Flow-Induced Constriction Is Independent of Endothelium and Tone in Isolated Rabbit Femoral Artery

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Accurate measurement of intraarterial pressure through radial artery catheters in neonates

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