Nicolaas Westerhof

Pressure and Flow Generated by the Left Ventricle against Different Impedances

To study selective changes in capacitive and resistive load under constant left atrial filling pressure, isolated cat hearts were loaded with a hydraulic model simulating the input impedance of the systemic arteries. The model was constructed so that resistive (peripheral resistance) and capacitive (total arterial compliance) characteristics could be changed independently. Aortic and left ventricular pressure and aortic flow, as generated by the left ventricle against the different impedances, were measured. An increase in resistance resulted in an increase in systolic, diastolic, and mean aortic pressure. A decrease in capacitance caused a small increase in systolic pressure and a decrease in diastolic and mean aortic pressure. Mean left ventricular pressure increased when resistance increased or capacitance decreased. Both peak flow and mean flow decreased when resistance increased or capacitance decreased. We attempted to explain these observations by the concept of source impedance. This concept had been, until now, incorrectly approached, because the nonlinearity arising from the aortic valves had been neglected. The correct computations met with difficulties, but it was shown that the isolated heart, with constant atrial filling pressure, behaved as neither a flow source nor a pressure source.

Matching between ventricle and arterial load. An evolutionary process.

The hemodynamic properties of the ventricle are related to those of the arterial load. However, the precise nature of this relation is not known. At least three different matching criteria have been described in the literature: optimization of heart rate, of power output, and of external efficiency. Although these suggestions are based on experimental findings, there is little understanding of the underlying principles. We now suggest that the balance between the ventricle and its load is a result of the evolutionary process. To support our view, three simple assumptions are proposed regarding the evolutionary determinants underlying the relation between ventricle and arterial load: 1) Arterial pressure and flow to be generated by the ventricular pump under normal (control) conditions are set by the demands of the body. 2) Mechanical properties of contractile machinery and arterial wall material are given. 3) The heart and arterial system should have minimum size. On the basis thereof, we argue that heart rate is related to maintenance of diastolic pressure and show that the ventricle operates close to optimum power and efficiency to attain minimum size.

Characterization of the Arterial System in the Time Domain

The impulse response function and the input impedance of the systemic arterial tree emphasize different aspects of this system. The impulse response function is calculated via inverse Fourier transformation of the input impedance. The effects of truncation of the impedance are reduced by subjecting the data to a Dolph-Chebyshev filter. The impulse response functions of a windkessel model, a uniform tube model, and of the arterial system of the dog, are given. The impulse response functions of the windkessel model and of the arterial system of the control dog show a sharp initial peak followed by an exponential decay (equal decay time as that of the diastolic pressure tracing). The height of the decay extrapolated to time zero is related to total arterial compliance. Total arterial compliance calculated in this way agrees with the value calculated from the ratio of the time constant of the diastolic pressure decay and peripheral resistance. The presence of peaks in the impulse response function indicates a distinct reflection site as shown in the uniform tube model and found in the dog with balloon occlusion of the descending aorta. The measurement of the time intervals between these peaks and the start of excitation together with the pulse wave velocity enable us to calculate the distance between the location of the reflecting site and the heart.

Cardiac high-energy phosphates adapt faster than oxygen consumption to changes in heart rate.

To investigate the dynamic control of cardiac ATP synthesis, we simultaneously determined the time course of mitochondrial oxygen consumption with the time course of changes in high-energy phosphates following steps in cardiac energy demand. Isolated isovolumically contracting rabbit hearts were perfused with Tyrodes solution at 28 degrees C (n = 7) or at 37 degrees C (n = 7). Coronary arterial and venous oxygen tensions were monitored with fast-responding oxygen electrodes. A cyclic pacing protocol in which we applied 64 step changes between two different heart rates was used. This enabled nuclear magnetic resonance measurement of the phosphate metabolites with a time resolution of approximately 2 seconds. Oxygen consumption changed after heart-rate steps with time constants of 14 +/- 1 (mean +/- SEM) seconds at 28 degrees C and 11 +/- 1 seconds at 37 degrees C, which are already corrected for diffusion and vascular transport delays. Doubling of the heart rate resulted in a significant decrease in phosphocreatine (PCr) content (11% at 28 degrees C, 8% at 37 degrees C), which was matched by an increase in inorganic phosphate (P(i)) content, although oxygen supply was shown to be nonlimiting. The time constants for the change of both P(i) and PCr content, approximately 5 seconds at 28 degrees C and 2.5 seconds at 37 degrees C, are significantly smaller than the respective time constants for oxygen consumption.(ABSTRACT TRUNCATED AT 250 WORDS)

A dynamic nonlinear lumped parameter model for skeletal muscle circulation

A dynamic nonlinear lumped parameter model of the circulation of skeletal muscle for constant vasoactive state is presented. This model consists of four compartments that represent the large arteries, the arterioles, the capillaries and venules, and the veins, respectively. The first compartment consists of a linear compliance (C1) and resistance (R1). The third compartment possesses no compliance and is represented by a linear resistance (R3). The second and fourth compartments each consist of a nonlinear pressure-volume relation, resulting in a pressure dependent compliance (C2, C4, respectively) and nonlinear resistance (R2, R4, respectively). The eleven model parameters were collected in a complementary way: they were partly obtained from a priori knowledge including, information at the microscopic level, and partly determined by means of an estimation algorithm. Estimated values of the compliances (in cm3·kPa−1·100 g−1, 1kPa=7.5 mmHg) and resistances (in kPa·s·cm−3·100 g) at an (arterial) inflow pressure of 10 kPa and a (venous) outflow pressure of 0 kPa were: C1: 0.014; R1: 6.6; C2: 0.565; R2: 84.6; R3: 37.9; C4: 1.044; R4: 24.5. The model (with the nonlinear pressure-volume relations) is able to predict the static and dynamic instantaneous (i.e., for constant vasomotor tone) pressure-flow relation and the instantaneous zero flow pressure intercept. These phenomena are therefore not necessarily the result of the rheological properties of blood. The secondary or delayed dilatation upon a positive inflow pressure step (or negative step in venous pressure) is predicted by the model implying that delayed dilatation is not necessarily related to changes in vasomotor tone. Venous outflow delay, upon a positive inflow pressure step (starting from zero flow), is also predicted by the model.

Systematic autoregulation counteracts the carotid baroreflex

The interaction between autoregulation and baroregulation and its effect on the gains of the short-term pressure regulatory system were studied by performing open- and closed-loop experiments in the same five anesthetized, vagotomized dogs and by analyzing the data using a novel model. With carotid pressure constant (no baroregulation), the pressure-flow data were convex to the flow axis, indicating the presence of autoregulation. When baroregulation was present, the data were convex to the pressure axis. The proposed model was able to fit the data as measured in both cases. From the fitting procedure, the zero-flow pressure intercept, the autoregulation resistance gain, and the baroregulation resistance gain were estimated. It is concluded that if autoregulation is present it affects the values of baroreflex gains estimated from both closed- and open-loop experiments. The autoregulation gain can be estimated from steady-state systemic pressure-flow data measured after vagotomy and with the carotid pressure constant. Then, from measurements of systemic pressure-flow data performed after restoring the hydraulic connection between carotid and aortic areas, the gains of the carotid baroreflex can be estimated with the aid of the proposed model.<<ETX>>

Mechanics of a thin walled collapsible microtube

The purpose of this study is to measure the transmural pressure-cross sectional area relation of micro tubes (240 μm diameter) and to compare the measured perfusion pressure-flow relation with the pressure-flow relation calculated from the experimental pressure-cross sectional area relation. The microtubes are made by dipping a glass mould in a latex solution and glueing their outside ends to the inside of glass pipettes. The pressure-cross sectional area relation is determined both with a microplethysmograph (pressure-volume relation) and the microscope (pressure-diameter relations). Heparinized blood is used to include the rheological properties of blood as a perfusion medium. Static pressure-flow relations are obtained with a constant velocity piston pump for two values of external pressure (0 and 10 kPa) and with two downstream resistor settings (0 and 380 kPa cm−3 sec). The calculated pressure-flow relations using length and the experimental pressure-cross sectional area relation, Poiseuilles law, and accounting for the diameter-and shear-dependent viscosity compared well with the relations obtained from the experiments. It is also found that the pressure-flow relation shows an apparent zero flow pressure axis intercept (the extrapolation of the pressure-flow relation to the pressure axis), which can therefore be explained on the basis of the shape of the pressure-area relations.

The four-element Windkessel model

In earlier studies the authors found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to correct estimates of the total arterial parameters such as the aortic characteristic impedance and total arterial compliance. To overcome this problem the authors add a fourth element, the total arterial inertance, to the three-element windkessel. The three- and four-element windkessels were tested against an extended model of the systemic circulation. The four-element windkessel described arterial pressure and flow most accurately and the estimated lumped parameters were typically within 10% of the actual values of the arterial system, The three- and four element windkessel model were also fit to in vivo human aortic pressure and flow waves. Again, the four-element windkessel fitted better and the estimated arterial parameter values were closer to values obtained with standard methods.

How cardiac contraction affects the coronary vasculature.

We modeled the influence of cardiac contraction on maximally dilated coronary blood vessels, whether single or in juxtaposition, taking into account the nonlinear material properties of both the vascular wall and the myocardium. We calculated pressure-area relations of single, embedded coronary blood vessels, and used these relations to calculate diastolic and systolic coronary pressure-flow relations in a model of the coronary vasculature. The model shows that the change in myocardial material properties during contraction can explain the decrease in coronary vessel area and coronary flow generally observed in experiments. The model also shows that arterioles can be protected from the compressive action of the cardiac muscle by the presence of accompanying venules, which is favorable for coronary blood flow.

Law of Poiseuille

With laminar and steady flow through a uniform tube of radius r i , the velocity profile over the cross-section is a parabola. The formula that describes the velocity (v) as a function of the radius, r is: