Fluid dynamics model of mitral valve flow: description with in vitro validation

A new method of haemodynamic assessment of mitral stenosis in atrial fibrillation: construction of a nomogram

Accurate haemodynamic assessment of mitral stenosis by hydraulic formulas requires measurement of the mean valve gradient and the cardiac output. The calculation is laborious, particularly in the presence of atrial fibrillation when averaged values obtained from multiple beat-to-beat determinations must be used. The relations between valve area, end diastolic gradient, and heart rate in 20 patients with mitral stenosis and atrial fibrillation were examined. In each patient the end diastolic pressure gradient for each cardiac cycle was related linearly to the RR interval of that cycle, and this relation was unchanged on exercise. The slope (S) and intercept (I) of this relation correlated with the degree of mitral stenosis as measured by the Gorlin valve area. The regression equations describing these relations were then used to construct a nomogram relating end diastolic pressure gradient to mitral valve area at different heart rates. When the nomogram was applied to catheterisation data from a further 30 patients the results correlated well with direct calculation of valve area by the Gorlin formula. The nomogram is simple to use, does not require measurement of cardiac output, and is independent of heart rate so that it is unnecessary for the patient to exercise during catheterisation.

Effects of nitroprusside on transmitral flow velocity patterns in extreme heart failure: a combined hemodynamic and Doppler echocardiographic study of varying loading conditions

To explore the mechanisms of change of left ventricular diastolic filling associated with preload and afterload reduction, the influence of nitroprusside on the transmitral flow velocity pattern, pulmonary capillary wedge pressure and left ventricular pressure interaction was studied in 11 patients with end-stage heart failure. Pulsed Doppler echocardiographic recordings of mitral inflow were obtained with simultaneous high fidelity left ventricular and phase-corrected pulmonary capillary wedge pressure recordings before and during levels of nitroprusside infusion. With nitroprusside, left ventricular systolic and end-diastolic pressures decreased by 14% and 41% (p less than 0.05, p less than 0.05), respectively, and cardiac output increased by 67% (p less than 0.05). The pulmonary capillary wedge-left ventricular crossover pressure decreased by 41% (p less than 0.05), but the time constant of isovolumetric left ventricular pressure decrease T was insignificantly changed. Isovolumetric relaxation time and acceleration and deceleration times of the early diastolic filling wave were significantly prolonged with nitroprusside infusion (p less than 0.05, p less than 0.05 and p less than 0.05, respectively). Peak early diastolic filling velocity was maintained (65 +/- 11 to 62 +/- 13 cm/s, p = NS) in spite of the decreased absolute crossover pressure. Changes in peak early diastolic filling velocity correlated weakly with changes in the crossover pressure (r = 0.48, p less than 0.05) and correlated better with the crossover to left ventricular minimal pressure difference (r = 0.78, p less than 0.05). Peak early diastolic filling velocity appears to be most affected by the early diastolic pulmonary capillary wedge to left ventricular pressure difference rather than the absolute pulmonary capillary wedge pressure. The lack of peak flow velocity change during nitroprusside infusion could be explained by either the associated decrease in left ventricular minimal pressure or downward shift of left ventricular diastolic pressure by the same amount as the decrease in pulmonary capillary wedge pressure. This may reflect a reduction of external constraint to ventricular distensibility produced by a reduction in filling volume in patients with a markedly dilated ventricle. Thus, a prolonged early diastolic filling period and preserved peak early diastolic filling velocity in spite of decreased left ventricular filling pressure and constant relaxation rate are associated with the beneficial effects of nitroprusside on left ventricular function in patients with severe congestive heart failure.

Analysis of the early transmitral Doppler velocity curve: effect of primary physiologic changes and compensatory preload adjustment

Left ventricular filling (as assessed by Doppler echocardiography) has previously been shown to depend in a complex fashion on ventricular diastolic function (compliance and relaxation) as well as other variables, such as atrial pressure and compliance, ventricular systolic function and mitral valve impedance. To study the effect of isolated physiologic alterations on individual Doppler indexes, a mathematic model of mitral flow was analyzed. By varying one physiologic variable at a time, it was shown that mitral velocity acceleration is affected directly by atrial pressure and inversely by the ventricular relaxation time constant, with relatively little impact of chamber compliance. Deceleration rate was directly influenced by mitral valve area, atrial pressure and ventricular systolic dysfunction and inversely affected by atrial and ventricular compliance relations, with little impact of relaxation unless it was so delayed as to be incomplete during deceleration. Peak velocity was directly affected most strongly by initial left atrial pressure, and lowered somewhat by prolonged relaxation, low atrial and ventricular compliance and systolic dysfunction. Strikingly different filling patterns emerged when the primary physiologic alterations were accompanied by simultaneous compensatory changes in atrial pressure designed to maintain stroke volume constant. Low ventricular compliance with preload compensation produced characteristic E waves with very short acceleration and deceleration times and high peak velocity. Thus, mathematic analysis of ventricular filling helps to explain the physical and physiologic basis for the transmitral velocity curve.

Analysis of different methods of assessing the stenotic mitral valve area with emphasis on the pressure gradient half-time concept

There are 2 different theoretical models that analyze factors influencing the transmitral pressure gradient half-time (T1/2), defined as the time needed for the pressure gradient to reach half its initial value. In this report the models and the assumptions inherent in them were summarized. One model includes left heart chamber compliance, the other does not. Although the models at a superficial glance seem to be contradictory, the conclusions drawn from them are similar: i.e., T1/2 is influenced not only by valve area, but also by initial maximal pressure gradient and by flow. Different clinical situations in which the T1/2 method for valve area estimation has been shown not to work are analyzed in the 2 models. It is concluded that these models have contributed to our understanding of the T1/2 concept and when it should not be used. We also advocate use of the continuity equation in these situations, since no assumptions then need be made.

Aortic regurgitation shortens Doppler pressure half-time in mitral stenosis: clinical evidence, in vitro simulation and theoretic analysis

Mitral valve areas determined by Doppler pressure half-time were compared with areas obtained by planimetry in two groups of patients with mitral stenosis: 24 patients without aortic regurgitation and 32 patients with more than grade 1 aortic regurgitation. The severity of aortic regurgitation was assessed by color flow mapping; 17 patients had grade 2, 10 had grade 3 and 5 had grade 4 aortic regurgitation. Regression equations for pressure half-time area versus planimetry mitral valve area were calculated separately for the aortic regurgitation (r = 0.88) and the nonaortic regurgitation group (r = 0.86); analysis of covariance revealed a significant (p less than 0.001) difference between the two groups leading to overestimation of planimetry area by the pressure half-time method in the aortic regurgitation group. The mitral valve areas in the group without regurgitation were best calculated with the expression 239/T1/2 (r = 0.77) as compared with a best fit of 195/T1/2 (r = 0.85) for the aortic regurgitation group. To elucidate the mechanisms affecting pressure half-time in aortic regurgitation, an in vitro model of mitral inflow in the presence of varying regurgitant volumes and different ventricular chamber compliances was used. Aortic regurgitation shortened directly measured pressure half-time proportional to the regurgitant fraction but an increase in left ventricular compliance could offset this effect. Finally, in a mathematic model of mitral inflow the competing effects of aortic regurgitation and chamber compliance could be confirmed. In conclusion, aortic regurgitation results clinically in a significant net shortening of pressure half-time leading to mitral valve area overestimation. However, the effect is moderate and individually unpredictable because of changes in chamber compliance.

Diastolic viscous properties of the intact canine left ventricle

The viscoelastic model of the ventricle predicts that the rate of change of volume (strain rate) is a determinant of the instantaneous pressure in the ventricle during diastole. Because relaxation is not complete before the onset of filling, one cannot distinguish the individual effects of relaxation and viscosity unless the passive and active components that determine the ventricular pressure are separated. To overcome this problem, we used the method of ventricular volume clamping to compare the pressures in the fully relaxed ventricle at a given volume at zero strain rate (static pressure) and high strain rate (dynamic pressure). Six open-chest, fentanyl-anesthetized dogs were instrumented with micromanometers and an electronically controlled mitral valve occluder in series with the electromagnetic flow probe. We reasoned as follows: If there were significant viscosity, then the dynamic pressure would be higher than the static pressure. The static pressure was measured when the ventricle was completely relaxed following a mitral valve occlusion after an arbitrary filling volume had been achieved. The dynamic pressure was determined by delaying the onset of filling until relaxation was complete and then measuring the pressure at the same volume that was achieved when the static pressure was measured. In 19 different hemodynamic situations, the dynamic and static pressures were identical (mean difference, 0.1 +/- 0.8 mm Hg), indicating that in the passive ventricle viscoelastic effects are insignificant and do not contribute to the left ventricular diastolic pressure under normal filling rates.

Impaired relationship between Doppler echocardiographic parameters of diastolic function and left ventricular filling pressure during acute ischemia

The relationship between left ventricular filling pressure and Doppler echocardiographic parameters of diastolic mitral flow (MF) was evaluated in patients with ischemic heart disease during acute ischemia induced by percutaneous transluminal coronary angioplasty (PTCA) of the left anterior descending artery. Thirty-two patients were examined by simultaneous recordings of the Doppler MF signal and the mean pulmonary capillary wedge pressure (PCm) as an approximation of left ventricular filling pressure. At rest PCm was correlated with the early/late velocity integral ratio (Ei/Ai: r = 0.62: p less than 0.0001; n = 32). In 25 of 32 patients the recordings during PTCA could be evaluated. At the end of the inflation (duration: 69 +/- 24 seconds) PCm increased from 11.2 +/- 5.5 to 17.2 +/- 7.2 mm Hg (p less than 0.001), and total MF integral as an index of systolic ventricular function decreased by 14.9 +/- 12.8% (p less than 0.001). Inasmuch as both early and late velocity integrals were reduced during PTCA, the Ei/Ai ratio did not change significantly (1.41 +/- 0.51 to 1.34 +/- 0.60; NS). In a subgroup of inflations without ECG signs of ischemia, Ei was decreased without a concomitant decrease in Ai, thus leading to a decrease in the Ei/Ai ratio (1.36 +/- 0.43 to 1.17 +/- 0.31; p less than 0.05). Summarizing the events during PTCA, a steady increase in PCm was observed, whereas the Ei/Ai ratio was slightly decreased. Thus the observation at rest that an elevated PCm was associated with an elevated Ei/Ai was no longer valid during PTCA (Ei/Ai: r = 0.28; NS). A significant correlation was found between parameters of Doppler MF and PCm in patients with ischemic heart disease at rest. During PTCA this relationship was attenuated. Therefore noninvasive assessment of left ventricular filling pressures during acute ischemia by Doppler echocardiography does not seem feasible.

Influence of orifice geometry and flow rate on effective valve area: an in vitro study

Fluid dynamics suggests that orifice geometry is a determinant of discharge properties and, therefore, should influence empiric constants in formulas (such as the Gorlin formula) to calculate stenotic valve area. An in vitro study utilizing a model of transmitral flow was conducted to investigate how the discharge coefficient changes with 1) orifice eccentricity (ratio of long to short diameter), 2) absolute area, 3) the presence of a nozzle-like inlet, and 4) varying flow. Twenty-three orifices with areas varying between 0.3 and 2.5 cm2 and eccentricities from 1:1, or circular, to 5:1, or elliptic, were tested. The calculated discharge coefficients ranged between 0.675 and 0.93. For a given area, the discharge coefficient decreased by a mean value (+/- SD) of 5.5 +/- 1.3% between circular orifices and 5:1 ellipses. Discharge coefficients increased by a mean of 8.9 +/- 3.5% from 0.3 to 2.5 cm2 area within each eccentricity class. A gradually tapering inlet (nozzle) raised the discharge coefficient by 8.8 +/- 3.9%, leading to a discharge coefficient between 0.81 and 0.93 for round orifices. The discharge coefficient did not change appreciably with flow. The concept of the discharge coefficient and its role in assessing restrictive orifices in general by hydraulic formulas (for example, the Gorlin and pressure half-time calculations) are discussed.

Quantification of jet flow by momentum analysis. An in vitro color Doppler flow study

Previous investigations have shown that the size of a regurgitant jet as assessed by color Doppler flow mapping is independently affected by the flow rate and velocity (or driving pressure) of the jet. Fluid dynamics theory predicts that jet momentum (given by the orifice flow rate multiplied by velocity) should best predict the appearance of the jet in the receiving chamber and also that this momentum should remain constant throughout the jet. To test this hypothesis, we measured jet area versus driving pressure, flow rate, velocity, orifice area, and momentum and showed that momentum is the optimal jet parameter: jet area = 1.25 (momentum).28, r = 0.989, p less than 0.0001. However, the very curvilinear nature of this function indicated that chamber constraint strongly affected jet area, which limited the ability to predict jet momentum from observed jet area. To circumvent this limitation, we analyzed the velocities per se within the Doppler flow map. For jets formed by 1-81-mm Hg driving pressure through 0.005-0.5-cm2 orifices, the velocity distribution confirmed the fluid dynamic prediction: Gaussian (bell-shaped) profiles across the jet at each level with the centerline velocity decaying inversely with distance from the orifice. Furthermore, momentum was calculated directly from the flow maps, which was relatively constant within the jet and in good agreement with the known jet momentum at the orifice (r = 0.99). Finally, the measured momentum was divided by orifice velocity to yield an accurate estimate of the orifice flow rate (r = 0.99). Momentum was also divided by the square of velocity to yield effective orifice area (r = 0.84). We conclude that momentum is the single jet parameter that best predicts the color area displayed by Doppler flow mapping. Momentum can be measured directly from the velocities within the flow map, and when combined with orifice velocity, momentum provides an accurate estimate of flow rate and orifice area.

Doppler assessment of prosthetic valves

Doppler evaluation of prosthetic valves is a complex process involving assessment of both forward and regurgitant flow. It is important to consider the type of prosthesis, its size, its position, its relationship to the ultrasound beam, and the patient's cardiac output and afterload condition in any evaluation of prosthetic valve function.