Experimental analysis of fluid mechanical energy losses in aortic valve stenosis: importance of pressure recovery

Current methods for assessing the severity of aortic stenosis depend primarily on measures of maximum systolic pressure drop at the aortic valve orifice and related calculations such as valve area. It is becoming increasingly obvious, however, that the impact of the obstruction on the left ventricle is equally important in assessing its severity and could potentially be influenced by geometric factors of the valve, causing variable degrees of downstream pressure recovery. The goal of this study was to develop a method for measuring fluid mechanical energy losses in aortic stenosis that could then be directly related to the hemodynamic load placed on the left ventricle. A control volume form of conservation of energy was theoretically analyzed and modified for application to aortic valve stenosis measurements. In vitro physiological pulsatile flow experiments were conducted with different types of aortic stenosis models, including a venturi meter, a nozzle, and 21-mm Medtronic-Hall tilting disc and St. Jude bileaflet mechanical valves. The energy loss created by each model was measured for a wide range of experimental conditions, simulating physiological variation. In all cases, there was more energy lost for the nozzle (mean = 0.27 J) than for any other model for a given stroke volume. The two prosthetic valves generated approximately the same energy losses (mean = 0.18 J), which were not statistically different, whereas the venturi meter had the lowest energy loss for all conditions (mean = 0.037 J). Energy loss correlated poorly with orifice pressure drop (r2 = 0.34) but correlated well with recovered pressure drop (r2 = 0.94). However, when the valves were considered separately, orifice and recovered pressure drop were both strongly correlated with energy loss (r2 = 0.99, 0.96). The results show that recovered pressure drop, not orifice pressure drop, is directly related to the energy loss that determines pump work and therefore is a more accurate measure of the hemodynamic significance of aortic stenosis.

Quasisteady behavior of pulsatile, confined, counterflowing jets: implications for the assessment of mitral and tricuspid regurgitation

Mitral and tricuspid regurgitation create turbulent jets within the atria. Clinically, for the purpose of estimating regurgitant severity, jet size is assumed to be proportional to peak jet flow rate and regurgitant volume. Unfortunately, the relationship is more complex because the determinants of jet size include interactions between jet pulsatility, jet momentum, atrial width, and the velocity of ambient atrial counterflows. These effects on fluorescent jet penetration were measured using an in vitro simulation. Both steady and pulsatile jets were driven into an opposing counterflow velocity field peak jet length (Ljp) measurements made as a function of (1) peak orifice velocity (Ujp), (2) the time required for the jet to accelerate from zero to peak velocity and begin to decelerate (Tjp), (3) jet orifice diameter (Dj), (4) counterflow velocity (Uc), and (5) counterflow tube diameter (Dc). A compact mathematical description was developed using dimensional analysis. Results showed that peak jet length was a function of the counterflow tube diameter, the ratio of peak jet to counterflow momentum, (Mjp/Mc) = (U2jpD2j)/(U2cD2c), and a previously undescribed jet pulsatility parameter, the pulsatility index (PI), PI = D2c/(TjpUjpDj). For the same jet orifice flow conditions, jet penetration decreased as chamber diameter decreased, as the jet PI increased, and as the momentum ratio decreased. These interactions provide insight into why regurgitant jet size is not always a good estimate of regurgitant severity.

How sensitive are jet centerline velocities to an opposing flow? Implications for using the centerline method to quantify regurgitant jet flow

A method for quantifying peak mitral and tricuspid regurgitant jet flow rate that utilizes a measure of jet orifice velocity (Uo, m s-1), a distal centerline velocity (Um, m s-1), and the intervening distance (X, cm) was recently developed. This method, however, modeled the regurgitant jet as a free jet, whereas many atrial jets are counterflowing jets because of jet opposing intra-atrial flow fields (counterflows). This study evaluated the feasibility of using the free jet quantification equation in the atrium where ambient flow fields may alter jet centerline velocities and therefore reduce the accuracy of jet flow rate calculations. A 4 cm wide chamber was used to pump counterflows of 0, 4, and 22 cm s-1 against jets of 2.3, 4.8, and 6.4 s-1 originating from a 2 mm diameter orifice. For each counterflow-jet combination, jet centerline velocities were measured using laser Doppler anemometry. For free jets (no counterflow), flow rate was calculated with 98% mean accuracy. For all jets in counterflow, the calculation was less accurate as (i) the ratio of jet orifice velocity to counterflow velocity decreased (Uo/Uc, where Uc is counterflow velocity), i.e. the counterflow was relatively more intense, an (ii) centerline measurements were mad further from the orifice. But although counterflow lowered jet centerline velocities beneath free jet values, it did so only significantly in the jet's distal portion, while the initial portion (X/D < 16, where D is jet orifice diameter) of a jet in counterflow behaved essentially as a free jet. Therefore, regurgitant jets, although not classically free because of systolic atrial inflow, will decay in their initial portions as free jets and hence are candidates for quantification with the centerline technique.

Three-dimensional reconstruction of the flow in a human left heart by using magnetic resonance phase velocity encoding

Intraventricular flows have been correlated with disease and are of interest to cardiologists as a possible means of diagnosis. This study extends a method that use magnetic resonance (MR) to measure the three-dimensional nature of these flows. Four coplanar, sagittal MR slices were located that spanned the left ventricle of a healthy human. All three velocity components were measured in each slice and 18 phases were obtained per beat. With use of the MR magnitude images, masks were created to isolate the velocity data within the heart. These data were read into the software package, Data Visualizer, and the data from the four slices were aligned so as to reconstruct the three-dimensional volume of the left ventricle and atrium. By representing the velocity in vectorial form, the three-dimensional intraventricular flow field was visualized. This revealed the presence of one large line vortex in the ventricle during late diastole but a more ordered flow during early diastole and systole. In conclusion, the use of MR velocity acquisition is a suitable method to obtain the complex intraventricular flow fields in humans and may lead to a better understanding of the importance of these flows.

Dynamics of systolic pulmonary venous flow in mitral regurgitation: mathematical modeling of the pulmonary venous system and atrium

The noninvasive assessment of mitral regurgitation has been an elusive clinical goal. Recent studies have highlighted the value of pulmonary venous (PV) flow reversal in indicating the presence of severe regurgitation. The purpose of this study was to explore the basic determinants of PV inflow in the presence and absence of regurgitation. In particular, the hypothesis that systolic PV flow depends on the interaction of regurgitant volume with atrial and PV properties (compliance, initial volume, total area of the pulmonary veins at the atrial junction, and the inertia of PV inflow) was tested and further, that the combination of these variables, rather than regurgitant volume alone, determines PV inflow. A mathematical model of the atrium and pulmonary veins was developed. Atrial and PV pressure were modeled as the product of chamber elastance and volume, where atrial elastance varied in time to simulate atrial relaxation and descent of the mitral anulus. A simplification of the modified unsteady Bernoulli equation was used to compute the PV velocities that resulted from the developed pressure gradient. The modeling was performed over a range of initial atrial elastances (0.77 to 0.2 mm Hg/cc), initial atrial volumes (20 to 75 cc), total PV areas (3.12 to 5.12 cm2), and PV inflow inertances (8 to 18 gm/cm2), with and without the addition of two regurgitant jets (regurgitant volume of 20 and 60 cc). The model realistically simulated the systolic PV waveform in magnitude and morphology. As the volume of regurgitation increased, PV peak flow velocity decreased, and eventually late systolic flow reversal occurred. However, the peak flow velocity, the time to peak flow, and the presence and magnitude of flow reversal were influenced by atrial compliance, volume, total atrial inlet area, and PV inflow inertia. This study found that PV flow blunting and reversal increased as atrial compliance, volume, and PV inertia decreased and as atrial inlet area increased. Atrial and PV properties (compliance, volume, total PV atrial inlet area, and PV inflow inertia), acting in combination, mediate the physiologic impact of the regurgitant lesion in terms of the resulting rise in atrial pressure as reflected by the pattern of systolic PV influx. For example, PV flow reversal is more likely in acute compared with chronic regurgitation because the atrium is less compliant and has a smaller initial volume. Therefore, the clinical assessment of mitral regurgitation using changes in systolic PV flow must be viewed in the context of atrial and PV properties.

Atrial inflow can alter regurgitant jet size: in vitro studies

Recent studies have attempted to predict the severity of regurgitant lesions from color Doppler jet size, which is a function of orifice momentum for free jets. Jets of mitral and tricuspid regurgitation, however, are opposed by flows entering the atria. Despite their low velocities, these counterflows may have considerable momentum that can limit jet penetration. The purpose of this study was to address the hypothesis that such counterflow fields influence regurgitant jet size. Steady flow was driven through 2.4- and 5.1-mm-diameter circular orifices at 2 to 6 m/s. At a constant orifice velocity and flow rate, the velocity of a uniform counterflow field was varied from 5 to 30 cm/s. Jet dimensions were measured by both fluorescent dye visualization and Doppler color flow mapping. The results showed that despite its relatively low velocities, counterflow dramatically curtailed jet length and area. Jet dimensions were functions of the ratio of jet to counterflow momentum. Thus, atrial inflow may participate in determining jet size and can alter the relation between jet size and lesion severity in mitral and tricuspid regurgitation.

Quantification of cardiac jets: theory and limitations

Jet flows are consequences of many cardiac lesions. With the advent of color Doppler flow mapping, these jet flows can be visualized noninvasively. Currently, an intense effort is underway to quantify cardiac jet flows as a means to assess the severity of jet forming lesions. Two techniques, PISA and jet centerline decay, have been suggested as methods to quantify jet flow volume. Although both techniques are theoretically sound, both formulations are based on ideal flow conditions that may not be completely realized in cardiac chambers. Thus, the complex dynamics of cardiac jet flows must be considered as they may diminish the accuracy of flow rate calculations. However, realistic in vitro experiments that mimic the impact of cardiac flow conditions on converging flows and jets, combined with carefully controlled in vivo testing of both PISA and centerline techniques, may eventually produce clinically useful quantification formulations.

Cardiac motion can alter proximal isovelocity surface area calculations of regurgitant flow

OBJECTIVES

This study addressed the hypothesis that motion of the surface containing a regurgitant orifice relative to the Doppler ultrasound transducer can cause differences between actual flow rate and calculations based on the proximal flow convergence technique.

BACKGROUND

In vitro studies quantitating regurgitant flow rate by proximal flow convergence have been limited to stationary orifices. Clinically, however, valve leaflets generally move relative to the ultrasound transducer during the cardiac cycle and can move at velocities important relative to the measured color aliasing velocities. The transducer therefore senses the vector sum of actual flow velocity toward the orifice and orifice velocity relative to the transducer. This can cause potential overestimation or underestimation of true flow rate, depending on the direction of surface motion.

METHODS

The hypothesis was explored computationally and tested by pumping fluid at a constant flow rate through an orifice in a plate moving at 0 to 8 cm/s (velocities comparable to those described clinically for mitral and tricuspid annulus motion toward an apical transducer).

RESULTS

Surface motion in the same direction as flow caused overestimation of the aliasing radius and calculated flow rate. Surface motion opposite to the direction of flow (typical for mitral and tricuspid regurgitation viewed from the apex or esophagus) caused underestimation of actual flow rate. The underestimation was greater for lower aliasing velocities (36 +/- 11% for 10 cm/s vs. 23 +/- 6% for 20 cm/s). Correcting for surface motion provided excellent agreement with actual values (y = 0.97x + 0.10, r = 0.99, SEE = 0.17 liters/min).

CONCLUSIONS

Physiologic motion of the surface containing a regurgitant orifice can cause substantial differences between actual flow rate and that calculated by the proximal flow convergence technique. Los aliasing velocities used to optimize that technique can magnify this effect. Such errors can be minimized by using higher aliasing velocities (compatible with the need to measure the aliasing radius) or eliminated by correcting for surface velocity determined by an M-mode ultrasound scan.