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

Prediction of haemodynamics after interatrial shunt for heart failure using the generalized circulatory equilibrium

Aims

Interatrial shunting (IAS) reduces left atrial pressure in patients with heart failure. Several clinical trials reported that IAS improved the New York Heart Association score and exercise capacity. However, its effects on haemodynamics vary depending on shunt size, cardiovascular properties, and stressed blood volume. To maximize the benefit of IAS, quantitative prediction of haemodynamics under IAS in individual patients is essential. The generalized circulatory equilibrium framework determines circulatory equilibrium as the intersection of the cardiac output curve and the venous return surface. By incorporating IAS into the framework, we predict the impact of IAS on haemodynamics.

Methods and results

In seven mongrel dogs, we ligated the left anterior descending artery and created impaired cardiac function with elevated left atrial pressure (baseline: 7.8 ± 1.0 vs. impaired: 11.9 ± 3.2 mmHg). We established extracorporeal left‐to‐right atrial shunting with a centrifugal pump. After recording pre‐IAS haemodynamics, we changed IAS flow stepwise to various levels and measured haemodynamics under IAS. To predict the impact of IAS on haemodynamics, we modelled the fluid mechanics of IAS by Newton's second law and incorporated IAS into the generalized circulatory equilibrium framework. Using pre‐IAS haemodynamic data obtained from the dogs, we predicted the impact of IAS flow on haemodynamics under IAS condition using a set of equations. We compared the predicted haemodynamic data with those measured. The predicted pulmonary flow [r² = 0.88, root mean squared error (RMSE) 11.4 mL/min/kg, P < 0.001), systemic flow (r² = 0.92, RMSE 11.2 mL/min/kg, P < 0.001), right atrial pressure (r² = 0.92, RMSE 0.71 mmHg, P < 0.001), and left atrial pressure (r² = 0.83, RMSE 0.95 mmHg, P < 0.001) matched well with those measured under normal and impaired cardiac function. Using this framework, we further performed a simulation study to examine the haemodynamic benefit of IAS in heart failure with preserved ejection fraction. We simulated the IAS haemodynamics under volume loading and exercise conditions. Volume loading and exercise markedly increased left atrial pressure. IAS size‐dependently attenuated the increase in left atrial pressure in both volume loading and exercise. These results indicate that IAS improves volume and exercise intolerance.

Conclusions

The framework developed in this study quantitatively predicts the haemodynamic impact of IAS. Simulation study elucidates how IAS improve haemodynamics under volume loading and exercise conditions. Quantitative prediction of IAS haemodynamics would contribute to maximizing the benefit of IAS in patients with heart failure.

The impact of cardiac rhythm on the mitral valve area and gradient in patients with mitral stenosis

OBJECTIVE

The aim of this study was to evaluate the effect of cardiac rhythm on the echocardiographic mitral valve area (MVA) and transmitral gradient calculation in relation to net atrioventricular compliance (Cn).

METHODS

Patients (n=22) with mild or moderate pure rheumatic mitral stenosis (MS) (MVA <2 cm2 and MVA >1 cm2) and atrial fibrillation (AF) were evaluated. All patients underwent transthoracic electrical DC cardioversion under amiodarone treatment. Nineteen of the 22 patients were successfully converted to sinus rhythm (SR). The patients were evaluated with transthoracic echocardiography before and two to three days after DC cardioversion. In order to deal with variable R-R intervals, the measurements were averaged on five to eight consecutive beats in AF. Cn was calculated with a previously validated equation [Cn (mL/mm Hg)=1.270 x MVA/E-wave downslope]. The Cn difference between AF and SR was calculated as follows: [(AF Cn-SR Cn)/AF Cn] x 100. The percentage gradient (mean or maximal) difference between AF and SR was calculated as follows: [AF gradient (mean or maximal) - SR gradient (mean or maximal)]/[AF gradient (mean or maximal)] x 100.

RESULTS

The MVA was lower (MVA planimetric; 1.62±0.29 vs. 1.54±0.27; p=.003, MVA PHT; 1.66±0.30 vs. 1.59±0.26; p=0.01) but transmitral gradient (mean gradient; 6.49±2.51 vs. 8.89±3.52; p=0.001, maximal gradient: 16.94±5.11 vs. 18.57±4.54; p=0.01) and Cn values (5.37±0.77 vs. 6.26±0.64; p<0.001) were higher in the AF than SR. There was a significant correlation between Cn difference and transmitral gradient difference (mean and maximal) (Cn difference-mean gradient difference; r=0.46; p=0.05; Cn difference-maximal gradient difference; r=0.72; p=0.001).

CONCLUSION

Cardiac rhythm has a significant impact on echocardiographic evaluation of MVA, transmitral gradient, and Cn in patients with MS.

Impact of net atrioventricular compliance on clinical outcome in mitral stenosis

BACKGROUND

Net atrioventricular compliance (Cn) has been reported to be an important determinant of pulmonary hypertension in mitral stenosis (MS). We hypothesized that it may be useful in assessing prognosis because Cn reflects hemodynamic consequences of MS. To date, limited data with an assumed Cn cutoff have indicated the need for larger prospective studies. This prospective study was designed to determine the impact of Cn on clinical outcome and its contribution to pulmonary pressure in MS. In addition, we aimed to identify a cutoff value of Cn for outcome prediction in this setting.

METHODS AND RESULTS

A total of 128 patients with rheumatic MS without other significant valve disease were prospectively enrolled. Comprehensive echocardiography was performed and Doppler-derived Cn estimated using a previously validated equation. The end point was either mitral valve intervention or death. Cn was an important predictor of pulmonary pressure, regardless of classic measures of MS severity. During a median follow-up of 22 months, the end point was reached in 45 patients (35%). Baseline Cn predicted outcome, adding prognostic information beyond that provided by mitral valve area and functional status. Cn ≤4 mL/mm Hg best predicted unfavorable outcome in derivation and validation sets. A subgroup analysis including only initially asymptomatic patients with moderate to severe MS without initial indication for intervention (40.6% of total) demonstrated that baseline Cn predicted subsequent adverse outcome even after adjustment for classic measures of hemodynamic MS severity (hazard ratio, 0.33; 95% confidence interval, 0.14-0.79; P=0.013).

CONCLUSIONS

Cn contributes to pulmonary hypertension beyond stenosis severity itself. In a wide spectrum of MS severity, Cn is a powerful predictor of adverse outcome, adding prognostic value to clinical data and mitral valve area. Importantly, baseline Cn predicts a progressive course with subsequent need for intervention in initially asymptomatic patients. Cn assessment therefore has potential value for clinical risk stratification and monitoring in MS patients.

Effect of left atrial compliance on pulmonary artery pressure: a case report

Background

Left ventricular diastolic dysfunction, with secondary atrial pressure elevation, is a well-known concept. On the contrary, effect of left atrial compliance on pulmonary pressure is rarely considered.

Case presentation

We report the echocardiographic case of a 9-year-old child who presented severe rheumatic mitral valve regurgitation with a giant left atrium, in contrast to a normal artery pulmonary pressure, testifying of the high left atrial compliance.

Conclusion

Left atrial compliance is an important determinant of symptoms and pulmonary artery pressure in mitral valve disease.

Effect of chamber capacitance on Doppler flow pattern across restrictive defects in obligatory atrial-level shunts

The right atrium has a significantly higher capacitance than the left atrium, and this may affect the Doppler flow pattern across an atrial septal defect (ASD) in unilateral atrioventricular (AV) valve atresia. This Doppler flow pattern is often used to assess ASD adequacy in this setting. We studied the effect of atrial capacitance and ASD size on the trans-ASD Doppler flow pattern in an in vivo flow model of alternate left or right AV valve atresia (LAVVA and RAVVA). We assessed trans-ASD Doppler flow patterns using the max/min velocity ratio and mean interatrial pressure gradients (PGs). In both models, ASD flow rate correlated with mean trans-ASD PG, but for similar flow rates the slope was higher in the LAVVA model. In LAVVA, a persistent PG was consistently observed, with low max/min ratio (median, 1.46; range, 1.03-3.13), whereas in RAVVA, phasic flow was common (median, 8.0; range, 2.8-20). Because atrial capacitance affects mean PG and Doppler flow pattern across the ASD, we propose that the assessment of ASD adequacy in RAVVA should not rely on Doppler findings.

Time-varying effective mitral valve area: prediction and validation using cardiac MRI and Doppler echocardiography in normal subjects

Precise knowledge of the volume and rate of early rapid left ventricular (LV) filling elucidates kinematic aspects of diastolic physiology. The Doppler E wave velocity-time integral (VTI) is conventionally used as the estimate of early, rapid-filling volume; however, this implicitly requires the assumption of a constant effective mitral valve area (EMVA). We sought to evaluate whether the EMVA is truly constant throughout early, rapid filling in 10 normal subjects using cardiac magnetic resonance imaging (MRI) and contemporaneous Doppler echocardiography, which were synchronized via ECG. LV volume measurements as a function of time were obtained via MRI, and transmitral flow values were measured via Doppler echocardiography. The synchronized data were used to predict EMVA as a function of time during early diastole. Validation involved EMVA determination using 1) the short-axis echocardiographic images near the mitral valve leaflet tips, 2) the distance between leaflet tips in the echocardiographic parasternal long-axis view, and 3) the distance between leaflet tips from the MRI LV outflow tract view. Predicted EMVA values varied substantially during early rapid filling, and observed EMVA values agreed well with predictions. We conclude that the EMVA is not constant, and its variation causes LV volume to increase faster than is reflected by the VTI. These results reveal the mechanism of early rapid volumetric increase and directly affect the significance and physiological interpretation of the VTI of the Doppler E wave. Application to subjects in selected pathophysiological subsets is in progress.

The wall-thinning to transmitral flow-velocity relation: derivation with in vivo validation

Motion of the endocardial surface in diastole is the resultant effect of wall thinning. Endocardial wall motion to transmitral flow (Doppler E-wave) relations that predict wall thinning are derived using conservation of myocardial volume, two simplified (spatiotemporally homogeneous) left ventricular (LV) geometric models and the constant-volume pump attribute of the heart. For validation, model-predicted vs. color M-mode recorded maximum rate of wall thinning was compared in (n = 15) normal controls. Excellent agreement for both models (r = 0.84, r = 0.86) was observed. For abnormal LV function (n = 15), model-predicted vs. M-mode recorded maximum rate of wall-thinning correlated poorly (r = -0.28, r = -0.22). We conclude that, in normal ventricles, the Doppler E-wave and wall thinning are related through the constant-volume attribute of the heart and its geometry. Pathologic cases are governed by the same principles, but the filling to wall-thinning relation is altered by spatiotemporal inhomogeneities in geometry and wall motion.

Spatio-temporal mapping of intracardiac pressure gradients. A solution to Euler's equation from digital postprocessing of color Doppler M-mode echocardiograms

Doppler assessment of intracardiac pressure gradients using the simplified Bernoulli equation is inaccurate in the absence of a restricted orifice. The purpose of this study is to develop a new general method to map instantaneous pressure gradients inside the heart using Doppler echocardiography. Color Doppler M-mode recordings are digitally postprocessed with a software algorithm that decodes flow velocity and fits a bivariate spatio-temporal tensor-product smoothing spline. Temporal and spatial accelerations are then calculated by analytical derivation of the fitted velocity data, allowing solution of both inertial and convective terms of Euler's equation. A database of 39 transmitral inflow and transaortic outflow color Doppler M-mode recordings from 20 patients with a number of cardiac conditions was analysed, along with matched pulsed-wave spectral recordings. A close agreement was observed between the spectral and postprocessed color Doppler velocity values (error = 0.8 +/- 11.7 cm/s), validating the data decoding and fitting process. Spatio-temporal pressure-gradient maps were obtained from all studies, allowing visualisation of instantaneous pressure gradients from the atrium to the apex during left ventricular filling, and from the apex to the outflow tract during ejection. Instantaneous pressure differences between localised intracardiac sample points closely matched previously published catheterization findings, both in magnitude and waveform shape. Our method shows that intracardiac instantaneous pressure gradients can be analysed noninvasively using color Doppler M-mode echocardiography combined with image postprocessing methods.

Impact of atrioventricular compliance on pulmonary artery pressure in mitral stenosis: an exercise echocardiographic study

BACKGROUND

The decay of the pressure gradient across a stenotic mitral valve is determined by the size of the orifice and net AV compliance (C(n)). We have observed a group of symptomatic patients, usually in sinus rhythm, characterized by pulmonary hypertension (particularly during exercise) despite a relatively large mitral valve area by pressure half-time. We speculated that this discrepancy was due to low atrial compliance causing both pulmonary hypertension and a steep decay of the transmitral pressure gradient despite significant stenosis. We therefore tested the hypothesis that C(n) is an important physiological determinant of pulmonary artery pressure at rest and during exercise in mitral stenosis.

METHODS AND RESULTS

Twenty patients with mitral stenosis were examined by Doppler echocardiography. C(n), calculated from the ratio of effective mitral valve area (continuity equation) and the E-wave downslope, ranged from 1.7 to 8.1 mL/mm Hg. Systolic pulmonary artery pressure (PAP) increased from 43+/-12 mm Hg at rest to 71+/-23 mm Hg (range, 40 to 110 mm Hg) during exercise. There was a particularly close correlation between C(n) and exercise PAP (r=-0.85). Patients with a low compliance were more symptomatic (P<0.025). Catheter- and Doppler-derived values for C(n), determined in 10 cases, correlated well (r=0.79).

CONCLUSIONS

C(n), which can be noninvasively assessed, is an important physiological determinant of PAP in mitral stenosis. Patients with low C(n) represent an important clinical entity, with symptoms corresponding to severe increases in PAP during stress echocardiography.

Modeling of diastole

Modeling methods have been employed to further characterize the physical and physiologic processes of filling and diastolic function. They have led to more detailed understanding of the effect of alteration of physiologic parameters on the Doppler E-wave contour as well as pulmonary vein flow. Depending on the modeling approach, different aspects of the filling process have been considered from AV gradient and net compliance to atrial appendage function to the mechanical suction pump attribute of the heart. The models have been applied for further characterization of diastolic function and elucidation of novel basic physiologic relations. We trust that readers recognize that this article could not serve as a comprehensive and global review of the state-of-the-art in physiologic modeling, but rather as a selective overview, with emphasis on the main modeling principles and options currently in use. Modeling of systems physiology, especially as it relates to the function of the four-chamber heart, remains a fertile area of investigation. Future progress is likely to have profound influence on (noninvasive) diagnosis and quantitation of the effect of therapy and lead to continued discovery of "new" (macroscopic, cellular, and molecular biologic) physiology.

Effect of aortic compliance on Doppler diastolic flow pattern in coarctation of the aorta

The spectral Doppler pattern at the site of an aortic coarctation (CoA) generally displays increased maximal velocity (Vmax) during systole with a slow velocity decay, resulting in the characteristic "sawtooth" pattern. If there is rapid velocity decay, the obstruction is often judged to be mild. The purpose of this study was to investigate if velocity decay is affected by proximal aortic compliance (C(p)). The relation between the velocity decay measured from the Doppler pattern and C(p) was studied with the use of an in vitro pulsatile flow model. The time (tau) between Vmax and 33% Vmax was the measure of velocity decay. The C(p) was varied from 0.7 to 2.6 mL/mm Hg for each of 4 levels of CoA severity. The various obstructions produced a Vmax range of 2.7 to 5.5 m/s. There was a positive linear relation between tau and C(p) (r(2) = 0.76). For a low C(p) (compliance = 0.7 mL/mm Hg), velocity decay was rapid (tau = 0.2 to 0.3 seconds) with no diastolic gradient. For equivalent obstructions, a high C(p) (2.6 mL/mm Hg) produced a persistent diastolic gradient and slow velocity decay (tau = 0.5 to 0.6 seconds). The Doppler pattern across a CoA is affected by C(p). Therefore, the absence of a sawtooth pattern should not exclude the diagnosis of significant CoA obstruction.

Balloon mitral valvuloplasty: comparison of haemodynamic and echocardiographic assessment of mitral stenosis at different heart rates in the catheterisation laboratory

AIMS

To compare echo-Doppler, Gorlin equation and haemodynamic methods of measuring mitral valve stenosis during right ventricular pacing-induced tachycardia before and after Inoue balloon mitral valvuloplasty to determine which method gave the most consistent results.

METHODS AND RESULTS

Measurements were made before and after valvuloplasty at: baseline heart rates, paced at 115 and then 145 beats/min. Mitral valve area by echo-Doppler was 1.1(+/-0.1) cm2 (mean +/- S.E.) before and 1.8(+/-0.2) cm2 after valvuloplasty; and by Gorlin equation: 0.9(+/-0.1) cm2 before and 1.5(+/-0.1) cm2 after. Echo-Doppler measurements were heart rate dependent but those by Gorlin measurements were not. At baseline, cardiac index was 2.08(+/-0.2) l min(-1), left atrial pressure 23.3(+/-7.9) mm Hg and mean mitral diastolic gradient 16.9(+/-9.9) mm Hg. After valvuloplasty, cardiac index was 2.31(+/-0.1) l min(-1), left atrial pressure fell to 19.2(+/-5.6) mm Hg and mean diastolic gradient was reduced to 8.5(+/-1.8) mm Hg.

CONCLUSIONS

The Gorlin mitral valve area appeared to be the most heart rate independent indicator of success following valvuloplasty.

Pulsed tissue Doppler evaluation of mitral annulus motion: a new window to assessment of diastolic function

Diastolic dysfunction is an important cause of cardiac heart failure. To date detailed assessment of diastolic left ventricular (LV) function has required invasive methods which are impractical in the clinical routine. The prevailing non-invasive method has been Doppler echocardiography with use of mitral inflow and pulmonary vein inflow parameters, measurements providing no direct assessment of either ventricular relaxation or compliance, and influenced by multiple haemodynamic factors. We sought to determine the tissue Doppler pattern from the mitral annulus motion in normals and in patients with expected LV-diastolic dysfunction. Using pulsed tissue Doppler we recorded peak velocities from the mitral annulus motion in 16 young normals, 10 older normals and in two groups of patients expected to have an LV-diastolic relaxation abnormality, i.e. 15 patients with systemic hypertension and 10 patients with significant aortic stenosis. The peak early diastolic (E) annulus velocity was significantly (P < 0.001) lower in older normals compared with young, and the late diastolic velocity (A) was higher (P < 0.01). Compared with the older normals, patients showed significantly lower E-velocities (P < 0.05 hypertensive patients), more pronounced in the patients with aortic stenosis (P < 0.001), but the A-velocities were not higher. In systole a decrease in peak velocity was noted with increasing age and in patients with aortic stenosis. In conclusion, pulsed tissue Doppler measurement of annulus motion seems to provide valuable and easily obtainable information about LV-diastolic function, and furthermore there is striking change in velocity pattern with increasing age which necessitates age-matched reference values.

New Doppler echocardiographic applications for the study of diastolic function

Doppler echocardiography is one of the most useful clinical tools for the assessment of left ventricular (LV) diastolic function. Doppler indices of LV filling and pulmonary venous (PV) flow are used not only for diagnostic purposes but also for establishing prognosis and evaluating the effect of therapeutic interventions. The utility of these indices is limited, however, by the confounding effects of different physiologic variables such as LV relaxation, compliance and filling pressure. Since alterations in these variables result in changes in Doppler indices of opposite direction, it is often difficult to determine the status of a given variable when a specific Doppler filling pattern is observed. Recently, color M-mode and tissue Doppler have provided useful insights in the study of diastolic function. These new Doppler applications have been shown to provide an accurate estimate of LV relaxation and appear to be relatively insensitive to the effects of preload compensation. This review will focus on the complementary role of color M-mode and tissue Doppler echocardiography and traditional Doppler indices of LV filling and PV flow in the assessment of diastolic function.

Left ventricular diastolic filling with an implantable ventricular assist device: beat to beat variability with overall improvement

OBJECTIVES

We studied the effects of left ventricular (LV) unloading by an implantable ventricular assist device on LV diastolic filling.

BACKGROUND

Although many investigators have reported reliable systemic and peripheral circulatory support with implantable LV assist devices, little is known about their effect on cardiac performance.

METHODS

Peak velocities of early diastolic filling, late diastolic filling, late to early filling ratio, deceleration time of early filling, diastolic filling period and atrial filling fraction were measured by intraoperative transesophageal Doppler echocardiography before and after insertion of an LV assist device in eight patients. A numerical model was developed to simulate this situation.

RESULTS

Before device insertion, all patients showed either a restrictive or a monophasic transmitral flow pattern. After device insertion, transmitral flow showed rapid beat to beat variation in each patient, from abnormal relaxation to restrictive patterns. However, when the average values obtained from 10 consecutive beats were considered, overall filling was significantly normalized from baseline, with early filling velocity falling from 87 +/- 31 to 64 +/- 26 cm/s (p < 0.01) and late filling velocity rising from 8 +/- 11 to 32 +/- 23 cm/s (p < 0.05), resulting in an increase in the late to early filling ratio from 0.13 +/- 0.18 to 0.59 +/- 0.38 (p < 0.01) and a rise in the atrial filling fraction from 8 +/- 10% to 26 +/- 17% (p < 0.01). The deceleration time (from 112 +/- 40 to 160 +/- 44 ms, p < 0.05) and the filling period corrected by the RR interval (from 39 +/- 8% to 54 +/- 10%, p < 0.005) were also significantly prolonged. In the computer model, asynchronous LV assistance produced significant beat to beat variation in filling indexes, but overall a normalization of deceleration time as well as other variables.

CONCLUSIONS

With LV assistance, transmitral flow showed rapidly varying patterns beat by beat in each patient, but overall diastolic filling tended to normalize with an increase of atrial contribution to the filling. Because of the variable nature of the transmitral flow pattern with the assist device, the timing of the device cycle must be considered when inferring diastolic function from transmitral flow pattern.

Quantitative assessment of diastolic filling function: a new Doppler echocardiographic method and in vitro validation

The effects of changes in preload and chamber compliance on the transmitral flow pattern was investigated with a fluid dynamics model. A decrease in compliance led to a steepening of the deceleration slope and a shortening of the pressure half-time in both restricted and nonrestricted valves. An increase in the preload led to a longer pressure half-time but did not affect the slope in the restricted valve. However, increased preload led to a shorter pressure half-time and a steeper slope in the nonrestricted valve. A mathematically derived method to measure the net atrioventricular compliance (-[annular area] va/[pvt [flow deceleration rate]]), where va and vt are flow velocities at the mitral anulus and the mitral tip levels) was then proposed. The values obtained by this method showed a strong correlation with true values (r2 = 0.89). A possibility of noninvasive quantitative assessment of diastolic filling function was implied.

Quantification of Mitral and Tricuspid Regurgitation Using Jet Centerline Velocities: An In Vitro Study of Jets in an Ambient Counterflow

A method for quantifying mitral and tricuspid regurgitant volume that utilizes a measure of jet orifice velocity U(0) - m/sec), a distal centerline velocity (U(m) - m/sec), and the intervening distance (X - cm) was recently developed; where jet flow rate (Q(cal) - L/min) is calculated as Q(cal) = (U(m)X)(2)/(26.46U(o)). 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 concentrated on the feasibility of using the free jet quantification equation in the atrium where ambient flow fields may alter jet centerline velocities and reduce the accuracy of jet flow rate calculations. A 4-cm wide chamber was used to pump counterflows of 0, 4, and 22 cm/sec against jets of 2.3, 4.8, and 6.4 m/sec 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 (U(o)/U(c), where U(c) is counterflow velocity), i.e., the counterflow was relatively more intense, and (ii) centerline measurements were made 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 (X/D > 16, i.e., >16 orifice diameters from the origin of the jet). Thus, the initial portion (X/D < 16) of a jet in counterflow behaved essentially as a free jet. As a result, even in significant counterflow, jet flow rate was calculated with >93% accuracy and >85% for jets typical of mitral and tricuspid regurgitation, respectively. Counterflow lowers jet centerline velocities beneath equivalent free jet values. This effect, however, is most significant in the distal portion of the jet. Therefore, regurgitant jets, although not classically free because of systolic atrial inflow or jet-induced intra-atrial swirling flows, will decay in their initial portions as free jets and thus are candidates for quantification with the centerline technique. (ECHOCARDIOGRAPHY, Volume 13, July 1996)

In vivo validation of a fluid dynamics model of mitral valve M-mode echocardiogram

A fluid dynamics model of mitral valve motion during diastolic filling of the left heart is described. Given a pulsed Doppler velocity pattern in the mitral annulus, the radius of circular mitral orifice, the length of leaflets and the end-systolic left ventricular volume, the numerical model predicts the time course of the mitral leaflets during diastole: the mitral valve M-mode echocardiogram. Results obtained by computer simulation have been validated with in vivo data. It is shown that mitral valve flow is essentially a fluid dynamics process of floating mitral valve leaflets with blood flow due to the atrioventricular pressure gradient. In addition, a partial opening of the mitral valve as the initial boundary condition is required to simulate the overshooting of the leaflets during early peak filling. Some back flow is a condition for perfect closing of the native mitral valve. The higher the unsteady character of mitral flow, the less efficient is the opening and closing processes of the mitral valve.

Newer Doppler measures of left ventricular diastolic function

Left ventricular (LV) diastolic dysfunction is an important cause of heart failure, and recent advances in the application of Doppler techniques allow a semiquantitative assessment of LV diastolic performance. This review discusses the use of Doppler echocardiography in the comprehensive assessment of LV diastolic function and performance in terms of the normal mitral and pulmonary venous flow profiles, their physiologic basis, and alterations in diseased states. There is also a discussion on the newer aspects of mitral flows such as relative durations of mitral A and pulmonary vein AR waves, E- and A- wave propagation inside the LV with their hemodynamic correlates, and derivation of ventricular dP/dt and Tau from the mitral regurgitation velocity profile. Analysis of these flow profiles and the other Doppler measures alluded to above allow one to make a fairly precise hemodynamic assessment of a patient in terms of left atrial pressure, LV relaxation and stiffness and the profile of LV diastolic pressure in terms of pre- 'a' wave and 'a' wave pressures and ventricular end-diastolic pressure.

Initial and subsequent angiographic outcome of percutaneous transluminal angioplasty performed on internal mammary artery grafts

OBJECTIVE

To estimate the initial outcome and incidence of restenosis of angioplasty of internal mammary artery grafts in a retrospective study.

METHODS

The study population consisted of 46 patients (48 lesions) who underwent first balloon angioplasty within the internal mammary artery graft. Most (37/48) were at the distal anastomosis. A few (8/48) were in the graft body. Six patients with the evidence of angiographic restenosis underwent a second angioplasty.

RESULTS

The success rate and the restenosis rate of the first angioplasty was 73% and 30% respectively. Of the 34 patients (35 lesions) with a successful first angioplasty, 30 underwent follow up angiography with a restenosis rate of 30% (9/30). A second angioplasty was performed on six of the nine restenotic lesions, with a success rate of 83% and no restenoses. The percent diameter stenosis of the recipient native coronary artery was significantly greater in the restenosis group, at 75 (SD 27)% v 89 (17)%, p < 0.05.

CONCLUSIONS

First angioplasty of 46 patients (48 lesions) within an internal mammary artery graft was performed with a success rate of 73% and a restenosis rate of 30% (follow up rate of 88%). The extent of the stenosis of the recipient native coronary artery may affect the restenosis rate.

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.

Comparison of proximal isovelocity surface area method with pressure half-time and planimetry in evaluation of mitral stenosis

OBJECTIVES

This study sought to 1) compare the accuracy of the proximal isovelocity surface area (PISA) and Doppler pressure half-time methods and planimetry for echocardiographic estimation of mitral valve area; 2) evaluate the effect of atrial fibrillation on the accuracy of the PISA method; and 3) assess factors used to correct PISA area estimates for leaflet angulation.

BACKGROUND

Despite recognized limitations of traditional echocardiographic methods for estimating mitral valve area, there has been no systematic comparison with the PISA method in a single cohort.

METHODS

Area estimates were obtained in patients with mitral stenosis by the Gorlin hydraulic formula, PISA and pressure half-time method in 48 patients and by planimetry in 36. Two different factors were used to correct PISA estimates for leaflet angle (theta): 1) plane-angle factor (theta/180 [theta in degrees]); and 2) solid-angle factor [1-cos(theta/2)].

RESULTS

After exclusion of patients with significant mitral regurgitation, the correlation between Gorlin and PISA areas (0.88) was significantly greater (p < 0.04) than that between Gorlin and pressure half-time (0.78) or Gorlin and planimetry (0.72). The correlation between Gorlin and PISA area estimates was lower in atrial fibrillation than sinus rhythm (0.69 vs. 0.93), but the standard error of the estimate was only slightly greater (0.24 vs. 0.19 cm2). The average ratio of the solid- to the plane-angle correction factors was approximately equal to previously reported values of the orifice contraction coefficient for tapering stenosis.

CONCLUSIONS

1) The accuracy of PISA area estimates in mitral stenosis is at least comparable to those of planimetry and pressure half-time. 2) Reasonable accuracy of the PISA method is possible in irregular rhythms. 3) A simple leaflet angle correction factor, theta/180 (theta in degrees), yields the physical orifice area because it overestimates the vena contracta area by a factor approximately equal to the contraction coefficient for a tapering stenosis.

Findings of automatic border detection in subjects with left ventricular diastolic dysfunction by Doppler echocardiography

Left ventricular automatic border detection (ABD) patterns were defined in the parasternal short-axis and the apical four-chamber views and were compared with pulsed-wave diastolic Doppler flow-velocity patterns of the mitral valve in 49 subjects (aged 39 to 87 years), 10 selected normal individuals, and 39 consecutive patients with high-quality echocardiographic Doppler studies and relaxation abnormalities (Doppler peak early diastolic velocity/peak late velocity ratio < 1). Both short-axis and apical four-chamber views were useful in the assessment of diastolic function by ABD. However, in subjects with high-quality two-dimensional echocardiographic Doppler studies, ABD was technically more feasible in the apical four-chamber view (97%; 38/39 subjects) than in the short-axis view (64%; 25/39 subjects) and correlated better with Doppler parameters. Compared with normal subjects, patients with abnormal Doppler relaxation patterns showed significant differences in diastolic filling indexes obtained by the ABD technique. The ratio of peak rapid filling rate/peak atrial filling rate (PRFR/PAFR) obtained from the dA/dt waveform in the apical four-chamber view had the highest correlation with Doppler indexes (r = 0.79). A PRFR/PAFR ratio of 1.5 best discriminated between normal individuals and subjects with relaxation abnormalities, with high sensitivity and specificity (95% and 100%, respectively). The PRFR/PAFR ratio obtained from the dA/dt waveform seemed to be a simple and useful method to distinguish between normal and abnormal left ventricular diastolic filling, as defined by Doppler echocardiography.

Comparison of diastolic filling models and their fit to transmitral Doppler contours

Anatomic/physiologic and kinematic mathematical models of diastolic filling which employ (lumped) parameters of diastolic function have been used to predict or characterize transmitral flow. The ability to determine model parameters from clinical transmitral flow, the Doppler velocity profile (DVP), is equivalent to solving the "inverse problem" of diastole. Systematic model-to-model and model-to-data comparison has never been carried out, in part due to the requirement that DVPs be digitized by hand. We developed, tested and verified a computerized method of DVP acquisition and reproduction, and carried out numerical determination of model-to-model and model-to-data goodness-of-fit. The transmitral flow velocity of two anatomic/physiologic models and one kinematic model were compared. Each model's ability to fit computer-acquired and reproduced transmitral DVPs was assessed. Results indicate that transmitral flow velocities generated by the three models are 'graphically indistinguishable and are able to fit the E-wave of clinical DVPs with comparable mean-square errors. Nonunique invertibility of the anatomic/physiologic models was verified, i.e., multiple sets of model parameters could be found that fit a single DVP with comparable mean-square error. The kinematic formulation permitted automated, unique, model-parameter determination, solving the "inverse problem" for the Doppler E-wave. We conclude that automated, quantitative characterization of clinical Doppler E-wave contours using this method is feasible. The relation of kinematic parameters to physiologic variables is a subject of current investigation.

Left ventricular systolic and diastolic function, and exercise capacity six to eight weeks after acute myocardial infarction. The DEFIANT Study Group. Doppler Flow and Echocardiography in Functional Cardiac Insufficiency: Assessment of Nisoldipine Therapy

Echocardiographic and Doppler-derived measurements of left ventricular (LV) function at rest were examined as predictors of maximal bicycle exercise capacity in a homogeneous group of 115 patients with mild to moderate LV dysfunction (ejection fraction 22 to 56%, median 43%) participating in the DEFIANT study of nisoldipine after acute myocardial infarction. Although the relations were not exact, peak exercise work load 7 weeks after infarction correlated with measurements of diastolic LV function at rest. Exercise work load was inversely related to peak late diastolic transmitral blood flow velocity (A wave) (slope -86.6; 95% confidence interval -120.9 to -52.2) and directly to the E/A ratio (slope 20.5; 95% confidence interval 6.0 to 35.1). The relations between exercise work load and peak late diastolic flow velocity remained significant after correction for age, sex, heart rate at rest, and use of beta-blocking drugs or nisoldipine. There was no relation between peak exercise work load and peak early diastolic transmitral flow velocity (E wave), isovolumic relaxation period or deceleration time. Measurements of systolic LV function (LV end-diastolic and end-systolic volumes, and ejection fraction, stroke volume and cardiac index) were also not significant as predictors of exercise capacity.

Echocardiographic description of the CarboMedics bileaflet prosthetic heart valve

OBJECTIVES

The aim of this study was to describe the echocardiographic appearance of the normal CarboMedics prosthesis in the aortic and mitral positions.

BACKGROUND

Echocardiography is the standard method of assessing prosthetic valves. However, new valve designs may still be marketed without an accompanying echocardiographic description. The CarboMedics prosthesis is in widespread use, but few noninvasive hemodynamic data have been published.

METHODS

Echocardiography was performed in 147 patients with a total of 96 normally functioning CarboMedics prostheses in the aortic position and 75 in the mitral position; in 24 patients, valves were implanted in both positions. The following variables were measured: peak and mean transvalvular velocities, peak and mean instantaneous gradient estimated from the modified Bernoulli equation, aortic acceleration slope, pressure half-time, transvalvular flow and effective orifice area using the continuity equation. Patterns of regurgitation were observed by transthoracic study in all valves and by transesophageal study in selected mitral valve prostheses.

RESULTS

For the aortic valve prostheses, estimated mean gradient ranged between 6 and 19 mm Hg. Effective area differed markedly among the anulus diameters (p < 0.001), with a mean value of 1 cm2 for the 19-mm valve and 2.6 cm2 for the 29-mm valve. For the mitral valve prostheses, mean gradient ranged from 3 to 7 mm Hg. There were a total of four washing leaks, one on either side of each pivotal point, and these lasted throughout systole or diastole. One jet was commonly more prominent than the other three.

CONCLUSIONS

The CarboMedics prosthesis offered relatively little resistance to forward flow except at small anulus diameters. The washing jets were prominent and would be easy to misdiagnose as a sign of paraprosthetic regurgitation.

Computer-controlled in vitro model of the human left heart

The decision for surgical intervention in the treatment of stenosis and for regurgitation of the mitral valve demands an objective and quantitative evaluation of the severity of mitral valve disease. The availability of ultrasound techniques capable of analysing flow velocities across valves and to produce representative images of valve orifices has increased the interest in the hydraulics of cardiac valves. To isolate and study the determinants of transmitral flow, an in vitro model of the human left heart was built. From the model it is possible to differentiate the influence of the different determinants of left heart performance on transmitral flow: preload, compliance of the left atrium and ventricle, peripheral resistance (afterload) and heart rate. The mechanical part of the model consists of a reservoir connected to an elastic closed circuit (Latex pulmonary veins, left atrium, left ventricle and aortic arch) with replaceable mitral and aortic valves. The electronic part of the model drives and controls the hydraulic part, allowing the independent regulation and monitoring of left atrial and left ventricular pressures p, volumes V and 'pV-loops' throughout the cardiac cycle at different cardiac rhythms. Left atrial filling pressure and aortic resistance are variable in a controlled fashion. Echo-Doppler study of the mitral valve and the transmitral valve flow is possible both from an atrial and a ventricular window in the model. This technical note describes the model.

Variation in the color Doppler area of a regurgitant jet with changes in the absolute chamber pressure: an in vitro study

The color Doppler appearance of a regurgitant jet depends on jet momentum, determined in part by the pressure difference between the two chambers. However, it is not clear if absolute chamber pressure has an independent effect on jet area. To test this question, an in vitro experiment was performed in which dynamically decaying jets were created with identical initial pressure gradients but five different levels of absolute chamber pressures. At every level of chamber pressure, color Doppler images were recorded with two different transducers (3.5 and 5.0 MHz) and jet areas were measured at four different flow rates (0 to 9.9 cm3/sec). A multilinear regression model was created with jet area as the dependent variable and jet flow rate, transducer frequency, and absolute chamber pressure as independent parameters. Jet area was most strongly predicted by flow rate (univariate r = 0.90) and transducer frequency (r = 0.32). Even after adjusting for these effects, however, a small but significant (p less than 0.0001) effect of absolute chamber pressure on jet area was seen with jet area rising by 0.89 cm2 for each 10 mm Hg increase in absolute chamber pressure (multivariate r = 0.96, p less than 0.0001). We conclude that the color Doppler area of a regurgitant jet is dependent not only on the relative pressure and flow between the two chambers but also on the absolute chamber pressure.

A theoretical model for the noninvasive assessment of the transmitral pressure-flow relation

The purpose of this paper is to formulate from the equations of fluid mechanics an equation which describes the transmitral pressure-flow relationship. According to the linear momentum equation applied to the atrioventricular coupling, the left-atrium-left-ventricle pressure difference (Pa-Pv) can be written as Pa-P v = A delta v/delta t + B v 2 + C v, where v is the transmitral blood velocity and A, B, and C are variables related to the geometry of the atrium, ventricle and mitral orifice, respectively. Based on this theory, Pa-Pv is calculated noninvasively in a patient with a nonobstructive mitral valve. Mitral flow and cardiac dimensions recorded by Doppler echocardiography are digitized and analyzed. Calculation shows that Pa-Pv reaches its peak value at the time of flow peak acceleration and has already considerably decreased at the time of peak velocity. The time course of calculated Pa-Pv is in close agreement with the published experimental catherization data. Numerical computation of early diastolic left atrium and left ventricle pressure curves based on the experimental data of others for the time constant of left ventricular relaxation, left atrial and ventricular chambers stiffness constants, combined with sine-waveform-simulated mitral flow, verifies the time course and the magnitude of Pa-Pv as predicted from flow equations. This paper provides a theoretical method for the noninvasive assessment of the transmitral pressure-flow relationship using ultrasound technique and might help to achieve a better understanding of the diastolic function as assessed by Doppler echocardiography.

The Hatle orifice area formula tested in normal bileaflet mechanical mitral prostheses

The Hatle formula was derived empirically in native mitral stenosis and may not be valid for normal prosthetic valves. Bileaflet mechanical prostheses open fully at low flows and have minimal interindividual variation in orifice area. In these valves effective area and measured manufacturer's area should be similar. We studied 60 patients aged 58 +/- 12 yr at a mean of 5 months after implantation with a CarboMedics prosthesis. There was a coexistent aortic prosthesis in 21. All diastolic measurements were averaged over 5 beats and stroke volume was calculated from the integral of the subaortic velocity trace and the cross-sectional area of the left ventricular outflow tract. For the whole group, area by the Hatle formula was 3.1 +/- 0.7 cm2 and measured area was 2.8 +/- 0.4 cm2. There was no significant correlation between these values (p = 0.329). Pressure half-time was more closely correlated with peak transmitral velocity (p = 0.012), RR interval (p = 0.015), diastolic time interval (p = 0.062) and stroke volume (p = 0.074). We conclude that the Hatle formula should not be applied to normal bileaflet mitral prostheses where pressure half-time reflects nonprosthetic factors more closely than orifice area.

Estimation of mitral valve area from regression analysis of the pressure gradient in mitral stenosis

Estimation of mitral valve area (MVA) in the cardiac catheterization laboratory is prone to pitfalls because of the time required for calculations and inaccuracies in the measurement of cardiac output. Because the rate of decrease in the mitral gradient directly correlates with the severity of mitral stenosis, an on-line estimate of MVA at the time of catheterization may be possible with regression analysis of digitized pressure recordings. A total of 61 comparisons of mitral gradient measurements and MVA were obtained in 37 patients at diagnostic catheterization and in 24 patients after balloon mitral valvotomy. Linear and nonlinear regression parameters yielded pressure half-time values and empiric constants similar to those used in Doppler echocardiography for estimation of MVA. The correlations derived from linear analysis were as good as those obtained from nonlinear analysis: from linear analysis, MVAregression = 0.79.MVAGorlin -0.03; r2 = 0.64, p = 0.0001; and from double exponential analysis, MVAregression = 0.86.MVAGorlin -0.07; r2 = 0.74; p = 0.0001. The correlations were not significantly affected by the presence of mild to moderate mitral regurgitation or whether they were obtained after balloon valvotomy. In summary, linear regression analysis yields accurate estimates of MVA despite the theoretical superiority of nonlinear methods. On-line digital analysis of mitral gradient tracings may thus be useful at the time of diagnostic cardiac catheterization or balloon mitral valvotomy to assess the severity of mitral stenosis and the response to interventions.

Calculation of atrioventricular compliance from the mitral flow profile: analytic and in vitro study

The quantitative assessment of ventricular diastolic function is an important goal of Doppler echocardiography. Hydrodynamic analysis predicts that the net compliance (Cn) of the left atrium and ventricle can be quantitatively predicted from the deceleration rate (dv/dt) of the mitral velocity profile by the simple expression: Cn = - A/rho dv/dt, where A is effective mitral valve area and rho is blood density. This formula was validated using an in vitro model of transmitral filling where mitral valve area ranged from 0.5 to 2.5 cm2 and net compliance from 0.012 to 0.023 cm3/(dynes/cm2) (15 to 30 cm3/mm Hg). In 34 experiments in which compliance was held constant throughout the filling period, net atrioventricular compliance was accurately calculated from the E wave downslope and mitral valve area (r = 0.95, p less than 0.0001). In a second group of experiments, chamber compliance was allowed to vary as a function of chamber pressure. When net compliance decreased during diastole (as when the ventricle moved to a steeper portion of its pressure-volume curve), the transorifice velocity profile was concave downward, whereas when net compliance increased, the velocity profile was concave upward. Application of the preceding formula to these curved profiles allowed instantaneous compliance to be calculated throughout the filling period (r = 0.93, p less than 0.001). Numeric application of a mathematic model of mitral filling demonstrated the accuracy of this approach in both restrictive and nonrestrictive orifices.(ABSTRACT TRUNCATED AT 250 WORDS)

Cardiac mechanics: basic and clinical contemporary research

This survey of cardiac hemodynamics updates evolving concepts of myocardial and ventricular systolic and diastolic loading and function. The pumping action of the heart and its interactions with arterial and venous systems in health and disease provide an extremely rich and challenging field of research, viewed from a fluid dynamic perspective. Many of the more important problems in this field, even if the fluid dynamics in them are considered in isolation, are found to raise questions which have not been asked in the history of fluid dynamics research. Biomedical engineering will increasingly contribute to their solution.

Numerical modeling of ventricular filling

The fluid dynamical and physiological assumptions underlying general mathematical modeling of ventricular filling are outlined. We then describe the use of a lumped parameter model and computer simulation to study how the early transmitral velocity profile is affected by isolated changes in ventricular compliance and relaxation, atrial pressure and compliance, and valvular morphology. We show that the transmitral velocity is fundamentally affected by two physical determinants: the transmitral pressure difference and the net compliance of the atrium and the ventricle. These physical determinants in turn are specified by the various physiologic parameters of interest. This approach has shown that peak velocity is most strongly affected by initial left atrial pressure, lowered somewhat by prolonged relaxation, low atrial and ventricular compliance, and systolic dysfunction. Peak acceleration is directly affected by atrial pressure and inversely affected by the time constant of isovolumic relaxation, with little influence of compliance, whereas the deceleration rate is almost purely given by mitral valve area divided by instantaneous atrioventricular compliance at the end of the rapid filling wave.

Alterations in transesophageal pulsed Doppler indexes of filling of the left ventricle after pericardiotomy

The impact of pericardial constraint on patterns of left ventricular filling was measured by transesophageal pulsed Doppler echocardiography in 30 patients undergoing elective nonvalvular cardiac surgery. Peak early left ventricular filling velocity increased from 0.52 +/- 0.11 to 0.56 +/- 0.15 m/s (p less than 0.05) and early left ventricular filling fraction increased from 60 +/- 9% to 65 +/- 9% (p less than 0.005) after pericardiotomy. The study group was retrospectively subdivided into two groups based on the prepericardiotomy mean right atrial pressure, an index of intrapericardial pressure and hence pericardial constraint. In 13 patients with a mean right atrial pressure less than 6 mm Hg, no significant changes in early left ventricular filling were evident after pericardiotomy. In 17 patients with a mean right atrial pressure greater than or equal to 6 mm Hg indicative of a greater degree of pericardial constraint before pericardiotomy, significant increases in peak early filling velocity (0.52 +/- 0.13 to 0.57 +/- 0.19 m/s, p less than 0.05), peak early filling rate (4.29 +/- 0.67 to 4.66 +/- 0.86 stroke volumes/s, p less than 0.05) and early left ventricular filling fraction (57 +/- 7% to 63 +/- 8%, p less than 0.001) were measured after pericardiotomy. Thus, the pericardium does constrain early left ventricular filling and its effects are more pronounced in patients with an elevated right atrial pressure.

Balloon expandable stent implantation of a stenosis at the origin of the left internal mammary artery graft: a case report

We describe a case of percutaneous transluminal coronary angioplasty in which we implanted a balloon expandable Palmaz-Schatz stent into a high-grade restenosed lesion at the origin of the left internal mammary graft.

Intravascular stenting of the right internal mammary artery

Despite its tortuous course and small caliber, percutaneous transluminal coronary angioplasty of the internal mammary artery can be performed with a high initial success rate (82-94%). The successful deployment of a balloon expandable coil stent at the mid-right internal mammary artery in a patient with recurrent stenosis of that graft is reported.

The effects of regurgitant orifice size, chamber compliance, and systemic vascular resistance on aortic regurgitant velocity slope and pressure half-time

The determinants of the aortic regurgitant velocity profile have been investigated using computer and in vitro simulations in which regurgitant orifice area, ventricular and aortic compliance, and systemic vascular resistance could be independently varied. In the study, regurgitant fraction was altered, either by changing the size of the regurgitant orifice or by holding the regurgitant orifice constant and changing chamber compliance or systemic vascular resistance. Upon increasing regurgitant fraction by increasing the size of the regurgitant orifice, the slope got steeper and the pressure half-time shortened, the response anticipated in current clinical practice. However, when the regurgitant orifice was kept constant and regurgitation fraction was increased by increasing the systemic vascular resistance or by increasing the compliance of the left ventricle, slope became less steep and pressure half-time lengthened. Multivariate analysis was used to quantify the relationship of regurgitant fraction to slope and pressure half-time. When orifice area was allowed to vary, slope was related directly (multiple r = 0.78, p less than 0.001) and half-time was related inversely (multiple r = 0.66, p less than 0.001) to regurgitant fraction. With the orifice area fixed, however, directionally opposite responses were seen; slope varied inversely (multiple r = 0.87, p less than 0.001), whereas half-time varied directly (multiple r = 0.88, p less than 0.001) with regurgitant fraction. This study suggests that the utility of the slope and pressure half-time of the regurgitant velocity tracing in clinical practice relates to their ability to discriminate regurgitant orifices of differing sizes.(ABSTRACT TRUNCATED AT 250 WORDS)

Impact of orifice geometry on the shape of jets: an in vitro Doppler color flow study

To investigate the influence of orifice geometry on the three-dimensional shape of jets, an in vitro Doppler color flow study was performed. Jets were formed by discharging blood through round orifices and through orifices with major/minor axis ratios of 2:1, 3:1 and 5:1. These were repeated with orifice areas of 0.1, 0.3 and 0.5 cm2. For turbulent and laminar jets formed by these orifices, Doppler color flow images were obtained from two orthogonal scanning planes aligned with the major and minor orifice axes. Jet width was measured at 1 cm intervals from 0 to 5 cm from the orifice and used to calculate jet eccentricity (ratio of major to minor axis widths) and the rate of divergence of the jet walls. Jets were observed to diverge more rapidly along walls aligned with the orifice minor axis rather than along the major axis. This differential spreading led to the development of circular symmetry at a short distance from the orifice. Jet divergence (theta) occurred more rapidly for turbulent jets and for jets formed by larger orifices: theta (zero) = 0.80 + 6.3.A + 7.0.T + 0.47.E-OR (r = 95, p less than 0.0001, n = 48), where A is orifice area (cm2); T is 0 for laminar jets, 1 for turbulent jets and E-OR combines orifice eccentricity and scanning orientation, ranging from -5 for 5:1 orifices imaged along the major axis, 0 for circular orifices to 5 for 5:1 orifices imaged along the minor axis. Within the jet, eccentricity decayed approximately exponentially with distance from the orifice, more rapidly for turbulent jets, more slowly for the larger and more eccentric orifices.(ABSTRACT TRUNCATED AT 250 WORDS)

Dialysis-induced alterations in left ventricular filling: mechanisms and clinical significance

Quantitative two-dimensional (2-D) and Doppler echocardiography were used to determine whether hemodialysis results in alterations in left ventricular (LV) diastolic filling that might contribute to dialysis-induced hypotension, as well as to assess whether any hemodynamic variables or indices of diastolic filling might be used to identify which patients were at the greatest risk of becoming hemodynamically unstable during dialysis. Sixteen male patients undergoing routine maintenance hemodialysis for end-stage renal disease were prospectively studied before and after hemodialysis. Following hemodialysis there was a significant prolongation (P less than 0.05) in LV isovolumetric relaxation time (IVRT), as well as a significant reduction in the rate and extent of early rapid ventricular filling (P less than 0.005); in contrast, late atrial-assisted filling did not change significantly. A multiple stepwise linear regression analysis of predialysis hemodynamic parameters and noninvasive indices of LV filling showed that there was a significant independent inverse relationship between the frequency of dialysis-related hypotensive episodes and the duration of early LV filling (r = -0.81; P less than 0.001). These results suggest that hemodialysis results in discrete alterations in early LV filling, with no significant compensatory increase in late atrial-assisted ventricular filling. Further, patients with the shortest early LV filling times appeared to have the greatest predilection for becoming hemodynamically unstable during dialysis.