Correlation Between Vortex Ring Formation and Mitral Annulus Dynamics During Ventricular Rapid Filling

A Hybrid Approach for Cardiac Blood Flow Vortex Ring Identification Based on Optical Flow and Lagrangian Averaged Vorticity Deviation

Objective: The measurement of cardiac blood flow vortex characteristics can help to facilitate the analysis of blood flow dynamics that regulates heart function. However, the complexity of cardiac flow along with other physical limitations makes it difficult to adequately identify the dominant vortices in a heart chamber, which play a significant role in regulating the heart function. Although the existing vortex quantification methods can achieve this goal, there are still some shortcomings: such as low precision, and ignoring the center of the vortex without the description of vortex deformation processes. To address these problems, an optical flow Lagrangian averaged vorticity deviation (Optical flow-LAVD) method is proposed.

Methodology: We examined the flow within the right atrium (RA) of the participants’ hearts, by using a single set of scans pertaining to a slice at two-chamber short-axis orientation. Toward adequate extraction of the vortex ring characteristics, a novel approach driven by the Lagrangian averaged vorticity deviation (LAVD) was implemented and applied to characterize the trajectory integral associated with vorticity deviation and the spatial mean of rings, by using phase-contrast magnetic resonance imaging (PC-MRI) datasets as a case study. To interpolate the time frames between every larger discrete frame and minimize the error caused by constructing a continuous velocity field for the integral process of LAVD, we implemented the optical flow as an interpolator and introduced the backward warping as an intermediate frame synthesis basis, which is then used to generate higher quality continuous velocity fields.

Results: Our analytical study results showed that the proposed Optical flow-LAVD method can accurately identify vortex ring and continuous velocity fields, based on optical flow information, for yielding high reconstruction outcomes. Compared with the linear interpolation and phased-based frame interpolation methods, our proposed algorithm can generate more accurate synthesized PC-MRI.

Conclusion: This study has developed a novel Optical flow-LAVD model to accurately identify cardiac vortex rings, and minimize the associated errors caused by the construction of a continuous velocity field. Our paper presents a superior vortex characteristics detection method that may potentially aid the understanding of medical experts on the dynamics of blood flow within the heart.

Alterations in Intracardiac Flow Patterns Affect Mitral Leaflets Dynamics in a Model of Ischemic Mitral Regurgitation

PURPOSE

This study was to evaluate the effects of ischemic mitral regurgitation (IMR) on vortex formation and leaflet dynamics using an established porcine infarct model of IMR.

METHODS

Using direct coronary ligation, five animals were subjected to a posterolateral myocardial infarction (MI) followed by an MRI at 12-weeks post MI. MR imaging consisted of 4D time-resolved left ventricular (LV) flow, full coverage 2D LV cine, and high resolution 2D cine of mitral valve dynamics. Five additional naïve animals underwent identical imaging protocols to serve as controls. Image analysis was performed to obtain mitral transvalvular flows as well as LV volumes throughout the cardiac cycle. In addition, anterior to posterior mid-leaflet tip distances were measured throughout the cardiac cycle for determination of temporal leaflet dynamics.

RESULTS

It was found IMR caused asymmetric vortex ring formation with the anterior vortex having a lower vorticity relative to its posterior counterpart. In contrast, normal ventricles create symmetric and tightly curled vortices in the basal chamber just underneath the mitral leaflets which conserve kinetic energy and aid in effective ejection. IMR animals were also evaluated for leaflet separation and were found to have a greater leaflet opening and achieved peak vorticity and peak leaflet opening later than control animals.

CONCLUSION

In conclusion, this study shows the effects that altered vortex formation, due to IMR, can have on ventricular filling and leaflet dynamics. These findings have important implications for understanding blood flow through the dilated heart and how ring annuloplasty and volume reduction interventions may influence mitral valve dynamics.

Lagrangian-averaged vorticity deviation of spiraling blood flow in the heart during isovolumic contraction and ejection phases

The formation of vortex rings in the left ventricular (LV) blood flow is a mechanism for optimized blood transport from the mitral valve inlet to aortic valve outlet, and the vorticity is an important measure of a well-functioning LV. However, due to lack of quantitative methods, the process of defining the boundary of a vortex in the LV and identifying the dominant vortex components has not been studied previously. The Lagrangian-averaged vorticity deviation (LAVD) can enable us to compute the trajectory integral of the normed difference of the vorticity from its spatial mean. Therefore, in this work, we have employed LAVD to identify the Lagrangian vortices and Eulerian vortices for measuring the vortex volume and vorticity in the LV blood flow. We found that during the LV ejection period, the positive (counterclockwise) and negative (clockwise) vorticity of patients are consistently stronger than those of the healthy groups, and the counterclockwise vortex volume of healthy groups (0.84+0.26 ml) is greater than that of patients (0.55+0.28 ml) during the pre-ejection period. Then, during the middle ejection phase, the counterclockwise vortex ring volume of patients (1.89+0.36 ml) exceeds that of healthy groups (1.38+0.43 ml). Finally, during the end-ejection period, the counterclockwise vortex ring volume of healthy subjects (0.61+0.17 ml) is the same as that of patients (0.60+0.19 ml). The results presented in this paper can provide new insights into the blood flow patterns within the LV. It can accurately indicate the role of vortices and vorticity values in intra-LV flow, and portray how cardiomyopathy (and its distorted contractile mechanism) can affect intra-LV flow patterns and mitigate adequate LV outflow.

Optimal vortex formation time index in mitral valve stenosis

Left ventricular vortex formation time (VFT) is a novel dimensionless index of flow propagation during left ventricular diastole, which has been demonstrated to be useful in heart failure and cardiomyopathy. In mitral stenosis (MS), flow propagation in the LV may be suboptimal. We studied VFT in varying degrees of MS. Echocardiography was performed on 20 healthy controls and 50 cases of rheumatic MS. Patients with atrial fibrillation, LV ejection fraction < 50% and other valvular heart diseases were excluded. VFT was obtained using the length-to-diameter ratio (L/D), where L is the continuous-wave Doppler velocity time integral stroke distance, divided by D, the mitral leaflet separation index. This was correlated against varying degrees of MS severity, left atrial (LA) volume and function. In controls, VFT was 3.92 ± 2.00 (optimal range) and was higher (suboptimal) with increasing severity of mitral stenosis (4.98 ± 2.43 in mild MS; 7.22 ± 2.98 in moderate MS; 11.55 ± 2.67 in severe MS, p < 0.001). VFT negatively correlated with mitral valve area (R² = 0.463, p < 0.001) and total LA emptying fraction (R² = 0.348, p < 0.001), and positively correlated with LA volume index (R² = 0.440, p < 0.001) and mean transmitral pressure gradient (R² = 0.336, p < 0.001). More severe MS correlated with suboptimal (higher) VFT. The restricted mitral valve opening may disrupt vortex formation and optimal fluid propagation in the LV. Despite the compensatory increase in LA size with increasingly severe MS, reduced LA function also contributed to the suboptimal LV vortex formation.

The Effect of Inflow Cannula Angle on the Intraventricular Flow Field of the Left Ventricular Assist Device-Assisted Heart: An In Vitro Flow Visualization Study

Previous studies have identified left ventricular assist device (LVAD) inflow cannula (IC) malposition as a significant risk for pump thrombosis. Thrombus development is a consequence of altered flow dynamics, which can produce areas of flow stasis or high shear that promote coagulation. The goal of this study was to measure the effect of IC orientation on the left ventricle (LV) flow field using a mock circulatory loop, and identify flow-based indices that are sensitive measures of cannula malposition. Experimental studies were performed with a customized silicone model of the dilated LV and the EVAHEART Centrifugal LVAS (Evaheart, Inc.; Houston TX). The velocity field of the LV midplane was measured for a transparent IC oriented parallel to and rotated 15° toward the septum under matched hemodynamic conditions. Vortex structures were analyzed and localized stasis calculated within the IC and combined with a map of normalized pulsatile velocity. The velocity fields revealed increased apical stasis and lower pulsatility with a small angulation of the IC. A significant change in vortex dynamics with the angled IC was observed, doubling the size of the counterclockwise (CCW) vortex while reducing the kinetic energy provided by LVAD support. A significant decrease in average and systolic velocities within the IC was found with cannula angulation, suggesting an increased resistance that affects primarily systolic flow and is worsened with increased LVAD support. These common echocardiographic indices offer the opportunity for immediate clinical application during ramp study assessment. Optimized IC positioning may be determined preoperatively using imaging techniques to develop patient-specific surgical recommendations.

Conducting Polymeric Nanocomposites with a Three-Dimensional Co-flow Microfluidics Platform

The nanoprecipitation of polymers is of great interest in biological and medicinal applications. Many approaches are available, but few generalized methods can fabricate structurally different biocompatible polymers into nanosized particles with a narrow distribution in a high-throughput manner. We simply integrate a glass slide, capillary, and metal needle into a simple microfluidics device. Herein, a detailed protocol is provided for using the glass capillary and slides to fabricate the microfluidics devices used in this work. To demonstrate the generality of our nanoprecipitation approach and platform, four (semi)natural polymers—acetalated dextran (Ac-DEX), spermine acetalated dextran (Sp-Ac-DEX), poly(lactic-co-glycolic acid) (PLGA), and chitosan—were tested and benchmarked by the polymeric particle size and polydispersity. More importantly, the principal objective was to explore the influence of some key parameters on nanoparticle size due to its importance for a variety of applications. The polymer concentration, the solvent/non-solvent volume rate/ratio, and opening of the inner capillary were varied so as to obtain polymeric nanoparticles (NPs). Dynamic light scattering (DLS), transmission electron microscopy (TEM), and optical microscopy are the main techniques used to evaluate the nanoprecipitation output. It turns out that the concentration of polymer most strongly determines the particle size and distribution, followed by the solvent/non-solvent volume rate/ratio, whereas the opening of the inner capillary shows a minor effect. The obtained NPs were smooth spheres with adjustable particle diameters and polymer-dependent surface potentials, both negative and positive.

Intraventricular Flow: More than Pretty Pictures

Patients with heart failure show myocardial, valvular, and electrical dysfunction, which results in enlarged cardiac chambers and increased intracardiac volume and pressure. Intracardiac flow analysis can provide information regarding the shape and wall properties, chamber dimensions, and flow efficiency throughout the cardiac cycle. There is increasing interest in vortex flow analysis for patients with heart failure to overcome limitations of conventional parameters. In conjunction with the conventional structural and functional parameters, vortex flow analysis-guided treatment in heart failure might be a novel option for cardiac physicians.

Advanced Age Attenuates Left Ventricular Filling Efficiency Quantified Using Vortex Formation Time: A Study of Octogenarians With Normal Left Ventricular Systolic Function Undergoing Coronary Artery Surgery

OBJECTIVE

Blood flow across the mitral valve during early left ventricular (LV) filling produces a 3-dimensional rotational fluid body, known as a vortex ring, that enhances LV filling efficiency. Diastolic dysfunction is common in elderly patients, but the influence of advanced age on vortex formation is unknown. The authors tested the hypothesis that advanced age is associated with a reduction in LV filling efficiency quantified using vortex formation time (VFT) in octogenarians undergoing coronary artery bypass graft (CABG) surgery.

DESIGN

Observational study.

SETTING

Veterans Affairs medical center.

PARTICIPANTS

After institutional review board approval, octogenarians (n = 7; 82 ± 2 year [mean ± standard deviation]; ejection fraction 56% ± 7%) without valve disease or atrial arrhythmias undergoing CABG were compared with a younger cohort (n = 7; 55 ± 6 year; ejection fraction 57% ± 7%) who were undergoing coronary revascularization.

INTERVENTIONS

None.

MEASUREMENTS AND MAIN RESULTS

All patients were monitored using radial and pulmonary arterial catheters and transesophageal echocardiography. Peak early LV filling (E) and atrial systole (A) blood flow velocities and their corresponding velocity-time integrals were obtained using pulse-wave Doppler echocardiography to determine E/A, atrial filling fraction (β), and E wave deceleration time. Pulse-wave Doppler also was used to measure pulmonary venous blood flow during systole and diastole. Mitral valve diameter (D) was calculated as the average of major and minor axis lengths obtained in the midesophageal LV bicommissural and long-axis transesophageal echocardiography imaging planes, respectively. VFT was calculated as 4 × (1 - β) × SV/(πD³), where SV is the stroke volume measured using thermodilution. Systemic and pulmonary hemodynamics, LV diastolic function, and VFT were determined during steady-state conditions 30 minutes before cardiopulmonary bypass. A delayed relaxation pattern of LV filling (E/A 0.81 ± 0.16 v 1.29 ± 0.19, p = 0.00015; β 0.44 ± 0.05 v 0.35 ± 0.03, p = 0.0008; E wave deceleration time 294 ± 58 v 166 ± 28 ms, p < 0.0001; ratio of peak pulmonary venous systolic and diastolic blood flow velocity 1.42 ± 0.23 v 1.14 ± 0.20, p = 0.0255) was observed in octogenarians compared with younger patients. Mitral valve diameter was similar between groups (2.7 ± 0.2 and 2.6 ± 0.2 cm, respectively, in octogenarians v younger patients, p = 0.299). VFT was reduced in octogenarians compared with younger patients (3.0 ± 0.9 v 4.5 ± 1.2; p = 0.0171). An inverse correlation between age and VFT was shown using linear regression analysis (VFT = -0.0627 × age + 8.24; r² = 0.408; p = 0.0139).

CONCLUSION

The results indicate that LV filling efficiency quantified using VFT is reduced in octogenarians compared with younger patients undergoing coronary artery bypass grafting.

The relationship between systolic vector flow mapping parameters and left ventricular cardiac function in healthy dogs

Vector flow mapping (VFM) is a novel echocardiographic technology that shows blood flow vectors and vortexes, enabled the hydrokinetic evaluation of hemodynamics within the left ventricle. VFM provides several unique parameters: circulation, vorticity, vortex area, and energy loss. The present study aims to reveal a relationship between VFM parameters and cardiac function. Five healthy Beagle dogs were anesthetized and administered with dobutamine (0, 2, 4, 8, 12 µg/kg/min). Pressure-volume diagrams were acquired to assess cardiac function using pressure-volume conductance catheter. Systolic maximum circulation, vorticity, vortex area, and energy loss were measured using VFM. The systolic maximum circulation, systolic vorticity, systolic vortex area, and systolic energy loss were increased by dobutamine administration. There was a strongly significant correlation between the systolic maximum circulation and ejection fraction (r = 0.76), maximal positive left ventricular (LV) pressure derivatives (dP/dt max) (r = 0.80), and end-systolic LV elastance (r = 0.73). Systolic vorticity and systolic vortex area were strongly correlated with ejection fraction (r = 0.76, 0.68) and dP/dt max (r = 0.76, 0.69), and end-systolic LV elastance (r = 0.62, 0.74), respectively. Systolic energy loss was strongly correlated with dP/dt max (r = 0.78), systolic maximum circulation (r = 0.81), and systolic vorticity (r = 0.82). The present study revealed that systolic VFM parameters are associated with the LV contractility. Furthermore, systolic energy loss was susceptible to the systolic vortex parameters such as systolic vorticity and systolic maximum circulation. Systolic VFM parameters are new hydrokinetic indices reflecting LV contractility.

Moderate Aortic Valvular Insufficiency Invalidates Vortex Formation Time as an Index of Left Ventricular Filling Efficiency in Patients With Severe Degenerative Calcific Aortic Stenosis Undergoing Aortic Valve Replacement

OBJECTIVE

Transmitral blood flow produces a vortex ring (quantified using vortex formation time [VFT]) that enhances the efficiency of left ventricular (LV) filling. VFT is attenuated in LV hypertrophy resulting from aortic valve stenosis (AS) versus normal LV geometry. Many patients with AS also have aortic insufficiency (AI). The authors tested the hypothesis that moderate AI falsely elevates VFT by partially inhibiting mitral leaflet opening in patients with AS.

DESIGN

Observational study.

SETTING

Veterans Affairs medical center.

PARTICIPANTS

Patients with AS in the presence or absence of moderate AI (n = 8 per group) undergoing aortic valve replacement (AVR) were studied after institutional review board approval.

INTERVENTIONS

None.

MEASUREMENTS AND MAIN RESULTS

Under general anesthesia, peak early LV filling (E) and atrial systole (A) blood flow velocities and their corresponding velocity-time integrals were obtained using pulse-wave Doppler transesophageal echocardiography (TEE) to determine E/A and atrial filling fraction (beta). Mitral valve diameter (D) was calculated as the average of major and minor axis lengths obtained in the midesophageal bicommissural (transcommissural anterior-lateral-posterior medial) and LV long-axis (anterior-posterior) TEE imaging planes, respectively. VFT was calculated as 4·(1-beta)·SV/πD(3), where SV = stroke volume measured using thermodilution. Hemodynamics, diastolic function, and VFT were determined during steady-state conditions before cardiopulmonary bypass. The severity of AS (mean and peak pressure gradients, peak transvalvular jet velocity, aortic valve area) and diastolic function (E/A, beta) were similar between groups. Moderate centrally directed AI was present in 8 patients with AS (ratio of regurgitant jet width to LV outflow tract diameter of 36±6%). Pulse pressure and mean pulmonary artery pressure were elevated in patients with versus without AI, but no other differences in hemodynamics were observed. Mitral valve minor and major axis lengths, diameter, and area were reduced in the presence versus the absence of AI. VFT was increased significantly (5.7±1.7 v 3.2±0.6; p = 0.00108) in patients with AS and AI compared with AS alone.

CONCLUSION

Moderate AI falsely elevates VFT in patients with severe AS undergoing AVR by partially inhibiting mitral valve opening. VFT may be an unreliable index of LV filling efficiency with competitive diastolic flow into the LV.

Emerging Trends in Heart Valve Engineering: Part IV. Computational Modeling and Experimental Studies

In this final portion of an extensive review of heart valve engineering, we focus on the computational methods and experimental studies related to heart valves. The discussion begins with a thorough review of computational modeling and the governing equations of fluid and structural interaction. We then move onto multiscale and disease specific modeling. Finally, advanced methods related to in vitro testing of the heart valves are reviewed. This section of the review series is intended to illustrate application of computational methods and experimental studies and their interrelation for studying heart valves.

The Influence of Mitral Annuloplasty on Left Ventricular Flow Dynamics

BACKGROUND

Mitral valve (MV) repair using annuloplasty rings is the preferred method of treatment for MV regurgitation, but the impact of annuloplasty ring placement on left ventricular intraventricular flow has not been studied.

METHODS

Annuloplasty rings of varying sizes were placed in 5 healthy sheep (intercommissural ring sizes were 24, 26, 28, 30, and 32 mm), and three-dimensional phase contrast magnetic resonance imaging (4D flow MRI) was performed before and 1 week after ring placement.

RESULTS

Normal diastolic flow consisted of diastolic intraventricular vortices that naturally unwound during systole. Postsurgical intraventricular flow was highly disturbed in all sheep, and the disturbance was greatest for undersized rings. Ring size was highly correlated with the diastolic inflow angle (Pearson's r = -0.62, p < 0.1, 95% confidence interval: -0.92 to 0.14). There was a mean angle increase of mean diastolic inflow angle increase of 12.3 degrees (< 30 mm, p < 0.01, 95% confidence interval: 4.8 to 19.6) for rings less than 30 mm. There was an inverse relationship between peak velocity and annuloplasty ring area (Pearson's r = -0.80, p < 0.05, 95% confidence interval: -0.96 to -0.2). Transmitral pressure gradients increased significantly from baseline 0.73 ± 0.18 mm Hg to after annuloplasty 2.31 ± 1.04 mm Hg (p < 0.05).

CONCLUSIONS

Mitral valve annuloplasty ring placement disturbs normal left ventricular intraventricular flow patterns, and the degree of disturbance is closely associated with annuloplasty ring size.

2-D left ventricular flow estimation by combining speckle tracking with Navier-Stokes-based regularization: an in silico, in vitro and in vivo study

Despite the availability of multiple ultrasound approaches to left ventricular (LV) flow characterization in two dimensions, this technique remains in its childhood and further developments seem warranted. This article describes a new methodology for tracking the 2-D LV flow field based on ultrasound data. Hereto, a standard speckle tracking algorithm was modified by using a dynamic kernel embedding Navier-Stokes-based regularization in an iterative manner. The performance of the proposed approach was first quantified in synthetic ultrasound data based on a computational fluid dynamics model of LV flow. Next, an experimental flow phantom setup mimicking the normal human heart was used for experimental validation by employing simultaneous optical particle image velocimetry as a standard reference technique. Finally, the applicability of the approach was tested in a clinical setting. On the basis of the simulated data, pointwise evaluation of the estimated velocity vectors correlated well (mean r = 0.84) with the computational fluid dynamics measurement. During the filling period of the left ventricle, the properties of the main vortex obtained from the proposed method were also measured, and their correlations with the reference measurement were also calculated (radius, r = 0.96; circulation, r = 0.85; weighted center, r = 0.81). In vitro results at 60 bpm during one cardiac cycle confirmed that the algorithm properly measures typical characteristics of the vortex (radius, r = 0.60; circulation, r = 0.81; weighted center, r = 0.92). Preliminary qualitative results on clinical data revealed physiologic flow fields.

Computational Study of Hemodynamic Effects of Abnormal E/A Ratio on Left Ventricular Filling

Three-dimensional numerical simulations are employed to investigate the hemodynamic effects of abnormal E/A ratios on left ventricular filling. The simulations are performed in a simplified geometric model of the left ventricle (LV) in conjunction with a specified endocardial motion. The model has been carefully designed to match the important geometric and flow parameters under the physiological conditions. A wide range of E/A ratios from 0 to infinity is employed with the aim to cover all the possible stages of left ventricle diastolic dysfunction (DD). The effects of abnormal E/A ratios on vortex dynamics, flow propagation velocity, energy consumption as well as flow transport and mixing are extensively discussed. Our results are able to confirm some common findings reported by the previous studies, and also uncover some interesting new features.

Intraventricular flow patterns and stasis in the LVAD-assisted heart

Left ventricular assist device (LVAD) support disrupts the natural blood flow path through the heart, introducing flow patterns associated with thrombosis, especially in the presence of medical devices. The aim of this study was to quantitatively evaluate the flow patterns in the left ventricle (LV) of the LVAD-assisted heart, with a focus on alterations in vortex development and stasis. Particle image velocimetry of a LVAD-supported LV model was performed in a mock circulatory loop. In the Pre-LVAD flow condition, a vortex ring initiating from the LV base migrated toward the apex during diastole and remained in the LV by the end of ejection. During LVAD support, vortex formation was relatively unchanged although vortex circulation and kinetic energy increased with LVAD speed, particularly in systole. However, as pulsatility decreased and aortic valve opening ceased, a region of fluid stasis formed near the left ventricular outflow tract. These findings suggest that LVAD support does not substantially alter vortex dynamics unless cardiac function is minimal. The altered blood flow introduced by the LVAD results in stasis adjacent to the LV outflow tract, which increases the risk of thrombus formation in the heart.

The vortex formation time to diastolic function relation: assessment of pseudonormalized versus normal filling

In early diastole, the suction pump feature of the left ventricle opens the mitral valve and aspirates atrial blood. The ventricle fills via a blunt profiled cylindrical jet of blood that forms an asymmetric toroidal vortex ring inside the ventricle whose growth has been quantified by the standard (dimensionless) expression for vortex formation time, VFT_standard = {transmitral velocity time integral}/{mitral orifice diameter}. It can differentiate between hearts having distinguishable early transmitral (Doppler E-wave) filling patterns. An alternative validated expression, VFT_kinematic reexpresses VFT_standard by incorporating left heart, near “constant-volume pump” physiology thereby revealing VFT_kinematic's explicit dependence on maximum rate of longitudinal chamber expansion (E′). In this work, we show that VFT_kinematic can differentiate between hearts having indistinguishable E-wave patterns, such as pseudonormal (PN; 0.75 < E/A < 1.5 and E/E′ > 8) versus normal. Thirteen age-matched normal and 12 PN data sets (738 total cardiac cycles), all having normal LVEF, were selected from our Cardiovascular Biophysics Laboratory database. Doppler E-, lateral annular E′-waves, and M-mode data (mitral leaflet separation, chamber dimension) was used to compute VFT_standard and VFT_kinematic. VFT_standard did not differentiate between groups (normal [3.58 ± 1.06] vs. PN [4.18 ± 0.79], P = 0.13). In comparison, VFT_kinematic for normal (3.15 ± 1.28) versus PN (4.75 ± 1.35) yielded P = 0.006. Hence, the applicability of VFT_kinematic for diastolic function quantitation has been broadened to include analysis of PN filling patterns in age-matched groups.

Chronic pressure-overload hypertrophy attenuates vortex formation time in patients with severe aortic stenosis and preserved left ventricular systolic function undergoing aortic valve replacement

OBJECTIVE

Transmitral blood flow produces a vortex ring that enhances the hydraulic efficiency of early left ventricular (LV) filling. The effect of pressure-overload hypertrophy on the duration of LV vortex ring formation (vortex formation time [VFT]) is unknown. The current investigation tested the hypothesis that chronic LV pressure-overload hypertrophy produced by severe aortic stenosis (AS) reduces VFT in patients with preserved LV systolic function undergoing aortic valve replacement.

DESIGN

Observational study.

SETTING

Veterans Affairs Medical Center.

PARTICIPANTS

After the Institutional Review Board's approval, 8 patients (7 men and 1 woman; age, 62±5 y; and ejection fraction, 59%±5%) with AS (peak pressure gradient, 81±22 mmHg; aortic valve area, 0.78±0.25 cm(2)) scheduled for aortic valve replacement were compared with 8 patients (all men; age, 63±3 y; and ejection fraction, 60%±7%) without AS undergoing coronary artery bypass graft surgery.

INTERVENTIONS

None.

MEASUREMENTS AND MAIN RESULTS

Under general anesthesia, peak early LV filling (E) and atrial systole (A) blood flow velocities and their corresponding velocity-time integrals were obtained using pulse-wave Doppler echocardiography to determine E/A and atrial filling fraction (β). Mitral valve diameter (D) was calculated as the average of minor and major axis lengths obtained in the midesophageal bicommissural and long-axis transesophageal echocardiography imaging planes, respectively. Posterior wall thickness (PWT) was measured at end-diastole using M-mode echocardiography. VFT was calculated as 4×(1-β)×SV/πD(3), where SV = stroke volume measured using thermodilution. Systemic and pulmonary hemodynamics, LV diastolic function, PWT, and VFT were determined during steady-state conditions 30 minutes before cardiopulmonary bypass. Early LV filling was attenuated in patients with AS (eg, E/A, 0.77±0.11 compared with 1.23±0.13; β, 0.43±0.09 compared with 0.35±0.02; p<0.05 for each). LV hypertrophy was observed (PWT, 1.4±0.1 cm compared with 1.1±0.2 cm; p<0.05) and VFT was lower (3.0±0.9 v 4.3±0.5; p<0.05) in patients with versus without AS. Linear regression analysis showed a significant correlation between VFT and PWT (VFT = -2.57 ×PWT + 6.81; r(2) = 0.345; p = 0.017).

CONCLUSION

The results indicated that pressure-overload hypertrophy produced by AS reduced VFT in patients with normal LV systolic function undergoing aortic valve replacement.

Vortices formed on the mitral valve tips aid normal left ventricular filling

For the left ventricle (LV) to function as an effective pump it must be able to fill from a low left atrial pressure. However, this ability is lost in patients with heart failure. We investigated LV filling by measuring the cardiac blood flow using 2D phase contrast magnetic resonance imaging and quantified the intraventricular pressure gradients and the strength and location of vortices. In normal subjects, blood flows towards the apex prior to the mitral valve opening, and the mitral annulus moves rapidly away after the valve opens, with both effects enhancing the vortex ring at the mitral valve tips. Instead of being a passive by-product of the process as was previously believed, this ring facilitates filling by reducing convective losses and enhancing the function of the LV as a suction pump. The virtual channel thus created by the vortices may help insure efficient mass transfer for the left atrium to the LV apex. Impairment of this mechanism contributes to diastolic dysfunction, with LV filling becoming dependent on left atrial pressure, which can lead to eventual heart failure. Better understanding of the mechanics of this progression may lead to more accurate diagnosis and treatment of this disease.

Vortex ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian coherent structures

Recent studies suggest that vortex ring formation during left ventricular (LV) rapid filling is an optimized mechanism for blood transport, and that the volume of the vortex ring is an important measure. However, due to lack of quantitative methods, the volume of the vortex ring has not previously been studied. Lagrangian Coherent Structures (LCS) is a new flow analysis method, which enables in vivo quantification of vortex ring volume. Therefore, we aimed to investigate if vortex ring volume in the human LV can be reliably quantified using LCS and magnetic resonance velocity mapping (4D PC-MR). Flow velocities were measured using 4D PC-MR in 9 healthy volunteers and 4 patients with dilated ischemic cardiomyopathy. LV LCS were computed from flow velocities and manually delineated in all subjects. Vortex volume in the healthy volunteers was 51 ± 6% of the LV volume, and 21 ± 5% in the patients. Interobserver variability was -1 ± 13% and interstudy variability was -2 ± 12%. Compared to idealized flow experiments, the vortex rings showed additional complexity and asymmetry, related to endocardial trabeculation and papillary muscles. In conclusion, LCS and 4D PC-MR enables measurement of vortex ring volume during rapid filling of the LV.

The left ventricular intracavitary vortex during the isovolumic contraction period as detected by vector flow mapping

AIMS

The purpose of this study was to characterize left ventricular (LV) intracavitary flow during the isovolumic contraction (IVC) period in humans using vector flow mapping.

METHODS

Color flow Doppler imaging was performed from the apical long-axis view in 61 patients with heart failure and 58 healthy volunteers. Doppler flow data obtained during IVC were analyzed offline with vector flow mapping.

RESULTS

A large vortex was formed from the LV inflow toward the outflow during IVC. In normal subjects, the area of the vortex was sustained, but the flow volume decreased significantly during IVC (P < 0.001). A significant apex-to-base flow velocity gradient was shown along the outflow axis on aortic valve opening. However, both the area and flow volume of the vortex decreased more severely during IVC in the patients (P < 0.001). The apex-to-base flow velocity gradient along the outflow axis disappeared and a reversed velocity gradient was observed at the basal-mid level on aortic valve opening. In multivariate models, a decreased LV ejection fraction was the only independent predictor of the percentage decrease in area of the vortex during the IVC (P < 0.001), and a larger QRS width (P = 0.028) and LV end-systolic long diameter (P = 0.002) were independent predictors of the percentage decrease in flow volume of the vortex.

CONCLUSIONS

The vortex across the LV inflow-outflow region during IVC facilitates the ejection of blood during early systole, and an unsustained vortex may be associated with impaired cardiac function.

Vortex formation time-to-left ventricular early rapid filling relation: model-based prediction with echocardiographic validation

During early rapid filling, blood aspirated by the left ventricle (LV) generates an asymmetric toroidal vortex whose development has been quantified using vortex formation time (VFT), a dimensionless index defined by the length-to-diameter ratio of the aspirated (equivalent cylindrical) fluid column. Since LV wall motion generates the atrioventricular pressure gradient resulting in the early transmitral flow (Doppler E-wave) and associated vortex formation, we hypothesized that the causal relation between VFT and diastolic function (DF), parametrized by stiffness, relaxation, and load, can be elucidated via kinematic modeling. Gharib et al. (Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO. Proc Natl Acad Sci USA 103: 6305–6308, 2006) approximated E-wave shape as a triangle and calculated VFTGharib as triangle (E-wave) area (cm) divided by peak (Doppler M-mode derived) mitral orifice diameter (cm). We used a validated kinematic model of filling for the E-wave as a function of time, parametrized by stiffness, viscoelasticity, and load. To calculate VFTkinematic, we computed the curvilinear E-wave area (using the kinematic model) and divided it by peak effective orifice diameter. The derived VFT-to-LV early rapid filling relation predicts VFT to be a function of peak E-wave-to-peak mitral annular tissue velocity (Doppler E′-wave) ratio as (E/E′)3/2. Validation utilized 262 cardiac cycles of simultaneous echocardiographic high-fidelity hemodynamic data from 12 subjects. VFTGharib and VFTkinematic were calculated for each subject and were well-correlated ( R2 = 0.66). In accordance with prediction, VFTkinematic to (E/E′)3/2 relationship was validated ( R 2 = 0.63). We conclude that VFTkinematic is a DF index computable in terms of global kinematic filling parameters of stiffness, viscoelasticity, and load. Validation of the fluid mechanics-to-chamber kinematics relation unites previously unassociated DF assessment methods and elucidates the mechanistic basis of the strong correlation between VFT and (E/E′)3/2.

Left Ventricular Vortex Under Mitral Valve Edge-to-Edge Repair

Mitral valve (MV) edge-to-edge repair (ETER) changes MV geometry by approximation of MV leaflets, and impacts left ventricle (LV) filling fluid mechanics. The purpose of this study was to investigate LV vortex with MV ETER during diastole. A computational MV-LV model was developed with MV ETER at the central free edges of the anterior and posterior leaflets. It was supposed that LV would elongate apically during diastole. The elongation deformation was controlled by the intraventricular flow rate. MV leaflets were modeled as a semi-prolate sphere with two symmetrical circular orifices and fixed at the maximum valve opening. MV chordae were neglected. FLUENT was used to simulate blood flow through the MV and in the LV. MV ETER generated two jets deflected laterally toward the LV wall in rapid LV filling. The jets impinged the LV wall obliquely and moved apically along the LV wall. Jet energy was primarily lost near the impingement. The jet from each MV orifice was surrounded by a vortex ring. The two vortex rings dissipated at the end of diastole. The total energy loss increased inversely with the MV orifice area. The atrio-ventricular pressure gradient was adverse near the end of diastole and possibly in diastasis. Reduction of the total orifice area led to more increment in the transmitral pressure drop than in the transmitral velocity. In conclusion, during diastole, two deflected jets from the MV under ETER impinged the LV wall. Major energy loss occurred around the jet impingement. Two vortex rings dissipated at the end of diastole with little storage of inflow energy for blood ejection in the following process of systole. MV ETER increased energy loss and lowered LV filling efficiency. The maintaining of a larger orifice area after ETER might not significantly increase energy loss in the LV during diastole and the transmitral pressure drop. The adverse pressure gradient from the atrium to the LV might be the mechanism of MV closure in the late diastole.

Two-dimensional intraventricular flow mapping by digital processing conventional color-Doppler echocardiography images

Doppler echocardiography remains the most extended clinical modality for the evaluation of left ventricular (LV) function. Current Doppler ultrasound methods, however, are limited to the representation of a single flow velocity component. We thus developed a novel technique to construct 2D time-resolved (2D+t) LV velocity fields from conventional transthoracic clinical acquisitions. Combining color-Doppler velocities with LV wall positions, the cross-beam blood velocities were calculated using the continuity equation under a planar flow assumption. To validate the algorithm, 2D Doppler flow mapping and laser particle image velocimetry (PIV) measurements were carried out in an atrio-ventricular duplicator. Phase-contrast magnetic resonance (MR) acquisitions were used to measure in vivo the error due to the 2D flow assumption and to potential scan-plane misalignment. Finally, the applicability of the Doppler technique was tested in the clinical setting. In vitro experiments demonstrated that the new method yields an accurate quantitative description of the main vortex that forms during the cardiac cycle (mean error for vortex radius, position and circulation). MR image analysis evidenced that the error due to the planar flow assumption is close to 15% and does not preclude the characterization of major vortex properties neither in the normal nor in the dilated LV. These results are yet to be confirmed by a head-to-head clinical validation study. Clinical Doppler studies showed that the method is readily applicable and that a single large anterograde vortex develops in the healthy ventricle while supplementary retrograde swirling structures may appear in the diseased heart. The proposed echocardiographic method based on the continuity equation is fast, clinically-compliant and does not require complex training. This technique will potentially enable investigators to study of additional quantitative aspects of intraventricular flow dynamics in the clinical setting by high-throughput processing conventional color-Doppler images.

Recent advances in the application of computational mechanics to the diagnosis and treatment of cardiovascular disease

During the last 30 years, research into the pathogenesis and progression of cardiovascular disease has had to employ a multidisciplinary approach involving a wide range of subject areas, from molecular and cell biology to computational mechanics and experimental solid and fluid mechanics. In general, research was driven by the need to provide answers to questions of critical importance for disease management. Ongoing improvements in the spatial resolution of medical imaging equipment coupled to an exponential growth in the capacity, flexibility and speed of computational techniques have provided a valuable opportunity for numerical simulations and complex experimental techniques to make a contribution to improving the diagnosis and clinical management of many forms of cardiovascular disease. This paper contains a review of recent progress in the numerical simulation of cardiovascular mechanics, focusing on three particular areas: patient-specific modeling and the optimization of surgery in pediatric cardiology, evaluating the risk of rupture in aortic aneurysms, and noninvasive characterization of intraventricular flow in the management of heart failure.

Biomechanics

This review covers research achievements in the field of biomechanics that have been obtained in the past few years and provides information to researchers in other fields of study.