Author + information
- Received March 8, 2014
- Revision received May 20, 2014
- Accepted June 2, 2014
- Published online October 21, 2014.
- Pablo Martínez-Legazpi, MEng, PhD∗,
- Javier Bermejo, MD, PhD†∗ (, )
- Yolanda Benito, DCS, DVM†,
- Raquel Yotti, MD, PhD†,
- Candelas Pérez del Villar, MD†,
- Ana González-Mansilla, MD, PhD†,
- Alicia Barrio, DCS, MBiol†,
- Eduardo Villacorta, MD†,
- Pedro L. Sánchez, MD, PhD†,
- Francisco Fernández-Avilés, MD, PhD† and
- Juan C. del Álamo, AeEng, PhD∗,‡
- ∗Mechanical and Aerospace Engineering Department, University of California, San Diego, La Jolla, California
- †Department of Cardiology, Hospital General Universitario Gregorio Marañón, Facultad de Medicina, Universidad Complutense de Madrid, and the Instituto de Investigación Sanitaria Gregorio Marañón, Madrid, Spain
- ‡Institute for Engineering in Medicine, University of California, San Diego, La Jolla, California
- ↵∗Reprint requests and correspondence:
Dr. Javier Bermejo, Department of Cardiology, Hospital General Universitario Gregorio Marañón, Dr. Esquerdo 46, 28007 Madrid, Spain.
Background Intraventricular fluid dynamics can be assessed clinically using imaging. The contribution of vortex structures to left ventricular (LV) diastolic function has never been quantified in vivo.
Objectives This study sought to understand the impact of intraventricular flow patterns on filling and to assess whether impaired fluid dynamics may be a source of diastolic dysfunction.
Methods Two-dimensional flow velocity fields from color Doppler echocardiographic sequences were obtained in 20 patients with nonischemic dilated cardiomyopathy (NIDCM), 20 patients with hypertrophic cardiomyopathy (HCM), and 20 control healthy volunteers. Using a flow decomposition method, we isolated the rotational velocity generated by the vortex ring from the surrounding flow in the left ventricle.
Results The vortex was responsible for entering 13 ± 6% of filling volume in the control group and 19 ± 8% in the NIDCM group (p = 0.004), but only 5 ± 5% in the HCM group (p < 0.0001 vs. controls). Favorable vortical effects on intraventricular pressure gradients were observed in the control and NIDCM groups but not in HCM patients. Differences in chamber sphericity explained variations in the vortex contribution to filling between groups (p < 0.005).
Conclusions The diastolic vortex is responsible for entering a significant fraction of LV filling volume at no energetic or pressure cost. Thus, intraventricular fluid mechanics are an important determinant of global chamber LV operative stiffness. Reduced stiffness in NIDCM is partially related to enhanced vorticity. Conversely, impaired vortex generation is an unreported mechanism of diastolic dysfunction in HCM and probably other causes of concentric remodeling.
Little is known about the relationship between diastolic function and the complex flow dynamics that occur during ventricular filling (1). The large vortical flow structures that develop during diastole appear particularly relevant. These vortices are a consequence of the heart’s chiral geometry and the interaction of the filling jet with the walls and mitral valve of the left ventricle (LV), but their effects on chamber hemodynamics remain incompletely understood. Once generated, vortices are relatively longstanding inertial flow structures capable of entraining fluid and decreasing pressure in their vicinity without an energetic cost of the driving system. Thus, a leading vortex can transport more mass than an equivalent straight jet of fluid (2,3). In the LV, vortices conserve kinetic energy between the intermittent periods of the cardiac cycle (4,5). Therefore, we hypothesized that vortex rings could play a major role in cardiac diastolic function.
Global LV chamber passive stiffness is determined by myocardial tissue material stiffness and thickness (6). In patients with hypertrophic cardiomyopathy (HCM), increased LV passive chamber stiffness is believed to be caused by stiffening and thickening of the cellular and extracellular components of the myocardium, whereas in nonischemic dilated cardiomyopathy (NIDCM), wall thinning contributes to typically seen reduced chamber stiffness (7). However, structural changes of the myocardium do not completely explain modifications in global chamber stiffness induced by chamber remodeling (8). Although chamber volume and shape additionally affect chamber stiffness, the mechanisms by which LV geometry influences such stiffness are not fully understood.
Given that vortex properties depend greatly on chamber geometry (5,9), we hypothesized that, in addition to structural changes in the myocardial compartment, modified flow dynamics, caused by abnormal chamber geometry, may contribute to the chamber stiffness characteristic of NIDCM and HCM. The present study was designed to assess the contribution of the intraventricular vortex to LV filling in normal and remodeled hearts. We used a previously validated algorithm to reconstruct the time-resolved 2-dimensional (2D+t) velocity field from color Doppler echocardiographic studies. By means of a velocity decomposition method, we were able to quantify, for the first time, the capacity of the diastolic vortex ring to transport LV filling volume in normal and abnormal ventricles.
Sixty subjects were prospectively selected (Table 1). Inclusion criteria for all study participants were: 1) the presence of sinus rhythm; 2) a suitable apical ultrasonic window; 3) absence of relevant aortic regurgitation (<2+); and 4) absence of E-A–wave fusion on the transmitral filling flow profile. Twenty patients with NIDCM were randomly selected from a large group recruited on the basis of angiographically proven absence of significant coronary artery disease and a stable clinical status (5). Another 20 patients with a firm diagnosis of HCM (based on clinical, familial, and genetic data) were selected from the outpatient clinic, 9 of which had obstructive disease (intraventricular pressure gradient of 51 ± 33 mm Hg in this subgroup). Twenty controls were also randomly selected from a large control population of normal subjects without known or suspected cardiovascular disease, with normal electrocardiographic and Doppler echocardiographic examinations, and with no history of hypertension or diabetes (5). The study was approved by the institutional review board, and all participants provided written informed consent.
Image acquisition and analysis
Comprehensive 2D echocardiographic examinations were performed using a Vivid 7 scanner and 2-4 MHz transducers (GE Healthcare, Waukesha, Wisconsin). LV volumes and ejection fraction were measured by the biplane Simpson method. Pulsed-wave tissue Doppler spectrograms were averaged from the septal and lateral mitral annulus (e′). Ventricular sphericity was computed as the ratio between the LV short and long axes from the parasternal long-axis and 4-chamber apical views, respectively. Longitudinal and transversal myocardial strain and strain rate were measured (EchoPac version 110.1.2, GE Healthcare) from the apical long-axis B-mode sequences used for providing the boundary conditions to the fluid-mechanics solver. Other conventional Doppler echocardiographic data were recorded following current recommendations (10).
2D-Flow image acquisition and processing
Image-processing steps are summarized in the Central Illustration. First, we recovered the 2D+t velocity field inside of the LV, using previously reported methods (5,11,12). We obtained images from the long-axis apical view, consecutively acquiring a color-Doppler sequence of 8 to 14 beats followed by a 2D cine-loop (4 beats) at a high frame rate, without tilting or displacing the probe. We used retrospective frame interleaving from multiple beats for the purpose of increasing temporal resolution (beats with >5% cycle-length variation were rejected) up to 150 to 200 frames/beat (11). The cross-beam flow velocity was calculated by integrating the continuity equation under a planar flow assumption and imposing nonpenetration at the myocardium-blood interface, which was obtained by speckle tracking (EchoPac). This modality has been previously validated in vitro (11) and in vivo (5). From the 2D+t flow velocity field, main (anteroseptal) and secondary (inferolateral) in-plane sections of the vortex ring were identified on the basis of the Q criterion (5,11,13). The reproducibility of this vortex-tracking algorithm to characterize main properties of the main and secondary vortex sections has been previously reported (5).
Flow velocity field decomposition
We decomposed the 2D+t flow velocity field into 2 complementary components: the vortex flow and the irrotational flow (Figure 1). The vortex flow was reconstructed via a vortex panel method, a well-established engineering methodology typically used in aeronautical and naval hydrodynamics. In biology, this method has been used to study vortex flow in undulatory fish swimming (14) but, to our knowledge, has never been implemented in the heart. Mathematically, in 2- or 3-dimensional flow, the vortex panel method can identify the velocity field caused by the presence of vortex structures inside of complex chamber geometries, given its size, circulation, and position (see the Online Appendix for details). Because the mitral valve leaflets are known to heavily condition vortex development, leaflet position was manually tracked frame-by-frame from the B-mode ultrasound sequences during the full filling period and entered in the flow decomposition algorithm for solving. We designated as vortex flow the velocity field induced by the LV vortices to the contiguous blood volume in the plane under study. This flow represents the velocity field that would be measured if a vortex of the same size, circulation, and location were artificially placed inside of a chamber of the same geometry. The irrotational flow designates the straight flow velocity directly related to the movements of the atrial and ventricular walls, as well as nonvortical inertial flow. This flow component was calculated subtracting vortex flow velocity fields from the measured total velocity field.
The total, vortex, and irrotational flow components were further processed to measure their contribution to filling blood volume and intracavitary pressure gradients. First, we averaged the 3 flow velocity components along the line connecting the mitral tips to obtain their respective LV filling velocity waveforms. To estimate the time evolution of LV filling, we integrated the velocity waveform from end-systolic to end-diastolic volume (Central Illustration) (15). We defined the vortex filling fraction as the proportion of total flow entering the LV that is transported by the vortex flow. Additionally, we identified the preferential streamlines of the LV filling jet core by semiautomatically tracing the streamlines with maximum values of inflow velocity in 20 equally spaced filling 2D+t velocity frames in the total flow field. These streamlines were then time-interpolated to the full sequence from mitral valve opening to mitral valve closing. We projected the total, vortex, and rotational velocity fields along these jet-core streamlines to obtain 1D+t (time-resolved 1-dimensional) representations of each of the flow velocity components (a curvilinear M-mode representation without the limitations of a straight flow and coaxial interrogation of conventional color Doppler M-mode echocardiography). Using these streamline projections and a previously validated algorithm (16,17), we calculated intraventricular diastolic pressure gradients and differences between the mitral annulus and LV apex. Because of the nonlinearity of the Euler governing equation, the decomposition of the velocity field into the vortex and irrotational ones entails the inclusion of a third pressure term that is physically related to the interaction between the 2 decomposed velocity fields. We designated this additional pressure component as the coupling component. The full mathematical derivation algorithm used for flow decomposition is summarized in the Online Appendix.
On the basis of the flow velocity waveform at the mitral tips, we determined the following periods: rapid filling (from mitral valve opening to peak E-wave velocity), E-wave deceleration plus diastasis if present (from peak E-wave to A-wave onset), A-wave acceleration (from A-wave onset to peak A-wave velocity), and A-wave deceleration (from peak A-wave velocity to mitral valve closing). Mean values of flow velocity, filling volume, and intraventricular diastolic pressure differences were estimated for each of these 4 periods for each of the flow components.
Variables are described as mean ± SD. Quantitative variables were compared using paired Student t tests and 1-way analysis of variance (ANOVA) followed by Dunnett contrasts against the control group, when appropriate. We analyzed the determinants of the vortex filling fraction using Pearson linear correlation analysis and multivariate linear regression of significant predictors (allowing for interactions), followed by backward stepwise elimination on the basis of Akaike’s information criteria. Standardized regression coefficients were calculated for variables entered into the final models. Statistical significance was established at the p < 0.05 level (R version 3.0.2, R Foundation for Statistical Computing, Vienna, Austria).
LV geometry and diastolic function
Increased LV mass was observed in patients with NIDCM and HCM (Table 1). Ventricular sphericity was abnormally high in the NIDCM group and abnormally low in patients with HCM. Most severe diastolic dysfunction was observed in the NIDCM group, as demonstrated by a prolonged isovolumic relaxation time, shortened deceleration time, and a low e′ and a high E/e′ ratio. The HCM group showed intermediate degrees of diastolic dysfunction, with normal isovolumic relaxation and deceleration times but a lower e′ and higher E/e′ ratio than control subjects. Both cardiomyopathy groups demonstrated abnormally low diastolic myocardial deformation parameters, with NIDCM patients showing the lowest values of early and late diastolic strain and strain rate (Table 1). Significant differences in vortex size, position, and circulation (i.e., rotational strength) of the main vortex section were found among the 3 populations (Table 2).
Vortex ring effects on filling flow and volume transport
The fraction of peak E-wave velocity generated by the vortex was 12 ± 10%, 18 ± 12%, and 8 ± 6% in the control, NIDCM (p = 0.05 vs. control), and HCM groups (p = 0.4 vs. control), respectively (ANOVA p = 0.001) (Figure 2). Compared with control subjects, the vortex filling fraction was significantly higher in the NIDCM group during all phases of diastole (Figure 3). Conversely, the HCM population’s vortex filling fraction was significantly lower than in control subjects during all phases. By the end of diastole, vortex flow was responsible for entering 13 ± 6% of filling volume across the mitral valve in the control population (range: 3% to 48%). This proportion was significantly higher in the NIDCM group (19 ± 8% [range: 7% to 58%]; p = 0.004 vs. control subjects) and significantly lower in HCM patients (5 ± 5% [range: 0% to 19%]; p = 0.0006 vs. control subjects; ANOVA p < 0.0001) (Figure 3).
Effects on intraventricular pressure distributions
During E-wave acceleration, the vortex induced a favorable pressure gradient towards the apex, with absolute values of the total pressure gradient significantly higher than the irrotational component for both the control and NIDCM groups (Figures 4 and 5⇓⇓). During E-wave deceleration, the vortex flow had a favorable effect in the NIDCM group and, to a lesser extent, in the control group by reducing pressure gradient reversal. During late filling, favorable significant effects of the vortex were observed in the NIDCM and control groups, increasing the absolute value of the negative pressure gradient during A-wave acceleration and reducing the adverse pressure gradient during A-wave deceleration (Figure 5). Representative examples of the effects of the velocity components on the velocity, filling volume, and intraventricular pressure gradients are shown in Figure 6.
Determinants of vortex-induced filling
Multivariate regression identified average diastolic values of circulation and long-axis position as the most important vortex properties related to volume transport (Table 3). Overall, differences among groups were related to differences in chamber sphericity (Figure 7).
The present study demonstrates that, by means of the diastolic vortex ring, structure-fluid interaction is a determinant of diastolic function in the human heart. By making use of this mechanism, the normal human ventricle can allocate 10% to 15% of its filling volume, without an energetic cost and without a negative impact on intraventricular diastolic pressure distributions. This mechanism of flow facilitation is enhanced in NIDCM but impaired in HCM.
Diastolic vortices as a filling transport mechanism
Ventricular filling results from the simultaneous and complementary action of negative (suction) and positive (pushing) pressure forces respectively generated in the ventricle and atrium. The pressure imbalance generated during isovolumic relaxation leads to mitral valve opening followed by filling jet development in the LV chamber. The jet evolves rapidly to a stable leading vortex ring inside the ventricle due to roll up of the fluid present in the vicinity of the mitral outlet and leaflets. During the remaining filling period, the vortex undergoes phases of longitudinal displacement and changes in size, but keeps contributing to blood transport across the mitral valve.
Although the time-evolving properties of this vortex ring have been well characterized in vivo (5,18,19), the present study is the first to quantify its capacity to transport blood across the mitral valve. Interestingly, initial speculations pointed toward a detrimental effect of the vortex ring on diastolic function by increasing pressure losses and energy dissipation (7). However, it was recently demonstrated that the diastolic vortex offers an advantage by confining the inflow jet and does not generate adverse pressure effects inside the LV (4,5,9). Our study demonstrates that the vortex additionally contributes to diastolic function by “pulling” blood from the LA and into the LV, particularly during the phases of E-wave deceleration, diastasis (whenever present), and late filling. At rest, 10% to 15% of filling flow is transported to the normal ventricle by this mechanism. During exercise, the vortex contribution is probably higher (20).
Despite the fact that the LV vortex acts as a functional mechanism to increase filling efficiency, it is improbable its abolition would lead to reduced cardiac output in most cases. In fact, despite a severely reduced vortex flow, stroke volume was within normal values in HCM patients. Seemingly, the heart can compensate for abolished vortex flow before compromising cardiac output. But, without modifying myocardial mechanical properties, this can only be achieved by increasing atrial pressure, accelerating the rate of relaxation, and/or boosting atrial thrust. In other words, it is possible for the heart to fill the LV by means of a vortex-free flow, but at the cost of increasing metabolic requirements and/or atrial pressure.
Transmitral flow-velocity measurement plays a pivotal role in the clinical assessment of cardiac hemodynamics. In particular, peak E-wave flow velocity is employed in most indexes for estimating LV filling pressures noninvasively (i.e., the recommended E/e′ method) (21,22). These Doppler-based indexes assume that peak E-wave velocity is determined by atrial pressure and the rate of LV relaxation (23). This assumption was derived from lumped-parameter models, and our study indicates a source of error caused by not accounting for inhomogeneous pressure-flow distributions inside of the chamber. Because the filling flow profile conditions vortex generation (9,24), and, in turn, the vortex is capable of modifying transmitral flow velocity, the structure-flow interaction that governs LV filling appears to be more complex than previously established. We speculate that the altered values of vortex-contributed flow we found in the NIDCM and HCM groups might help explain the inaccuracy of the E/e′ method previously reported in these 2 populations (25,26). Future studies exploring the utility of flow decomposition methods for predicting LV filling pressures noninvasively are warranted.
Fluid dynamics, chamber stiffness, and remodeling
Vortex-mediated blood transport was significantly modified in abnormal ventricles. This finding closely agrees with pioneering in vitro and in vivo studies showing the impact of chamber geometry on the generation of the diastolic vortex ring (5,24). In fact, the NIDCM group displaying enhanced vortex transport also showed the lowest values of myocardial diastolic deformation metrics. Therefore, beyond myocardial structure, filling flow dynamics have an independent role per se in determining global diastolic operative stiffness.
For given myocardium mechanical properties, chamber geometries favoring the vortical organization of flow inertia would show lower global operative stiffness than ventricles filled exclusively by vortex-free flow. In other words, a normal ventricle’s operative stiffness would be higher if it were to be filled statically (e.g., during an infinitely long filling period and hence without flow inertia). Thus, by modulating the level of vortex development, the degree of chamber sphericity determines its operative stiffness. We believe our measurements of vortex-induced flow facilitation demonstrate that changes in vortex development account for the previously reported sensitivity of diastolic function to the degree of concentric chamber remodeling (27) and are not an epiphenomenon of smaller chamber volumes.
The intraventricular vortex’s impact on filling has important implications and may explain several previously poorly understood findings. “L-waves” were described long ago as additional forward-velocity waves being recorded in transmitral pulsed-wave Doppler tracings during diastasis of normal subjects (28). Our findings support that L-waves are generated by vortex-mediated transport, not caused by the propagation of pulmonary vein flow as previously suggested (28) (Figure 4). In hypertensive patients, flow propagation velocity is frequently paradoxically fast (29). Because flow propagation velocity is related not only to relaxation but also to diastolic vortex strength (30,31), abolishing late flow propagation is probably the consequence of a predominant vortex-free filling jet in concentrically remodeled ventricles (Figure 4). In patients with atrial fibrillation or asynchronous pacing, disturbed intraventricular vortex formation may contribute to frequently elevated filling pressures. In patients with HCM undergoing remodeling surgery, restoring physiological vortex formation may be one of the mechanisms leading to the improvement of diastolic function demonstrated for this therapy (32). Regarding mitral valve repair or replacement, impairment of physiological intraventricular flow dynamics may play a role in the suboptimal hemodynamics frequently observed in the clinical setting (33). Additional studies are necessary to assess the implications of nonphysiological intraventricular fluid dynamics in these and other scenarios. Flow-decomposition algorithms, as introduced in this study, are suitable methods for this purpose.
The vortex ring is a 3-dimensional structure, but our study utilizes a 2D flow decomposition method. This planar flow simplification may lead to inaccuracy in estimating vortex-entered volume or filling fraction. However, a 2D approach offers important practical advantages. First, in our method, the theoretical planar constraint is relaxed by the numerical benefits of the minimization function used for solving the continuity equation (5,11). Ad-hoc validation studies against particle image velocimetry (11) and phase-contrast magnetic resonance (5) have demonstrated good agreement against reference techniques even in abnormal ventricles. Second, the computational requirements of the flow decomposition method are greatly reduced when implemented in 2D. Third, 2D methods can estimate the intraventricular flow field at the high spatial and temporal resolutions that are necessary to accurately estimate intraventricular pressure gradient fields (34). And finally, compared with similar physiological studies using phase-contrast magnetic resonance (1,4,35–37), we were able to study a relatively large number of patients in each group. Consequently, although the exact figures presented herein need to be interpreted with caution, we do not believe that our study’s conclusions would change qualitatively using more complex 3D techniques.
We did not measure chamber pressures, metabolic uptake, or intrinsic diastolic properties directly. However, we believe that the hemodynamic implications discussed in the previous text can be reliably deduced from the pressure gradient and flow data measured experimentally. Notice that, by definition, entering a given filling fraction at no pressure reduces overall chamber stiffness by the same proportion. Comprehensive mathematical models, probably combined with refined simulation methods, should be useful to analyze additional mechanisms of the reciprocal effects of fluid and myocardial mechanics on chamber diastolic function.
Using the intraventricular vortex ring, the normal ventricle in sinus rhythm enters 10% to 15% of its filling volume at no metabolic or pressure cost. Thus, the physiological diastolic vortex provides a useful mechanism to reduce global chamber operative stiffness. The amount of vortex facilitation is determined by the degree of ventricular chamber sphericity. Consequently, enhanced vortex function reduces chamber operative stiffness in conditions of eccentrically remodeled ventricles, such as NIDCM. Conversely, reduction of vortex-mediated filling is a mechanism of diastolic dysfunction in severe concentric remodeling diseases such as HCM.
COMPETENCY IN MEDICAL KNOWLEDGE: Digital processing of conventional color Doppler ultrasound sequences can be used to measure vortex facilitation and LV sphericity, providing insight into myocardial diastolic function.
TRANSLATIONAL OUTLOOK: Impaired vortex flow can be used to evaluate interventions and devices that influence diastolic intraventricular flow and global diastolic function in patients with various forms of acute and chronic cardiac disease.
Full mathematical derivation of the algorithms used for the flow decomposition and the further calculations can be found in the online version of this article.
This study was supported by grants PI12/02885, PIS09/02603, RD12/0042 (Red de Investigación Cardiovascular), and CM12/00273 (to Dr. Pérez del Villar) from the Instituto de Salud Carlos III–Ministerio de Economía y Competitividad, Spain, and National Institutes of Health grant 1R21 HL108268-01 (to Dr. del Álamo). Drs. Pérez del Villar and González-Mansilla have been partially supported by grants from the Fundación para Investigación Biomédica Gregorio Marañón, Madrid, Spain. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.
- Abbreviations and Acronyms
- time-resolved 2-dimensional
- analyses of variance
- diastolic intraventricular pressure difference (gradient)
- hypertrophic cardiomyopathy
- left ventricle/ventricular
- nonischemic dilated cardiomyopathy
- Received March 8, 2014.
- Revision received May 20, 2014.
- Accepted June 2, 2014.
- American College of Cardiology Foundation
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