E-wave asymmetry elucidates diastolic ventricular stiffness-relaxation coupling: model-based prediction with in vivo validation.

Load, chamber stiffness, and relaxation are the three established determinants of global diastolic function (DF). Coupling of systolic stiffness and isovolumic relaxation has been hypothesized; however, diastolic stiffness-relaxation coupling (DSRC) remains unknown. The parametrized diastolic filling (PDF) formalism, a validated DF model incorporates DSRC. PDF model-predicted DSRC was validated by analysis of 159 Doppler E-waves from a published data set (22 healthy volunteers undergoing bicycle exercise). E-waves at varying (46-120 bpm) heart rates (HR) demonstrated variation in acceleration time (AT), deceleration time (DT), and E-wave peak velocity. AT, DT, and Epeak were converted into PDF parameters: stiffness ([Formula: see text]), relaxation ([Formula: see text]), and load (xo) using published numerical methods. Univariate linear regression showed that over a twofold increase in HR, AT, and DT decrease ([Formula: see text] = -0.44; P < 0.001 and r = -0.42; P < 0.001, respectively), while, DT/AT remains constant (r = -0.04; P = 0.67). Similarly, [Formula: see text] increases with HR (r = 0.55; P < 0.001), while [Formula: see text] has no significant correlation with HR (r = 0.08; P = 0.32). However, the dimensionless DSRC parameter ψ = c2/4k shows no significant correlation with HR (r = -0.03; P = 0.7). Furthermore, ψ is uniquely determined by DT/AT rather than AT or DT independently. Constancy of ψ in spite of a twofold increase in HR establishes that stiffness (k) and relaxation (c) are coupled and manifest via a HR-invariant parameter of E-wave asymmetry and should not be considered independent of each other. The manifestation of DSRC through E-wave asymmetry via ψ underscores the value of DT/AT as a physiological, mechanism-derived index of DF.NEW & NOTEWORTHY: Although diastolic stiffness and relaxation are considered independent chamber properties, the cardio-hemic inertial oscillation that generates E-waves obeys Newton's law. E-waves vary with heart rate requiring simultaneous change in stiffness and relaxation. By retrospective analysis of human heart-rate varying transmitral Doppler-data, we show that diastolic stiffness and relaxation are coupled and that the coupling manifests through E-wave asymmetry, quantified through a parametrized diastolic filling model-derived dimensionless parameter, which only depends on deceleration time and acceleration time, readily obtainable via standard echocardiography.

Alternative diastolic function models of ventricular longitudinal filling velocity are mathematically identical.

The spatiotemporal features of normal in vivo cardiac motion are well established. Longitudinal velocity has become a focus of diastolic function (DF) characterization, particularly the tissue Doppler e'-wave, manifesting in early diastole when the left ventricle (LV) is a mechanical suction pump (dP/dV < 0). To characterize DF and elucidate mechanistic features, several models have been proposed and have been previously compared algebraically, numerically, and in their ability to fit physiological velocity data. We analyze two previously noncompared models of early rapid-filling lengthening velocity (Doppler e'-wave): parametrized diastolic filling (PDF) and force balance model (FBM). Our initial numerical experiments sampled FBM-generated e'(t) contours as input to determine PDF model predicted fit. The resulting exact numerical agreement [standard error of regression (SER) = 9.06 × 10-16] was not anticipated. Therefore, we analyzed all published FBM-generated e'(t) contours and observed identical agreement. We re-expressed FBM's algebraic expressions for e'(t) and observed for the first time that model-based predictions for lengthening velocity by the FBM and the PDF model are mathematically identical: e'(t) = γe-αtsinh(ßt), thereby providing exact algebraic relations between the three PDF parameters and the six FBM parameters. Previous pioneering experiments have independently established the unique determinants of e'(t) to be LV relaxation, restoring forces (stiffness), and load. In light of the exact intermodel agreement, we conclude that the three PDF parameters, relaxation, stiffness (restoring forces), and load, are unique determinants of DF and e'(t). Thus, we show that only the PDF formalism can compute the three unique, independent, physiological determinants of long-axis LV myocardial velocity from e'(t).NEW & NOTEWORTHY We show that two separate, independently derived physiological (kinematic) models predict mathematically identical expressions for LV-lengthening velocity (Doppler e'-wave), indicating that damped harmonic oscillatory motion is a physiologically accurate model of diastolic function. Although both models predict the same "overdamped" velocity contour, only one model solves the "inverse problem" and generates unique, lumped parameters of relaxation, stiffness (restoring force), and load from the e'-wave.

Vortex-ring mixing as a measure of diastolic function of the human heart: Phantom validation and initial observations in healthy volunteers and patients with heart failure.

PURPOSE: To present and validate a new method for 4D flow quantification of vortex-ring mixing during early, rapid filling of the left ventricle (LV) as a potential index of diastolic dysfunction and heart failure. MATERIALS AND METHODS: 4D flow mixing measurements were validated using planar laser-induced fluorescence (PLIF) in a phantom setup. Controls (n = 23) and heart failure patients (n = 23) were studied using 4D flow at 1.5T (26 subjects) or 3T (20 subjects) to determine vortex volume (VV) and inflowing volume (VVinflow ). The volume mixed into the vortex-ring was quantified as VVmix-in = VV-VVinflow . The mixing ratio was defined as MXR = VVmix-in /VV. Furthermore, we quantified the fraction of the end-systolic volume (ESV) mixed into the vortex-ring (VVmix-in /ESV) and the fraction of the LV volume at diastasis (DV) occupied by the vortex-ring (VV/DV). RESULTS: PLIF validation of MXR showed fair agreement (R(2) = 0.45, mean ± SD 1 ± 6%). MXR was higher in patients compared to controls (28 ± 11% vs. 16 ± 10%, P < 0.001), while VVmix-in /ESV and VV/DV were lower in patients (10 ± 6% vs. 18 ± 12%, P < 0.01 and 25 ± 8% vs. 50 ± 6%, P < 0.0001). CONCLUSION: Vortex-ring mixing can be quantified using 4D flow. The differences in mixing parameters observed between controls and patients motivate further investigation as indices of diastolic dysfunction. J. Magn. Reson. Imaging 2016;43:1386-1397.

What global diastolic function is, what it is not, and how to measure it.

Despite Leonardo da Vinci's observation (circa 1511) that "the atria or filling chambers contract together while the pumping chambers or ventricles are relaxing and vice versa," the dynamics of four-chamber heart function, and of diastolic function (DF) in particular, are not generally appreciated. We view DF from a global perspective, while characterizing it in terms of causality and clinical relevance. Our models derive from the insight that global DF is ultimately a result of forces generated by elastic recoil, modulated by cross-bridge relaxation, and load. The interaction between recoil and relaxation results in physical wall motion that generates pressure gradients that drive fluid flow, while epicardial wall motion is constrained by the pericardial sac. Traditional DF indexes (τ, E/E', etc.) are not derived from causal mechanisms and are interpreted as approximating either stiffness or relaxation, but not both, thereby limiting the accuracy of DF quantification. Our derived kinematic models of isovolumic relaxation and suction-initiated filling are extensively validated, quantify the balance between stiffness and relaxation, and provide novel mechanistic physiological insight. For example, causality-based modeling provides load-independent indexes of DF and reveals that both stiffness and relaxation modify traditional DF indexes. The method has revealed that the in vivo left ventricular equilibrium volume occurs at diastasis, predicted novel relationships between filling and wall motion, and quantified causal relationships between ventricular and atrial function. In summary, by using governing physiological principles as a guide, we define what global DF is, what it is not, and how to measure it.

Spatio-temporal attributes of left ventricular pressure decay rate during isovolumic relaxation.

Global left ventricular (LV) isovolumic relaxation rate has been characterized: 1) via the time constant of isovolumic relaxation τ or 2) via the logistic time constant τ(L). An alternate kinematic method, characterizes isovolumic relaxation (IVR) in accordance with Newton's Second Law. The model's parameters, stiffness E(k), and damping/relaxation µ result from best fit of model-predicted pressure to in vivo data. All three models (exponential, logistic, and kinematic) characterize global relaxation in terms of pressure decay rates. However, IVR is inhomogeneous and anisotropic. Apical and basal LV wall segments untwist at different times and rates, and transmural strain and strain rates differ due to the helically variable pitch of myocytes and sheets. Accordingly, we hypothesized that the exponential model (τ) or kinematic model (µ and E(k)) parameters will elucidate the spatiotemporal variation of IVR rate. Left ventricular pressures in 20 subjects were recorded using a high-fidelity, multipressure transducer (3 cm apart) catheter. Simultaneous, dual-channel pressure data was plotted in the pressure phase-plane (dP/dt vs. P) and τ, µ, and E(k) were computed in 1631 beats (average: 82 beats per subject). Tau differed significantly between the two channels (P < 0.05) in 16 of 20 subjects, whereas µ and E(k) differed significantly (P < 0.05) in all 20 subjects. These results show that quantifying the relaxation rate from data recorded at a single location has limitations. Moreover, kinematic model based analysis allows characterization of restoring (recoil) forces and resistive (crossbridge uncoupling) forces during IVR and their spatio-temporal dependence, thereby elucidating the relative roles of stiffness vs. relaxation as IVR rate determinants.

The thermodynamics of diastole: kinematic modeling-based derivation of the P-V loop to transmitral flow energy relation with in vivo validation.

Pressure-volume (P-V) loop-based analysis facilitates thermodynamic assessment of left ventricular function in terms of work and energy. Typically these quantities are calculated for a cardiac cycle using the entire P-V loop, although thermodynamic analysis may be applied to a selected phase of the cardiac cycle, specifically, diastole. Diastolic function is routinely quantified by analysis of transmitral Doppler E-wave contours. The first law of thermodynamics requires that energy (ε) computed from the Doppler E-wave (εE-wave) and the same portion of the P-V loop (εP-V E-wave) be equivalent. These energies have not been previously derived nor have their predicted equivalence been experimentally validated. To test the hypothesis that εP-V E-wave and εE-wave are equivalent, we used a validated kinematic model of filling to derive εE-wave in terms of chamber stiffness, relaxation/viscoelasticity, and load. For validation, simultaneous (conductance catheter) P-V and echocadiographic data from 12 subjects (205 total cardiac cycles) having a range of diastolic function were analyzed. For each E-wave, εE-wave was compared with εP-V E-wave calculated from simultaneous P-V data. Linear regression yielded the following: εP-V E-wave=αεE-wave+b (R2=0.67), where α=0.95 and b=6e(-5). We conclude that E-wave-derived energy for suction-initiated early rapid filling εE-wave, quantitated via kinematic modeling, is equivalent to invasive P-V-defined filling energy. Hence, the thermodynamics of diastole via εE-wave generate a novel mechanism-based index of diastolic function suitable for in vivo phenotypic characterization.

Elucidation of spatially distinct compensatory mechanisms in diastole: radial compensation for impaired longitudinal filling in left ventricular hypertrophy.

Cardiac output maintenance is so fundamental that, when regional systolic function is impaired, as during ischemia, nonischemic segments compensate by becoming hypercontractile. By analogy, diastolic compensatory mechanisms that maintain filling volume must exist but remain to be fully elucidated. Viewing filling in spatially distinct (longitudinal, radial) mechanistic terms facilitates elucidation of diastolic compensatory mechanisms. Because impairment of longitudinal (long axis) diastolic function (DF) in left ventricular hypertrophy (LVH) is established, we hypothesized that to maintain filling volume, radial (short-axis) filling function would compensate. In 20 normal left ventricular ejection fraction (LVEF) subjects (10 with LVH, 10 without LVH), we analyzed longitudinal function via Doppler tissue imaging of mitral annular motion and radial function as change in short-axis endocardial dimension via M-mode. The spatial (long axis, short axis) endocardial LV dimensions and their changes allowed assignment of E-wave filling volume into (cylindrical geometry-based) longitudinal and radial components. Despite indistinguishable (P = 0.70) E-wave velocity-time integrals (E-wave filling volume surrogate), systolic stroke volumes, and end-diastolic volumes in the LVH and control groups, longitudinal volume in absolute terms and the percent of E-wave volume accommodated longitudinally were reduced in the LVH group (P < 0.05 and P < 0.01, respectively), whereas the percent of E-wave volume accommodated radially was enhanced (P < 0.01). We conclude that, in normal LVEF (decreased longitudinal volume accommodation) LVH subjects vs. controls, spatially distinct compensatory mechanisms in diastole manifest as increased radial volume accommodation per unit of E-wave filling volume. Assessment of spatially distinct diastolic compensatory mechanisms in other pathophysiological subsets is warranted.

Quantifying Diastolic Function: From E-Waves as Triangles to Physiologic Contours via the 'Geometric Method'.

Conventional echocardiographic diastolic function (DF) assessment approximates transmitral flow velocity contours (Doppler E-waves) as triangles, with peak (Epeak), acceleration time (AT), and deceleration time (DT) as indexes. These metrics have limited value because they are unable to characterize the underlying physiology. The parametrized diastolic filling (PDF) formalism provides a physiologic, kinematic mechanism based characterization of DF by extracting chamber stiffness (k), relaxation (c), and load (x o ) from E-wave contours. We derive the mathematical relationship between the PDF parameters and Epeak, AT, DT and thereby introduce the geometric method (GM) that computes the PDF parameters using Epeak, AT, and DT as input. Numerical experiments validated GM by analysis of 208 E-waves from 31 datasets spanning the full range of clinical diastolic function. GM yielded indistinguishable average parameter values per subject vs. the gold-standard PDF method (k: R2 = 0.94, c: R2 = 0.95, x o : R2 = 0.95, p < 0.01 all parameters). Additionally, inter-rater reliability for GM-determined parameters was excellent (k: ICC = 0.956 c: ICC = 0.944, x o : ICC = 0.993). Results indicate that E-wave symmetry (AT/DT) may comprise a new index of DF. By employing indexes (Epeak, AT, DT) that are already in standard clinical use the GM capitalizes on the power of the PDF method to quantify DF in terms of physiologic chamber properties.

Contraction-relaxation coupling mechanism characterization in the thermodynamic phase plane: normal vs. impaired left ventricular ejection fraction.

Using simultaneous pressure-volume measurements obtained during cardiac catheterization, we employ the thermodynamic phase-plane (TPP) method to characterize global contraction-relaxation coupling (CRC) between normal and impaired left ventricular (LV) ejection fraction (LVEF) groups. The cardiac cycle inscribes a closed loop in the TPP defined by the coordinates "potential" power [V(dP/dt), ergs/s] and "kinetic" power [P(dV/dt), ergs/s]. The TPP-derived indexes kappa and rho define the chamber's contractile and CRC attributes, respectively. Data from 33 subjects dichotomized as normal control (n = 22, >50% LVEF) and impaired LVEF (n = 11, <50% LVEF) were analyzed. The results were as follows: kappa = 3.0 +/- 1.1 and rho = -0.38 +/- 0.21 for controls and kappa = 5.4 +/- 1.6 and rho = -1.14 +/- 0.47 for the impaired LVEF group; kappa and rho are significantly higher for impaired LVEF than for control (P < 0.001 for both). As kappa increased, rho decreased (r = -0.69) for all subjects. Hence, ventricles with impaired LVEF are thermodynamically less efficient because they require more potential power per unit of delivered kinetic power than controls. We conclude that TPP-derived indexes of CRC facilitate assessment of chamber efficiency in thermodynamic terms and elucidate the dominant differentiating features in terms of CRC indexes.

Stiffness- and relaxation-based quantitation of radial left ventricular oscillations: elucidation of regional diastolic function mechanisms.

Traditionally, global and longitudinal (i.e., regional) left ventricular (LV) diastolic function (DF) assessment has utilized features of transmitral Doppler E and A waves or Doppler tissue imaging (DTI)-derived mitral annular E' and A' waves, respectively. Quantitation of regional DF has included M-mode echocardiography-based approaches and strain and strain rate imaging (in selected imaging planes), while analysis of mitral annular "oscillations" has recently provided a new window into longitudinal (long-axis) function. The remaining major spatial degree of kinematic freedom during diastole, radial (short-axis) motion, has not been fully characterized, nor has it been exploited for its potential to provide radial LV stiffness (k'(rad)) and relaxation/damping (c'(rad)) indexes. Prior characterization of regional (longitudinal) DF used only annular E'- and A'-wave peak velocities or, alternatively, myocardial strain and strain rate. By kinematically modeling short-axis tissue motion as damped radial oscillation, we present a novel method of estimating k'(rad) and c'(rad) during early filling. As required by the (near) constant-volume property of the heart and tissue/blood incompressibility, in subjects (n = 10) with normal DF, we show that oscillation duration-determined longitudinal (k'(long) and c'(long)) and radial (k'(long) and c'(rad)) parameters are highly correlated (R = 0.69 and 0.92, respectively). Selected examples of diabetic and LV hypertrophic subjects yield radial (k'(long) and c'(rad)) parameters that differ substantially from controls. Results underscore the utility of the incompressibility-based causal relation between DTI-determined mitral annular long-axis (longitudinal mode) and short-axis (radial mode) oscillations in healthy subjects. Selected pathological examples provide mechanistic insight and illustrate the value and potential role of regional (longitudinal and radial) DF indexes in fully characterizing normal vs. impaired DF states.

The kinematic filling efficiency index of the left ventricle: contrasting normal vs. diabetic physiology.

An index of filling efficiency incorporating stiffness and relaxation (S&R) parameters has not been derived or validated, although numerous studies have focused on the effects of altered relaxation or stiffness on early rapid filling and diastolic function. Previous studies show that S&R parameters can be obtained from early rapid filling (Doppler E-wave) via kinematic modeling. E-wave contours are governed by harmonic oscillatory motion modeled via the parameterized diastolic filling (PDF) formalism. The previously validated model determines three (unique) oscillator parameters from each E-wave having established physiological analogues: x(o) (load), c (relaxation/viscoelasticity) and k (chamber stiffness). We define the dimensionless, filling-volume-based kinematic filling efficiency index (KFEI) as the ratio of the velocity-time integral (VTI) of the actual clinical E-wave contour fit via PDF to the VTI of the PDF model-predicted ideal E-wave contour having the same x(o) and k, but with no resistance to filling (c = 0). To validate the new index, Doppler E-waves from 36 patients with normal ventricular function, 17 diabetic and 19 well-matched non-diabetic controls, were analyzed. E-wave parameters x(o), c and k and KFEI were computed for each patient and compared. In concordance with prior human and animal studies in which c differentiated between normal and diabetic hearts, KFEI differentiated (p < 0.001) between nondiabetics (55.8% +/- 3.3%) and diabetics (49.1% +/- 3.3%). Thus, the new index introduces and validates the concept of filling efficiency, and, using diabetes as a working example, provides quantitative and mechanistic insight into how S&R affect ventricular filling efficiency.

The quest for load-independent left ventricular chamber properties: exploring the normalized pressure-volume loop.

Left ventricular (LV) pressure-volume (P-V) loop analysis is the gold standard for chamber function assessment. To advance beyond traditional P-V and pressure phase plane (dP/dt-P) analysis in the quest for novel load-independent chamber properties, we introduce the normalized P-V loop. High-fidelity LV pressure and volume data (161 P-V loops) from 13 normal control subjects were analyzed. Normalized LV pressure (PN) was defined by 0 ≤ P(t) ≤ 1. Normalized LV volume (VN) was defined as VN=V(t)/Vdiastasis, since the LV volume at diastasis (Vdiastasis) is the in-vivo equilibrium volume relative to which the LV volume oscillates. Plotting PN versus VN for each cardiac cycle generates normalized P-V loops. LV volume at the peak LV ejection rate and at the peak LV filling rate (peak -dV/dt and peak +dV/dt, respectively) were determined for conventional and normalized loops. VN at peak +dV/dt was inscribed at 64 ± 5% of normalized equilibrium (diastatic) volume with an inter-subject variation of 8%, and had a reduced intra-subject (beat-to-beat) variation compared to conventional P-V loops (9% vs. 13%, respectively; P < 0.005), thereby demonstrating load-independent attributes. In contrast, VN at peak -dV/dt was inscribed at 81 ± 9% with an inter-subject variation of 11%, and had no significant change in intra-subject (beat-to-beat) variation compared to conventional P-V loops (17% vs. 17%, respectively; P = 0.56), therefore failing to demonstrate load-independent tendencies. Thus, the normalized P-V loop advances the quest for load-independent LV chamber properties. VN at the peak LV filling rate (≈sarcomere length at the peak sarcomere lengthening rate) manifests load-independent properties. This novel method may help to elucidate and quantify new attributes of cardiac and cellular function. It merits further application in additional human and animal physiologic and pathophysiologic datasets.

Hydraulic forces contribute to left ventricular diastolic filling.

Myocardial active relaxation and restoring forces are known determinants of left ventricular (LV) diastolic function. We hypothesize the existence of an additional mechanism involved in LV filling, namely, a hydraulic force contributing to the longitudinal motion of the atrioventricular (AV) plane. A prerequisite for the presence of a net hydraulic force during diastole is that the atrial short-axis area (ASA) is smaller than the ventricular short-axis area (VSA). We aimed (a) to illustrate this mechanism in an analogous physical model, (b) to measure the ASA and VSA throughout the cardiac cycle in healthy volunteers using cardiovascular magnetic resonance imaging, and (c) to calculate the magnitude of the hydraulic force. The physical model illustrated that the anatomical difference between ASA and VSA provides the basis for generating a hydraulic force during diastole. In volunteers, VSA was greater than ASA during 75-100% of diastole. The hydraulic force was estimated to be 10-60% of the peak driving force of LV filling (1-3 N vs 5-10 N). Hydraulic forces are a consequence of left heart anatomy and aid LV diastolic filling. These findings suggest that the relationship between ASA and VSA, and the associated hydraulic force, should be considered when characterizing diastolic function and dysfunction.

Consequences of increasing heart rate on deceleration time, the velocity-time integral, and E/A.

The ascendancy of diastolic heart failure to "epidemic" proportions has increased the use of and reliance on Doppler echocardiography as a source for diagnosis and as the preferred method for determining indexes of diastolic function (DF). Current indexes are primarily derived from shape-based features of Doppler E and A waves, such as their amplitudes, slopes, durations, and areas. Load dependence and pathologic correlates of these indexes have been considered, but DF indexes are not routinely corrected for heart rate (HR). To determine the dependence of selected Doppler-derived indexes of DF on HR, transmitral Doppler flow velocities and electrocardiograms were simultaneously recorded during supine bicycle exercise in 21 young, healthy volunteers. Standard E- and A-wave shape-based indexes (acceleration time, deceleration time [DT], peak E, peak A) were measured using triangle approximation. Velocity-time integrals (VTIs) were calculated by trapezoidal and triangular approximations. A-wave peak velocity (A) was measured conventionally, relative to baseline, and also using 2 alternative methods: A*, measured relative to the E@A velocity, and Ac, relative to the E-wave deceleration value at peak A-wave velocity. E/A was calculated conventionally and by using A* and Ac. The results showed that DF indexes derived from individual E waves are essentially HR independent. DT showed a mere 20% decrease for a 100% increase in HR. A triangular approximation for the E-wave VTI and the corrected E/Ac were found to be nearly HR independent. In conclusion, on the basis of the established continuity of cardiac output as a function of increasing HR and the observed data, Doppler-derived indexes of DF (DT, VTIs, E/Ac) can be treated as essentially HR independent only if the VTI and A-wave peak are corrected for HR as described.

Quantitation of mitral annular oscillations and longitudinal "ringing" of the left ventricle: a new window into longitudinal diastolic function.

For diastolic function (DF) quantification, transmitral flow velocity has been characterized in terms of the geometric features of a triangle (heights, widths, areas, durations) approximating the E-wave contour, whereas mitral annular velocity has only been characterized by E'-wave peak amplitude. The fact that E-waves convey global DF information, whereas annular E'-waves provide longitudinal DF information, has not been fully characterized, nor has the physiological legitimacy of combining fluid motion (E)- and tissue motion (E')-derived measurements into routinely used indexes (E/E') been fully elucidated. To place these Doppler echo measurements on a firmer causal, physiological, and clinical basis, we examined features of the E'-wave (and annular motion in general), including timing, amplitude, duration, and contour (shape), in kinematic terms. We derive longitudinal rather than global indexes of stiffness and relaxation of the left ventricle and explain the observed difference between E- and E'-wave durations. On the basis of the close agreement between model prediction and E'-wave contour for subjects having normal physiology, we propose damped harmonic oscillation as the proper paradigm in which to view and analyze the motion of the mitral annulus during early filling. Novel, longitudinal indexes of left ventricular stiffness, relaxation, viscosity, and stored (end-systolic) elastic strain can be determined from the E'-wave (and any subsequent waves) by modeling annular motion during early filling as damped harmonic oscillation. A subgroup exploratory analysis conducted in diabetic subjects (n = 9) and nondiabetic controls (n = 12) indicates that longitudinal DF indexes differentiate between these groups on the basis of longitudinal damping (P < 0.025) and longitudinal stored elastic strain (P < 0.005).

Load-independent index of diastolic filling: model-based derivation with in vivo validation in control and diastolic dysfunction subjects.

Maximum elastance is an experimentally validated, load-independent systolic function index stemming from the time-varying elastance paradigm that decoupled extrinsic load from (intrinsic) contractility. Although Doppler echocardiography is the preferred method of diastolic function (DF) assessment, all echo-derived indexes are load dependent, and no invasive or noninvasive load-independent index of filling (LIIF) exists. In this study, we derived and experimentally validated a LIIF. We used a kinematic filling paradigm (the parameterized diastolic filling formalism) to predict and derive the (dimensionless) dynamic diastolic efficiency M, defined by the slope of the peak driving force [maximum driving force (kx(o)) proportional, variant peak atrioventricular (AV) gradient] to maximum viscoelastic resistive force [peak resistive force (cE(peak))] relation. To validate load independence, we analyzed E-waves recorded while load was varied via tilt table (head up, horizontal, and head down) in 16 healthy volunteers. For the group, linear regression of E-wave derived kx(o) vs. cE(peak) yielded kx(o) = M (cE(peak)) + B, r2 = 0.98; where M = 1.27 +/- 0.09 and B = 5.69 +/- 1.70. Effects of diastolic dysfunction (DD) on M were assessed by analysis of preexisting simultaneous cath-echo data in six DD vs. five control subjects. Average M for the DD group (M = 0.98 +/- 0.07) was significantly lower than controls (M = 1.17 +/- 0.05, P < 0.001). We conclude that M is a LIIF because it uncouples intrinsic DF (i.e., the pressure-flow relation) from extrinsic load (left ventricular end-diastolic pressure). Larger M values imply better DF in that increasing AV pressure gradient results in relatively smaller increases in peak resistive losses (cE(peak)). Conversely, lower M implies that increasing AV gradient leads to larger increases in resistive losses. Further prospective validation characterizing M in well-defined pathological states is warranted.

Isovolumic pressure-to-early rapid filling decay rate relation: model-based derivation and validation via simultaneous catheterization echocardiography.

Transmitral Doppler echocardiography is the preferred method of noninvasive diastolic function assessment. Correlations between catheterization-based measures of isovolumic relaxation (IVR) and transmitral, early rapid filling (Doppler E-wave)-derived parameters have been observed, but no model-based, causal explanation has been offered. IVR has also been characterized in terms of its duration as IVR time (IVRT) and by tau, the time-constant of IVR, by approximating the terminal left ventricular IVR pressure contour as Pt= Pinfinity + P(o)e(-t/tau), where Pt is the continuity of pressure, Pinfinity and Po are constants, t is time, and tau is the time constant of IVR. To characterize the relation between IVR and early rapid filling more fully, simultaneous (micromanometric) left ventricular pressure and transmitral Doppler E-wave data from 25 subjects undergoing elective cardiac catheterization and having normal physiology were analyzed. The time constant tau was determined from the dP/dt vs. P (phase) plane and, simultaneous Doppler E-waves provided global indexes of chamber viscosity/relaxation (c), chamber stiffness (k), and load (xo). We hypothesize that temporal continuity of pressure decay at mitral valve opening and physiological constraints permit the algebraic derivation of linear relations relating 1/tau to both peak atrioventricular pressure gradient (kxo) and E-wave-derived viscosity/relaxation (c) but does not support a similar, causal (linear) relation between deceleration time and tau or IVRT. Both predicted linear relations were observed: kxo to 1/tau (r = 0.71) and viscosity/relaxation to 1/tau (r = 0.71). Similarly, as anticipated, only a weak linear correlation between deceleration time and IVRT or tau was observed (r = 0.41). The observed in vivo relationship provides insight into the isovolumic mechanism of relaxation and the changing-volume mechanism of early rapid filling via a link of the respective relaxation properties.

Vortex ring behavior provides the epigenetic blueprint for the human heart.

The laws of fluid dynamics govern vortex ring formation and precede cardiac development by billions of years, suggesting that diastolic vortex ring formation is instrumental in defining the shape of the heart. Using novel and validated magnetic resonance imaging measurements, we show that the healthy left ventricle moves in tandem with the expanding vortex ring, indicating that cardiac form and function is epigenetically optimized to accommodate vortex ring formation for volume pumping. Healthy hearts demonstrate a strong coupling between vortex and cardiac volumes (R(2) = 0.83), but this optimized phenotype is lost in heart failure, suggesting restoration of normal vortex ring dynamics as a new, and possibly important consideration for individualized heart failure treatment. Vortex ring volume was unrelated to early rapid filling (E-wave) velocity in patients and controls. Characteristics of vortex-wall interaction provide unique physiologic and mechanistic information about cardiac diastolic function that may be applied to guide the design and implantation of prosthetic valves, and have potential clinical utility as therapeutic targets for tailored medicine or measures of cardiac health.

Quantitative assessment of atrial conduit function: a new index of diastolic dysfunction.

BACKGROUND: Heart failure (HF) epidemic has increased need for accurate diastolic dysfunction (DD) quantitation. Cardiac MRI can elucidate left atrial (LA) phasic function, and accurately quantify its conduit contribution to left ventricular (LV) filling, but has limited availability. We hypothesized that the percentage of LV stroke volume due to atrial conduit volume (LACV), as assessed using 3D-echocardiography, can differentiate among progressive degrees of DD in HF patients. METHODS AND RESULTS: Sixty-three subjects (66 ± 12 years) with DD and ejection fraction (EF) ranging 14-62% underwent full-volume 3D-echocardiography. Simultaneous LA and LV volume curves as function of time (t) were calculated, with LACV as LACV(t) = [LV(t) - LV minimum] - [LA maximum LA(t)], expressed as % of stroke volume. Patients were assigned to four (0-3, from none to severe) DD grades, according to classical Doppler parameters. In this population DD is linked to LACV, with progressively higher percentages of conduit contribution to stroke volume associated with higher degrees of DD (p = 0.0007). Patients were then dichotomized into no-mild (n = 26) or severe (n = 37) DD groups. Apart from atrial volume, larger (p < 0.02) in severe DD group, no differences between groups were found for LV diastolic and stroke volume, EF, mass and flow propagation velocity. However, a significant difference was found for LACV expressed as % of LV stroke volume (29 ± 15 vs. 43 ± 23%, p = 0.016). CONCLUSIONS: Our study confirms that LACV contribution to stroke volume increases along with worsening DD, as assessed in the context of (near) constant-volume four-chamber heart physiology. Thus, LACV can serve as new parameter for DD grading severity in HF patients.