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Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism

Quantitative cardiac function assessment remains a challenge for physiologists and clinicians.&#160;Although historically invasive methods have comprised ...

Washington University in St. Louis

The filling (diastolic) function of the human left ventricle is most commonly assessed by echocardiography, a non-invasive imaging modality. To quantify diastolic function (DF) empiric indices are obtained from the features (height, duration, area) of transmitral flow velocity contour, obtained by echocardiography. The parameterized diastolic filling (PDF) formalism is a kinematic model developed by Kovács et. al. which incorporates the suction pump attribute of the left ventricle and facilitates DF quantitation by analysis of echocardiographic transmitral flow velocity contours in terms of stiffness (k), relaxation (c) and load (x(0)). A complementary approach developed by Gharib et. al., uses fluid mechanics and characterizes DF in terms of vortex formation time (T*) derived from streamline features formed by the jet of blood aspirated into the ventricle. Both of these methods characterize DF using a causality-based approach. In this paper, we derive T*'s kinematic analogue T*(kinematic) in terms of k, c and x(0). A comparison between T*(kinematic) and T*(fluid) (mechanic) obtained from averaged transmitral velocity and mitral annulus diameter, is presented. We found that T* calculated by the two methods were comparable and T*(kinematic) correlated with the peak LV recoil driving force kx(0).

Determination of early diastolic LV vortex formation time (T*) via the PDF formalism: a kinematic model of filling.

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 VFT(Gharib) 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 VFT(kinematic), 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. VFT(Gharib) and VFT(kinematic) were calculated for each subject and were well-correlated (R(2) = 0.66). In accordance with prediction, VFT(kinematic) to (E/E')(3/2) relationship was validated (R(2) = 0.63). We conclude that VFT(kinematic) 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).

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

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.

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

Flow impedance has been used to characterize the physical properties of the vascular system by assessing its phasic flow response to pulsatile pressure input in terms of resistance as a function of frequency. Impedance has also been used to characterize global diastolic left ventricular (LV) chamber properties. In early diastole the LV is a mechanical suction pump and accommodates filling by simultaneously expanding in two principal spatial directions: longitudinal (base-to-apex, long-axis) and transverse (radial, short-axis). Total (characteristic) impedance Z(C) is the product of longitudinal (Z(L)) and transverse (Z(T)) impedance as Z(C)(2)=Z(L)Z(T) where the two impedances reflect the relative spatial propensity for volume accommodation. In this work we compute Z(L) and Z(T) for the LV in early diastole. We analyze simultaneously recorded dual pressure-transducer and transthoracic echocardiographic flow data obtained during cardiac catheterization in 11 subjects. We found that Z(L) was 2 orders of magnitude smaller than Z(T) in all subjects, providing the first hemodynamic evidence, in concordance with cine-MRI imaging data that longitudinal volume accommodation is indeed, nature's preferred spatial filling mechanism. We also investigated the effect of impaired diastolic function on directional impedances and found that Z(L) increased (becomes worse) while Z(T) decreased (becomes better) indicating that as diastolic function becomes impaired radial filling compensates for decreased longitudinal volume accommodation to preserve stroke volume. These results provide mechanistic insight and show that normal diastolic function defines a properly impedance matched state and that diastolic dysfunction is equivalent to a state of impedance mismatch.

Quantitative assessment of left ventricular diastolic function via longitudinal and transverse flow impedances.

Impedance has been used in vascular biology to characterize the frequency dependent opposition the circulatory system presents to blood flow in response to a pulsatile pressure gradient. It has also been used to characterize diastolic function (DF) via the early, diastolic left ventricular (LV) pressure-flow relation. In a normal LV, early filling volume is accommodated primarily by wall-thinning and ascent of the mitral annulus relative to the spatially fixed apex (longitudinal chamber expansion). Simultaneously, the endocardial (transverse or short axis) dimension also increases while epicardial (transverse) external dimension remains essentially constant. To quantify these directional filling attributes, we compute longitudinal (Z(L)) and transverse (Z(T)) impedances during early rapid-filling (Doppler E-wave). Z(L) and Z(T) were calculated from 578 cardiac cycles of simultaneous transmitral flow and high fidelity LV pressure data in 17 subjects with normal LV function. Average Z(L) was 0.7 ± 0.4 mmHg s/cm(4) and average Z(T) was 238 ± 316 mmHg s/cm(2). Direct comparison, in the same units is achieved by computing Z(T) over the ≈10 cm(2) cross-sectional area of LV (denoted ŽT) revealing that Z(L) is ≈34 times smaller than Ž(T). This quantifies the physiologic preference for longitudinal LV volume accommodation. Lowest Z(L) and Z(T) values occurred in the first harmonic with monotonically increasing values with higher harmonics. We conclude that Z(L) and Z(T) characterize longitudinal and transverse chamber properties of DF and therefore, diastolic dysfunction can be viewed as a state of impedance mismatch.

Early left ventricular diastolic function quantitation using directional impedances.

-Heart failure with preserved ejection fraction (HFPEF) involves failure of cardiovascular reserve in multiple domains. In HFPEF animal models, dietary sodium restriction improves ventricular and vascular stiffness and function. We hypothesized that the sodium-restricted Dietary Approaches to Stop Hypertension diet (DASH/SRD) would improve left ventricular diastolic function, arterial elastance, and ventricular-arterial (V-A) coupling in hypertensive HFPEF.

Low-Sodium DASH Diet Improves Diastolic Function and Ventricular-Arterial Coupling in Hypertensive Heart Failure with Preserved Ejection Fraction.

The pressure phase plane (PPP), defined by dP(t)/dt versus P(t) coordinates has revealed novel physiologic relationships not readily obtainable from conventional, time domain analysis of left ventricular pressure (LVP). We extend the methodology by introducing the normalized pressure phase plane (nPPP), defined by 0 ≤ P ≤ 1 and -1 ≤ dP/dt ≤ +1. Normalization eliminates load-dependent effects facilitating comparison of conserved features of nPPP loops. Hence, insight into load-invariant systolic and diastolic chamber properties and their coupling to load can be obtained. To demonstrate utility, high-fidelity P(t) data from 14 subjects (4234 beats) was analyzed. PNR, the nPPP (dimensionless) pressure, where -dP/dtpeak occurs, was 0.61 and had limited variance (7%). The relative load independence of PNR was corroborated by comparison of PPP and nPPP features of normal sinus rhythm (NSR) and (ejecting and nonejecting) premature ventricular contraction (PVC) beats. PVCs had lower P(t)max and lower peak negative and positive dP(t)/dt values versus NSR beats. In the nPPP, +dP/dtpeak occurred at higher (dimensionless) P in PVC beats than in regular beats (0.44 in NSR vs. 0.48 in PVC). However, PNR for PVC versus NSR remained unaltered (PNR = 0.64; P > 0.05). Possible mechanistic explanation includes a (near) load-independent (constant) ratio of maximum cross-bridge uncoupling rate to instantaneous wall stress. Hence, nPPP analysis reveals LV properties obscured by load and by conventional temporal P(t) and dP(t)/dt analysis. nPPP identifies chamber properties deserving molecular and cellular physiologic explanation.

The quest for load-independent left ventricular chamber properties: Exploring the normalized pressure phase plane.

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, VFTstandard = {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, VFTkinematic reexpresses VFTstandard by incorporating left heart, near "constant-volume pump" physiology thereby revealing VFTkinematic's explicit dependence on maximum rate of longitudinal chamber expansion (E'). In this work, we show that VFTkinematic 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 VFTstandard and VFTkinematic. VFTstandard did not differentiate between groups (normal [3.58 ± 1.06] vs. PN [4.18 ± 0.79], P = 0.13). In comparison, VFTkinematic for normal (3.15 ± 1.28) versus PN (4.75 ± 1.35) yielded P = 0.006. Hence, the applicability of VFTkinematic for diastolic function quantitation has been broadened to include analysis of PN filling patterns in age-matched groups.

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

The Doppler echocardiographic E-wave is generated when the left ventricle's suction pump attribute initiates transmitral flow. In some subjects E-waves are accompanied by L-waves, the occurrence of which has been correlated with diastolic dysfunction. The mechanisms for L-wave generation have not been fully elucidated. We propose that the recirculating diastolic intraventricular vortex ring generates L-waves and based on this mechanism, we predict the presence of L-waves in the right ventricle (RV). We imaged intraventricular flow using Doppler echocardiography and phase-contrast magnetic resonance imaging (PC-MRI) in 10 healthy volunteers. L-waves were recorded in all subjects, with highest velocities measured typically 2 cm below the annulus. Fifty-five percent of cardiac cycles (189 of 345) had L-waves. Color M-mode images eliminated mid-diastolic transmitral flow as the cause of the observed L-waves. Three-dimensional intraventricular flow patterns were imaged via PC-MRI and independently validated our hypothesis. Additionally as predicted, L-waves were observed in the RV, by both echocardiography and PC-MRI. The re-entry of the E-wave-generated vortex ring flow through a suitably located echo sample volume can be imaged as the L-wave. These waves are a general feature and a direct consequence of LV and RV diastolic fluid mechanics.

Erina Ghosh

Department of Biomedical Engineering,
Cardiovascular Biophysics Lab

Washington University in St. Louis

Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism

Erina Ghosh

.css-o250i3{font-size:18px;font-family:Open Sans,sans-serif;line-height:21.6px;}Department of Biomedical Engineering,Cardiovascular Biophysics Lab

Washington University in St. Louis

Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism

Department of Biomedical Engineering,
Cardiovascular Biophysics Lab