Kinematic modeling-based left ventricular diastatic (passive) chamber stiffness determination with in-vivo validation

Mechanistic validation of the 2016 American Society of Echocardiography/European Association of Cardiovascular Imaging Guidelines for the assessment of diastolic dysfunction in heart failure with reduced ejection fraction

Background

The American Society for Echocardiography/European Association of Cardiovascular Imaging (ASE/EACVI) 2016 guidelines for assessment of diastolic dysfunction (DD) are based primarily on the effects of diastolic dysfunction on left ventricular filling hemodynamics. However, these measures do not provide quantifiable mechanistic information about diastolic function. The Parameterized Diastolic Filling (PDF) formalism is a validated theoretical framework that describes DD in terms of the physical properties of left ventricular filling.

Aims

We hypothesized that PDF analysis can provide mechanistic insight into the mechanical properties governing higher grade DD.

Methods

Patients referred for echocardiography showing reduced left ventricular ejection fraction (< 45%) were prospectively classified into DD grade according to 2016 ASE/EACVI guidelines. Serial E-waves acquired during free breathing using pulsed wave Doppler of transmitral blood flow were analyzed using the PDF formalism.

Results

Higher DD grade (grade 2 or 3, n = 20 vs grade 1, n = 30) was associated with increased chamber stiffness (261 ± 71 vs 169 ± 61 g/s², p < 0.001), increased filling energy (2.0 ± 0.9 vs 1.0 ± 0.5 mJ, p < 0.001) and greater peak forces resisting filling (median [interquartile range], 18 [15–24] vs 11 [8–14] mN, p < 0.001). DD grade was unrelated to chamber viscoelasticity (21 ± 4 vs 20 ± 6 g/s, p = 0.32). Stiffness was inversely correlated with ejection fraction (r = − 0.39, p = 0.005).

Conclusions

Higher grade DD was associated with changes in the mechanical properties that determine the physics of poorer left ventricular filling. These findings provide mechanistic insight into, and independent validation of the appropriateness of the 2016 guidelines for assessment of DD.

Right Ventricular Myocardial Stiffness and Relaxation Components by Kinematic Model-Based Transtricuspid Flow Analysis in Children and Adolescents with Pulmonary Arterial Hypertension

We hypothesized that the kinematic model-based parameters obtained from the transtricuspid E-wave would be useful for evaluating the right ventricular diastolic property in pediatric pulmonary arterial hypertension (PAH) patients. The model was parametrized by stiffness/elastic recoil k, relaxation/damping c and load x. These parameters were determined as the solution of m⋅d²x/dt² + c⋅dx/dt + kx = 0, which is based on the theory that the E-wave contour is determined by the interplay of stiffness/restoring force, damping/relaxation force and load. The PAH group had a significantly higher k and c compared with the control group (182.5 ± 72.4 g/s vs. 135.7 ± 49.5 g/s², p = 0.0232, and 21.9 ± 6.5 g/s vs. 10.6 ± 5.2 g/s, p <0.0001, respectively). These results indicate that in the PAH group, the right ventricle had higher stiffness/elastic recoil and inferior cross-bridge relaxation. The present findings indicate the feasibility and utility of using kinematic model parameters to assess right ventricular diastolic function.

Fractionating E-Wave Deceleration Time Into Its Stiffness and Relaxation Components Distinguishes Pseudonormal From Normal Filling

Background—

Pseudonormal Doppler E-wave filling patterns indicate diastolic dysfunction but are indistinguishable from the normal filling pattern. For accurate classification, maneuvers to alter load or to additionally measure peak E ′ are required. E-wave deceleration time (DT) has been fractionated into its stiffness (DT s ) and relaxation (DT r ) components (DT=DT s +DT r ) by analyzing E-waves via the parametrized diastolic filling formalism. The method has been validated with DT s and DT r correlating with simultaneous catheterization-derived stiffness (dP/dV) and relaxation ( τ ) with r =0.82 and r =0.94, respectively. We hypothesize that DT fractionation can (1) distinguish between unblinded ( E ′ known) normal versus pseudonormal age-matched groups with normal left ventricular ejection fraction, and (2) distinguish between blinded ( E ′ unknown) normal versus pseudonormal groups, based solely on E-wave analysis.

Methods and Results—

Data (763 E-waves) from 15 age-matched, pseudonormal (elevated E / E ′) and 15 normal subjects were analyzed. Conventional echocardiographic and parametrized diastolic filling stiffness ( k ) and relaxation ( c ) parameters and DT s and DT r were compared. Conventional diastolic function parameters did not differentiate between unblinded groups, whereas k , c ( P <0.001) and DT s , DT r ( P <0.001) did. Independent, blinded ( E ′ not provided) analysis of 42 subjects (30 subjects from unblinded training set and 12 additional subjects from validation set, 581 E-waves) showed that R (=DT r /DT) had high sensitivity (0.90) and specificity (0.86) in differentiating pseudonormal from normal once E ′ revealed actual classification.

Conclusions—

arametrized diastolic filling–based E-wave analysis ( k , c or DT s and DT r ) can differentiate normal versus pseudonormal filling patterns without requiring knowledge of E ′.

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. Although historically invasive methods have comprised the only means available, the development of noninvasive imaging modalities (echocardiography, MRI, CT) having high temporal and spatial resolution provide a new window for quantitative diastolic function assessment. Echocardiography is the agreed upon standard for diastolic function assessment, but indexes in current clinical use merely utilize selected features of chamber dimension (M-mode) or blood/tissue motion (Doppler) waveforms without incorporating the physiologic causal determinants of the motion itself. The recognition that all left ventricles (LV) initiate filling by serving as mechanical suction pumps allows global diastolic function to be assessed based on laws of motion that apply to all chambers. What differentiates one heart from another are the parameters of the equation of motion that governs filling. Accordingly, development of the Parametrized Diastolic Filling (PDF) formalism has shown that the entire range of clinically observed early transmitral flow (Doppler E-wave) patterns are extremely well fit by the laws of damped oscillatory motion. This permits analysis of individual E-waves in accordance with a causal mechanism (recoil-initiated suction) that yields three (numerically) unique lumped parameters whose physiologic analogues are chamber stiffness (k), viscoelasticity/relaxation (c), and load (xo). The recording of transmitral flow (Doppler E-waves) is standard practice in clinical cardiology and, therefore, the echocardiographic recording method is only briefly reviewed. Our focus is on determination of the PDF parameters from routinely recorded E-wave data. As the highlighted results indicate, once the PDF parameters have been obtained from a suitable number of load varying E-waves, the investigator is free to use the parameters or construct indexes from the parameters (such as stored energy 1/2kxo(2), maximum A-V pressure gradient kxo, load independent index of diastolic function, etc.) and select the aspect of physiology or pathophysiology to be quantified.

Diastolic Function in Normal Sinus Rhythm vs. Chronic Atrial Fibrillation: Comparison by Fractionation of E-wave Deceleration Time into Stiffness and Relaxation Components

Although the electrophysiologic derangement responsible for atrial fibrillation (AF) has been elucidated, how AF remodels the ventricular chamber and affects diastolic function (DF) has not been fully characterized. The previously validated Parametrized Diastolic Filling (PDF) formalism models suction-initiated filling kinematically and generates error-minimized fits to E-wave contours using unique load (x_o), relaxation (c), and stiffness (k) parameters. It predicts that E-wave deceleration time (DT) is a function of both stiffness and relaxation. Ascribing DT_s to stiffness and DTr to relaxation such that DT=DT_s+DT_r is legitimate because of causality and their predicted and observed high correlation (r=0.82 and r=0.94) with simultaneous (diastatic) chamber stiffness (dP/dV) and isovolumic relaxation (tau), respectively. We analyzed simultaneous echocardiography-cardiac catheterization data and compared 16 age matched, chronic AF subjects to 16, normal sinus rhythm (NSR) subjects (650 beats). All subjects had diastatic intervals. Conventional DF parameters (DT, AT, E_peak, E_dur, E-VTI, E/E') and E-wave derived PDF parameters (c, k, DT_s, DT_r) were compared. Total DT and DT_s, DT_r in AF were shorter than in NSR (p<0.005), chamber stiffness, (k) in AF was higher than in NSR (p<0.001). For NSR, 75% of DT was due to stiffness and 25% was due to relaxation whereas for AF 81% of DT was due to stiffness and 19% was due to relaxation (p<0.005). We conclude that compared to NSR, increased chamber stiffness is one measurable consequence of chamber remodeling in chronic, rate controlled AF. A larger fraction of E-wave DT in AF is due to stiffness compared to NSR. By trending individual subjects, this method can elucidate and characterize the beneficial or adverse long-term effects on chamber remodeling due to alternative therapies in terms of chamber stiffness and relaxation.

The isovolumic relaxation to early rapid filling relation: kinematic model based prediction with in vivo validation

Although catheterization is the gold standard, Doppler echocardiography is the preferred diastolic function (DF) characterization method. The physiology of diastole requires continuity of left ventricular pressure (LVP)‐generating forces before and after mitral valve opening (MVO). Correlations between isovolumic relaxation (IVR) indexes such as tau (time‐constant of IVR) and noninvasive, Doppler E‐wave‐derived metrics, such as peak A‐V gradient or deceleration time (DT), have been established. However, what has been missing is the model‐predicted causal link that connects isovolumic relaxation (IVR) to suction‐initiated filling (E‐wave). The physiology requires that model‐predicted terminal force of IVR (F_tIVR) and model‐predicted initial force of early rapid filling (F_{i E‐wave}) after MVO be correlated. For validation, simultaneous (conductance catheter) P‐V and E‐wave data from 20 subjects (mean age 57 years, 13 men) having normal LV ejection fraction (LVEF>50%) and a physiologic range of LV end‐diastolic pressure (LVEDP) were analyzed. For each cardiac cycle, the previously validated kinematic (Chung) model for isovolumic pressure decay and the Parametrized Diastolic Filling (PDF) kinematic model for the subsequent E‐wave provided F_tIVR and F_{i E‐wave} respectively. For all 20 subjects (15 beats/subject, 308 beats), linear regression yielded F_tIVR = α F_{i E‐wave} + b (R = 0.80), where α = 1.62 and b = 1.32. We conclude that model‐based analysis of IVR and of the E‐wave elucidates DF mechanisms common to both. The observed in vivo relationship provides novel insight into diastole itself and the model‐based causal mechanistic relationship that couples IVR to early rapid filling.

The Challenge of Chamber Stiffness Determination in Chronic Atrial Fibrillation vs. Normal Sinus Rhythm: Echocardiographic Prediction with Simultaneous Hemodynamic Validation

Echocardiographic diastolic function (DF) assessment remains a challenge in atrial fibrillation (AF), because indexes such as E/A cannot be used and because chronic, rate controlled AF causes chamber remodeling. To determine if echocardiography can accurately characterize diastolic chamber properties we compared 15 chronic AF subjects to 15, age matched normal sinus rhythm (NSR) subjects using simultaneous echocardiography-cardiac catheterization (391 beats analyzed). Conventional DF parameters (DT, Epeak, AT, Edur, E-VTI, E/E') and validated, E-wave derived, kinematic modeling based chamber stiffness parameter (k), were compared. For validation, chamber stiffness (dP/dV) was independently determined from simultaneous, multi-beat P-V loop data. Results show that neither AT, Epeak nor E-VTI differentiated between groups. Although DT, Edur and E/E' did differentiate between groups (DTNSR vs. DTAF p < 0.001, EdurNSR vs. EdurAF p < 0.001, E/E'NSR vs. E/E'AF p < 0.05), the model derived chamber stiffness parameter k was the only parameter specific for chamber stiffness, (kNSR vs. kAF p <0.005). The invasive gold standard determined end-diastolic stiffness in NSR was indistinguishable from end-diastolic (i.e. diastatic) stiffness in AF (p = 0.84). Importantly, the analysis provided mechanistic insight by showing that diastatic stiffness in AF was significantly greater than diastatic stiffness in NSR (p < 0.05). We conclude that passive (diastatic) chamber stiffness is increased in normal LVEF chronic, rate controlled AF hearts relative to normal LVEF NSR controls and that in addition to DT, the E-wave derived, chamber stiffness specific index k, differentiates between AF vs. NSR groups, even when invasively determined end-diastolic chamber stiffness fails to do so.

Low-sodium DASH diet improves diastolic function and ventricular-arterial coupling in hypertensive heart failure with preserved ejection fraction

BACKGROUND

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 coupling in hypertensive HFPEF.

METHODS AND RESULTS

Thirteen patients with treated hypertension and compensated HFPEF consumed the DASH/SRD (target sodium, 50 mmol/2100 kcal) for 21 days. We measured baseline and post-DASH/SRD brachial and central blood pressure (via radial arterial tonometry) and cardiovascular function with echocardiographic measures (all previously invasively validated). Diastolic function was quantified via the parametrized diastolic filling formalism that yields relaxation/viscoelastic (c) and passive/stiffness (k) constants through the analysis of Doppler mitral inflow velocity (E-wave) contours. Effective arterial elastance (Ea) end-systolic elastance (Ees) and ventricular-arterial coupling (defined as the ratio Ees:Ea) were determined using previously published techniques. Wilcoxon matched-pairs signed-rank tests were used for pre-post comparisons. The DASH/SRD reduced clinic and 24-hour brachial systolic pressure (155 ± 35 to 138 ± 30 and 130 ± 16 to 123 ± 18 mm Hg; both P=0.02), and central end-systolic pressure trended lower (116 ± 18 to 111 ± 16 mm Hg; P=0.12). In conjunction, diastolic function improved (c=24.3 ± 5.3 to 22.7 ± 8.1 g/s; P=0.03; k=252 ± 115 to 170 ± 37 g/s(2); P=0.03), Ea decreased (2.0 ± 0.4 to 1.7 ± 0.4 mm Hg/mL; P=0.007), and ventricular-arterial coupling improved (Ees:Ea=1.5 ± 0.3 to 1.7 ± 0.4; P=0.04).

CONCLUSIONS

In patients with hypertensive HFPEF, the sodium-restricted DASH diet was associated with favorable changes in ventricular diastolic function, arterial elastance, and ventricular-arterial coupling.

CLINICAL TRIAL REGISTRATION

URL: http://www.clinicaltrials.gov. Unique identifier: NCT00939640.

Diastolic chamber properties of the left ventricle assessed by global fitting of pressure-volume data: improving the gold standard of diastolic function

In cardiovascular research, relaxation and stiffness are calculated from pressure-volume (PV) curves by separately fitting the data during the isovolumic and end-diastolic phases (end-diastolic PV relationship), respectively. This method is limited because it assumes uncoupled active and passive properties during these phases, it penalizes statistical power, and it cannot account for elastic restoring forces. We aimed to improve this analysis by implementing a method based on global optimization of all PV diastolic data. In 1,000 Monte Carlo experiments, the optimization algorithm recovered entered parameters of diastolic properties below and above the equilibrium volume (intraclass correlation coefficients = 0.99). Inotropic modulation experiments in 26 pigs modified passive pressure generated by restoring forces due to changes in the operative and/or equilibrium volumes. Volume overload and coronary microembolization caused incomplete relaxation at end diastole (active pressure > 0.5 mmHg), rendering the end-diastolic PV relationship method ill-posed. In 28 patients undergoing PV cardiac catheterization, the new algorithm reduced the confidence intervals of stiffness parameters by one-fifth. The Jacobian matrix allowed visualizing the contribution of each property to instantaneous diastolic pressure on a per-patient basis. The algorithm allowed estimating stiffness from single-beat PV data (derivative of left ventricular pressure with respect to volume at end-diastolic volume intraclass correlation coefficient = 0.65, error = 0.07 ± 0.24 mmHg/ml). Thus, in clinical and preclinical research, global optimization algorithms provide the most complete, accurate, and reproducible assessment of global left ventricular diastolic chamber properties from PV data. Using global optimization, we were able to fully uncouple relaxation and passive PV curves for the first time in the intact heart.