Diabetes and diastolic function: stiffness and relaxation from transmitral flow

Diastolic function: modeling left ventricular untwisting as a damped harmonic oscillator

Objective.We developed a method using cardiovascular magnetic resonance imaging to model the untwisting of the left ventricle (LV) as a damped torsional harmonic oscillator to estimate shear modulus (intrinsic myocardial stiffness) and frictional damping, then applied this method to evaluate the torsional stiffness of patients with resistant hypertension (RHTN) compared to a control group.Approach.The angular displacement of the LV during diastole was measured. Myocardial shear modulus and damping constant were determined by solving a system of equations modeling the diastolic untwisting as a damped, unforced harmonic oscillator, in 100 subjects with RHTN and 36 control subjects.Main Results.Though overall torsional stiffness was increased in RHTN (41.7 (27.1-60.7) versus 29.6 (17.3-35.7) kdyn*cm;p = 0.001), myocardial shear modulus was not different between RHTN and control subjects (0.34 (0.23-0.50) versus 0.33 (0.22-0.46) kPa;p= 0.758). RHTN demonstrated an increase in overall diastolic frictional damping (6.13 ± 3.77 versus 3.35 ± 1.70 kdyn*cm*s;p< 0.001), but no difference in damping when corrected for the overlap factor (74.3 ± 25.9 versus 68.0 ± 24.0 dyn*s/cm3;p = 0.201). There was an increase in the polar moment (geometric component of stiffness; 11.47 ± 6.95 versus 7.58 ± 3.28 cm4;p<0.001).Significance.We have developed a phenomenological method, estimating the intrinsic stiffness and relaxation properties of the LV based on restorative diastolic untwisting. This model finds increased overall stiffness in RHTN and points to hypertrophy, rather than tissue- level changes, as the major factor leading to increased stiffness.

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.

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(βt), 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.

Normal Reference Values for Assessing Diastolic Function Using the Parameterized Diastolic Filling Formalism Method in Patients with Normal Results of Rest and Stress Echocardiography

The parameterized diastolic filling (PDF) method can be used to study the mechanics of early diastolic left ventricular (LV) filling. However, there are no publications describing the reference ranges of the PDF parameters. This study retrospectively recruited patients with normal results on rest and stress echocardiography and no diabetes or hypertension (n=138, 45% female). DICOM images of the resting E-wave from transmitral pulsed wave Doppler flow velocities were analyzed using freely available software. Viscoelastic energy loss (c) and stiffness (k) were higher in males compared to females (p≤0.001 for both). There were no correlations between any of the PDF parameters and age (p>0.05 for all). In males, stiffness was correlated with systolic blood pressure (r=0.24, p=0.04), and load and filling energy were correlated with diastolic blood pressure (r=-0.27, p=0.02, and r=-0.29, p=0.01, respectively). Sex-specific normal 95% reference limits for PDF analysis of early LV filling are presented for clinical use.

Cardiac Amyloidosis Shows Decreased Diastolic Function as Assessed by Echocardiographic Parameterized Diastolic Filling

Cardiac amyloidosis is a rare but serious condition with poor survival. One of the early findings by echocardiography is impaired diastolic function, even before the development of cardiac symptoms. Early diagnosis is important, permitting initiation of treatment aimed at improving survival. The parameterized diastolic filling (PDF) formalism entails describing the left ventricular filling pattern during early diastole using the mathematical equation for the motion of a damped harmonic oscillator. We hypothesized that echocardiographic PDF analysis could detect differences in diastolic function between patients with amyloidosis and controls. Pulsed-wave Doppler echocardiography of transmitral flow was measured in 13 patients with amyloid heart disease and 13 age- and gender matched controls. E- waves (2 to 3 per subject) were analyzed using in-house developed software. Nine PDF-derived parameters were obtained in addition to conventional echocardiographic parameters of diastolic function. Compared to controls, cardiac amyloidosis patients had a larger left atrial area (23.7 ± 7.5 cm² vs. 18.5 ± 4.8 cm², p = 0.04), greater interventricular septum wall thickness (14.4 ± 2.6 mm vs. 9.3 ± 1.3 mm, p < 0.001), lower e' (0.06 ± 0.02 m/s vs. 0.09 ± 0.02 m/s, p < 0.001) and higher E/e' (18.0 ± 12.9 vs. 7.7 ± 1.3, p = 0.001). The PDF parameter peak resistive force was greater in cardiac amyloidosis patients compared to controls (17.9 ± 5.7 mN vs. 13.1 ± 3.1 mN, p = 0.03), and other PDF parameters did not differ. PDF analysis revealed that patients with cardiac amyloidosis had a greater peak resistive force compared to controls, consistent with a greater degree of diastolic dysfunction. PDF analysis may be useful in characterizing diastolic function in amyloid heart disease.

Kinematic analysis of diastolic function using the freely available software Echo E-waves - feasibility and reproducibility

BACKGROUND

Early diastolic left ventricular (LV) filling can be accurately described using the same methods used in classical mechanics to describe the motion of a loaded spring as it recoils, a validated method also referred to as the Parameterized Diastolic Filling (PDF) formalism. With this method, each E-wave recorded by pulsed wave (PW) Doppler can be mathematically described in terms of three constants: LV stiffness (k), viscoelasticity (c), and load (x ₀). Also, additional parameters of physiological and diagnostic interest can be derived. An efficient software application for PDF analysis has not been available. We aim to describe the structure, feasibility, time efficiency and intra-and interobserver variability for use of such a solution, implemented in Echo E-waves, a freely available software application ( www.echoewaves.org ).

RESULTS

An application was developed, with the ability to open DICOM files from different vendors, as well as rapid semi-automatic analysis and export of results. E-waves from 20 patients were analyzed by two investigators. Analysis time for a median of 34 (interquartile range (IQR) 29-42) E-waves per patient (representing 63 %, IQR 56-79 % of the recorded E-waves per patient) was 4.3 min (IQR 4.0-4.6 min). Intra-and intraobserver variability was good or excellent for 12 out of 14 parameters (coefficient of variation 2.5-18.7 %, intraclass correlation coefficient 0.80-0.99).

CONCLUSION

Kinematic analysis of diastolic function using the PDF method for Doppler echocardiography implemented in freely available semiautomatic software is highly feasible, time efficient, and has good to excellent intra-and interobserver variability.

Acceleration rate of mitral inflow E wave: a novel transmitral doppler index for assessing diastolic function

Background

We performed comprehensive transmitral and pulmonary venous Doppler echocardiographic studies to devise a novel index of diastolic function. This is the first study to assess the utility of the acceleration rate (AR) of the E wave of mitral inflow as a primary diagnostic modality for assessing diastolic function.

Methods

Study group consisted of 84 patients (53 + 11 years) with left ventricle (LV) diastolic dysfunction and 34 healthy people (35 ± 9 years) as control group, who were referred for clinically indicated two-dimensional transthoracic echocardiogram (TTE) during 2012 and 2013 to Imam Hospital. Normal controls were defined as patients without clinical evidence of cardiac disease and had normal TTE. LV diastolic function was determined according to standardized protocol of American Society of Echocardiography (ASE). As our new parameter, AR of E wave of mitral inflow was also measured in all patients. It was represented by the slope of the line between onset of E wave and peak of it. Correlation between AR of E wave and LV diastolic function grade was measured using the Spearman correlation coefficient. Receiver operating characteristic (ROC) curve was used to determine the sensitivity and specificity of AR of E wave in diagnosing LV diastolic dysfunction in randomly selected two-thirds of population then its derived cutoff was evaluated in rest of the population. The institutional review board of the hospital approved the study protocol. All participants gave written informed consent. This investigation was in accordance with the Declaration of Helsinki.

Results

The mean value of AR was 1010 ± 420 cm/s² in patients whereas the mean value for the normal controls was 701 ± 210 cm/s². There was a strong and graded relation between AR of E wave of mitral inflow and LV diastolic function grade (Spearman P ≤0.0001, r_s =0.69). ROC curve analysis revealed that AR of E wave of mitral inflow =750 cm/s² predicted moderate or severe LV diastolic dysfunction with 89 % sensitivity and 89 % specificity (area under curve [AUC] = 0.903, P <0.0001). Application of this cutoff on test group showed 96 % sensitivity and 77 % specificity with AUC = 0.932 and P <0.0001.

Conclusion

AR of E wave of mitral inflow could be used for assessment of diastolic function, especially moderate or severe diastolic dysfunction. However, before its clinical application, external validation should be considered.

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.

Diastolic function in heart failure

Heart failure has reached epidemic proportions, and diastolic heart failure or heart failure with preserved ejection fraction (HFpEF) constitutes about 50% of all heart failure admissions. Long-term prognosis of both reduced ejection fraction heart failure and HFpEF are similarly dismal. No pharmacologic agent has been developed that actually treats or repairs the physiologic deficit(s) responsible for HFpEF. Because the physiology of diastole is both subtle and counterintuitive, its role in heart failure has received insufficient attention. In this review, the focus is on the physiology of diastole in heart failure, the dominant physiologic laws that govern the process in all hearts, how all hearts work as a suction pump, and, therefore, the elucidation and characterization of what actually is meant by "diastolic function". The intent is for the reader to understand what diastolic function actually is, what it is not, and how to measure it. Proper measurement of diastolic function requires one to go beyond the usual E/A, E/E', etc. phenomenological metrics and employ more rigorous causality (mathematical modeling) based parameters of diastolic function. The method simultaneously provides new physiologic insight into the meaning of in vivo "equilibrium volume" of the left ventricle (LV), longitudinal versus transverse volume accommodation of the chamber, diastatic "ringing" of the mitral annulus, and the mechanism of L-wave generation, as well as availability of a load-independent index of diastolic function (LIIDF). One important consequence of understanding what diastolic function is, is the recognition that all that current therapies can do is basically alter the load, rather than actually "repair" the functional components (chamber stiffness, chamber relaxation). If beneficial (biological/structural/metabolic) remodeling due to therapy does manifest ultimately as improved diastolic function, it is due to resumption of normal physiology (as in alleviation of ischemia) or activation of compensatory pathways already devised by evolution. In summary, meaningful quantitative characterization of diastolic function in any clinical setting, including heart failure, requires metrics based on physiologic mechanisms that quantify the suction pump attribute of the heart. This requires advancing beyond phenomenological global indexes such as E/A, E/E', Vp, etc. and employing causality (mathematical modeling) based parameters of diastolic function easily obtained via the parametrized diastolic function (PDF) formalism.

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.

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.

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

The slope of the diastatic pressure-volume relationship (D-PVR) defines passive left ventricular (LV) stiffness κ. Although κ is a relative measure, cardiac catheterization, which is an absolute measurement method, is used to obtain the former. Echocardiography, including transmitral flow velocity (Doppler E-wave) analysis, is the preferred quantitative diastolic function (DF) assessment method. However, E-wave analysis can provide only relative, rather than absolute pressure information. We hypothesized that physiologic mechanism-based modeling of E-waves allows derivation of the D-PVR(E-wave) whose slope, κ(E-wave), provides E-wave-derived diastatic, passive chamber stiffness. Our kinematic model of filling and Bernoulli's equation were used to derive expressions for diastatic pressure and volume on a beat-by-beat basis, thereby generating D-PVR(E-wave), and κ(E-wave). For validation, simultaneous (conductance catheter) P-V and echocardiographic E-wave data from 30 subjects (444 total cardiac cycles) having normal LV ejection fraction (LVEF) were analyzed. For each subject (15 beats average) model-predicted κ(E-wave) was compared to experimentally measured κ(CATH) via linear regression yielding as follows: κ(E-wave) = ακ(CATH) + b (R(2) = 0.92), where, α = 0.995 and b = 0.02. We conclude that echocardiographically determined diastatic passive chamber stiffness, κ(E-wave), provides an excellent estimate of simultaneous, gold standard (P-V)-defined diastatic stiffness, κ(CATH). Hence, in chambers at diastasis, passive LV stiffness can be accurately determined by means of suitable analysis of Doppler E-waves (transmitral flow).

The diastolic function to cyclic variation of myocardial ultrasonic backscatter relation: the influence of parameterized diastolic filling (PDF) formalism determined chamber properties

Myocardial tissue characterization represents an extension of currently available echocardiographic imaging. The systematic variation of backscattered energy during the cardiac cycle (the "cyclic variation" of backscatter) has been employed to characterize cardiac function in a wide range of investigations. However, the mechanisms responsible for observed cyclic variation remain incompletely understood. As a step toward determining the features of cardiac structure and function that are responsible for the observed cyclic variation, the present study makes use of a kinematic approach of diastolic function quantitation to identify diastolic function determinants that influence the magnitude and timing of cyclic variation. Echocardiographic measurements of 32 subjects provided data for determination of the cyclic variation of backscatter to diastolic function relation characterized in terms of E-wave determined, kinematic model-based parameters of chamber stiffness, viscosity/relaxation and load. The normalized time delay of cyclic variation appears to be related to the relative viscoelasticity of the chamber and predictive of the kinematic filling dynamics as determined using the parameterized diastolic filling formalism (with r-values ranging from .44 to .59). The magnitude of cyclic variation does not appear to be strongly related to the kinematic parameters.

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 = 6 e−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.

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

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

An evaluation of transmitral and pulmonary venous Doppler indices for assessing murine left ventricular diastolic function

With the continued development of genetically engineered mouse models of cardiac disease, further advancement of noninvasive techniques for evaluating cardiac diastolic dysfunction in these models would be valuable. Therefore, we performed comprehensive transmitral and pulmonary venous Doppler echocardiographic studies to devise novel indices of diastolic function in a mouse model with cardiac hypertrophy, which were validated against invasively measured hemodynamic parameters. We examined 10 HopX(Tg) transgenic mice with diastolic dysfunction and 10 age-matched controls sedated with 1% to 2% isoflurane (male, age 14-18 weeks). These studies revealed that the acceleration time of the transmitral Doppler E-wave was the best Doppler parameter for unmasking LV diastolic dysfunction in HopX(Tg) mice. This is the first study to assess the utility of the acceleration time of the E-wave and pulmonary venous Doppler echocardiography as a primary diagnostic modality for assessing murine diastolic function.

The E-wave delayed relaxation pattern to LV pressure contour relation: model-based prediction with in vivo validation

The transmitral Doppler E-wave "delayed relaxation" (DR) pattern is an established sign of diastolic dysfunction (DD). Furthermore, chambers exhibiting a DR filling pattern are also expected to have a prolonged time-constant of isovolumic relaxation (tau). The simultaneous observation of a DR pattern and normal tau in the same heart is not uncommon, however. The simultaneous hemodynamic equivalent of the DR pattern has not been proposed. To determine the feature of the left ventricular (LV) pressure contour during the E-wave that is causally related to its DR pattern we applied kinematic and fluid mechanics based arguments to derive the pressure recovery ratio (PRR). The PRR is dimensionless and is defined by the left ventricular pressure difference between diastasis and minimum pressure, normalized to the pressure difference between a fiducial diastolic filling pressure and minimum pressure [PRR=(P(Diastasis)-P(Min))/(P(Fiducial)-P(Min))]. We analyzed 354 cardiac cycles from 40 normal sinus rhythm (NSR) subjects and 113 beats from nine atrial fibrillation (AF) subjects from our database of simultaneous transmitral flow-micromanometric LV pressure recordings. The fiducial pressure is defined by the end diastolic pressure in NSR and by the pressure at dP/dt(MIN) in the setting of AF. Consistent with derivation, PRR was linearly related to a DR pattern related, model-based relaxation parameter (R(2) = 0.77, 0.83 in NSR and AF, respectively). Furthermore, the PRR successfully differentiated subjects with a DR pattern from subjects with partial DR or normal E-wave pattern (p < 0.05). We conclude that the PRR may differentiate between subjects having a DR pattern and subjects with normal E-waves, even when tau cannot.

The age dependence of left ventricular filling efficiency

Echocardiography has emerged as the preferred modality by which diastolic function (DF) is assessed for clinical or research purposes. Echocardiographic indexes and parameters of DF such as E/A, DT, E/E', etc., deteriorate with advancing age. Whether the efficiency of filling depends on age is unknown. To better characterize the filling process and DF in causal rather than correlative terms, we have previously modeled diastole kinematically. We introduced and validated a dimensionless measure of DF termed the kinematic filling efficiency index (KFEI). In the present study, we determined the effect of aging on DF in terms of KFEI in 72 control subjects without cardiovascular-related diseases or pathologies. We also evaluated the age dependence of other conventional parameters of DF. In concordance with other noninvasive DF measures known to decrease with age, KFEI decreases and correlates very strongly with age (R2=0.80). Multivariate analysis showed that age is the single most important contributor to KFEI (p=0.003). We conclude that KFEI provides novel insight into DF impairment mechanisms because of aging. These results support the clinical value of KFEI and advance our ability to characterize DF in mechanistic and quantitative terms based on the efficiency of filling.

Transmitral flow velocity-contour variation after premature ventricular contractions: a novel test of the load-independent index of diastolic filling

The new echocardiography-based, load-independent index of diastolic filling (LIIDF) M was assessed using load-/shape-varying E-waves after premature ventricular contractions (PVCs). Twenty-six PVCs in 15 subjects from a preexisting simultaneous echocardiography-catheterization database were selected. Perturbed load-state beats, defined as the first two post-PVC E-waves, and steady-state E-waves, were subjected to conventional and model-based analysis. M, a dimensionless index, defined by the slope of the peak driving-force vs. peak (filling-opposing) resistive-force regression, was determined from steady-state E-waves alone, and from load-perturbed E-waves combined with a matched number of subsequent beats. Despite high degrees of E-wave shape variation, M derived from load-varying, perturbed beats and M derived from steady-state beats alone were indistinguishable. Because the peak driving-force vs. peak resistive-force relation determining M remains highly linear in the extended E-wave shape and load variation regime observed, we conclude that M is a robust LIIDF.

Noninvasive methods for determining pulmonary vascular function in children with pulmonary arterial hypertension: application of a mechanical oscillator model

OBJECTIVE

Noninvasive diagnostics for pulmonary arterial hypertension (PAH) have traditionally sought to predict main pulmonary artery pressure from qualitative or direct quantitative measures of the flow velocity pattern obtained from spectral Doppler ultrasound examination of the main pulmonary artery. A more detailed quantification of flow velocity patterns in the systemic circuit has been obtained by parameterizing the flow trace with a simple dynamic system model. Here, we investigate such a model's utility as a noninvasive predictor of total right heart afterload and right heart function.

DESIGN

Flow velocity and pressure was measured within the main pulmonary artery during right heart catheterization of patients with normal hemodynamics (19 subjects, 20 conditions) and those with PAH undergoing reactivity evaluation (34 patients, 69 conditions). Our model parameters were obtained by least-squares fitting the model velocity to the measured flow velocity.

RESULTS

Five parameter means displayed significant (P < .05) differences between normotensive and hypertensive groups. The model stiffness parameter correlated to actual pulmonary vascular resistance (r = 0.4924), pulmonary vascular stiffness (r = 0.6811), pulmonary flow (r = 0.6963), and stroke work (r = 0.7017), while the model initial displacement parameter had good correlation to stiffness (r = 0.6943) and flow (r = 0.6958).

CONCLUSIONS

As predictors of total right heart afterload (resistance and stiffness) and right ventricle work, the model parameters of stiffness and initial displacement offer more comprehensive measures of the disease state than previous noninvasive methods and may be useful in routine diagnostic monitoring of patients with PAH.

The effects of caloric restriction- and exercise-induced weight loss on left ventricular diastolic function

Little is known about the effects of weight loss on diastolic function. Furthermore, it is not known whether both caloric restriction (CR)- and exercise (Ex)-induced weight loss have salutary effects on diastolic function. Therefore, we assessed the effects of yearlong CR ( n = 12) and Ex ( n = 13) interventions, which induced ∼12% weight loss, on diastolic function in healthy, nonobese (body mass index = 23.5–29.9 kg/m2) men and women aged 50 to 60 yr. Recordings of Doppler transmitral flow and Doppler tissue imaging were acquired and analyzed by conventional approaches and a validated parameterized diastolic filling (PDF) formalism. Isovolumic relaxation time decreased after weight loss in both groups ( P < 0.05). Septal peak early mitral annular velocity (E′) increased ( P < 0.01) and peak E-wave velocity/E′ decreased ( P < 0.05) after weight loss in the CR group. Based on the PDF-derived indexes, CR resulted in a decrease in global ventricular stiffness ( k) and increases in longitudinal (septal annulus motion) stored elastic strain ( x′o), peak force ( k′ x′o), and peak stored strain energy (1/2 k′ xoprime;2). In the Ex group, k was unchanged, although septal x′o and 1/2 k′ xo′2 increased significantly and k′ x′o ( P = 0.13) tended to increase. We conclude that weight loss, whether induced by CR or Ex, has salutary effects on diastolic function.

E-wave deceleration time may not provide an accurate determination of LV chamber stiffness if LV relaxation/viscoelasticity is unknown

Average left ventricular (LV) chamber stiffness (ΔPavg/ΔVavg) is an important diastolic function index. An E-wave-based determination of ΔPavg/ΔVavg (Little WC, Ohno M, Kitzman DW, Thomas JD, Cheng CP. Circulation 92: 1933–1939, 1995) predicted that deceleration time (DT) determines stiffness as follows: ΔPavg/ΔVavg = N(π/DT)2 (where N is constant), which implies that if the DTs of two LVs are indistinguishable, their stiffness is indistinguishable as well. We observed that LVs with indistinguishable DTs may have markedly different ΔPavg/ΔVavg values determined by simultaneous echocardiography-catheterization. To elucidate the mechanism by which LVs with indistinguishable DTs manifest distinguishable chamber stiffness, we use a validated, kinematic E-wave model (Kovács SJ, Barzilai B, Perez JE. Am J Physiol Heart Circ Physiol 252: H178–H187, 1987) with stiffness ( k) and relaxation/viscoelasticity ( c) parameters. Because the predicted linear relation between k and ΔPavg/ΔVavg has been validated, we reexpress the DT-stiffness (ΔPavg/ΔVavg) relation of Little et al. as follows: DT k ≈ [Formula: see text]. Using the kinematic model, we derive the general DT-chamber stiffness/viscoelasticity relation as follows: DT k, c = [Formula: see text](where c and k are determined directly from the E-wave), which reduces to DT k when c ≪ k. Validation involved analysis of 400 E-waves by determination of five-beat averaged k and c from 80 subjects undergoing simultaneous echocardiography-catheterization. Clinical E-wave DTs were compared with model-predicted DT k and DT k, c. Clinical DT was better predicted by stiffness and relaxation/viscoelasticity ( r2 = 0.84, DT vs. DT k, c) jointly rather than by stiffness alone ( r2 = 0.60, DT vs. DT k). Thus LVs can have indistinguishable DTs but significantly different ΔPavg/ΔVavg if chamber relaxation/viscoelasticity differs. We conclude that DT is a function of both chamber stiffness and chamber relaxation viscoelasticity. Quantitative diastolic function assessment warrants consideration of simultaneous stiffness and relaxation/viscoelastic effects.

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.

Absence of diastolic mitral annular oscillations is a marker for relaxation-related diastolic dysfunction

Although Doppler tissue imaging frequently indicates the presence of mitral annular oscillations (MAO) following the E' wave (E'' wave, etc.), only recently was it shown that annular "ringing" follows the rules of damped harmonic oscillatory motion. Oscillatory model-based analysis of E' and E'' waves provides longitudinal left ventricular (LV) stiffness (k'), relaxation/viscoelasticity (c'), and stored elastic strain (x(o)') parameters. We tested the hypothesis that presence (MAO(+)) vs. absence (MAO(-)) of diastolic MAO is an index of superior LV relaxation by analyzing simultaneous echocardiographic-hemodynamic data from 35 MAO(+) and 20 MAO(-) normal ejection fraction (EF) subjects undergoing cardiac catheterization. Echocardiographic annular motion and transmitral flow data were analyzed with a previously validated kinematic model of filling. Invasive and noninvasive diastolic function (DF) indexes differentiated between MAO(+) and MAO(-) groups. Specifically, the MAO(+) group had a shorter time constant of isovolumic relaxation [tau; 51 (SD 13) vs. 67 (SD 27) ms; P<0.01] and isovolumic relaxation time [63 (SD 16) vs. 82 (SD 17) ms; P<0.001] and greater ratio of peak E-wave to peak A-wave velocity [1.19 (SD 0.31) vs. 0.97 (SD 0.31); P<0.05]. The MAO(+) group had greater peak lateral mitral annulus velocity [E'; 17.5 (SD 3.1) vs. 13.5 (SD 3.8) cm/s; P<0.001] and LVEF [71.2 (SD 7.5)% vs. 65.4 (SD 9.1)%; P<0.05] and lower heart rate [65 (SD 9) vs. 74 (SD 9) beats/min, P<0.001]. Additional conventional and kinematic modeling-derived indexes were highly concordant with these findings. We conclude that absence of early diastolic MAO is an easily discernible marker for relaxation-related diastolic dysfunction. Quantitation of MAO via stiffness and relaxation/viscoelasticity parameters facilitates quantitative assessment of regional (i.e., longitudinal) DF and may improve diagnosis of diastolic dysfunction.

Role of Diastolic Dyssynchrony in the Delayed Relaxation Pattern of Left Ventricular Filling

We investigated the extent to which diastolic dyssynchrony contributes to the delayed relaxation pattern of left ventricular filling and limitation in exercise capacity. In 100 patients with diabetes, preserved left ventricular systolic function, normal filling pressure, and no coronary disease, we measured magnitude of early diastolic tissue lengthening (tissue velocity and strain rate) and diastolic dyssynchrony (SD in QRS to peak early diastolic tissue velocity interval across 4 basal myocardial segments). From transmitral flow patients were divided into those with normal filling (50 patients) and delayed relaxation (50 patients). Myocardial lengthening was reduced and SD in interval from QRS onset to peak early diastolic tissue velocity across all segments was higher in patients with delayed relaxation compared with control patients. Myocardial lengthening was the only predictor of delayed relaxation and correlation with exercise capacity was better for lengthening indices than SD in interval from QRS onset to peak early diastolic tissue velocity across all segments. Therefore, in this group a reduced rate of myocardial lengthening plays a more important role in delayed relaxation than diastolic dyssynchrony.

Diastolic ventricular-vascular stiffness and relaxation relation: elucidation of coupling via pressure phase plane-derived indexes

Because systole and diastole are coupled and systolic ventricular-vascular coupling has been characterized, we hypothesize that diastolic ventricular-vascular coupling (DVVC) exists and can be characterized in terms of relaxation and stiffness. To characterize and elucidate DVVC mechanisms, we introduce time derivative of pressure (dP/d t) vs. time-varying pressure [P( t)] (pressure phase plane, PPP)-derived analogs of ventricular and vascular “stiffness” and relaxation parameters. Although volume change (dV) = 0 during isovolumic periods, and time-varying left ventricular (LV) stiffness, typically expressed as change in pressure per unit change in volume (dP/dV), is undefined, our formulation allows determination of a PPP-derived stiffness analog during isovolumic contraction and relaxation. Similarly, an aortic stiffness analog is also derivable from the PPP. LV relaxation was characterized via τ, the time constant of isovolumic relaxation, and vascular (aortic pressure decay) relaxation was characterized in terms of its equivalent (windkessel) exponential decay time constant κ. The results show that PPP-derived systolic and diastolic ventricular and vascular stiffness are strongly coupled [Formula: see text]. In support of the DVVC hypothesis, a strong linear correlation between relaxation (rate of pressure decay) indexes κ and τ (κ = 9.89τ − 90.3, r = 0.81) was also observed. The correlations observed underscore the role of long-term, steady-state DVVC as a diastolic function determinant. Awareness of the PPP-derived DVVC parameters provides insight into mechanisms and facilitates quantification of arterial stiffening and associated increase in diastolic chamber stiffness. The PPP method provides a tool for quantitative assessment and determination of the functional coupling of the vasculature to diastolic function.

Frequency-based analysis of the early rapid filling pressure-flow relation elucidates diastolic efficiency mechanisms

Stiffness- and relaxation-based diastolic function (DF) assessment can characterize the presence, severity, and mechanism of dysfunction. Although frequency-based characterization of arterial function is routine (input impedance, characteristic impedance, arterial wave reflection), DF assessment via frequency-based methods incorporating optimization/efficiency criteria is lacking. By definition, optimal filling maximizes (E wave) volume and minimizes "loss" at constant stored elastic strain energy (which initiates mechanical, recoil-driven filling). In thermodynamic terms, optimal filling delivers all oscillatory power (rate of work) at the lowest harmonic. To assess early rapid filling optimization, simultaneous micromanometric left ventricular pressure and echocardiographic transmitral flow (Doppler E wave) were Fourier analyzed in 31 subjects. A validated kinematic filling model provided closed-form expressions for E wave contours and model parameters. Relaxation-based DF impairment is indicated by prolonged E wave deceleration time (DT). Optimization was assessed via regression between the dimensionless ratio of 2nd (Q2) and 3rd flow harmonics (Q3) to the lowest harmonic (Q1), i.e., (Q2/Q1) or (Q3/Q1) vs. DT or c, the filling model's viscosity/damping (energy loss) parameter. Results show that DT prolongation or increased c generated increased oscillatory power at higher harmonics (Q2/Q1 = 0.00091DT + 0.09837, r = 0.70; Q3/Q1 = 0.00053DT + 0.02747, r = 0.60; Q2/Q1 = 0.00614c + 0.15527, r = 0.91; Q3/Q1 = 0.00396c + 0.05373, r = 0.87). Because ideal filling is achieved when all oscillatory power is delivered at the lowest harmonic, the observed increase in power at higher harmonics is a measure of filling inefficiency. We conclude that frequency-based analysis facilitates assessment of filling efficiency and elucidates the mechanism by which diastolic dysfunction associated with prolonged DT impairs optimal filling.

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.