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.

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.

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.

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.

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.

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.

The impact of 6 weeks of atrial fibrillation on left atrial and ventricular structure and function.

OBJECTIVE: The impact of prolonged episodes of atrial fibrillation on atrial and ventricular function has been incompletely characterized. The purpose of this study was to investigate the influence of atrial fibrillation on left atrial and ventricular function in a rapid paced porcine model of atrial fibrillation. METHODS: A control group of pigs (group 1, n = 8) underwent left atrial and left ventricular conductance catheter studies and fibrosis analysis. A second group (group 2, n = 8) received a baseline cardiac magnetic resonance imaging to characterize left atrial and left ventricular function. The atria were rapidly paced into atrial fibrillation for 6 weeks followed by cardioversion and cardiac magnetic resonance imaging. RESULTS: After 6 weeks of atrial fibrillation, left atrial contractility defined by atrial end-systolic pressure-volume relationship slope was significantly lower in group 2 than in group 1 (1.1 ± 0.5 vs 1.7 ± 1.0; P = .041), whereas compliance from the end-diastolic pressure-volume relationship was unchanged (1.5 ± 0.9 vs 1.6 ± 1.3; P = .733). Compared with baseline, atrial fibrillation resulted in a significantly higher contribution of left atrial reservoir volume to stroke volume (32% vs 17%; P = .005) and lower left atrial booster pump volume contribution to stroke volume (19% vs 28%; P = .029). Atrial fibrillation also significantly increased maximum left atrial volume (206 ± 41 mL vs 90 ± 21 mL; P < .001). Left atrial fibrosis in group 2 was significantly higher than in group 1. Atrial fibrillation decreased left ventricular ejection fraction (29% ± 9% vs 58 ± 8%; P < .001), but left ventricular stroke volume was unchanged. CONCLUSIONS: In a chronic model of atrial fibrillation, the left atrium demonstrated significant structural remodeling and decreased contractility. These data suggest that early intervention in patients with persistent atrial fibrillation might mitigate against adverse atrial and ventricular structural remodeling.

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 (DTs) and relaxation (DTr) components (DT=DTs+DTr) by analyzing E-waves via the parametrized diastolic filling formalism. The method has been validated with DTs and DTr 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 DTs and DTr were compared. Conventional diastolic function parameters did not differentiate between unblinded groups, whereas k, c (P<0.001) and DTs, DTr (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 (=DTr/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 DTs and DTr) 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.

E-wave generated intraventricular diastolic vortex to L-wave relation: model-based prediction with in vivo validation.

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.

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

Abstract 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 (Ft IVR) and model-predicted initial force of early rapid filling (Fi 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 Ft IVR and Fi E-wave respectively. For all 20 subjects (15 beats/subject, 308 beats), linear regression yielded Ft IVR = α Fi 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.

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 (xo), relaxation (c), and stiffness (k) parameters. It predicts that E-wave deceleration time (DT) is a function of both stiffness and relaxation. Ascribing DTs to stiffness and DTr to relaxation such that DT=DTs+DTr 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, Epeak, Edur, E-VTI, E/E') and E-wave derived PDF parameters (c, k, DTs, DTr) were compared. Total DT and DTs, DTr 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 quest for load-independent left ventricular chamber properties: Exploring the normalized pressure phase plane.

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.