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

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

In early diastole, the suction pump feature of the left ventricle opens the mitral valve and aspirates atrial blood. The ventricle fills via a blunt profiled cylindrical jet of blood that forms an asymmetric toroidal vortex ring inside the ventricle whose growth has been quantified by the standard (dimensionless) expression for vortex formation time, VFT_standard = {transmitral velocity time integral}/{mitral orifice diameter}. It can differentiate between hearts having distinguishable early transmitral (Doppler E-wave) filling patterns. An alternative validated expression, VFT_kinematic reexpresses VFT_standard by incorporating left heart, near “constant-volume pump” physiology thereby revealing VFT_kinematic's explicit dependence on maximum rate of longitudinal chamber expansion (E′). In this work, we show that VFT_kinematic can differentiate between hearts having indistinguishable E-wave patterns, such as pseudonormal (PN; 0.75 < E/A < 1.5 and E/E′ > 8) versus normal. Thirteen age-matched normal and 12 PN data sets (738 total cardiac cycles), all having normal LVEF, were selected from our Cardiovascular Biophysics Laboratory database. Doppler E-, lateral annular E′-waves, and M-mode data (mitral leaflet separation, chamber dimension) was used to compute VFT_standard and VFT_kinematic. VFT_standard did not differentiate between groups (normal [3.58 ± 1.06] vs. PN [4.18 ± 0.79], P = 0.13). In comparison, VFT_kinematic for normal (3.15 ± 1.28) versus PN (4.75 ± 1.35) yielded P = 0.006. Hence, the applicability of VFT_kinematic for diastolic function quantitation has been broadened to include analysis of PN filling patterns in age-matched groups.

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.

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.

Stiffness and relaxation components of the exponential and logistic time constants may be used to derive a load-independent index of isovolumic pressure decay

In current practice, empirical parameters such as the monoexponential time constant tau or the logistic model time constant tauL are used to quantitate isovolumic relaxation. Previous work indicates that tau and tauL are load dependent. A load-independent index of isovolumic pressure decline (LIIIVPD) does not exist. In this study, we derive and validate a LIIIVPD. Recently, we have derived and validated a kinematic model of isovolumic pressure decay (IVPD), where IVPD is accurately predicted by the solution to an equation of motion parameterized by stiffness (Ek), relaxation (tauc), and pressure asymptote (Pinfinity) parameters. In this study, we use this kinematic model to predict, derive, and validate the load-independent index MLIIIVPD. We predict that the plot of lumped recoil effects [Ek.(P*max-Pinfinity)] versus resistance effects [tauc.(dP/dtmin)], defined by a set of load-varying IVPD contours, where P*max is maximum pressure and dP/dtmin is the minimum first derivative of pressure, yields a linear relation with a constant (i.e., load independent) slope MLIIIVPD. To validate the load independence, we analyzed an average of 107 IVPD contours in 25 subjects (2,669 beats total) undergoing diagnostic catheterization. For the group as a whole, we found the Ek.(P*max-Pinfinity) versus tauc.(dP/dtmin) relation to be highly linear, with the average slope MLIIIVPD=1.107+/-0.044 and the average r2=0.993+/-0.006. For all subjects, MLIIIVPD was found to be linearly correlated to the subject averaged tau (r2=0.65), tauL(r2=0.50), and dP/dtmin (r2=0.63), as well as to ejection fraction (r2=0.52). We conclude that MLIIIVPD is a LIIIVPD because it is load independent and correlates with conventional IVPD parameters. Further validation of MLIIIVPD in selected pathophysiological settings is warranted.