Leonid Shmuylovich

Point: Left ventricular volume during diastasis is the physiological in vivo equilibrium volume and is related to diastolic suction.

> “ Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” (Sherlock Holmes; Ref. [6a][1]) The truth regarding ventricular equilibrium and diastolic suction has been elusive since Galen ([26][2]) observed blood moving into the ventricle with a force

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.

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=6e(-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.

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.

Determination of early diastolic LV vortex formation time (T∗) via the PDF formalism: A kinematic model of filling

The filling (diastolic) function of the human left ventricle is most commonly assessed by echocardiography, a non-invasive imaging modality. To quantify diastolic function (DF) empiric indices are obtained from the features (height, duration, area) of transmitral flow velocity contour, obtained by echocardiography. The parameterized diastolic filling (PDF) formalism is a kinematic model developed by Kovács et al which incorporates the suction pump attribute of the left ventricle and facilitates DF quantitation by analysis of echocardiographic transmitral flow velocity contours in terms of stiffness (k), relaxation (c) and load (x<inf>o</inf>). A complementary approach developed by Gharib et al, uses fluid mechanics and characterizes DF in terms of vortex formation time (T∗) derived from streamline features formed by the jet of blood aspirated into the ventricle. Both of these methods characterize DF using a causality-based approach. In this paper, we derive T∗s kinematic analogue T∗<inf>kinematic</inf> in terms of k, c and x<inf>o</inf>. A comparison between T∗<inf>kinematic</inf> and T∗<inf>fluid</inf> <inf>mechanic</inf> obtained from averaged transmitral velocity and mitral annulus diameter, is presented. We found that T∗ calculated by the two methods were comparable and T∗<inf>kinematic</inf> correlated with the peak LV recoil driving force kx<inf>o</inf>.

Last word on point: Counterpoint: Left ventricular volume during diastasis is the physiological in vivo equilibrium volume and is related to diastolic suction.

to the editor: We thank the commentators for sharing their perspectives and we would like to expand on them as a group–with a focus on causation. Although equilibrium volume definitions may appear semantic, disagreement leads to experimentally differentiable consequences about suction, which as

Point: Counterpoint: Left ventricular volume during diastasis is/is not the physiological in vivo equilibrium volume and is/is not related to diastolic suction

> “ Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” (Sherlock Holmes; Ref. [6a][1]) The truth regarding ventricular equilibrium and diastolic suction has been elusive since Galen ([26][2]) observed blood moving into the ventricle with a force

Early detection of abnormal left ventricular relaxation in acute myocardial ischemia with a quadratic model. Med Eng Phys 2014;36(September (9)):1101–5 by Morimont et al.

[ Dear Editor, We read with interest the article by Morimont et al., who quantitatively address an important issue in cardiovascular physiology and medicine. They note that the conventional method of characterizing the pressure decline in the left ventricle during isovolumic relaxation (IVR) provides poor curve-fits, especially in pathophysiologic settings such as acute myocardial infarction. While their findings are compelling, some comments regarding limitations of their method are in order. The authors rightly utilize the pressure phase plane (PPP, a plot of dP/dt versus P) to graphically illustrate and thereby elucidate and characterize the fall of left ventricular pressure during IVR [1]. As a basis, the authors cite a curve fitting method proposed by Matsubara et al., who noted that IVR segments of PPP plots are often curvilinear instead of linear [2]. The conventional method of characterization uses a monoexponential to fit the data, which can only inscribe a linear fit to the IVR segment in the PPP, and thereby can fail to accurately quantify the relaxation process in some cases [2–4]. We have previously noted the difficulties encountered in fitting both monoexponential and logistic (quadratic) equations to the IVR portion of PPP trajectories even to data from the same heart [4]. Instead of employing a curve-fit approach, we derived a model of isovolumic relaxation that incorporates two known properties of the heart: (1) elastic recoil drives the ventricle to return to its passive state [5–7] and (2) myosin-actin cross-bridge inactivation (uncoupling) modulates relaxation [8]. Like the logistic equation used by Morimont et al., our model has two parameters instead of the one used in the conventional monoexponential method. However, our parameters are kinematic analogs of physical properties (stiffness derived from elastic elements and viscous resistance (relaxation) derived from cross-bridge uncoupling). Our model-predicted fit to the data has several benefits over mechanism independent curve-fitting methods [4]. First, the model was derived with a physical basis for its stiffness and relaxation parameters. Second, it can fit a portion of the IVR segment prior to minimum dP/dt (i.e. peak negative dP/dt). Third, we have shown that this model more accurately characterizes the spatiotemporal attributes of LV pressure decay rate during IVR [9]. Importantly, this model correctly predicts both linear and curvilinear shaped IVR segments of PPP trajectories, including those of non-ejecting premature ventricular contractions [4]. This capability is a result of the interplay between the elastic (stiffness) and viscous (relaxation) terms in the governing differential equation. Our approach revealed that the monoexponential (linear IVR) versus logistic model (curvilinear IVR) are actually parametric limits of our kinematic model—thereby elucidating the relative role of stiffness versus relaxation as IVR determinants [4].

Left ventricular volume during diastasis is/is not the physiological in vivo equilibrium volume and is/is not related to diastolic suction: Point: Left ventricular volume during diastasis is the physiological in vivo equilibrium volume and is related to diastolic suction

> “ Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” (Sherlock Holmes; Ref. [6a][1]) The truth regarding ventricular equilibrium and diastolic suction has been elusive since Galen ([26][2]) observed blood moving into the ventricle with a force

Automated method for calculation of a load-independent index of isovolumic pressure decay from left ventricular pressure data

Diastolic heart failure (DHF) is present in over 50% of hospitalized heart failure patients, and diastolic dysfunction is known to play a critical pathophysiologic role. Measurement of left-ventricular pressure (LVP) via catheterization is the gold standard for diastolic function (DF) evaluation, but current methods fail to fully capitalize on the complete information content of the pressure contour. We have previously demonstrated that a kinematic model of isovolumic pressure decay (IVPD), which accounts for restoring force (stiffness) and resistance (viscoelasticity/relaxation), provides mechanistic insight into IVPD physiology and provides an accurate fit to the recorded contour. Recently we derived a novel load-independent index of isovolumic pressure decay (LIIIVPD) involving IVPD kinematic model stiffness and resistance parameters. In this work we detail methods and provide guidelines by which LIIIVPD computation may be achieved in real-time from the pressure contour recorded during cardiac catheterization.