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Articles by Leonid Shmuylovich in JoVE

Quantification of Global Diastolic Function by Kinematic Modelingbased Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism
Sina Mossahebi^{2,5}, Simeng Zhu^{2,5}, Howard Chen^{1,5}, Leonid Shmuylovich^{3,5}, Erina Ghosh^{1,5}, Sándor J. Kovács^{4,5}
^{1}Department of Biomedical Engineering, Washington University in St. Louis, ^{2}Department of Physics, Washington University in St. Louis, ^{3}Division of Biology and Biomedical Sciences, Washington University in St. Louis, ^{4}Department of Medicine, Cardiovascular Division, Washington University in St. Louis, ^{5}Cardiovascular Biophysics Lab, Washington University in St. Louis
Accurate, causalitybased quantification of global diastolic function has been achieved by kinematic modelingbased analysis of transmitral flow via the Parametrized Diastolic Filling (PDF) formalism. PDF generates unique stiffness, relaxation, and load parameters and elucidates 'new' physiology while providing sensitive and specific indexes of dysfunction.
Other articles by Leonid Shmuylovich on PubMed

Loadindependent Index of Diastolic Filling: Modelbased Derivation with in Vivo Validation in Control and Diastolic Dysfunction Subjects
Journal of Applied Physiology (Bethesda, Md. : 1985).
Jul, 2006 
Pubmed ID: 16575023 Maximum elastance is an experimentally validated, loadindependent systolic function index stemming from the timevarying elastance paradigm that decoupled extrinsic load from (intrinsic) contractility. Although Doppler echocardiography is the preferred method of diastolic function (DF) assessment, all echoderived indexes are load dependent, and no invasive or noninvasive loadindependent 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 Ewaves recorded while load was varied via tilt table (head up, horizontal, and head down) in 16 healthy volunteers. For the group, linear regression of Ewave 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 cathecho 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 pressureflow relation) from extrinsic load (left ventricular enddiastolic 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 welldefined pathological states is warranted.

Ewave Deceleration Time May Not Provide an Accurate Determination of LV Chamber Stiffness if LV Relaxation/viscoelasticity is Unknown
American Journal of Physiology. Heart and Circulatory Physiology.
Jun, 2007 
Pubmed ID: 17220184 Average left ventricular (LV) chamber stiffness (Delta P(avg)/Delta V(avg)) is an important diastolic function index. An Ewavebased determination of Delta P(avg)/Delta V(avg) (Little WC, Ohno M, Kitzman DW, Thomas JD, Cheng CP. Circulation 92: 19331939, 1995) predicted that deceleration time (DT) determines stiffness as follows: Delta P(avg)/Delta V(avg) = N(pi/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 Delta P(avg)/Delta V(avg) values determined by simultaneous echocardiographycatheterization. To elucidate the mechanism by which LVs with indistinguishable DTs manifest distinguishable chamber stiffness, we use a validated, kinematic Ewave model (Kovács SJ, Barzilai B, Perez JE. Am J Physiol Heart Circ Physiol 252: H178H187, 1987) with stiffness (k) and relaxation/viscoelasticity (c) parameters. Because the predicted linear relation between k and Delta P(avg)/Delta V(avg) has been validated, we reexpress the DTstiffness (Delta P(avg)/Delta V(avg)) relation of Little et al. as follows: DT(k) approximately pi/(2k). Using the kinematic model, we derive the general DTchamber stiffness/viscoelasticity relation as follows: DT(k,c) = pi/(2skrt[k])+c/(2k)(where c and k are determined directly from the Ewave), which reduces to DT(k) when c < k. Validation involved analysis of 400 Ewaves by determination of fivebeat averaged k and c from 80 subjects undergoing simultaneous echocardiographycatheterization. Clinical Ewave DTs were compared with modelpredicted DT(k) and DT(k,c). Clinical DT was better predicted by stiffness and relaxation/viscoelasticity (r(2) = 0.84, DT vs. DT(k,c)) jointly rather than by stiffness alone (r(2) = 0.60, DT vs. DT(k)). Thus LVs can have indistinguishable DTs but significantly different Delta P(avg)/Delta V(avg) 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
Ultrasound in Medicine & Biology.
Jun, 2007 
Pubmed ID: 17478033 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 Ewave) via kinematic modeling. Ewave 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 Ewave having established physiological analogues: x(o) (load), c (relaxation/viscoelasticity) and k (chamber stiffness). We define the dimensionless, fillingvolumebased kinematic filling efficiency index (KFEI) as the ratio of the velocitytime integral (VTI) of the actual clinical Ewave contour fit via PDF to the VTI of the PDF modelpredicted ideal Ewave contour having the same x(o) and k, but with no resistance to filling (c = 0). To validate the new index, Doppler Ewaves from 36 patients with normal ventricular function, 17 diabetic and 19 wellmatched nondiabetic controls, were analyzed. Ewave 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.


Transmitral Flow Velocitycontour Variation After Premature Ventricular Contractions: a Novel Test of the Loadindependent Index of Diastolic Filling
Ultrasound in Medicine & Biology.
Dec, 2008 
Pubmed ID: 18692298 The new echocardiographybased, loadindependent index of diastolic filling (LIIDF) M was assessed using load/shapevarying Ewaves after premature ventricular contractions (PVCs). Twentysix PVCs in 15 subjects from a preexisting simultaneous echocardiographycatheterization database were selected. Perturbed loadstate beats, defined as the first two postPVC Ewaves, and steadystate Ewaves, were subjected to conventional and modelbased analysis. M, a dimensionless index, defined by the slope of the peak drivingforce vs. peak (fillingopposing) resistiveforce regression, was determined from steadystate Ewaves alone, and from loadperturbed Ewaves combined with a matched number of subsequent beats. Despite high degrees of Ewave shape variation, M derived from loadvarying, perturbed beats and M derived from steadystate beats alone were indistinguishable. Because the peak drivingforce vs. peak resistiveforce relation determining M remains highly linear in the extended Ewave shape and load variation regime observed, we conclude that M is a robust LIIDF.

Stiffness and Relaxation Components of the Exponential and Logistic Time Constants May Be Used to Derive a Loadindependent Index of Isovolumic Pressure Decay
American Journal of Physiology. Heart and Circulatory Physiology.
Dec, 2008 
Pubmed ID: 18952715 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 loadindependent 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 loadindependent index MLIIIVPD. We predict that the plot of lumped recoil effects [Ek.(P*maxPinfinity)] versus resistance effects [tauc.(dP/dtmin)], defined by a set of loadvarying 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*maxPinfinity) 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 Ewave Delayed Relaxation Pattern to LV Pressure Contour Relation: Modelbased Prediction with in Vivo Validation
Ultrasound in Medicine & Biology.
Mar, 2010 
Pubmed ID: 20172449 The transmitral Doppler Ewave "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 timeconstant 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 Ewave 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 flowmicromanometric 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, modelbased 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 Ewave pattern (p < 0.05). We conclude that the PRR may differentiate between subjects having a DR pattern and subjects with normal Ewaves, even when tau cannot.


Vortex Formation Timetoleft Ventricular Early Rapid Filling Relation: Modelbased Prediction with Echocardiographic Validation
Journal of Applied Physiology (Bethesda, Md. : 1985).
Dec, 2010 
Pubmed ID: 20864560 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 lengthtodiameter ratio of the aspirated (equivalent cylindrical) fluid column. Since LV wall motion generates the atrioventricular pressure gradient resulting in the early transmitral flow (Doppler Ewave) 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: 63056308, 2006) approximated Ewave shape as a triangle and calculated VFT(Gharib) as triangle (Ewave) area (cm) divided by peak (Doppler Mmode derived) mitral orifice diameter (cm). We used a validated kinematic model of filling for the Ewave as a function of time, parametrized by stiffness, viscoelasticity, and load. To calculate VFT(kinematic), we computed the curvilinear Ewave area (using the kinematic model) and divided it by peak effective orifice diameter. The derived VFTtoLV early rapid filling relation predicts VFT to be a function of peak Ewavetopeak mitral annular tissue velocity (Doppler E'wave) ratio as (E/E')(3/2). Validation utilized 262 cardiac cycles of simultaneous echocardiographic highfidelity hemodynamic data from 12 subjects. VFT(Gharib) and VFT(kinematic) were calculated for each subject and were wellcorrelated (R(2) = 0.66). In accordance with prediction, VFT(kinematic) to (E/E')(3/2) relationship was validated (R(2) = 0.63). We conclude that VFT(kinematic) is a DF index computable in terms of global kinematic filling parameters of stiffness, viscoelasticity, and load. Validation of the fluid mechanicstochamber kinematics relation unites previously unassociated DF assessment methods and elucidates the mechanistic basis of the strong correlation between VFT and (E/E')(3/2).

The Thermodynamics of Diastole: Kinematic Modelingbased Derivation of the PV Loop to Transmitral Flow Energy Relation with in Vivo Validation
American Journal of Physiology. Heart and Circulatory Physiology.
Feb, 2011 
Pubmed ID: 21076022 Pressurevolume (PV) loopbased 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 PV 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 Ewave contours. The first law of thermodynamics requires that energy (ε) computed from the Doppler Ewave (εEwave) and the same portion of the PV loop (εPV Ewave) be equivalent. These energies have not been previously derived nor have their predicted equivalence been experimentally validated. To test the hypothesis that εPV Ewave and εEwave are equivalent, we used a validated kinematic model of filling to derive εEwave in terms of chamber stiffness, relaxation/viscoelasticity, and load. For validation, simultaneous (conductance catheter) PV and echocadiographic data from 12 subjects (205 total cardiac cycles) having a range of diastolic function were analyzed. For each Ewave, εEwave was compared with εPV Ewave calculated from simultaneous PV data. Linear regression yielded the following: εPV Ewave=αεEwave+b (R2=0.67), where α=0.95 and b=6e(5). We conclude that Ewavederived energy for suctioninitiated early rapid filling εEwave, quantitated via kinematic modeling, is equivalent to invasive PVdefined filling energy. Hence, the thermodynamics of diastole via εEwave generate a novel mechanismbased index of diastolic function suitable for in vivo phenotypic characterization.

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