Isovolumic pressure-to-early rapid filling decay rate relation: model-based derivation and validation via simultaneous catheterization echocardiography

The Structure of Left Ventricular Relaxation in Case of Ventriculography

AIM

To study the relaxation structure of the left ventricle (LV) in patients who underwent ventriculography.

MATERIAL AND METHODS

LV ventriculography was performed in 37 patients. Before catheterization, echocardiography was performed in each patient. In 6 patients, the LV ejection fraction (EF) was below 40%; these patients with systolic dysfunction were not included in the study. In 31 patients, the LV EF was higher than 50%. In this group, 13 patients had NYHA functional class (FC) 2-3 chronic heart failure (CHF); the rest of the patients had FC 1 CHF. Eighteen of 31 patients had stable ischemic heart disease; 50% of these patients had a history of myocardial infarction; the rest of the patients had hypertension and atrial and ventricular arrhythmias. The dynamics of the LV pressure decrease was analyzed from the moment of the maximum rate of pressure drop, which usually coincides with the closure of the aortic valves. The pressure drop curve was logarithmized with natural logarithms and divided into 4-5 sections with different degrees of curve slope. The relaxation time constant was calculated for each section. Its inverse value characterizes the relaxation time constant (tau).

RESULTS

In 31 patients with LV EF 52-60%, three types of the dynamics of the relaxation rate constant were identified during the pressure decrease in the isovolumic phase: in 9 patients, the isovolumic relaxation constant (IRC) steadily increased as the pressure decreased; in 13 patients, it continuously decreased; and in 9 patients, the dynamics of IRC change was intermediate, with an initial increase followed by a decrease.

CONCLUSION

In diastolic dysfunction, one group of patients had an adaptation type associated with an increase in the LV wall elasticity, while the other group had a different type of adaptation associated with its decrease. Each type has advantages and disadvantages. This is probably due to changes in the structure of the sarcomeric protein connectin (titin).

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.

Myocardial relaxation is accelerated by fast stretch, not reduced afterload

Fast relaxation of cross-bridge generated force in the myocardium facilitates efficient diastolic function. Recently published research studying mechanisms that modulate the relaxation rate has focused on molecular factors. Mechanical factors have received less attention since the 1980s when seminal work established the theory that reducing afterload accelerates the relaxation rate. Clinical trials using afterload reducing drugs, partially based on this theory, have thus far failed to improve outcomes for patients with diastolic dysfunction. Therefore, we reevaluated the protocols that suggest reducing afterload accelerates the relaxation rate and identified that myocardial relengthening was a potential confounding factor. We hypothesized that the speed of myocardial relengthening at end systole (end systolic strain rate), and not afterload, modulates relaxation rate and tested this hypothesis using electrically-stimulated trabeculae from mice, rats, and humans. We used load-clamp techniques to vary afterload and end systolic strain rate independently. Our data show that the rate of relaxation increases monotonically with end systolic strain rate but is not altered by afterload. Computer simulations mimic this behavior and suggest that fast relengthening quickens relaxation by accelerating the detachment of cross-bridges. The relationship between relaxation rate and strain rate is novel and upends the prevailing theory that afterload modifies relaxation. In conclusion, myocardial relaxation is mechanically modified by the rate of stretch at end systole. The rate of myocardial relengthening at end systole may be a new diagnostic indicator or target for treatment of diastolic dysfunction.

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 ′.

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

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 (F_tIVR) and model‐predicted initial force of early rapid filling (F_{i 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 F_tIVR and F_{i E‐wave} respectively. For all 20 subjects (15 beats/subject, 308 beats), linear regression yielded F_tIVR = α F_{i 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.

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.

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.

The diastatic pressure-volume relationship is not the same as the end-diastolic pressure-volume relationship

The end-diastolic pressure-volume (P-V) relationship (EDPVR) is routinely used to determine the passive left ventricular (LV) stiffness, although the diastatic P-V relationship (D-PVR) has also been measured. Based on the physiological difference between diastasis (the LV and atrium are relaxed and static) and end diastole (LV volume increased by atrial systole and the atrium is contracted), we hypothesized that, although both D-PVR and EDPVR include LV chamber stiffness information, they are two different, distinguishable P-V relations. Cardiac catheterization determined LV pressures, and conductance volumes in 31 subjects were analyzed. Physiological, beat-to-beat variation of the diastatic and end-diastolic P-V points were fit by linear and exponential functions to generate the D-PVR and EDPVR. The extrapolated exponential D-PVR underestimated LVEDP in 82% of the heart beats (P < 0.001). The extrapolated EDPVR overestimated pressure at diastasis in 84% of the heart beats (P < 0.001). If each subject's diastatic and end-diastolic P-V data were combined to form a continuous data set to be fit by one exponential relation, the goodness of fit was always worse than if the diastatic and end-diastolic data were grouped separately and fit by two distinct exponential relations. Diastatic chamber stiffness was less than EDPVR stiffness (defined by the slope of P-V relation) for all 31 subjects (0.16 +/- 0.11 vs. 0.24 +/- 0.15 mmHg/ml, P < 0.001). We conclude that the D-PVR and EDPVR are distinguishable. Because it is not coupled to a contracted atrium, the D-PVR conveys passive LV stiffness better than the EDPVR. Additional studies that fully elucidate the physiology and biology of diastasis in health and disease are in progress.

Physical determinants of left ventricular isovolumic pressure decline: model prediction with in vivo validation

The rapid decline in pressure during isovolumic relaxation (IVR) is traditionally fit algebraically via two empiric indexes: τ, the time constant of IVR, or τL, a logistic time constant. Although these indexes are used for in vivo diastolic function characterization of the same physiological process, their characterization of IVR in the pressure phase plane is strikingly different, and no smooth and continuous transformation between them exists. To avoid the parametric discontinuity between τ and τL and more fully characterize isovolumic relaxation in mechanistic terms, we modeled ventricular IVR kinematically, employing a traditional, lumped relaxation (resistive) and a novel elastic parameter. The model predicts IVR pressure as a function of time as the solution of d2P/d t2 + (1/μ)dP/d t + EkP = 0, where μ (ms) is a relaxation rate (resistance) similar to τ or τL and Ek (1/s2) is an elastic (stiffness) parameter (per unit mass). Validation involved analysis of 310 beats (10 consecutive beats for 31 subjects). This model fit the IVR data as well as or better than τ or τL in all cases (average root mean squared error for dP/d t vs. t: 29 mmHg/s for model and 35 and 65 mmHg/s for τ and τL, respectively). The solution naturally encompasses τ and τL as parametric limits, and good correlation between τ and 1/μ Ek (τ = 1.15/μ Ek − 11.85; r2 = 0.96) indicates that isovolumic pressure decline is determined jointly by elastic ( Ek) and resistive (1/μ) parameters. We conclude that pressure decline during IVR is incompletely characterized by resistance (i.e., τ and τL) alone but is determined jointly by elastic ( Ek) and resistive (1/μ) mechanisms.

Elucidation of spatially distinct compensatory mechanisms in diastole: radial compensation for impaired longitudinal filling in left ventricular hypertrophy

Cardiac output maintenance is so fundamental that, when regional systolic function is impaired, as during ischemia, nonischemic segments compensate by becoming hypercontractile. By analogy, diastolic compensatory mechanisms that maintain filling volume must exist but remain to be fully elucidated. Viewing filling in spatially distinct (longitudinal, radial) mechanistic terms facilitates elucidation of diastolic compensatory mechanisms. Because impairment of longitudinal (long axis) diastolic function (DF) in left ventricular hypertrophy (LVH) is established, we hypothesized that to maintain filling volume, radial (short-axis) filling function would compensate. In 20 normal left ventricular ejection fraction (LVEF) subjects (10 with LVH, 10 without LVH), we analyzed longitudinal function via Doppler tissue imaging of mitral annular motion and radial function as change in short-axis endocardial dimension via M-mode. The spatial (long axis, short axis) endocardial LV dimensions and their changes allowed assignment of E-wave filling volume into (cylindrical geometry-based) longitudinal and radial components. Despite indistinguishable (P = 0.70) E-wave velocity-time integrals (E-wave filling volume surrogate), systolic stroke volumes, and end-diastolic volumes in the LVH and control groups, longitudinal volume in absolute terms and the percent of E-wave volume accommodated longitudinally were reduced in the LVH group (P < 0.05 and P < 0.01, respectively), whereas the percent of E-wave volume accommodated radially was enhanced (P < 0.01). We conclude that, in normal LVEF (decreased longitudinal volume accommodation) LVH subjects vs. controls, spatially distinct compensatory mechanisms in diastole manifest as increased radial volume accommodation per unit of E-wave filling volume. Assessment of spatially distinct diastolic compensatory mechanisms in other pathophysiological subsets is warranted.

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.

Derivation and Left Ventricular Pressure Phase Plane Based Validation of a Time Dependent Isometric Crossbridge Attachment Model

Huxley's crossbridge attachment model predicts tension (contractile force) development in isometric (fixed length) cells using constant attachment and detachment rates. Alternative models incorporating time-varying calcium concentrations are complex (coupled linear differential equations) and use time-dependent inputs (calcium, elastance, etc.) to model multiple states. We hypothesize that by incorporating the known significant rise and fall in intracellular calcium, via either an asymmetric damped function or a symmetric Gaussian function, into a time-varying, rather than constant, attachment rate function, the Huxley model prediction for tension (i.e., chamber pressure) in isovolumic (isometric) non-ejecting beats will improve. To test the hypothesis that the time-dependent model-predicted (TDM) pressure fits the in vivo isometric (isovolumic) LV pressure phase-plane (PPP) contour better than the constant attachment rate predicted pressure, we used the TDM to fit non-ejecting, premature ventricular contraction (PVC) PPP contours in 6 subjects. Conventional model fit was poor (relative error 74.0%+/-12.5%), while the asymmetric damped TDM rate function provided slight improvement relative to the conventional time-independent model (relative error 55.4%+/-9.8%). The symmetric Gaussian rate function TDM provided the best PPP fit to all non-ejecting beats tested (relative error 19.8%+/-4.8%). We conclude that approximating the lumped attachment rate via a time-varying, rather than constant, rate function generates a physiologically viable model of crossbridge behavior. The PPP provides the optimal arena for alternate mathematical formulation assessment of LVP contour prediction by time-dependent attachment rate functions and facilitates modeling of cardiac contraction and relaxation.

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.