The thermodynamics of diastole: kinematic modeling-based derivation of the P-V loop to transmitral flow energy relation with in vivo validation

Kinetic energy of left ventricular blood flow across heart failure phenotypes and in subclinical diastolic dysfunction

BACKGROUND

Kinetic energy (KE) of intracardiac blood flow reflects myocardial work spent on accelerating blood and provides a mechanistic window into diastolic filling dynamics. Diastolic dysfunction may represent an early stage in the development of heart failure (HF). Here we evaluated the hemodynamic effects of impaired diastolic function in subjects with and without HF, testing the hypothesis that left ventricular KE differs between controls, subjects with subclinical diastolic dysfunction (SDD), and HF patients.

METHODS

We studied 77 subjects (16 controls, 20 subjects with SDD, 16 HFpEF, 9 HFmrEF, and 16 HFrEF patients, age- and sex-matched at the group level). Cardiac magnetic resonance at 1.5T included intracardiac 4D flow and cine imaging. Left ventricular KE was calculated as 0.5*m*v².

RESULTS

Systolic KE was similar between groups (p>0.4), also after indexing to stroke volume (p=0.25), and was primarily driven by ventricular emptying rate (p<0.0001, R²=0.52). Diastolic KE was higher in heart failure patients than controls (p<0.05) but similar between SDD and HFpEF (p>0.18), correlating with inflow conditions (E-wave velocity, p<0.0001, R²=0.24) and end-diastolic volume (p=0.0003, R²=0.17) but not with average e' (p=0.07).

CONCLUSIONS

Diastolic KE differs between controls and heart failure, suggesting more work is spent filling the failing ventricle, while systolic KE does not differentiate between well-matched groups with normal ejection fraction even in the presence of relaxation abnormalities and heart failure. Mechanistically, KE reflects the acceleration imparted on the blood and is driven by variations in ventricular emptying and filling rates, volumes, and heart rate, regardless of underlying pathology.

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.

Quantification of left and right atrial kinetic energy using four-dimensional intracardiac magnetic resonance imaging flow measurements

Kinetic energy (KE) of atrial blood has been postulated as a possible contributor to ventricular filling. Therefore, we aimed to quantify the left (LA) and right (RA) atrial blood KE using cardiac magnetic resonance (CMR). Fifteen healthy volunteers underwent CMR at 3 T, including a four-dimensional phase-contrast flow sequence. Mean LA KE was lower than RA KE (1.1 ± 0.1 vs. 1.7 ± 0.1 mJ, P < 0.01). Three KE peaks were seen in both atria: one in ventricular systole, one during early ventricular diastole, and one during atrial contraction. The systolic LA peak was significantly smaller than the RA peak ( P < 0.001), and the early diastolic LA peak was larger than the RA peak ( P < 0.05). Rotational flow contained 46 ± 7% of total KE and conserved energy better than nonrotational flow did. The KE increase in early diastole was higher in the LA ( P < 0.001). Systolic KE correlated with the combination of atrial volume and systolic velocity of the atrioventricular plane displacement ( r2 = 0.57 for LA and r2 = 0.64 for RA). Early diastolic KE of the LA correlated with left ventricle (LV) mass ( r2 = 0.28), however, no such correlation was found in the right heart. This suggests that LA KE increases during early ventricular diastole due to LV elastic recoil, indicating that LV filling is dependent on diastolic suction. Right ventricle (RV) relaxation does not seem to contribute to atrial KE. Instead, RA KE generated during ventricular systole may be conserved in a hydraulic “flywheel” and transferred to the RV through helical flow, which may contribute to RV filling.

Quantification of left and right ventricular kinetic energy using four-dimensional intracardiac magnetic resonance imaging flow measurements

We aimed to quantify kinetic energy (KE) during the entire cardiac cycle of the left ventricle (LV) and right ventricle (RV) using four-dimensional phase-contrast magnetic resonance imaging (MRI). KE was quantified in healthy volunteers (n = 9) using an in-house developed software. Mean KE through the cardiac cycle of the LV and the RV were highly correlated (r(2) = 0.96). Mean KE was related to end-diastolic volume (r(2) = 0.66 for LV and r(2) = 0.74 for RV), end-systolic volume (r(2) = 0.59 and 0.68), and stroke volume (r(2) = 0.55 and 0.60), but not to ejection fraction (r(2) < 0.01, P = not significant for both). Three KE peaks were found in both ventricles, in systole, early diastole, and late diastole. In systole, peak KE in the LV was lower (4.9 ± 0.4 mJ, P = 0.004) compared with the RV (7.5 ± 0.8 mJ). In contrast, KE during early diastole was higher in the LV (6.0 ± 0.6 mJ, P = 0.004) compared with the RV (3.6 ± 0.4 mJ). The late diastolic peaks were smaller than the systolic and early diastolic peaks (1.3 ± 0.2 and 1.2 ± 0.2 mJ). Modeling estimated the proportion of KE to total external work, which comprised ∼0.3% of LV external work and 3% of RV energy at rest and 3 vs. 24% during peak exercise. The higher early diastolic KE in the LV indicates that LV filling is more dependent on ventricular suction compared with the RV. RV early diastolic filling, on the other hand, may be caused to a higher degree of the return of the atrioventricular plane toward the base of the heart. The difference in ventricular geometry with a longer outflow tract in the RV compared with the LV explains the higher systolic KE in the RV.

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).

Pressure-volume relation analysis of mouse ventricular function

Nearly 40 years ago, the Sagawa laboratory spawned a renaissance in the use of instantaneous ventricular pressure-volume (P-V) relations to assess cardiac function. Since then, this analysis has taken hold as the most comprehensive way to quantify ventricular chamber function and energetics and cardiovascular interactions. First studied in large mammalian hearts and later in humans employing a catheter-based method, P-V analysis was translated to small rodents in the late 1990s by the Kass laboratory. Over the past decade, this approach has become a gold standard for comprehensive examination of in vivo cardiac function in mice, facilitating a new era of molecular cardiac physiology. The catheter-based method remains the most widely used approach in mice. In this brief review, we discuss this instrumentation, the theory behind its use, and how volume signals are calibrated and discuss elements of P-V analysis. The goal is to provide a convenient summary of earlier investigations and insights for users whose primary interests lie in genetic/molecular studies rather than in biomedical engineering.