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

Analysis of Right Ventricular Myocardial Stiffness and Relaxation Components in Children and Adolescents With Pulmonary Arterial Hypertension

Background

The rate of left ventricular pressure decrease during isovolumic relaxation is traditionally assessed algebraically via 2 empirical indices: the monoexponential and logistic time constants (τ_E and τ_L). Since the pattern of right ventricular (RV) pressure decrease is quite different from that of the left ventricular, we hypothesized that novel kinematic model parameters are more appropriate and useful to evaluate RV diastolic dysfunction.

Methods and Results

Eight patients with pulmonary arterial hypertension (age 12.5±4.8 years) and 20 normal subjects (control group; age 12.3±4.4 years) were enrolled. The kinematic model was parametrized by stiffness/restoring Ek and damping/relaxation μ. The model predicts isovolumic relaxation pressure as a function of time as the solution of d²P/dt²+(1/μ)dP/dt+EkP=0, based on the theory that the pressure decay is determined by the interplay of inertial, stiffness/restoring, and damping/relaxation forces. In the assessment of RV diastolic function, τ_E and τ_L did not show significant differences between the pulmonary arterial hypertension and control groups (46.8±15.5 ms versus 32.5±14.6 ms, and 19.6±5.9 ms versus 14.5±7.2 ms, respectively). The pulmonary arterial hypertension group had a significantly higher Ek than the control group (915.9±84.2 s⁻² versus 487.0±99.6 s⁻², P<0.0001) and a significantly lower μ than the control group (16.5±4.3 ms versus 41.1±10.4 ms, P<0.0001). These results show that the RV has higher stiffness/elastic recoil and lower cross‐bridge relaxation in pulmonary arterial hypertension.

Conclusions

The present findings indicate the feasibility and utility of kinematic model parameters for assessing RV diastolic function.

The quest for load-independent left ventricular chamber properties: exploring the normalized pressure-volume loop

Left ventricular (LV) pressure–volume (P–V) loop analysis is the gold standard for chamber function assessment. To advance beyond traditional P–V and pressure phase plane (dP/dt‐P) analysis in the quest for novel load‐independent chamber properties, we introduce the normalized P–V loop. High‐fidelity LV pressure and volume data (161 P‐V loops) from 13 normal control subjects were analyzed. Normalized LV pressure (P_N) was defined by 0 ≤ P(t) ≤ 1. Normalized LV volume (V_N) was defined as V_N=V(t)/V_diastasis, since the LV volume at diastasis (V_diastasis) is the in‐vivo equilibrium volume relative to which the LV volume oscillates. Plotting P_N versus V_N for each cardiac cycle generates normalized P‐V loops. LV volume at the peak LV ejection rate and at the peak LV filling rate (peak −dV/dt and peak +dV/dt, respectively) were determined for conventional and normalized loops. V_N at peak +dV/dt was inscribed at 64 ± 5% of normalized equilibrium (diastatic) volume with an inter‐subject variation of 8%, and had a reduced intra‐subject (beat‐to‐beat) variation compared to conventional P‐V loops (9% vs. 13%, respectively; P < 0.005), thereby demonstrating load‐independent attributes. In contrast, V_N at peak −dV/dt was inscribed at 81 ± 9% with an inter‐subject variation of 11%, and had no significant change in intra‐subject (beat‐to‐beat) variation compared to conventional P‐V loops (17% vs. 17%, respectively; P = 0.56), therefore failing to demonstrate load‐independent tendencies. Thus, the normalized P‐V loop advances the quest for load‐independent LV chamber properties. V_N at the peak LV filling rate (≈sarcomere length at the peak sarcomere lengthening rate) manifests load‐independent properties. This novel method may help to elucidate and quantify new attributes of cardiac and cellular function. It merits further application in additional human and animal physiologic and pathophysiologic datasets.

Assessment of pulmonary arterial compliance evaluated using harmonic oscillator kinematics

We hypothesized that K_PA, a harmonic oscillator kinematics-derived spring constant parameter of the pulmonary artery pressure (PAP) profile, reflects PA compliance in pediatric patients. In this prospective study of 33 children (age range = 0.5–20 years) with various cardiac diseases, we assessed the novel parameter designated as K_PA calculated using the pressure phase plane and the equation K_PA = (dP/dt_max)²/([Pmax – Pmin])/2)², where dP/dt_max is the peak derivative of PAP, and Pmax – Pmin is the difference between the minimum and maximum PAP. PA compliance was also calculated using two conventional methods: systolic PA compliance (sPAC) was expressed as the stroke volume/Pmax – Pmin; and diastolic PA compliance (dPAC) was determined according to a two-element Windkessel model of PA diastolic pressure decay. In addition, data were recorded during abdominal compression to determine the influence of preload on K_PA. A significant correlation was observed between K_PA and sPAC (r = 0.52, P = 0.0018), but not dPAC. Significant correlations were also seen with the time constant (τ) of diastolic PAP (r = −0.51, P = 0.0026) and the pulmonary vascular resistance index (r = −0.39, P = 0.0242). No significant difference in K_PA was seen between before and after abdominal compression. K_PA had a higher intraclass correlation coefficient than other compliance and resistance parameters for both intra-observer and inter-observer variability (0.998 and 0.997, respectively). These results suggest that K_PA can provide insight into the underlying mechanisms and facilitate the quantification of PA compliance.

Temperature-dependent inotropic and lusitropic indices based on half-logistic time constants for four segmental phases in isovolumic left ventricular pressure–time curve in excised, cross-circulated canine heart

Varying temperature affects cardiac systolic and diastolic function and the left ventricular (LV) pressure–time curve (PTC) waveform that includes information about LV inotropism and lusitropism. Our proposed half-logistic (h-L) time constants obtained by fitting using h-L functions for four segmental phases (Phases I–IV) in the isovolumic LV PTC are more useful indices for estimating LV inotropism and lusitropism during contraction and relaxation periods than the mono-exponential (m-E) time constants at normal temperature. In this study, we investigated whether the superiority of the goodness of h-L fits remained even at hypothermia and hyperthermia. Phases I–IV in the isovolumic LV PTCs in eight excised, cross-circulated canine hearts at 33, 36, and 38 °C were analyzed using h-L and m-E functions and the least-squares method. The h-L and m-E time constants for Phases I–IV significantly shortened with increasing temperature. Curve fitting using h-L functions was significantly better than that using m-E functions for Phases I–IV at all temperatures. Therefore, the superiority of the goodness of h-L fit vs. m-E fit remained at all temperatures. As LV inotropic and lusitropic indices, temperature-dependent h-L time constants could be more useful than m-E time constants for Phases I–IV.

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.

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.

Acute initial haemodynamic changes in a rat isoprenaline model of cardiotoxicity

The synthetic catecholamine isoprenaline (ISO) has been used as an inductor in the acute myocardial infarction model for more than a half century. Despite the fact that many articles were published on this topic, precise early haemodynamic pathology remains unknown. Acute haemodynamic changes were measured in rats; first, in preliminary experiments by the thermodilution method; and second, in main experiments continuously for 2 h using a Millar catheter. Animals received saline or ISO in the cardiotoxic dose (100 mg/kg, subcutaneously). Also, additional experiments were performed with salbutamol in order to evaluate the role of β2-receptors. ISO caused a rapid, within 1 min, approximately 40% decrease in arterial blood pressures, 30% increase in the heart rate, and 30% decrease in the stroke volume. Within the first 2 min, the changes were followed by decreases in afterload (−40%), preload (−10%), diastolic relaxation (−50%), diastolic filling (−40%), and a marked, but short-term, increase in the left ventricle contractility (+100%). Ejection fraction did not significantly change, suggesting diastolic dysfunction. Salbutamol, with the exception of diastolic pressure and afterload, did not substantially influence other parameters. In conclusion, this study demonstrated that diastolic dysfunction precedes systolic dysfunction and β2-receptor stimulation alone is not sufficient for an early induction of diastolic dysfunction.

Spatio-temporal attributes of left ventricular pressure decay rate during isovolumic relaxation

Global left ventricular (LV) isovolumic relaxation rate has been characterized: 1) via the time constant of isovolumic relaxation τ or 2) via the logistic time constant τ L. An alternate kinematic method, characterizes isovolumic relaxation (IVR) in accordance with Newton's Second Law. The model's parameters, stiffness Ek, and damping/relaxation μ result from best fit of model-predicted pressure to in vivo data. All three models (exponential, logistic, and kinematic) characterize global relaxation in terms of pressure decay rates. However, IVR is inhomogeneous and anisotropic. Apical and basal LV wall segments untwist at different times and rates, and transmural strain and strain rates differ due to the helically variable pitch of myocytes and sheets. Accordingly, we hypothesized that the exponential model (τ) or kinematic model (μ and Ek) parameters will elucidate the spatiotemporal variation of IVR rate. Left ventricular pressures in 20 subjects were recorded using a high-fidelity, multipressure transducer (3 cm apart) catheter. Simultaneous, dual-channel pressure data was plotted in the pressure phase-plane (dP/d t vs. P) and τ, μ, and Ek were computed in 1631 beats (average: 82 beats per subject). Tau differed significantly between the two channels ( P < 0.05) in 16 of 20 subjects, whereas μ and Ek differed significantly ( P < 0.05) in all 20 subjects. These results show that quantifying the relaxation rate from data recorded at a single location has limitations. Moreover, kinematic model based analysis allows characterization of restoring (recoil) forces and resistive (crossbridge uncoupling) forces during IVR and their spatio-temporal dependence, thereby elucidating the relative roles of stiffness vs. relaxation as IVR rate determinants.

Quantitative assessment of left ventricular diastolic function via longitudinal and transverse flow impedances

Flow impedance has been used to characterize the physical properties of the vascular system by assessing its phasic flow response to pulsatile pressure input in terms of resistance as a function of frequency. Impedance has also been used to characterize global diastolic left ventricular (LV) chamber properties. In early diastole the LV is a mechanical suction pump and accommodates filling by simultaneously expanding in two principal spatial directions: longitudinal (base-to-apex, long-axis) and transverse (radial, short-axis). Total (characteristic) impedance Z(C) is the product of longitudinal (Z(L)) and transverse (Z(T)) impedance as Z(C)(2)=Z(L)Z(T) where the two impedances reflect the relative spatial propensity for volume accommodation. In this work we compute Z(L) and Z(T) for the LV in early diastole. We analyze simultaneously recorded dual pressure-transducer and transthoracic echocardiographic flow data obtained during cardiac catheterization in 11 subjects. We found that Z(L) was 2 orders of magnitude smaller than Z(T) in all subjects, providing the first hemodynamic evidence, in concordance with cine-MRI imaging data that longitudinal volume accommodation is indeed, nature's preferred spatial filling mechanism. We also investigated the effect of impaired diastolic function on directional impedances and found that Z(L) increased (becomes worse) while Z(T) decreased (becomes better) indicating that as diastolic function becomes impaired radial filling compensates for decreased longitudinal volume accommodation to preserve stroke volume. These results provide mechanistic insight and show that normal diastolic function defines a properly impedance matched state and that diastolic dysfunction is equivalent to a state of impedance mismatch.

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.