Diastolic chamber properties of the left ventricle assessed by global fitting of pressure-volume data: improving the gold standard of diastolic function

Abstract

In cardiovascular research, relaxation and stiffness are calculated from pressure-volume (PV) curves by separately fitting the data during the isovolumic and end-diastolic phases (end-diastolic PV relationship), respectively. This method is limited because it assumes uncoupled active and passive properties during these phases, it penalizes statistical power, and it cannot account for elastic restoring forces. We aimed to improve this analysis by implementing a method based on global optimization of all PV diastolic data. In 1,000 Monte Carlo experiments, the optimization algorithm recovered entered parameters of diastolic properties below and above the equilibrium volume (intraclass correlation coefficients = 0.99). Inotropic modulation experiments in 26 pigs modified passive pressure generated by restoring forces due to changes in the operative and/or equilibrium volumes. Volume overload and coronary microembolization caused incomplete relaxation at end diastole (active pressure > 0.5 mmHg), rendering the end-diastolic PV relationship method ill-posed. In 28 patients undergoing PV cardiac catheterization, the new algorithm reduced the confidence intervals of stiffness parameters by one-fifth. The Jacobian matrix allowed visualizing the contribution of each property to instantaneous diastolic pressure on a per-patient basis. The algorithm allowed estimating stiffness from single-beat PV data (derivative of left ventricular pressure with respect to volume at end-diastolic volume intraclass correlation coefficient = 0.65, error = 0.07 ± 0.24 mmHg/ml). Thus, in clinical and preclinical research, global optimization algorithms provide the most complete, accurate, and reproducible assessment of global left ventricular diastolic chamber properties from PV data. Using global optimization, we were able to fully uncouple relaxation and passive PV curves for the first time in the intact heart.

Keywords: diastole; diastolic function; diastolic stiffness; hemodynamics; left ventricle; mechanical properties; pressure; relaxation.

Figures

Fig. 1.

Theoretical model decoupling of active (yellow) and passive (green) left ventricular (LV) diastolic pressures. Total pressure is shown in red. Early filling is shown in detail in the inset. Pa, active diastolic pressure; Pp, passive diastolic pressure; AVC, aortic valve closing; MVO, mitral valve opening; V, LV volume; V0, equilibrium volume; P̂, estimated pressure; Psystole, systole pressure.

Fig. 2.

Full characterization of passive diastolic pressure-volume (PV) relationship. A: three phases obtained during hemodynamic interventions in a representative animal experiment. B: curves obtained from a control subject (red) and a dilated cardiomyopathy (DCM) patient (blue). Dotted lines represent the full PV relationship, whereas solid lines represent the curve operated by the ventricle during the cardiac cycle. C–E: uncertainty of stiffness parameters measured from the DCM patient in B. Charts show the scatter plot (C) and distribution functions (D and E) results of Monte Carlo estimation of stiffness parameters obtained by the end-diastolic PV relationship (EDPVR) (blue) and global methods (red) for that particular data set. Notice the narrowing in confidence intervals and reduction in cross-correlation between parameters obtained using the global optimization method. dP/dV, derivative of LV pressure with respect to volume; EDV, end-diastolic volume.

Fig. 3.

Full characterization of LV main diastolic properties by PV analysis in a control subject. A: PV data sets of 9 beats obtained during inferior vena cava (IVC) occlusion. B: beat-by-beat representation of each measured diastolic PV curve (black), fitted pressure (red), as well as active (yellow) and passive (green) contributions to total pressure. End-diastolic PV points for all beats are also shown (black dots).

Fig. 4.

Sensitivity analysis of LV main diastolic properties. A: normalized Jacobian matrix of a control subject. Measured pressure is shown in the black dotted line. The impact of each diastolic index on instantaneous pressure is shown as the partial derivative of fitted pressure with respect to each index, normalized by its value. Elastic restoring forces are shown in green [constant of diastolic elastic recoil (S−) and LV minimum dead volume (Vd)], diastolic stiffness in blue [constant of diastolic passive stiffness (S+) and LV maximal achievable volume (Vm)], V0 in red, time constant of relaxation (τ) in yellow, and LV pressure at the onset of diastole (P0) in gray. Notice that early filling is governed by P0, τ, V0, and elastic restoring forces, whereas late filling is only influenced by V0 and diastolic stiffness. B: identical analysis as in A, in a patient with DCM. This ventricle does not contract below V0, so there is no contribution to filling of restoring forces. Additionally, notice that relaxation is not completed by end diastole, so end-diastolic pressure (EDP) is partially influenced by τ. C–F: resolution matrices of isovolumic relaxation (C and E) and full diastolic period (D and F). In this representation, the degree of autocorrelation among parameters is shown as the hue of gray, from no relationship (black) to full correlation (white).

Fig. 5.

Alternative mathematical model fittings for pressure data during isovolumic relaxation shown in the pressure phase plane. The results of adjusting pressure-time data using the optimization algorithm implementing different relaxation functions are shown in a representative animal data set of 14 beats obtained during IVC occlusion. Active relaxation is described using the exponential (Eq. A1, green), the logistic (Eq. A9, blue), and the kinematic models (Eq. A10, red), overlaid on measured pressure (black, from peak LV pressure to end diastole). In the pressure-phase plane, these models are depicted as linear, one parameter curvilinear, and two parameter curvilinear, respectively. Beats 1, 7, and 14 are shown. Notice that, by design, the optimization algorithm estimates a single set of relaxation parameters [τ, τ-logistic, and μ (resistive parameter equivalent to τ) and Ek (lumped elastic parameter accounting for the elastic restoring force)] for the exponential, logistic, and kinematic models, respectively, from the 14 beats in the data set. Thus individual beat fitting results are necessarily worse than if each beat were fitted independently. dP/dt, minimal derivative of LV pressure with respect to time.

Fig. 6.

Impact of passive pressure during the isovolumic phase on the estimation of relaxation. A: Bland-Altman plot of pooled data of all beats from all animal experiments showing the bias (solid line) ± SD (dashed line) showing the individual variation of passive pressure from AVC to MVO. The lack of full agreement demonstrates volume-mediated changes in passive pressure in this phase. B: scatterplot between asymptotic pressure obtained by single-beat analysis using Eq. A7 (horizontal axis) and average isovolumic passive pressure obtained by the global optimization method (vertical axis). The lack of correlation demonstrates the limitations of the conventional method for measuring relaxation to accurately uncouple passive pressure during the isovolumic phase. C: impact of the uncertainty of estimating passive pressure during the isovolumic phase for the characterization of relaxation using the conventional exponential method (Eq. A7 analytic derivative solved for a τ value of 50 ms and P0 of 80 mmHg). Notice that 1-mmHg error in the estimation of Pp induces an error up to 4.5 ms in measured τ. As shown in B, these errors are frequently much higher. We believe that this mechanism may partially account for the preload dependence of relaxation previously reported using the conventional single-beat isovolumic method.

Fig. 7.

Example of Monte Carlo synthetic PV curves generated from an animal volume data set. Pressure is generated from instantaneous volumes using random values for indexes of active and passive diastolic properties, and random noise is added, as detailed in the text. End-diastolic PV values are shown in the black dots. The global fitting passive pressure curve is shown in red.