Predictive Modeling of Secondary Pulmonary Hypertension in Left Ventricular Diastolic Dysfunction

Abstract

Diastolic dysfunction is a common pathology occurring in about one third of patients affected by heart failure. This condition may not be associated with a marked decrease in cardiac output or systemic pressure and therefore is more difficult to diagnose than its systolic counterpart. Compromised relaxation or increased stiffness of the left ventricle induces an increase in the upstream pulmonary pressures, and is classified as secondary or group II pulmonary hypertension (2018 Nice classification). This may result in an increase in the right ventricular afterload leading to right ventricular failure. Elevated pulmonary pressures are therefore an important clinical indicator of diastolic heart failure (sometimes referred to as heart failure with preserved ejection fraction, HFpEF), showing significant correlation with associated mortality. However, accurate measurements of this quantity are typically obtained through invasive catheterization and after the onset of symptoms. In this study, we use the hemodynamic consistency of a differential-algebraic circulation model to predict pulmonary pressures in adult patients from other, possibly non-invasive, clinical data. We investigate several aspects of the problem, including the ability of model outputs to represent a sufficiently wide pathologic spectrum, the identifiability of the model's parameters, and the accuracy of the predicted pulmonary pressures. We also find that a classifier using the assimilated model parameters as features is free from the problem of missing data and is able to detect pulmonary hypertension with sufficiently high accuracy. For a cohort of 82 patients suffering from various degrees of heart failure severity, we show that systolic, diastolic, and wedge pulmonary pressures can be estimated on average within 8, 6, and 6 mmHg, respectively. We also show that, in general, increased data availability leads to improved predictions.

Keywords: adaptive Markov chain Monte Carlo; computational physiology; data assimilation; lumped parameter hemodynamic modeling; model-based disease detection; predictive models for pulmonary pressures.

Figure 1

Lumped parameter hemodynamic model with RC pulmonary circuit.

Figure 2

Histogram of data availability among the 82 patients (A) and missing data pattern (B). Note how each row of the heat map is normalized to a zero to one range, highlighting the relative magnitude of the clinical target.

Figure 3

KL divergence between predicted and assumed clinical targets for varying heart failure severity.

Figure 4

Variation of mean parameter values and associated confidence intervals under increasing heart failure severity. Right and left ventricular model parameters shown in the Figure are the ventricular passive curve slope K_pas,i,1, exponent factor K_pas,i,2, active curve slope E_max,i and unstressed ventricular volume V_i,0 (where i ∈ {rv, lv}). Also shown: R_pa (pulmonary resistance), R_sys,a (arterial systemic resistance), R_sys,v (venous systemic resistance).

Figure 5

Average local sensitivities using a perturbation factor of 1%. (A) Average local sensitivity table for all parameters and model outputs. (B) Average local sensitivities table for all parameters and pulmonary outputs only. The values in each row are scaled to make their sum equal to 100.0 and two cutoffs are used equal to 25 and 12.5 for (A,B), respectively.

Figure 6

Histograms of (A) right ventricular, (B) left ventricular, and (C) pulmonary and systemic resistance model parameters from MCMC and default parameter values (vertical dashed lines) used to assess structural identifiability.

Figure 7

Bar plot of the coefficient of variation (CV) alongside the learning factor, (θ) for each parameter. a and b represent the minimum and maximum bound of each parameter uniform marginal prior.

Figure 8

(Row 1) pressure time histories over one heart cycle for aortic, pulmonary and left ventricular pressure. (Row 2) flow time histories over one heart cycle for left ventricular outflow and pulmonary flow as well as left ventricular pressure-volume loop.

Figure 9

(A) Scatter plot of eigenvalues vs. eigenvectors for all patients. Red horizontal line represents selected cut-off value. FIM eigenvalues at identified parameters plotted in increasing order. (B) Plot of number of patients selected (eigenvalues less than cut-off) for each eigenvector. (C,D) Selection of two of the 17 total radar plots of all parameters whose eigenvalues are less than the selected cut-off. (C) Example of unimportant initial condition, i.e., whose perturbation has no effect on the model results. (D) Example of non-identifiable parameter combinations where no dominant parameter can be identified and where the combination significantly changes across patients.

Figure 10

(A,B) Bland-Altman plots of sPAP, dPAP, mPAP, and PVR for clinical targets, and as predicted from models trained with and without pulmonary targets, respectively. Solid horizontal lines represent the mean of all differences, while dashed lines are drawn at 1.96 times the standard deviation. Predictions associated with gray markers in the Bland-Altman plots result from using less than 15 clinical targets. (C) Predictive performance for pulmonary pressure. Absence of PAP targets in average prediction errors is represented using dashed lines. The shaded region represents the area bounded by the 5th and 95th percentile from 5,000 random subsamples from MCMC. (D) Zoom on average errors which correspond to patients with more than 15 available clinical targets.

Figure 11

(A) Target ranking with minimum prediction error. (B) Target ranking and associated occurrence.

Figure 12

(A) Ranks of clinical targets for each patient in order of importance (i.e., green more important, red less important). (B) Minimum combined prediction error associated with the introduction of each clinical target for all the patients included in the study. Note how blank entries correspond to missing clinical targets.

Figure 13

Accuracy of a naïve Bayes classifiers for pulmonary hypertension using different approaches for multiple imputation.

Figure 14

Principal component decomposition (left) along with the contingency table (right) for the unbalanced data and balanced through centroid clustering.

Figure 15

Accuracy of a Naïve Bayes classifiers for pulmonary hypertension, using identified lumped parameters as features, and various methods to handle unbalanced data. The methods used were Random Over-sampling (ros), Random Under-sampling (rus), an over-sampling method: SMOTE (Synthetic Minority Oversampling TEchnique) (sm), two under-sampling methods: Tomek Links (tl) and Cluster Centroids (cc), and a hybrid approach that performs over-sampling followed by under-sampling using SMOTE followed by Tomek Links (smt).