Patient‐Specific Lumped‐Parameter Model for Quantifying Vessel‐Specific Remodeling and Predicting Right Ventricular Function in Pulmonary Hypertension

Figures

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  FIGURE 1. Schematic representation of right heart catheterization, and echocardiography. In a semi‐recumbent position, pulmonary artery pressure was measured via RHC, RVOT flow was measured using pulsed‐wave Doppler echocardiography. Pulmonary artery pressure (PAP) and RVOT flow (Q RVOT) wave forms were used for parameter estimation. P, pressure; RHC, right heart catheterization; RVOT, right ventricular outflow tract.

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  FIGURE 2. Schematic representation of the lumped‐parameter model. The model incorporates six compartments representing the RA, RV, PA, PC, PV, and LA with resistive elements (Rval,T, Rval,P, RPA, RPC, RPV) and compliant elements (CPA, CPC, CPV) as indicated. The RV chamber is modeled using a time‐varying elastance function (ERVt) to capture systolic and diastolic pressure–volume relationships. Pressures (P) and flows (Q) are defined for each compartment, with fixed boundary conditions at PRA and PLA derived from literature and the minimum of the PAWP and diastolic PAP, respectively. C, compliance; CPA, compliance of the pulmonary artery; CPC, compliance of the pulmonary capillaries; CPV, compliance of the pulmonary veins; ERV, right ventricular elastance; LA, left atrium; P, pressure; PA, pulmonary artery; PAP, pulmonary artery pressure; PAWP, pulmonary arterial wedge pressure; PC, pulmonary capillaries; PV, pulmonary veins; PLA, left atrial pressure; PRA, right atrial pressure; Q, flow; R, resistance; RA, right atrium; RPA, resistance from the pulmonary arteries to the pulmonary capillaries; RPC, resistance from the pulmonary capillaries to the pulmonary veins; RPV resistance from the…

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  FIGURE 3. Sensitivity analysis of model parameters on pulmonary hemodynamics. Relative sensitivity of key model parameters on two primary output metrics: Pulmonary artery pressure (PPA) and blood flow across the pulmonary valve (Qval,P). The top plot illustrates the sensitivity of PPA to variations in model parameters, including resistances, compliances, and elastance, with each parameter's influence visualized along the x‐axis. The relative sensitivity is calculated by measuring the change in PPA as each parameter is perturbed. The bottom plot shows the sensitivity analysis for Qval,P, which represents the flow across the pulmonary valve into the PA, highlighting the most influential parameters on pulmonary flow. These sensitivity analyses provide insight into the model's robustness and identify the parameters that most significantly affect the outputs.

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  FIGURE 4. Time‐series pressure and flow fits for representative subjects from each phenotype are shown: (A) Pre‐capillary PH (#4), (B) Ipc‐PH (#11), (C) Cpc‐PH (#20), and (D) No PH (#23). Blue solid and dashed lines represent clinical and model‐predicted pulmonary arterial pressure, respectively, while red solid and dashed lines denote clinical and model‐RVOT flow.

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  FIGURE 5. Parity plots comparing model‐predicted and measured values for (A) diastolic pressure, (B) systolic pressure, and (C) systolic flow. Each point represents an individual subject, color‐coded by phenotype: red = Pre‐capillary PH, blue = Ipc‐PH, black = Cpc‐PH, and green = No PH. The close alignment of data points along the identity line indicates strong model–data agreement, particularly for pressure metrics.

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  FIGURE 6. Simulated Right Ventricle (RV) PV loop data for representative subjects from each of the four phenotypes. Model‐derived PV loop metrics revealed distinct differences across groups red = Pre‐capillary PH, blue = Ipc‐PH, black = Cpc‐PH, and green = No PH.

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  FIGURE 7. Comparison of model parameters across pulmonary hypertension phenotypes. (A) RPA (pulmonary arterial resistance), (B) RPC(pulmonary capillary resistance), (C) RPV (pulmonary venous resistance), (D) CPA (pulmonary arterial compliance), (E) CPC (pulmonary capillary compliance), (F) CPV (pulmonary venous compliance), (G) Rval,T (tricuspid valve resistance), (H) Emax (maximum elastance of the right ventricle) and (I 45) Emin (minimum elastance of the right ventricle) for all 25 participants: 5 Cpc‐PH, 12 Ipc‐PH, 5 pre‐capillary PH, and 3 No PH. Boxplots represent the median (purple line), interquartile range (boxes), and outliers (red plus signs). *p < 0.05, **p < 0.01 for inter‐group comparisons between PH phenotypes.

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  FIGURE 8. 2D LDA projections illustrating phenotype separability using (A) clinical data, (B) model‐derived features, and (C) combined clinical and model features. The combined feature set shows the most distinct clustering across PH phenotypes: Pre‐capillary PH (red), Ipc‐PH (blue), Cpc‐PH (black), and No PH (green).