Lumped-parameter models of the pulmonary vasculature during the progression of pulmonary arterial hypertension

Computer simulation of surgical interventions for the treatment of refractory pulmonary hypertension

This paper describes computer models of three interventions used for treating refractory pulmonary hypertension (RPH). These procedures create either an atrial septal defect, a ventricular septal defect or, in the case of a Potts shunt, a patent ductus arteriosus. The aim in all three cases is to generate a right-to-left shunt, allowing for either pressure or volume unloading of the right side of the heart in the setting of right ventricular failure, while maintaining cardiac output. These shunts are created, however, at the expense of introducing de-oxygenated blood into the systemic circulation, thereby lowering the systemic arterial oxygen saturation. The models developed in this paper are based on compartmental descriptions of human hemodynamics and oxygen transport. An important parameter included in our models is the cross-sectional area of the surgically created defect. Numerical simulations are performed to compare different interventions and various shunt sizes and to assess their impact on hemodynamic variables and oxygen saturations. We also create a model for exercise and use it to study exercise tolerance in simulated pre-intervention and post-intervention RPH patients.

Parameter inference in a computational model of haemodynamics in pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.

An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle

In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies.

Computational models of ventricular mechanics and adaptation in response to right-ventricular pressure overload

Pulmonary arterial hypertension (PAH) is associated with substantial remodeling of the right ventricle (RV), which may at first be compensatory but at a later stage becomes detrimental to RV function and patient survival. Unlike the left ventricle (LV), the RV remains understudied, and with its thin-walled crescent shape, it is often modeled simply as an appendage of the LV. Furthermore, PAH diagnosis is challenging because it often leaves the LV and systemic circulation largely unaffected. Several treatment strategies such as atrial septostomy, right ventricular assist devices (RVADs) or RV resynchronization therapy have been shown to improve RV function and the quality of life in patients with PAH. However, evidence of their long-term efficacy is limited and lung transplantation is still the most effective and curative treatment option. As such, the clinical need for improved diagnosis and treatment of PAH drives a strong need for increased understanding of drivers and mechanisms of RV growth and remodeling (G&R), and more generally for targeted research into RV mechanics pathology. Computational models stand out as a valuable supplement to experimental research, offering detailed analysis of the drivers and consequences of G&R, as well as a virtual test bench for exploring and refining hypotheses of growth mechanisms. In this review we summarize the current efforts towards understanding RV G&R processes using computational approaches such as reduced-order models, three dimensional (3D) finite element (FE) models, and G&R models. In addition to an overview of the relevant literature of RV computational models, we discuss how the models have contributed to increased scientific understanding and to potential clinical treatment of PAH patients.

Relative Contributions of Matrix and Myocytes to Biaxial Mechanics of the Right Ventricle in Pulmonary Arterial Hypertension

Pulmonary arterial hypertension (PAH) commonly leads to right ventricular (RV) hypertrophy and fibrosis that affect the mechanical properties of the RV myocardium (MYO). To investigate the effects of PAH on the mechanics of the RV MYO and extracellular matrix (ECM), we compared RV wall samples, isolated from rats in which PAH was induced using the SuHx protocol, with samples from control animals before and after the tissues were decellularized. Planar biaxial mechanical testing, a technique first adapted to living soft biological tissues by Fung, was performed on intact and decellularized samples. Fung's anisotropic exponential strain energy function fitted the full range of biaxial test results with high fidelity in control and PAH samples both before and after they were decellularized. Mean RV myocardial apex-to-outflow tract and circumferential stresses during equibiaxial strain were significantly greater in PAH than control samples. Mean RV ECM circumferential but not apex-to-outflow tract stresses during equibiaxial strain were significantly greater in the PAH than control group. The ratio of ECM to myocardial stresses at matched strains did not change significantly between groups. Circumferential stresses were significantly higher than apex-to-outflow tract stresses for all groups. These findings confirm the predictions of a mathematical model based on changes in RV hemodynamics and morphology in rat PAH, and may provide a foundation for a new constitutive analysis of the contributions of ECM remodeling to changes in RV filling properties during PAH.

Lumped-parameter models of the pulmonary vasculature during the progression of pulmonary arterial hypertension

A longitudinal study of monocrotaline-induced pulmonary arterial hypertension (PAH) was carried out in Sprague-Dawley rats to investigate the changes in impedance (comprising resistance and compliance) produced by elevated blood pressure. Using invasively measured blood flow as an input, blood pressure was predicted using 3- and 4-element Windkessel (3WK, 4WK) type lumped-parameter models. Resistance, compliance, and inductance model parameters were obtained for the five different treatment groups via least-squares errors. The treated animals reached levels of hypertension, where blood pressure increased two folds from control to chronic stage of PAH (mean pressure went from 24 ± 5 to 44 ± 6 mmHg, P < 0.0001) but blood flow remained overall unaffected. Like blood pressure, the wave-reflection coefficient significantly increased at the advanced stage of PAH (0.26 ± 0.09 to 0.52 ± 0.09, P < 0.0002). Our modeling efforts revealed that resistances and compliance changed during the disease progression, where changes in compliance occur before the changes in resistance. However, resistance and compliance are not directly inversely related. As PAH develops, resistances increase nonlinearly (R_d exponentially and R at a slower rate) while compliance linearly decreases. And while 3WK and 4WK models capture the pressure-flow relation in the pulmonary vasculature during PAH, results from Akaike Information Criterion and sensitivity analysis allow us to conclude that the 3WK is the most robust and accurate model for this system. Ninety-five percent confidence intervals of the predicted model parameters are included for the population studied. This work establishes insight into the complex remodeling process occurring in PAH.