Impact of pulmonary vascular stiffness and vasodilator treatment in pediatric pulmonary hypertension: 21 patient-specific fluid-structure interaction studies

Simulating Multi-Scale Pulmonary Vascular Function by Coupling Computational Fluid Dynamics With an Anatomic Network Model

The function of the pulmonary circulation is truly multi-scale, with blood transported through vessels from centimeter to micron scale. There are scale-dependent mechanisms that govern the flow in the pulmonary vascular system. However, very few computational models of pulmonary hemodynamics capture the physics of pulmonary perfusion across the spatial scales of functional importance in the lung. Here we present a multi-scale model that incorporates the 3-dimensional (3D) complexities of pulmonary blood flow in the major vessels, coupled to an anatomically-based vascular network model incorporating the multiple contributing factors to capillary perfusion, including gravity. Using the model we demonstrate how we can predict the impact of vascular remodeling and occlusion on both macro-scale functional drivers (flow distribution between lungs, and wall shear stress) and micro-scale contributors to gas exchange. The model predicts interactions between 3D and 1D models that lead to a redistribution of blood between postures, both on a macro- and a micro-scale. This allows us to estimate the effect of posture on left and right pulmonary artery wall shear stress, with predictions varying by 0.75-1.35 dyne/cm² between postures.

Patient-Specific Computational Analysis of Hemodynamics in Adult Pulmonary Hypertension

Pulmonary hypertension (PH) is a progressive disease characterized by elevated pressure and vascular resistance in the pulmonary arteries. Nearly 250,000 hospitalizations occur annually in the US with PH as the primary or secondary condition. A definitive diagnosis of PH requires right heart catheterization (RHC) in addition to a chest computed tomography, a walking test, and others. While RHC is the gold standard for diagnosing PH, it is invasive and posseses inherent risks and contraindications. In this work, we characterized the patient-specific pulmonary hemodynamics in silico for diverse PH WHO groups. We grouped patients on the basis of mean pulmonary arterial pressure (mPAP) into three disease severity groups: at-risk ([Formula: see text], denoted with A), mild ([Formula: see text], denoted with M), and severe ([Formula: see text], denoted with S). The pulsatile flow hemodynamics was simulated by evaluating the three-dimensional Navier-Stokes system of equations using a flow solver developed by customizing OpenFOAM libraries (v5.0, The OpenFOAM Foundation). Quasi patient-specific boundary conditions were implemented using a Womersley inlet velocity profile and transient resistance outflow conditions. Hemodynamic indices such as spatially averaged wall shear stress ([Formula: see text]), wall shear stress gradient ([Formula: see text]), time-averaged wall shear stress ([Formula: see text]), oscillatory shear index ([Formula: see text]), and relative residence time ([Formula: see text]), were evaluated along with the clinical metrics pulmonary vascular resistance ([Formula: see text]), stroke volume ([Formula: see text]) and compliance ([Formula: see text]), to assess possible spatiotemporal correlations. We observed statistically significant decreases in [Formula: see text], [Formula: see text], and [Formula: see text], and increases in [Formula: see text] and [Formula: see text] with disease severity. [Formula: see text] was moderately correlated with [Formula: see text] and [Formula: see text] at the mid-notch stage of the cardiac cycle when these indices were computed using the global pulmonary arterial geometry. These results are promising in the context of a long-term goal of identifying computational biomarkers that can serve as surrogates for invasive diagnostic protocols of PH.

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called 'model mismatch'). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure-area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

Simulation of unsteady blood flows in a patient-specific compliant pulmonary artery with a highly parallel monolithically coupled fluid-structure interaction algorithm

Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient-specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems but need improvements when the problems become harder when (a) the geometry becomes complex (eg, a few branches to a full pulmonary artery), (b) the model becomes more complex (eg, fluid-only to coupled fluid-structure interaction), (c) both the fluid and wall models become highly nonlinear, and (d) the computer on which we run the simulation is a supercomputer with tens of thousands of processor cores. To push the limit of CFD in all four fronts, in this paper, we develop and study a highly parallel algorithm for solving a monolithically coupled fluid-structure system for the modeling of the interaction of the blood flow and the arterial wall. As a case study, we consider a patient-specific, full size pulmonary artery obtained from computed tomography (CT) images, with an artificially added layer of wall with a fixed thickness. The fluid is modeled with a system of incompressible Navier-Stokes equations, and the wall is modeled by a geometrically nonlinear elasticity equation. As far as we know, this is the first time the unsteady blood flow in a full pulmonary artery is simulated without assuming a rigid wall. The proposed numerical algorithm and software scale well beyond 10 000 processor cores on a supercomputer for solving the fluid-structure interaction problem discretized with a stabilized finite element method in space and an implicit scheme in time involving hundreds of millions of unknowns.

An efficient parallel simulation of unsteady blood flows in patient-specific pulmonary artery

Simulation of blood flows in the pulmonary artery provides some insight into certain diseases by examining the relationship between some continuum metrics, eg, the wall shear stress acting on the vascular endothelium, which responds to flow-induced mechanical forces by releasing vasodilators/constrictors. V. Kheyfets, in his previous work, studies numerically a patient-specific pulmonary circulation to show that decreasing wall shear stress is correlated with increasing pulmonary vascular impedance. In this paper, we develop a scalable parallel algorithm based on domain decomposition methods to investigate an unsteady model with patient-specific pulsatile waveforms as the inlet boundary condition. The unsteady model offers tremendously more information about the dynamic behavior of the flow field, but computationally speaking, the simulation is a lot more expensive since a problem which is similar to the steady-state problem has to be solved many times, and therefore, the traditional sequential approach is not suitable anymore. We show computationally that simulations using the proposed parallel approach with up to 10 000 processor cores can be obtained with much reduced compute time. This makes the technology potentially usable for the routine study of the dynamic behavior of blood flows in the pulmonary artery, in particular, the changes of the blood flows and the wall shear stress in the spatial and temporal dimensions.

Diagnosis, Evaluation and Treatment of Pulmonary Arterial Hypertension in Children

Pulmonary Hypertension (PH), the syndrome of elevated pressure in the pulmonary arteries, is associated with significant morbidity and mortality for affected children. PH is associated with a wide variety of potential underlying causes, including cardiac, pulmonary, hematologic and rheumatologic abnormalities. Regardless of the cause, for many patients the natural history of PH involves progressive elevation in pulmonary arterial resistance and pressure, right ventricular dysfunction, and eventually heart failure. In recent years, a number of pulmonary arterial hypertension (PAH)-targeted therapies have become available to reduce pulmonary artery pressure and improve outcome. A growing body of evidence in both the adult and pediatric literature demonstrates enhanced quality of life, functional status, and survival among treated patients. This review provides a description of select etiologies of PH seen in pediatrics and an update on the most recent data pertaining to evaluation and management of children with PH/PAH. The available evidence for specific classes of PAH-targeted therapies in pediatrics is additionally discussed.

Image-based computational assessment of vascular wall mechanics and hemodynamics in pulmonary arterial hypertension patients

Pulmonary arterial hypertension (PAH) is a disease characterized by an elevated pulmonary arterial (PA) pressure. While several computational hemodynamic models of the pulmonary vasculature have been developed to understand PAH, they are lacking in some aspects, such as the vessel wall deformation and its lack of calibration against measurements in humans. Here, we describe a computational modeling framework that addresses these limitations. Specifically, computational models describing the coupling of hemodynamics and vessel wall mechanics in the pulmonary vasculature of a PAH patient and a normal subject were developed. Model parameters, consisting of linearized stiffness E of the large vessels and Windkessel parameters for each outflow branch, were calibrated against in vivo measurements of pressure, flow and vessel wall deformation obtained, respectively, from right-heart catheterization, phase-contrast and cine magnetic resonance images. Calibrated stiffness E of the proximal PA was 2.0 and 0.5 MPa for the PAH and normal models, respectively. Calibrated total compliance C_T and resistance R_T of the distal vessels were, respectively, 0.32 ml/mmHg and 11.3 mmHg∗min/l for the PAH model, and 2.93 ml/mmHg and 2.6 mmHg∗min/l for the normal model. These results were consistent with previous findings that the pulmonary vasculature is stiffer with more constricted distal vessels in PAH patients. Individual effects on PA pressure due to remodeling of the distal and proximal compartments of the pulmonary vasculature were also investigated in a sensitivity analysis. The analysis suggests that the remodeling of distal vasculature contributes more to the increase in PA pressure than the remodeling of proximal vasculature.

Pulmonary Hypertension in Children

The prevalence of PH is increasing in the pediatric population, because of improved recognition and increased survival of patients, and remains a significant cause of morbidity and mortality. Recent studies have improved the understanding of pediatric PH, but management remains challenging because of a lack of evidence-based clinical trials. The growing contribution of developmental lung disease requires dedicated research to explore the use of existing therapies as well as the creation of novel therapies. Adequate study of pediatric PH will require multicenter collaboration due to the small numbers of patients, multifactorial disease causes, and practice variability.

Validation of an arterial constitutive model accounting for collagen content and crosslinking

During the progression of pulmonary hypertension (PH), proximal pulmonary arteries (PAs) increase in both thickness and stiffness. Collagen, a component of the extracellular matrix, is mainly responsible for these changes via increased collagen fiber amount (or content) and crosslinking. We sought to differentiate the effects of collagen content and cross-linking on mouse PA mechanical changes using a constitutive model with parameters derived from experiments in which collagen content and cross-linking were decoupled during hypoxic pulmonary hypertension (HPH). We employed an eight-chain orthotropic element model to characterize collagen's mechanical behavior and an isotropic neo-Hookean form to represent elastin. Our results showed a strong correlation between the material parameter related to collagen content and measured collagen content (R(2)=0.82, P<0.0001) and a moderate correlation between the material parameter related to collagen crosslinking and measured crosslinking (R(2)=0.24, P=0.06). There was no significant change in either the material parameter related to elastin or the measured elastin content from histology. The model-predicted pressure at which collagen begins to engage was ∼25mmHg, which is consistent with experimental observations. We conclude that this model may allow us to predict changes in the arterial extracellular matrix from measured mechanical behavior in PH patients, which may provide insight into prognoses and the effects of therapy.

STATEMENT OF SIGNIFICANCE

The literature has proposed several constitutive models to describe the mechanical effects of arterial collagen but none separates collagen content from crosslinking. Given that both are critical to arterial mechanics, the novel model described here does so. Furthermore, our novel model is well tested by experimental data; model parameters were reasonably correlated with measured collagen content and crosslinking and the model-predicted collagen transition stretch was consistent with that obtained experimentally. Given that arterial collagen structural changes and collagen engagement are critical to arterial stiffening in several disease states, this model, by linking mechanical and biological properties, may allow us to predict important biological changes during disease progression from measured mechanical behavior.

Patient-specific computational modeling of blood flow in the pulmonary arterial circulation

Computational fluid dynamics (CFD) modeling of the pulmonary vasculature has the potential to reveal continuum metrics associated with the hemodynamic stress acting on the vascular endothelium. It is widely accepted that the endothelium responds to flow-induced stress by releasing vasoactive substances that can dilate and constrict blood vessels locally. The objectives of this study are to examine the extent of patient specificity required to obtain a significant association of CFD output metrics and clinical measures in models of the pulmonary arterial circulation, and to evaluate the potential correlation of wall shear stress (WSS) with established metrics indicative of right ventricular (RV) afterload in pulmonary hypertension (PH). Right Heart Catheterization (RHC) hemodynamic data and contrast-enhanced computed tomography (CT) imaging were retrospectively acquired for 10 PH patients and processed to simulate blood flow in the pulmonary arteries. While conducting CFD modeling of the reconstructed patient-specific vasculatures, we experimented with three different outflow boundary conditions to investigate the potential for using computationally derived spatially averaged wall shear stress (SAWSS) as a metric of RV afterload. SAWSS was correlated with both pulmonary vascular resistance (PVR) (R(2)=0.77, P<0.05) and arterial compliance (C) (R(2)=0.63, P<0.05), but the extent of the correlation was affected by the degree of patient specificity incorporated in the fluid flow boundary conditions. We found that decreasing the distal PVR alters the flow distribution and changes the local velocity profile in the distal vessels, thereby increasing the local WSS. Nevertheless, implementing generic outflow boundary conditions still resulted in statistically significant SAWSS correlations with respect to both metrics of RV afterload, suggesting that the CFD model could be executed without the need for complex outflow boundary conditions that require invasively obtained patient-specific data. A preliminary study investigating the relationship between outlet diameter and flow distribution in the pulmonary tree offers a potential computationally inexpensive alternative to pressure based outflow boundary conditions.

The role of wall shear stress in the assessment of right ventricle hydraulic workload

Pulmonary hypertension (PH) is a devastating disease affecting approximately 15-50 people per million, with a higher incidence in women. PH mortality is mostly attributed to right ventricle (RV) failure, which results from RV hypotrophy due to an overburdened hydraulic workload. The objective of this study is to correlate wall shear stress (WSS) with hemodynamic metrics that are generally accepted as clinical indicators of RV workload and are well correlated with disease outcome. Retrospective right heart catheterization data for 20 PH patients were analyzed to derive pulmonary vascular resistance (PVR), arterial compliance (C), and an index of wave reflections (Γ). Patient-specific contrast-enhanced computed tomography chest images were used to reconstruct the individual pulmonary arterial trees up to the seventh generation. Computational fluid dynamics analyses simulating blood flow at peak systole were conducted for each vascular model to calculate WSS distributions on the endothelial surface of the pulmonary arteries. WSS was found to be decreased proportionally with elevated PVR and reduced C. Spatially averaged WSS (SAWSS) was positively correlated with PVR (R (2) = 0.66), C (R (2) = 0.73), and Γ (R (2) = 0.5) and also showed promising preliminary correlations with RV geometric characteristics. Evaluating WSS at random cross sections in the proximal vasculature (main, right, and left pulmonary arteries), the type of data that can be acquired from phase-contrast magnetic resonance imaging, did not reveal the same correlations. In conclusion, we found that WSS has the potential to be a viable and clinically useful noninvasive metric of PH disease progression and RV health. Future work should be focused on evaluating whether SAWSS has prognostic value in the management of PH and whether it can be used as a rapid reactivity assessment tool, which would aid in selection of appropriate therapies.

A novel in vivo approach to assess radial and axial distensibility of large and intermediate pulmonary artery branches

Pulmonary arteries (PAs) distend to accommodate increases in cardiac output. PA distensibility protects the right ventricle (RV) from excessive increases in pressure. Loss of PA distensibility plays a critical role in the fatal progression of pulmonary arterial hypertension (PAH) toward RV failure. However, it is unclear how PA distensibility is distributed across the generations of PA branches, mainly because of the lack of appropriate in vivo methods to measure distensibility of vessels other than the large, conduit PAs. In this study, we propose a novel approach to assess the distensibility of individual PA branches. The metric of PA distensibility we used is the slope of the stretch ratio-pressure relationship. To measure distensibility, we combined invasive measurements of mean PA pressure with angiographic imaging of the PA network of six healthy female dogs. Stacks of 2D images of the PAs, obtained from either contrast enhanced magnetic resonance angiography (CE-MRA) or computed tomography digital subtraction angiography (CT-DSA), were used to reconstruct 3D surface models of the PA network, from the first bifurcation down to the sixth generation of branches. For each branch of the PA, we calculated radial and longitudinal stretch between baseline and a pressurized state obtained via acute embolization of the pulmonary vasculature. Our results indicated that large and intermediate PA branches have a radial distensibility consistently close to 2%/mmHg. Our axial distensibility data, albeit affected by larger variability, suggested that the PAs distal to the first generation may not significantly elongate in vivo, presumably due to spatial constraints. Results from both angiographic techniques were comparable to data from established phase-contrast (PC) magnetic resonance imaging (MRI) and ex vivo mechanical tests, which can only be used in the first branch generation. Our novel method can be used to characterize PA distensibility in PAH patients undergoing clinical right heart catheterization (RHC) in combination with MRI.

Numerical simulation of patient-specific left ventricular model with both mitral and aortic valves by FSI approach

Intraventricular flow is important in understanding left ventricular function; however, relevant numerical simulations are limited, especially when heart valve function is taken into account. In this study, intraventricular flow in a patient-specific left ventricle has been modelled in two-dimension (2D) with both mitral and aortic valves integrated. The arbitrary Lagrangian-Eulerian (ALE) approach was employed to handle the large mesh deformation induced by the beating ventricular wall and moving leaflets. Ventricular wall deformation was predefined based on MRI data, while leaflet dynamics were predicted numerically by fluid-structure interaction (FSI). Comparisons of simulation results with in vitro and in vivo measurements reported in the literature demonstrated that numerical method in combination with MRI was able to predict qualitatively the patient-specific intraventricular flow. To the best of our knowledge, we are the first to simulate patient-specific ventricular flow taking into account both mitral and aortic valves.

Influence of distal resistance and proximal stiffness on hemodynamics and RV afterload in progression and treatments of pulmonary hypertension: a computational study with validation using animal models

We develop a simple computational model based on measurements from a hypoxic neonatal calf model of pulmonary hypertension (PH) to investigate the interplay between vascular and ventricular measures in the setting of progressive PH. Model parameters were obtained directly from in vivo and ex vivo measurements of neonatal calves. Seventeen sets of model-predicted impedance and mean pulmonary arterial pressure (mPAP) show good agreement with the animal measurements, thereby validating the model. Next, we considered a predictive model in which three parameters, PVR, elastic modulus (EM), and arterial thickness, were varied singly from one simulation to the next to study their individual roles in PH progression. Finally, we used the model to predict the individual impacts of clinical (vasodilatory) and theoretical (compliance increasing) PH treatments on improving pulmonary hemodynamics. Our model (1) displayed excellent patient-specific agreement with measured global pulmonary parameters; (2) quantified relationships between PVR and mean pressure and PVS and pulse pressure, as well as studiying the right ventricular (RV) afterload, which could be measured as a hydraulic load calculated from spectral analysis of pulmonary artery pressure and flow waves; (3) qualitatively confirmed the derangement of vascular wall shear stress in progressive PH; and (4) established that decreasing proximal vascular stiffness through a theoretical treatment of reversing proximal vascular remodeling could decrease RV afterload.

Wall shear stress measured by phase contrast cardiovascular magnetic resonance in children and adolescents with pulmonary arterial hypertension

BACKGROUND

Pulmonary arterial hypertension (PAH) is a devastating disease with significant morbidity and mortality. At the macroscopic level, disease progression is observed as a complex interplay between mean pulmonary artery pressure, pulmonary vascular resistance, pulmonary vascular stiffness, arterial size, and flow. Wall shear stress (WSS) is known to mediate or be dependent on a number of these factors. Given that WSS is known to promote architectural vessel remodeling, it is imperative that the changes of this factor be quantified in the presence of PAH.

METHODS

In this study, we analyzed phase contrast imaging of the right pulmonary artery derived from cardiovascular magnetic resonance to quantify the local, temporal and circumferentially averaged WSS of a PAH population and a pediatric control population. In addition, information about flow and relative area change were derived.

RESULTS

Although the normotensive and PAH shear waveform exhibited a WSS profile which is uniform in magnitude and direction along the vessel circumference at systole, time-averaged WSS (2.2 ± 1.6 vs. 6.6 ± 3.4 dynes/cm(2), P = 0.018) and systolic WSS (8.2 ± 5.0 v. 20.0 ± 9.1 dynes/cm(2), P = 0.018) was significantly depressed in the PAH population as compared to the controls. BSA-indexed PA diameter was significantly larger in the PAH population (1.5 ± 0.4 vs. 0.7 ± 0.1 cm/m(2), P = 0.003).

CONCLUSIONS

In the presence of preserved flow rates through a large PAH pulmonary artery, WSS is significantly decreased. This may have implications for proximal pulmonary artery remodeling and cellular function in the progression of PAH.

Considerations for numerical modeling of the pulmonary circulation--a review with a focus on pulmonary hypertension

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.