Estimating pulmonary arterial remodeling via an animal-specific computational model of pulmonary artery stenosis

Pulmonary artery stenosis (PAS) often presents in children with congenital heart disease, altering blood flow and pressure during critical periods of growth and development. Variability in stenosis onset, duration, and severity result in variable growth and remodeling of the pulmonary vasculature. Computational fluid dynamics (CFD) models enable investigation into the hemodynamic impact and altered mechanics associated with PAS. In this study, a one-dimensional (1D) fluid dynamics model was used to simulate hemodynamics throughout the pulmonary arteries of individual animals. The geometry of the large pulmonary arteries was prescribed by animal-specific imaging, whereas the distal vasculature was simulated by a three-element Windkessel model at each terminal vessel outlet. Remodeling of the pulmonary vasculature, which cannot be measured in vivo, was estimated via model-fitted parameters. The large artery stiffness was significantly higher on the left side of the vasculature in the left pulmonary artery (LPA) stenosis group, but neither side differed from the sham group. The sham group exhibited a balanced distribution of total distal vascular resistance, whereas the left side was generally larger in the LPA stenosis group, with no significant differences between groups. In contrast, the peripheral compliance on the right side of the LPA stenosis group was significantly greater than the corresponding side of the sham group. Further analysis indicated the underperfused distal vasculature likely moderately decreased in radius with little change in stiffness given the increase in thickness observed with histology. Ultimately, our model enables greater understanding of pulmonary arterial adaptation due to LPA stenosis and has potential for use as a tool to noninvasively estimate remodeling of the pulmonary vasculature.

Remodeling of Murine Branch Pulmonary Arteries Under Chronic Hypoxia and Short-Term Normoxic Recovery

Chronic hypoxia plays a central role in diverse pulmonary pathologies, but its effects on longitudinal changes in the biomechanical behavior of proximal pulmonary arteries remain poorly understood. Similarly, effects of normoxic recovery have not been well studied. Here, we report hypoxia-induced changes in composition, vasoactivity, and passive biaxial mechanics in the main branch pulmonary artery of male C57BL/6J mice exposed to 10% FiO2 for 1, 2, or 3 weeks. We observed significant changes in extracellular matrix, and consequently wall mechanics, as early as 1 week of hypoxia. While circumferential stress and stiffness returned toward normal values by 2-3 weeks of hypoxia, area fractions of cytoplasm and thin collagen fibers did not return toward normal until after 1 week of normoxic recovery. By contrast, elastic energy storage and overall distensibility remained reduced after 3 weeks of hypoxia as well as following 1 week of normoxic recovery. While smooth muscle and endothelial cell responses were attenuated under hypoxia, smooth muscle but not endothelial cell responses recovered following 1 week of subsequent normoxia. Collectively, these data suggest that homeostatic processes were unable to preserve or restore overall function, at least over a brief period of normoxic recovery. Longitudinal changes are critical in understanding large pulmonary artery remodeling under hypoxia, and its reversal, and will inform predictive models of vascular adaptation.

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images

One-dimensional (1D) cardiovascular models offer a non-invasive method to answer medical questions, including predictions of wave-reflection, shear stress, functional flow reserve, vascular resistance and compliance. This model type can predict patient-specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty in in vivo imaging introduces variability in network size and vessel dimensions, affecting haemodynamic predictions. Understanding the influence of variation in image-derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three-dimensional surfaces and construct vessel centrelines. Still, there is no exact way to generate vascular trees from the centrelines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labelled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D haemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore haemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analysing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high-fidelity patient-specific haemodynamics models. KEY POINTS: This study introduces novel algorithms for generating labelled directed trees from medical images, focusing on accurate junction node placement and radius extraction using change points to provide haemodynamic predictions with uncertainty within expected measurement error. Geometric features, such as vessel dimension (length and radius) and network size, significantly impact pressure and flow predictions in both pulmonary and aortic arterial networks. Standardizing networks to a consistent number of vessels is crucial for meaningful comparisons and decreases haemodynamic uncertainty. Change points are valuable to understanding structural transitions in vascular data, providing an automated and efficient way to detect shifts in vessel characteristics and ensure reliable extraction of representative vessel radii.

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Efficient uncertainty quantification in a spatially multiscale model of pulmonary arterial and venous hemodynamics

Pulmonary hypertension (PH) is a debilitating disease that alters the structure and function of both the proximal and distal pulmonary vasculature. This alters pressure-flow relationships in the pulmonary arterial and venous trees, though there is a critical knowledge gap in the relationships between proximal and distal hemodynamics in disease. Multiscale computational models enable simulations in both the proximal and distal vasculature. However, model inputs and measured data are inherently uncertain, requiring a full analysis of the sensitivity and uncertainty of the model. Thus, this study quantifies model sensitivity and output uncertainty in a spatially multiscale, pulse-wave propagation model of pulmonary hemodynamics. The model includes fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. We quantify uncertainty in blood pressure, blood flow rate, wave intensity, wall shear stress, and cyclic stretch. The latter two are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal arterial and venous circulations.

Reconstructing microvascular network skeletons from 3D images: What is the ground truth?

Structural changes to microvascular networks are increasingly highlighted as markers of pathogenesis in a wide range of disease, e.g. Alzheimer's disease, vascular dementia and tumour growth. This has motivated the development of dedicated 3D imaging techniques, alongside the creation of computational modelling frameworks capable of using 3D reconstructed networks to simulate functional behaviours such as blood flow or transport processes. Extraction of 3D networks from imaging data broadly consists of two image processing steps: segmentation followed by skeletonisation. Much research effort has been devoted to segmentation field, and there are standard and widely-applied methodologies for creating and assessing gold standards or ground truths produced by manual annotation or automated algorithms. The Skeletonisation field, however, lacks widely applied, simple to compute metrics for the validation or optimisation of the numerous algorithms that exist to extract skeletons from binary images. This is particularly problematic as 3D imaging datasets increase in size and visual inspection becomes an insufficient validation approach. In this work, we first demonstrate the extent of the problem by applying 4 widely-used skeletonisation algorithms to 3 different imaging datasets. In doing so we show significant variability between reconstructed skeletons of the same segmented imaging dataset. Moreover, we show that such a structural variability propagates to simulated metrics such as blood flow. To mitigate this variability we introduce a new, fast and easy to compute super metric that compares the volume, connectivity, medialness, bifurcation point identification and homology of the reconstructed skeletons to the original segmented data. We then show that such a metric can be used to select the best performing skeletonisation algorithm for a given dataset, as well as to optimise its parameters. Finally, we demonstrate that the super metric can also be used to quickly identify how a particular skeletonisation algorithm could be improved, becoming a powerful tool in understanding the complex implication of small structural changes in a network.

A computational growth and remodeling framework for adaptive and maladaptive pulmonary arterial hemodynamics

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step toward predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

A topological data analysis study on murine pulmonary arterial trees with pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure above 20 mmHg in the main pulmonary artery, is a cardiovascular disease impacting the pulmonary vasculature. PH is accompanied by chronic vascular remodeling, wherein vessels become stiffer, large vessels dilate, and smaller vessels constrict. Some types of PH, including hypoxia-induced PH (HPH), also lead to microvascular rarefaction. This study analyzes the change in pulmonary arterial morphometry in the presence of HPH using novel methods from topological data analysis (TDA). We employ persistent homology to quantify arterial morphometry for control and HPH mice characterizing normalized arterial trees extracted from micro-computed tomography (micro-CT) images. We normalize generated trees using three pruning algorithms before comparing the topology of control and HPH trees. This proof-of-concept study shows that the pruning method affects the spatial tree statistics and complexity. We find that HPH trees are stiffer than control trees but have more branches and a higher depth. Relative directional complexities are lower in HPH animals in the right, ventral, and posterior directions. For the radius pruned trees, this difference is more significant at lower perfusion pressures enabling analysis of remodeling of larger vessels. At higher pressures, the arterial networks include more distal vessels. Results show that the right, ventral, and posterior relative directional complexities increase in HPH trees, indicating the remodeling of distal vessels in these directions. Strahler order pruning enables us to generate trees of comparable size, and results, at all pressure, show that HPH trees have lower complexity than the control trees. Our analysis is based on data from 6 animals (3 control and 3 HPH mice), and even though our analysis is performed in a small dataset, this study provides a framework and proof-of-concept for analyzing properties of biological trees using tools from Topological Data Analysis (TDA). Findings derived from this study bring us a step closer to extracting relevant information for quantifying remodeling in HPH.

A multiscale framework for defining homeostasis in distal vascular trees: applications to the pulmonary circulation

Pulmonary arteries constitute a low-pressure network of vessels, often characterized as a bifurcating tree with heterogeneous vessel mechanics. Understanding the vascular complexity and establishing homeostasis is important to study diseases such as pulmonary arterial hypertension (PAH). The onset and early progression of PAH can be traced to changes in the morphometry and structure of the distal vasculature. Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature. Accordingly, the goal of this study is to provide a multiscale modeling framework that embeds the essential features of arterial wall constituents coupled with the hemodynamics within an arterial network characterized by an extension of Murray's law. This framework will be used to establish the homeostatic baseline characteristics of a pulmonary arterial tree, including important parameters such as vessel radius, wall thickness and shear stress. To define the vascular homeostasis and hemodynamics in the tree, we consider two timescales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization, which integrates a metabolic cost function minimization, the stress equilibrium, and hemodynamics, is performed at the slow timescale. In the fast timescale, the pulsatile blood flow dynamics is described by a Womersley's deformable wall analytical solution. Illustrative examples for symmetric and asymmetric trees are presented that provide baseline characteristics for the normal pulmonary arterial vasculature. The results are compared with diverse literature data on morphometry, structure, and mechanics of pulmonary arteries. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling of PAH.

A Computational Growth and Remodeling Framework for Adaptive and Maladaptive Pulmonary Arterial Hemodynamics

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step towards predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

A computational study of aortic reconstruction in single ventricle patients

Patients with hypoplastic left heart syndrome (HLHS) are born with an underdeveloped left heart. They typically receive a sequence of surgeries that result in a single ventricle physiology called the Fontan circulation. While these patients usually survive into early adulthood, they are at risk for medical complications, partially due to their lower than normal cardiac output, which leads to insufficient cerebral and gut perfusion. While clinical imaging data can provide detailed insight into cardiovascular function within the imaged region, it is difficult to use these data for assessing deficiencies in the rest of the body and for deriving blood pressure dynamics. Data from patients used in this paper include three-dimensional, magnetic resonance angiograms (MRA), time-resolved phase contrast cardiac magnetic resonance images (4D-MRI) and sphygmomanometer blood pressure measurements. The 4D-MRI images provide detailed insight into velocity and flow in vessels within the imaged region, but they cannot predict flow in the rest of the body, nor do they provide values of blood pressure. To remedy these limitations, this study combines the MRA, 4D-MRI, and pressure data with 1D fluid dynamics models to predict hemodynamics in the major systemic arteries, including the cerebral and gut vasculature. A specific focus is placed on studying the impact of aortic reconstruction occurring during the first surgery that results in abnormal vessel morphology. To study these effects, we compare simulations for an HLHS patient with simulations for a matched control patient that has double outlet right ventricle (DORV) physiology with a native aorta. Our results show that the HLHS patient has hypertensive pressures in the brain as well as reduced flow to the gut. Wave intensity analysis suggests that the HLHS patient has irregular circulatory function during light upright exercise conditions and that predicted wall shear stresses are lower than normal, suggesting the HLHS patient may have hypertension.

Virtual Transcatheter Interventions for Peripheral Pulmonary Artery Stenosis in Williams and Alagille Syndromes

Background

Despite favorable outcomes of surgical pulmonary artery (PA) reconstruction, isolated proximal stenting of the central PAs is common clinical practice for patients with peripheral PA stenosis in association with Williams and Alagille syndromes. Given the technical challenges of PA reconstruction and the morbidities associated with transcatheter interventions, the hemodynamic consequences of all treatment strategies must be rigorously assessed. Our study aims to model, assess, and predict hemodynamic outcomes of transcatheter interventions in these patients.

Methods and Results

Isolated proximal and “extensive” interventions (stenting and/or balloon angioplasty of proximal and lobar vessels) were performed in silico on 6 patient‐specific PA models. Autoregulatory adaptation of the cardiac output and downstream arterial resistance was modeled in response to intervention‐induced hemodynamic perturbations. Postintervention computational fluid dynamics predictions were validated in 2 stented patients and quantitatively assessed in 4 surgical patients. Our computational methods accurately predicted postinterventional PA pressures, the primary indicators of success for treatment of peripheral PA stenosis. Proximal and extensive treatment achieved median reductions of 14% and 40% in main PA systolic pressure, 27% and 56% in pulmonary vascular resistance, and 10% and 45% in right ventricular stroke work, respectively.

Conclusions

In patients with Williams and Alagille syndromes, extensive transcatheter intervention is required to sufficiently reduce PA pressures and right ventricular stroke work. Transcatheter therapy was shown to be ineffective for long‐segment stenosis and pales hemodynamically in comparison with published outcomes of surgical reconstruction. Regardless of the chosen strategy, a virtual treatment planning platform could identify lesions most critical for optimizing right ventricular afterload.

Numerical predictions of shear stress and cyclic stretch in pulmonary hypertension due to left heart failure

Isolated post-capillary pulmonary hypertension (Ipc-PH) occurs due to left heart failure, which contributes to 1 out of every 9 deaths in the United States. In some patients, through unknown mechanisms, Ipc-PH transitions to combined pre-/post-capillary PH (Cpc-PH) and is associated with a dramatic increase in mortality. Altered mechanical forces and subsequent biological signaling in the pulmonary vascular bed likely contribute to the transition from Ipc-PH to Cpc-PH. However, even in a healthy pulmonary circulation, the mechanical forces in the smallest vessels (the arterioles, capillary bed, and venules) have not been quantitatively defined. This study is the first to examine this question via a computational fluid dynamics model of the human pulmonary arteries, arterioles, venules, and veins. Using this model, we predict temporal and spatial dynamics of cyclic stretch and wall shear stress with healthy and diseased hemodynamics. In the normotensive case for large vessels, numerical simulations show that large arteries have higher pressure and flow than large veins, as well as more pronounced changes in area throughout the cardiac cycle. In the microvasculature, shear stress increases and cyclic stretch decreases as vessel radius decreases. When we impose an increase in left atrial pressure to simulate Ipc-PH, shear stress decreases and cyclic stretch increases as compared to the healthy case. Overall, this model predicts pressure, flow, shear stress, and cyclic stretch that providing a way to analyze and investigate hypotheses related to disease progression in the pulmonary circulation.

A multiscale model of vascular function in chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension (CTEPH) is caused by recurrent or unresolved pulmonary thromboemboli, leading to perfusion defects and increased arterial wave reflections. CTEPH treatment aims to reduce pulmonary arterial pressure and reestablish adequate lung perfusion, yet patients with distal lesions are inoperable by standard surgical intervention. Instead, these patients undergo balloon pulmonary angioplasty (BPA), a multisession, minimally invasive surgery that disrupts the thromboembolic material within the vessel lumen using a catheter balloon. However, there still lacks an integrative, holistic tool for identifying optimal target lesions for treatment. To address this insufficiency, we simulate CTEPH hemodynamics and BPA therapy using a multiscale fluid dynamics model. The large pulmonary arterial geometry is derived from a computed tomography (CT) image, whereas a fractal tree represents the small vessels. We model ring- and web-like lesions, common in CTEPH, and simulate normotensive conditions and four CTEPH disease scenarios; the latter includes both large artery lesions and vascular remodeling. BPA therapy is simulated by simultaneously reducing lesion severity in three locations. Our predictions mimic severe CTEPH, manifested by an increase in mean proximal pulmonary arterial pressure above 20 mmHg and prominent wave reflections. Both flow and pressure decrease in vessels distal to the lesions and increase in unobstructed vascular regions. We use the main pulmonary artery (MPA) pressure, a wave reflection index, and a measure of flow heterogeneity to select optimal target lesions for BPA. In summary, this study provides a multiscale, image-to-hemodynamics pipeline for BPA therapy planning for patients with inoperable CTEPH. NEW & NOTEWORTHY This article presents novel computational framework for predicting pulmonary hemodynamics in chronic thromboembolic pulmonary hypertension. The mathematical model is used to identify the optimal target lesions for balloon pulmonary angioplasty, combining simulated pulmonary artery pressure, wave intensity analysis, and a new quantitative metric of flow heterogeneity.