Evolution of hemodynamic forces in the pulmonary tree with progressively worsening pulmonary arterial hypertension in pediatric patients

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.

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.

Computational haemodynamics for pulmonary valve replacement by means of a reduced fluid-structure interaction model

Pulmonary valve replacement (PVR) consists of substituting a patient's original valve with a prosthetic one, primarily addressing pulmonary valve insufficiency, which is crucially relevant in Tetralogy of Fallot repairment. While extensive clinical and computational literature on aortic and mitral valve replacements is available, PVR's post-procedural haemodynamics in the pulmonary artery and the impact of prosthetic valve dynamics remain significantly understudied. Addressing this gap, we introduce a reduced Fluid-Structure Interaction (rFSI) model, applied for the first time to the pulmonary valve. This model couples a three-dimensional computational representation of pulmonary artery haemodynamics with a one-degree-of-freedom model to account for valve structural mechanics. Through this approach, we analyse patient-specific haemodynamics pre and post PVR. Patient-specific geometries, reconstructed from CT scans, are virtually equipped with a template valve geometry. Boundary conditions for the model are established using a lumped-parameter model, fine-tuned based on clinical patient data. Our model accurately reproduces patient-specific haemodynamic changes across different scenarios: pre-PVR, six months post-PVR, and a follow-up condition after a decade. It effectively demonstrates the impact of valve implantation on sustaining the diastolic pressure gradient across the valve. The numerical results indicate that our valve model is able to reproduce overall physiological and/or pathological conditions, as preliminary assessed on two different patients. This promising approach provides insights into post-PVR haemodynamics and prosthetic valve effects, shedding light on potential implications for patient-specific outcomes.

Impact and mechanisms of drag-reducing polymers on shear stress regulation in pulmonary hypertension

BACKGROUND

Pulmonary hypertension (PH) is a refractory disease characterized by elevated pulmonary artery pressure and resistance. Drag-reducing polymers (DRPs) are blood-soluble macromolecules that reduce vascular resistance by altering the blood dynamics and rheology. Our previous work indicated that polyethylene oxide (PEO) can significantly reduce the medial wall thickness and vascular resistance of the pulmonary arteries, but the specific mechanism is still unclear.

METHODS

This study was designed to investigate the role and mechanism of PEO on intracellular calcium [Ca2 +] i and cytoskeletal proteins of endothelial cells (ECs) induced by low shear stress (LSS) in PH. Primary Pulmonary Artery Endothelial Cells (PAECs) were subjected to steady LSS (1 dyn/cm2) or physiological shear stress (SS) (10 dyn/cm2) for 20 h in a BioFlux 200 flow system. Calcium influx assays were conducted to evaluate the mechanisms of PEO on [Ca2 +] i. Subsequently, taking the key protein that induces cytoskeletal remodeling, the regulatory light chain (RLC) phosphorylation, as the breakthrough point, this study focused on the two key pathways of PEO that regulate phosphorylation of RLC: Myosin light chain kinase (MLCK) and Rho-associated kinase (ROCK) pathways.

RESULTS

Our current research revealed that PEO at LSS (1 dyn/cm2) significantly suppressed LSS-induced [Ca2 +] i and the expression level of transient receptor potential channel 1(TRPC1). In addition, ECs convert LSS stimuli into the upregulation of cytoskeletal proteins, including filamentous actin (F-actin), MLCK, ROCK, p-RLC, and pp-RLC. Further experiments using pharmacological inhibitors demonstrated that PEO at the LSS downregulated cytoskeleton-related proteins mainly through the ROCK and MLCK pathways.

CONCLUSIONS

This study considered intracellular calcium and cytoskeleton rearrangement as entry points to study the application of PEO in the biomedical field, which has important theoretical significance and practical application value for the treatment of PH.

Subject-specific one-dimensional fluid dynamics model of chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension (CTEPH) develops due to the accumulation of blood clots in the lung vasculature that obstructs flow and increases pressure. The mechanobiological factors that drive progression of CTEPH are not understood, in part because mechanical and hemodynamic changes in the small pulmonary arteries due to CTEPH are not easily measurable. Using previously published hemodynamic measurements and imaging from a large animal model of CTEPH, we applied a subject-specific one-dimensional (1D) computational fluid dynamic (CFD) approach to investigate the impact of CTEPH on pulmonary artery stiffening, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) in extralobar (main, right, and left) pulmonary arteries and intralobar (distal to the extralobar) arteries. Our results demonstrate that CTEPH increases pulmonary artery wall stiffness and decreases TAWSS in extralobar and intralobar arteries. Moreover, CTEPH increases the percentage of the intralobar arterial network with both low TAWSS and high OSI, quantified by the novel parameter φ , which is related to thrombogenicity. Our analysis reveals a strong positive correlation between increases in mean pulmonary artery pressure (mPAP) and φ from baseline to CTEPH in individual subjects, which supports the suggestion that increased φ drives disease severity. This subject-specific experimental-computational framework shows potential as a predictor of the impact of CTEPH on pulmonary arterial hemodynamics and pulmonary vascular mechanics. By leveraging advanced modeling techniques and calibrated model parameters, we predict spatial distributions of flow and pressure, from which we can compute potential physiomarkers of disease progression. Ultimately, this approach can lead to more spatially targeted interventions that address the needs of individual CTEPH patients.

A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.

Computational approaches for mechanobiology in cardiovascular development and diseases

The cardiovascular development in vertebrates evolves in response to genetic and mechanical cues. The dynamic interplay among mechanics, cell biology, and anatomy continually shapes the hydraulic networks, characterized by complex, non-linear changes in anatomical structure and blood flow dynamics. To better understand this interplay, a diverse set of molecular and computational tools has been used to comprehensively study cardiovascular mechanobiology. With the continual advancement of computational capacity and numerical techniques, cardiovascular simulation is increasingly vital in both basic science research for understanding developmental mechanisms and disease etiologies, as well as in clinical studies aimed at enhancing treatment outcomes. This review provides an overview of computational cardiovascular modeling. Beginning with the fundamental concepts of computational cardiovascular modeling, it navigates through the applications of computational modeling in investigating mechanobiology during cardiac development. Second, the article illustrates the utility of computational hemodynamic modeling in the context of treatment planning for congenital heart diseases. It then delves into the predictive potential of computational models for elucidating tissue growth and remodeling processes. In closing, we outline prevailing challenges and future prospects, underscoring the transformative impact of computational cardiovascular modeling in reshaping cardiovascular science and clinical practice.

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.

Subject-specific one-dimensional fluid dynamics model of chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension (CTEPH) develops due to the accumulation of blood clots in the lung vasculature that obstruct flow and increase pressure. The mechanobiological factors that drive progression of CTEPH are not understood, in part because mechanical and hemodynamic changes in the pulmonary vasculature due to CTEPH are not easily measurable. Using previously published hemodynamic measurements and imaging from a large animal model of CTEPH, we developed a subject-specific one-dimensional (1D) computational fluid dynamic (CFD) models to investigate the impact of CTEPH on pulmonary artery stiffening, time averaged wall shear stress (TAWSS), and oscillatory shear index (OSI). Our results demonstrate that CTEPH increases pulmonary artery wall stiffness and decreases TAWSS in extralobar (main, right and left pulmonary arteries) and intralobar vessels. Moreover, CTEPH increases the percentage of the intralobar arterial network with both low TAWSS and high OSI. This subject-specific experimental-computational framework shows potential as a predictor of the impact of CTEPH on pulmonary arterial hemodynamics and pulmonary vascular mechanics. By leveraging advanced modeling techniques and calibrated model parameters, we predict spatial distributions of flow and pressure, from which we can compute potential physiomarkers of disease progression, including the combination of low mean wall shear stress with high oscillation. Ultimately, this approach can lead to more spatially targeted interventions that address the needs of individual CTEPH patients.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

A Computational Study of Blood Flow Dynamics in the Pulmonary Arteries

In this work we study the blood dynamics in the pulmonary arteries by means of a 3D-0D geometric multiscale approach, where a detailed 3D model for the pulmonary arteries is coupled with a lumped parameters (0D) model of the cardiovascular system. We propose to investigate three strategies for the numerical solution of the 3D-0D coupled problem: the Splitting-Explicit and Implicit algorithms, where information are exchanged between 3D and 0D models at each time step at the interfaces, and the One-Way algorithm, where the 0D is solved first off-line. In our numerical experiments performed in a realistic patient-specific 3D domain with a physiologically calibrated 0D model, we discuss first the issue on instabilities that may arise when not suitable connections are considered between 3D and 0D models; second we compare the performance and accuracy of the three proposed numerical strategies. Finally, we report a comparison between a healthy and a hypertensive case, providing a preliminary result highlighting how our method could be used in future for clinical purposes.

Loss of lung microvascular endothelial Piezo2 expression impairs NO synthesis, induces EndMT, and is associated with pulmonary hypertension

Mechanical forces are translated into biochemical stimuli by mechanotransduction channels, such as the mechanically activated cation channel Piezo2. Lung Piezo2 expression has recently been shown to be restricted to endothelial cells. Hence, we aimed to investigate the role of Piezo2 in regulation of pulmonary vascular function and structure, as well as its contribution to development of pulmonary arterial hypertension (PAH). The expression of Piezo2 was significantly reduced in pulmonary microvascular endothelial cells (MVECs) from patients with PAH, in lung tissue from mice with a Bmpr2^+/R899X knock-in mutation commonly found in patients with pulmonary hypertension, and in lung tissue of monocrotaline (MCT) and sugen-hypoxia-induced PH (SuHx) PAH rat models, as well as from a swine model with pulmonary vein banding. In MVECs, Piezo2 expression was reduced in response to abnormal shear stress, hypoxia, and TGFβ stimulation. Functional studies in MVECs exposed to shear stress illustrated that siRNA-mediated Piezo2 knockdown impaired endothelial alignment, calcium influx, phosphorylation of AKT, and nitric oxide production. In addition, siPiezo2 reduced the expression of the endothelial marker PECAM-1 and increased the expression of vascular smooth muscle markers ACTA2, SM22a, and calponin. Thus, Piezo2 acts as a mechanotransduction channel in pulmonary MVECs, stimulating shear-induced production of nitric oxide and is essentially involved in preventing endothelial to mesenchymal transition. Its blunted expression in pulmonary hypertension could impair the vasodilator capacity and stimulate vascular remodeling, indicating that Piezo2 might be an interesting therapeutic target to attenuate progression of the disease.NEW & NOTEWORTHY The mechanosensory ion channel Piezo2 is exclusively expressed in lung microvascular endothelial cells (MVECs). Patient MVECs as well as animal models of pulmonary (arterial) hypertension showed lower expression of Piezo2 in the lung. Mechanistically, Piezo2 is required for calcium influx and NO production in response to shear stress, whereas stimuli known to induce endothelial to mesenchymal transition (EndMT) reduce Piezo2 expression in MVECs, and Piezo2 knockdown induces a gene and protein expression pattern consistent with EndMT.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

Compromised Cardiopulmonary Function in Fibulin-5 Deficient Mice

Competent elastic fibers are critical to the function of the lung and right circulation. Murine models of elastopathies can aid in understanding the functional roles of the elastin and elastin-associated glycoproteins that constitute elastic fibers. Here, we quantify together lung and pulmonary arterial structure, function, and mechanics with right heart function in a mouse model deficient in the elastin-associated glycoprotein fibulin-5. Differences emerged as a function of genotype, sex, and arterial region. Specifically, functional studies revealed increased lung compliance in fibulin-5 deficiency consistent with a histologically observed increased alveolar disruption. Biaxial mechanical tests revealed that the primary branch pulmonary arteries exhibit decreased elastic energy storage capacity and wall stress despite only modest differences in circumferential and axial material stiffness in the fibulin-5 deficient mice. Histological quantifications confirm a lower elastic fiber content in the fibulin-5 deficient pulmonary arteries, with fragmented elastic laminae in the outer part of the wall - likely the reason for reduced energy storage. Ultrasound measurements confirm sex differences in compromised right ventricular function in the fibulin-5 deficient mice. These results reveal compromised right heart function, but opposite effects of elastic fiber dysfunction on the lung parenchyma (significantly increased compliance) and pulmonary arteries (trend toward decreased distensibility), and call for further probing of ventilation-perfusion relationships in pulmonary pathologies. Amongst many other models, fibulin-5 deficient mice can contribute to our understanding of the complex roles of elastin in pulmonary health and disease.

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.

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.

A Personalized Pulmonary Circulation Model to Non-Invasively Calculate Fractional Flow Reserve for Artery Stenosis Detection

OBJECTIVE

Fractional Flow Reserve (FFR) is regarded as a fundamental index to assess pulmonary artery stenosis. The application of FFR can increase the accuracy of detection of pulmonary artery stenosis. However, the invasive examination may carry a number of physiological risks for patients. Therefore, we propose a personalized pulmonary circulation model to non- invasively calculate FFR of pulmonary artery stenosis. Method- ology: We employed a personalized pulmonary circulation model to non-invasively calculate FFR using only computed tomography angiogram (CTA) data. This model combined boundary conditions estimation and 3D pulmonary artery morphology reconstruction for CFD simulation. First, we obtained patient-specific boundary conditions by adapting the right ventricle stroke volume and main pulmonary artery pressure feature points (systolic, diastolic, and mean pressure). Secondly, the 3D pulmonary artery morphology was reconstructed by threshold segmentation. The CFD simulation was then performed to obtain pressure distribution in the entire pulmonary artery. Finally, the FFR in pulmonary artery stenoses was calculated as the ratio of distal pressure and proximal pres- sure.

RESULTS

To validate our model, we compared the calculated FFR with measured FFR by pressure guide wires examination of 8 patients. The FFR calculated by our model showed a good agreement with measured FFR by pressure guide wires exami- nation. The average accuracy rate was 91.41%.

CONCLUSION

The proposed personalized pulmonary model is capable of reasonably non-invasively calculating FFR with sufficient accuracy.

SIGNIFICANCE

FFR calculated in our model may contribute to non-invasive detection of pulmonary artery stenosis and to the assessment of invasive interventions.

Computational simulation-derived hemodynamic and biomechanical properties of the pulmonary arterial tree early in the course of ventricular septal defects

Untreated ventricular septal defects (VSDs) can lead to pulmonary arterial hypertension (PAH) characterized by elevated pulmonary artery (PA) pressure and vascular remodeling, known as PAH associated with congenital heart disease (PAH-CHD). Though previous studies have investigated hemodynamic effects on vascular mechanobiology in late-stage PAH, hemodynamics leading to PAH-CHD initiation have not been fully quantified. We hypothesize that abnormal hemodynamics from left-to-right shunting in early stage VSDs affects PA biomechanical properties leading to PAH initiation. To model PA hemodynamics in healthy, small, moderate, and large VSD conditions prior to the onset of vascular remodeling, computational fluid dynamics simulations were performed using a 3D finite element model of a healthy 1-year-old's proximal PAs and a body-surface-area-scaled 0D distal PA tree. VSD conditions were modeled with increased pulmonary blood flow to represent degrees of left-to-right shunting. In the proximal PAs, pressure, flow, strain, and wall shear stress (WSS) increased with increasing VSD size; oscillatory shear index decreased with increasing VSD size in the larger PA vessels. WSS was higher in smaller diameter vessels and increased with VSD size, with the large VSD condition exhibiting WSS >100 dyn/cm[Formula: see text], well above values typically used to study dysfunctional mechanotransduction pathways in PAH. This study is the first to estimate hemodynamic and biomechanical metrics in the entire pediatric PA tree with VSD severity at the stage leading to PAH initiation and has implications for future studies assessing effects of abnormal mechanical stimuli on endothelial cells and vascular wall mechanics that occur during PAH-CHD initiation and progression.

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.

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient-specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed-form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state-of-the-art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long-term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Patient-Specific Computational Analysis of Hemodynamics and Wall Mechanics and Their Interactions in Pulmonary Arterial Hypertension

Vascular wall stiffness and hemodynamic parameters are potential biomechanical markers for detecting pulmonary arterial hypertension (PAH). Previous computational analyses, however, have not considered the interaction between blood flow and wall deformation. Here, we applied an established computational framework that utilizes patient-specific measurements of hemodynamics and wall deformation to analyze the coupled fluid-vessel wall interaction in the proximal pulmonary arteries (PA) of six PAH patients and five control subjects. Specifically, we quantified the linearized stiffness (E), relative area change (RAC), diastolic diameter (D), regurgitant flow, and time-averaged wall shear stress (TAWSS) of the proximal PA, as well as the total arterial resistance (R t ) and compliance (C t ) at the distal pulmonary vasculature. Results found that the average proximal PA was stiffer [median: 297 kPa, interquartile range (IQR): 202 kPa vs. median: 75 kPa, IQR: 5 kPa; P = 0.007] with a larger diameter (median: 32 mm, IQR: 5.25 mm vs. median: 25 mm, IQR: 2 mm; P = 0.015) and a reduced RAC (median: 0.22, IQR: 0.10 vs. median: 0.42, IQR: 0.04; P = 0.004) in PAH compared to our control group. Also, higher total resistance (R t ; median: 6.89 mmHg × min/l, IQR: 2.16 mmHg × min/l vs. median: 3.99 mmHg × min/l, IQR: 1.15 mmHg × min/l; P = 0.002) and lower total compliance (C t ; median: 0.13 ml/mmHg, IQR: 0.15 ml/mmHg vs. median: 0.85 ml/mmHg, IQR: 0.51 ml/mmHg; P = 0.041) were observed in the PAH group. Furthermore, lower TAWSS values were seen at the main PA arteries (MPAs) of PAH patients (median: 0.81 Pa, IQR: 0.47 Pa vs. median: 1.56 Pa, IQR: 0.89 Pa; P = 0.026) compared to controls. Correlation analysis within the PAH group found that E was directly correlated to the PA regurgitant flow (r = 0.84, P = 0.018) and inversely related to TAWSS (r = -0.72, P = 0.051). Results suggest that the estimated elastic modulus E may be closely related to PAH hemodynamic changes in pulmonary arteries.

Longitudinal Evolution of Pulmonary Artery Wall Shear Stress in a Swine Model of Pulmonary Artery Stenosis and Stent Interventions

Branch pulmonary artery stenosis (PAS) commonly occurs in congenital heart disease and it has previously been hypothesized that in branch PAS the pulmonary arteries (PAs) remodel their lumen diameter to maintain constant wall shear stress (WSS). We quantified the longitudinal progression of PA WSS in a swine model of unilateral PAS and two different intervention time courses to test this hypothesis. To quantify WSS in the entire pulmonary tree we used 4D Flow MRI for the large-proximal PAs and a structured tree model for the small-distal PAs. Our results only partially supported the hypothesis that in branch PAS the PAs remodel their lumen diameter to maintain WSS homeostasis. Proximal PA WSS was similar between groups at the final study time-point but WSS of mid-sized (5 mm to 500 μm) PA segments was found to be different between the sham and LPAS groups. This suggests that WSS homeostasis may only be achieved for the large-proximal PAs. Additionally, our results do not show WSS homeostasis being achieved over shorter periods of time suggesting that any potential WSS dependent changes in PA lumen diameter were a long-term remodeling response rather than a short-term vasodilation response. Future studies should confirm if these findings hold true in humans and investigate the impacts of WSS at different levels of the pulmonary tree on growth.

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.

Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood

Pulmonary artery (PA) morphometry has been extensively explored in adults, with particular focus on intra-acinar arteries. However, scaling law relationships for length and diameter of extensive preacinar PAs by age have not been previously reported for in vivo human data. To understand preacinar PA growth spanning children to adults, we performed morphometric analyses of all PAs visible in the computed tomography (CT) and magnetic resonance (MR) images from a healthy subject cohort [n = 16; age: 1-51 yr; body surface area (BSA): 0.49-2.01 m²]. Subject-specific anatomic PA models were constructed from CT and MR images, and morphometric information-diameter, length, tortuosity, bifurcation angle, and connectivity-was extracted and sorted into diameter-defined Strahler orders. Validation of Murray's law, describing optimal scaling exponents of radii for branching vessels, was performed to determine how closely PAs conform to this classical relationship. Using regression analyses of vessel diameters and lengths against orders and patient metrics (BSA, age, height), we found that diameters increased exponentially with order and allometrically with patient metrics. Length increased allometrically with patient metrics, albeit weakly. The average tortuosity index of all vessels was 0.026 ± 0.024, average bifurcation angle was 28.2 ± 15.1°, and average Murray's law exponent was 2.92 ± 1.07. We report a set of scaling laws for vessel diameter and length, along with other morphometric information. These provide an initial understanding of healthy structural preacinar PA development with age, which can be used for computational modeling studies and comparison with diseased PA anatomy.NEW & NOTEWORTHY Pulmonary artery (PA) morphometry studies to date have focused primarily on large arteries and intra-acinar arteries in either adults or children, neglecting preacinar arteries in both populations. Our study is the first to quantify in vivo preacinar PA morphometry changes spanning infants to adults. For preacinar arteries > 1 mm in diameter, we identify scaling laws for vessel diameters and lengths with patient metrics of growth and establish a healthy PA morphometry baseline for most preacinar PAs.

Structural and hemodynamic properties of murine pulmonary arterial networks under hypoxia-induced pulmonary hypertension

Detection and monitoring of patients with pulmonary hypertension, defined as a mean blood pressure in the main pulmonary artery above 25 mmHg, requires a combination of imaging and hemodynamic measurements. This study demonstrates how to combine imaging data from microcomputed tomography images with hemodynamic pressure and flow waveforms from control and hypertensive mice. Specific attention is devoted to developing a tool that processes computed tomography images, generating subject-specific arterial networks in which one-dimensional fluid dynamics modeling is used to predict blood pressure and flow. Each arterial network is modeled as a directed graph representing vessels along the principal pathway to ensure perfusion of all lobes. The one-dimensional model couples these networks with structured tree boundary conditions representing the small arteries and arterioles. Fluid dynamics equations are solved in this network and compared to measurements of pressure in the main pulmonary artery. Analysis of microcomputed tomography images reveals that the branching ratio is the same in the control and hypertensive animals, but that the vessel length-to-radius ratio is significantly lower in the hypertensive animals. Fluid dynamics predictions show that in addition to changed network geometry, vessel stiffness is higher in the hypertensive animal models than in the control models.

Fluid-structure interaction modeling of blood flow in the pulmonary arteries using the unified continuum and variational multiscale formulation

In this work, we present a computational fluid-structure interaction (FSI) study for a healthy patient-specific pulmonary arterial tree using the unified continuum and variational multiscale (VMS) formulation we previously developed. The unified framework is particularly well-suited for FSI, as the fluid and solid sub-problems are addressed in essentially the same manner and can thus be uniformly integrated in time with the generalized-α method. In addition, the VMS formulation provides a mechanism for large-eddy simulation in the fluid sub-problem and pressure stabilization in the solid sub-problem. The FSI problem is solved in a quasi-direct approach, in which the pressure and velocity in the unified continuum body are first solved, and the solid displacement is then obtained via a segregated algorithm and prescribed as a boundary condition for the mesh motion. Results of the pulmonary arterial FSI simulation are presented and compared against those of a rigid wall simulation.

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.

A canonical correlation analysis of the relationship between clinical attributes and patient-specific hemodynamic indices in adult pulmonary hypertension

Pulmonary hypertension (PH) is a progressive disease affecting approximately 10-52 cases per million, with a higher incidence in women, and with a high mortality associated with right ventricle (RV) failure. In this work, we explore the relationship between hemodynamic indices, calculated from in silico models of the pulmonary circulation, and clinical attributes of RV workload and pathological traits. Thirty-four patient-specific pulmonary arterial tree geometries were reconstructed from computed tomography angiography images and used for volume meshing for subsequent computational fluid dynamics (CFD) simulations. Data obtained from the CFD simulations were post-processed resulting in hemodynamic indices representative of the blood flow dynamics. A retrospective review of medical records was performed to collect the clinical variables measured or calculated from standard hospital examinations. Statistical analyses and canonical correlation analysis (CCA) were performed for the clinical variables and hemodynamic indices. Systolic pulmonary artery pressure (sPAP), diastolic pulmonary artery pressure (dPAP), cardiac output (CO), and stroke volume (SV) were moderately correlated with spatially averaged wall shear stress (0.60 ≤ R² ≤ 0.66; p < 0.05). Similarly, the CCA revealed a linear and strong relationship (ρ = 0.87; p << 0.001) between 5 clinical variables and 2 hemodynamic indices. To this end, in silico models of PH blood flow dynamics have a high potential for predicting the relevant clinical attributes of PH if analyzed in a group-wise manner using CCA.

Medical Image-Based Hemodynamic Analyses in a Study of the Pulmonary Artery in Children With Pulmonary Hypertension Related to Congenital Heart Disease

Objective: Pulmonary hypertension related to congenital heart disease (PH-CHD) is a devastating disease caused by hemodynamic disorders. Previous hemodynamic research in PH-CHD mainly focused on wall shear stress (WSS). However, energy loss (EL) is a vital parameter in evaluation of hemodynamic status. We investigated if EL of the pulmonary artery (PA) is a potential biomechanical marker for comprehensive assessment of PH-CHD. Materials and Methods: Ten PH-CHD patients and 10 age-matched controls were enrolled. Subject-specific 3-D PA models were reconstructed based on computed tomography. Transient flow, WSS, and EL in the PA were calculated using non-invasive computational fluid dynamics. The relationship between body surface area (BSA)-normalized EL ( E . ) and PA morphology and PA flow were analyzed. Results: Morphologic analysis indicated that the BSA-normalized main PA (MPA) diameter (D_MPAnorm), MPA/aorta diameter ratio (D_MPA/D_AO), and MPA/(left PA + right PA) [D_MPA/D_(LPA+RPA)] diameter ratio were significantly larger in PH-CHD patients. Hemodynamic results showed that the velocity of the PA branches was higher in PH-CHD patients, in whom PA flow rate usually increased. WSS in the MPA was lower and E . was higher in PH-CHD patients. E . was positively correlated with D_MPAnorm, D_MPA/D_AO, and D_MPA/D_(LPA+RPA) ratios and the flow rate in the PA. E . was a sensitive index for the diagnosis of PH-CHD. Conclusion: E . is a potential biomechanical marker for PH-CHD assessment. This hemodynamic parameter may lead to new directions for revealing the potential pathophysiologic mechanism of PH-CHD.