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

Rapid estimation of left ventricular contractility with a physics-informed neural network inverse modeling approach

Physics-based computer models based on numerical solutions of the governing equations generally cannot make rapid predictions, which in turn limits their applications in the clinic. To address this issue, we developed a physics-informed neural network (PINN) model that encodes the physics of a closed-loop blood circulation system embedding a left ventricle (LV). The PINN model is trained to satisfy a system of ordinary differential equations (ODEs) associated with a lumped parameter description of the circulatory system. The model predictions have a maximum error of less than 5% when compared to those obtained by solving the ODEs numerically. An inverse modeling approach using the PINN model is also developed to rapidly estimate model parameters (in ∼ 3 min) from single-beat LV pressure and volume waveforms. Using synthetic LV pressure and volume waveforms generated by the PINN model with different model parameter values, we show that the inverse modeling approach can recover the corresponding ground truth values for LV contractility indexed by the end-systolic elastance Ees with a 1% error, which suggests that this parameter is unique. The estimated Ees is about 58% to 284% higher for the data associated with dobutamine compared to those without, which implies that this approach can be used to estimate LV contractility using single-beat measurements. The PINN inverse modeling can potentially be used in the clinic to simultaneously estimate LV contractility and other physiological parameters from single-beat measurements.

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.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

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.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

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.

Uncertainty Quantification in the In Vivo Image-Based Estimation of Local Elastic Properties of Vascular Walls

Introduction: Patient-specific computational models are a powerful tool for planning cardiovascular interventions. However, the in vivo patient-specific mechanical properties of vessels represent a major source of uncertainty. In this study, we investigated the effect of uncertainty in the elastic module (E) on a Fluid–Structure Interaction (FSI) model of a patient-specific aorta. Methods: The image-based χ-method was used to compute the initial E value of the vascular wall. The uncertainty quantification was carried out using the generalized Polynomial Chaos (gPC) expansion technique. The stochastic analysis was based on four deterministic simulations considering four quadrature points. A deviation of about ±20% on the estimation of the E value was assumed. Results: The influence of the uncertain E parameter was evaluated along the cardiac cycle on area and flow variations extracted from five cross-sections of the aortic FSI model. Results of stochastic analysis showed the impact of E in the ascending aorta while an insignificant effect was observed in the descending tract. Conclusions: This study demonstrated the importance of the image-based methodology for inferring E, highlighting the feasibility of retrieving useful additional data and enhancing the reliability of in silico models in clinical practice.

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.

Blood flow analysis with computational fluid dynamics and 4D-flow MRI for vascular diseases

Both computational fluid dynamics (CFD) and time-resolved, three-dimensional, phase-contrast, magnetic resonance imaging (4D-flow MRI) enable visualization of time-varying blood flow structures and quantification of blood flow in vascular diseases. However, they are totally different. CFD is a method to calculate blood flow by solving the governing equations of fluid mechanics, so the obtained flow field is somewhat virtual. On the other hand, 4D-flow MRI measures blood flow in vivo, thus the flow is real. Recently, with the development and enhancement of computers, medical imaging techniques, and related software, blood flow analysis has become more accessible to clinicians and its usefulness in vascular diseases has been demonstrated. In this review, we have outlined the methods and characteristics of CFD and 4D-flow MRI, respectively. We have discussed the differences in the characteristics between both methods; reviewed the milestones achieved by blood flow analysis in various vascular diseases; and discussed the usefulness, challenges, and limitations of blood flow analysis. We have discussed the difficulties and limitations of current blood flow analysis. We have also discussed our views on future directions.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

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.