Reproducing Patient-Specific Hemodynamics in the Blalock-Taussig Circulation Using a Flexible Multi-Domain Simulation Framework: Applications for Optimal Shunt Design

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.

Using a reduced-order model to investigate the effect of the heart rate on the aortic dissection

The computational cost of a three-dimensional (3D) fluid-structure interaction (FSI) simulation of a dissected aorta has prevented researchers from investigating the effect of a wide range of the heart rate on the hemodynamic quantities in the disease. We have presented a systematic procedure to develop a zero-dimensional (0D) model for a dissected aorta. A series of numerical experiments were used to calculate the values for the resistance, inertance, and compliance of each lumen with irregular geometries. Having validated the results from the 0D model against those from the 3D model for one heart rate, we used the 0D model to investigate the effect of the heart rate of 50-150 bpm on the flow rates and the pressures in an idealized geometry of an aortic dissection. The 0D model showed acceptable accuracy when compared with the 3D FSI simulation. For instance, at peak systole, 7.18% relative error in the flow rate in the true lumen was observed for 0D and 3D simulations. The flow rate in the true lumen showed a stronger dependency on the heart rate, that is, 300% for the true lumen and 1.5% for the false lumen. The pressure difference between the lumina increased non-monotonically as the heart beats faster. Because of its efficiency, the reported procedure can be used for uncertainty and sensitivity analysis of the hemodynamic quantities in a diseased aorta with complex geometries such as that of the aortic dissection.

The Effects of the Mechanical Properties of Vascular Grafts and an Anisotropic Hyperelastic Aortic Model on Local Hemodynamics during Modified Blalock-Taussig Shunt Operation, Assessed Using FSI Simulation

Cardiovascular surgery requires the use of state-of-the-art artificial materials. For example, microporous polytetrafluoroethylene grafts manufactured by Gore-Tex^® are used for the treatment of cyanotic heart defects (i.e., modified Blalock–Taussig shunt). Significant mortality during this palliative operation has led surgeons to adopt mathematical models to eliminate complications by performing fluid–solid interaction (FSI) simulations. To proceed with FSI modeling, it is necessary to know either the mechanical properties of the aorta and graft or the rheological properties of blood. The properties of the aorta and blood can be found in the literature, but there are no data about the mechanical properties of Gore-Tex^® grafts. Experimental studies were carried out on the mechanical properties vascular grafts adopted for modified pediatric Blalock–Taussig shunts. Parameters of two models (the five-parameter Mooney–Rivlin model and the three-parameter Yeoh model) were determined by uniaxial experimental curve fitting. The obtained data were used for patient-specific FSI modeling of local blood flow in the “aorta-modified Blalock–Taussig shunt–pulmonary artery” system in three different shunt locations: central, right, and left. The anisotropic model of the aortic material showed higher stress values at the peak moment of systole, which may be a key factor determining the strength characteristics of the aorta and pulmonary artery. Additionally, this mechanical parameter is important when installing a central shunt, since it is in the area of the central anastomosis that an increase in stress on the aortic wall is observed. According to computations, the anisotropic model shows smaller values for the displacements of both the aorta and the shunt, which in turn may affect the success of preoperative predictions. Thus, it can be concluded that the anisotropic properties of the aorta play an important role in preoperative modeling.

Tunable Blood Shunt for Neonates With Complex Congenital Heart Defects

Despite advancements in procedures and patient care, mortality rates for neonatal recipients of the Norwood procedure, a palliation for single ventricle congenital malformations, remain high due to the use of a fixed-diameter blood shunt. In this study, a new geometrically tunable blood shunt was investigated to address limitations of the current treatment paradigm (e.g., Modified Blalock-Taussig Shunt) by allowing for controlled modulation of blood flow through the shunt to accommodate physiological changes due to the patient’s growth. First, mathematical and computational cardiovascular models were established to investigate the hemodynamic requirements of growing neonatal patients with shunts and to inform design criteria for shunt diameter changes. Then, two stages of prototyping were performed to design, build and test responsive hydrogel systems that facilitate tuning of the shunt diameter by adjusting the hydrogel’s degree of crosslinking. We examined two mechanisms to drive crosslinking: infusion of chemical crosslinking agents and near-UV photoinitiation. The growth model showed that 15–18% increases in shunt diameter were required to accommodate growing patients’ increasing blood flow; similarly, the computational models demonstrated that blood flow magnitudes were in agreement with previous reports. These target levels of diameter increases were achieved experimentally with model hydrogel systems. We also verified that the photocrosslinkable hydrogel, composed of methacrylated dextran, was contact-nonhemolytic. These results demonstrate proof-of-concept feasibility and reflect the first steps in the development of this novel blood shunt. A tunable shunt design offers a new methodology to rebalance blood flow in this vulnerable patient population during growth and development.

Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary conditions. The contributions of this work are threefold:1.To demonstrate that neural networks can be efficient aggregators of whole families of parametric solutions to physical problems, trained using data created with traditional, trusted numerical methods such as finite elements. Advantages include extremely fast evaluation of pressure and velocity at any point in physical and parameter space (asymptotically, ∼3 μs/query), and data compression (the network requires 99% less storage space compared to its own training data).2.To demonstrate that the neural networks can accurately interpolate between finite element solutions in parameter space, allowing them to be instantly queried for pressure and velocity field solutions to problems for which traditional simulations have never been performed.3.To introduce an active learning algorithm, so that during training, a finite element solver can automatically be queried to obtain additional training data in locations where the neural network's predictions are in most need of improvement, thus autonomously acquiring and efficiently distributing training data throughout parameter space. In addition to the obvious utility of Item 2, above, we demonstrate an application of the network in rapid parameter sweeping, very precisely predicting the degree of narrowing in a tube which would result in a 50% increase in end-to-end pressure difference at a given flow rate. This capability could have applications in both medical diagnosis of arterial disease, and in computer-aided design.

Characterization of Post-Operative Hemodynamics Following the Norwood Procedure Using Population Data and Multi-Scale Modeling

Children with hypoplastic left heart syndrome (HLHS) must undergo multiple surgical stages to reconstruct the anatomy to a sustainable single ventricle system. Stage I palliation, or the Norwood procedure, provides circulation to both pulmonary and systemic vasculature. The aorta is reconstructed and attached to the right ventricle and a fraction of systemic flow is redirected to the pulmonary arteries (PAs) through a systemic-to-PA shunt. Despite abundant hemodynamic data available 4-5 months after Norwood palliation, data is very scarce immediately following stage I. This data is critical in determining post-operative success. In this work, we combined population data and computational fluid dynamics (CFD) to characterize hemodynamics immediately following stage I (post-stage I) and prior to stage II palliation (pre-stage II). A patient-specific model was constructed as a baseline geometry, which was then scaled to reflect population-based morphological data at both time-points. Population-based hemodynamic data was then used to calibrate each model to reproduce blood flow representative of HLHS patients. The post-stage I simulation produced a PA pressure of 22 mmHg and high-frequency oscillations within the flow field indicating highly disturbed hemodynamics. Despite PA mean pressure dropping to 14 mmHg, the pre-stage II model also produced high-frequency flow components and PA wall shear stress increases. These suboptimal conditions may be necessary to ensure adequate PA flow throughout the pre-stage II period, as the shunt becomes relatively smaller compared to the patient's somatic growth. In the future, CFD can be used to optimize shunt design and minimize these suboptimal conditions.

CRIMSON: An open-source software framework for cardiovascular integrated modelling and simulation

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization.

Multiscale modeling of a modified Blalock-Taussig surgery in a patient-specific tetralogy of Fallot

Tetralogy of Fallot (TOF) is a congenital heart anomaly that causes a drastic reduction in the oxygen level. In this study, we coupled a lumped-parameter model with a patient-specific three-dimensional (3D) model which included a modified Blalock-Taussig (MBT) shunt. By forming a closed loop, we investigated the effects of certain parameters on the flow rates and the pressures at different locations of the developed network. A local sensitivity analysis on an initial zero-dimensional (0D) closed-loop model was conducted. The 0D lumped parameter (LP) model was then refined based on the results of the multiscale 0D-3D model and the local sensitivity analysis was repeated for the refined 0D model. It was shown that the maximum pressure of the pulmonary bed had the highest sensitivity of 94% to the diameter of MBT shunt. We observed that the existence of the flow in the shunt during the diastole caused an elevated wall shear stress (WSS) in the pulmonary artery. In this work, we calculated the flow velocity and pressure field in a 3D patient-specific aorta with an MBT shunt, and then we used the results to increase the accuracy of our LP model to simulate numerous 0D simulations in a significantly shorter time, which is potentially applicable for medical decision-making.

A flexible framework for sequential estimation of model parameters in computational hemodynamics

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A "Netlist" implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Péclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical instabilities when backflow occurs at Neumann boundaries, we propose an approach based on the prescription of the total flux. In addition, we introduce a "consistent flux" outflow boundary condition and demonstrate its superior performance over the traditional zero diffusive flux boundary condition. Lastly, we discuss discontinuity capturing (DC) stabilization techniques to address the well-known oscillatory behavior of the solution near the concentration front in advection-dominated flows. We present numerical examples in both idealized and patient-specific geometries to demonstrate the efficacy of the proposed procedures. The three contributions discussed in this paper successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.

Emerging 3D technologies and applications within congenital heart disease: teach, predict, plan and guide

3D visualization technologies have evolved to become a mainstay in the management of congenital heart disease (CHD) with a growing presence within multiple facets. Printed and virtual 3D models allow for a more comprehensive approach to educating trainees and care team members. Computational fluid dynamics can take 3D modeling to the next level, by predicting post-procedural outcomes and helping to determine surgical approach. 3D printing and extended reality are developing resources for pre-procedural planning and intra-procedural guidance with the potential to revolutionize decision-making and procedural success. Challenges still remain within existing technologies and their applications to the CHD field. Addressing these gaps, both by those within and outside of CHD, will transform education and patient care within our field.

The Use of Biophysical Flow Models in the Surgical Management of Patients Affected by Chronic Thromboembolic Pulmonary Hypertension

Introduction: Chronic Thromboembolic Pulmonary Hypertension (CTEPH) results from progressive thrombotic occlusion of the pulmonary arteries. It is treated by surgical removal of the occlusion, with success rates depending on the degree of microvascular remodeling. Surgical eligibility is influenced by the contributions of both the thrombus occlusion and microvasculature remodeling to the overall vascular resistance. Assessing this is challenging due to the high inter-individual variability in arterial morphology and physiology. We investigated the potential of patient-specific computational flow modeling to quantify pressure gradients in the pulmonary arteries of CTEPH patients to assist the decision-making process for surgical eligibility.

Methods: Detailed segmentations of the pulmonary arteries were created from postoperative chest Computed Tomography scans of three CTEPH patients. A focal stenosis was included in the original geometry to compare the pre- and post-surgical hemodynamics. Three-dimensional flow simulations were performed on each morphology to quantify velocity-dependent pressure changes using a finite element solver coupled to terminal 2-element Windkessel models. In addition to transient flow simulations, a parametric modeling approach based on constant flow simulations is also proposed as faster technique to estimate relative pressure drops through the proximal pulmonary vasculature.

Results: An asymmetrical flow split between left and right pulmonary arteries was observed in the stenosed models. Removing the proximal obstruction resulted in a reduction of the right-left pressure imbalance of up to 18%. Changes were also observed in the wall shear stresses and flow topology, where vortices developed in the stenosed model while the non-stenosed retained a helical flow. The predicted pressure gradients from constant flow simulations were consistent with the ones measured in the transient flow simulations.

Conclusion: This study provides a proof of concept that patient-specific computational modeling can be used as a noninvasive tool for assisting surgical decisions in CTEPH based on hemodynamics metrics. Our technique enables determination of the proximal relative pressure, which could subsequently be compared to the total pressure drop to determine the degree of distal and proximal vascular resistance. In the longer term this approach has the potential to form the basis for a more quantitative classification system of CTEPH types.