Fluid-structure interaction simulations of the Fontan procedure using variable wall properties

Biomechanical Analysis of Age-Dependent Changes in Fontan Power Loss

The hemodynamics in Fontan patients with single ventricles rely on favorable flow and energetics, especially in the absence of a subpulmonary ventricle. Age-related changes in energetics for extracardiac and lateral tunnel Fontan procedures are not well understood. Vorticity (VOR) and viscous dissipation rate (VDR) are two descriptors that can provide insights into flow dynamics and dissipative areas in Fontan pathways, potentially contributing to power loss. This study examined power loss and its correlation with spatio-temporal flow descriptors (vorticity and VDR). Data from 414 Fontan patients were used to establish a relationship between the superior vena cava (SVC) to inferior vena cava (IVC) flow ratio and age. Computational flow modeling was conducted for both extracardiac conduits (ECC, n = 16) and lateral tunnels (LT, n = 25) at different caval inflow ratios of 2, 1, and 0.5 that corresponded with ages 3, 8, and 15+. In both cohorts, vorticity and VDR correlated well with PL, but ECC cohort exhibited a slightly stronger correlation for PL-VOR (>0.83) and PL-VDR (>0.89) than that for LT cohort (>0.76 and > 0.77, respectively) at all ages. Our data also suggested that absolute and indexed PL increase (p < 0.02) non-linearly as caval inflow changes with age and are highly patient-specific. Comparison of indexed power loss between our ECC and LT cohort showed that while ECC had a slightly higher median PL for all 3 caval inflow ratio examined (3.3, 8.3, 15.3) as opposed to (2.7, 7.6, 14.8), these differences were statistically non-significant. Lastly, there was a consistent rise in pressure gradient across the TCPC with age-related increase in IVC flows for both ECC and LT Fontan patient cohort. Our study provided hemodynamic insights into Fontan energetics and how they are impacted by age-dependent change in caval inflow. This workflow may help assess the long-term sustainability of the Fontan circulation and inform the design of more efficient Fontan conduits.

Computational fluid-structure interaction analysis of the end-to-side radio-cephalic arteriovenous fistula

BACKGROUND AND OBJECTIVE

In the current work, we present a descriptive fluid-structure interaction computational study of the end-to-side radio-cephalic arteriovenous fistula. This allows us to account for the different thicknesses and elastic properties of the radial artery and cephalic vein.

METHODS

The core of the work consists in simulating different arteriovenous fistula configurations obtained by virtually varying the anastomosis angle, i.e. the angle between the end of the cephalic vein and the side of the radial artery. Since the aim of the work is to understand the blood dynamics in the very first days after the surgical intervention, the radial artery is considered stiffer and thicker than the cephalic vein.

RESULTS

Our results demonstrate that both the diameter of the cephalic vein and the anastomosis angle play a crucial role to obtain a blood dynamics without re-circulation regions that could prevent fistula failure.

CONCLUSIONS

When an anastomosis angle close to the perpendicular direction with respect to the radial artery is combined with a large diameter of the cephalic vein, the recirculation regions and the low Wall Shear Stress (WSS) zones are reduced. Conversely, from a structural point of view, a low anastomosis angle with a large diameter of the cephalic vein reduces the mechanical stress acting on the vessel walls.

Non-invasive Estimation of Pressure Drop Across Aortic Coarctations: Validation of 0D and 3D Computational Models with In Vivo Measurements

Blood pressure gradient ( Δ P ) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of Δ P estimates derived non-invasively using patient-specific 0D and 3D deformable wall simulations. Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N = 17). 0D simulations were performed first and used to tune boundary conditions and initialize 3D simulations. Δ P across the CoA estimated using both 0D and 3D simulations were compared to invasive catheter-based pressure measurements for validation. The 0D simulations were extremely efficient ( ∼ 15 s computation time) compared to 3D simulations ( ∼ 30 h computation time on a cluster). However, the 0D Δ P estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0D model classified patients with severe CoA requiring intervention (defined as Δ P ≥ 20 mmHg) with 76% accuracy and 3D simulations improved this to 88%. Overall, a combined approach, using 0D models to efficiently tune and launch 3D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.

Impact of Age-Related Change in Caval Flow Ratio on Hepatic Flow Distribution in the Fontan Circulation

BACKGROUND

The Fontan operation is a palliative technique for patients born with single ventricle heart disease. The superior vena cava (SVC), inferior vena cava (IVC), and hepatic veins are connected to the pulmonary arteries in a total cavopulmonary connection by an extracardiac conduit or a lateral tunnel connection. A balanced hepatic flow distribution (HFD) to both lungs is essential to prevent pulmonary arteriovenous malformations and cyanosis. HFD is highly dependent on the local hemodynamics. The effect of age-related changes in caval inflows on HFD was evaluated using cardiac magnetic resonance data and patient-specific computational fluid dynamics modeling.

METHODS

SVC and IVC flow from 414 patients with Fontan were collected to establish a relationship between SVC:IVC flow ratio and age. Computational fluid dynamics modeling was performed in 60 (30 extracardiac and 30 lateral tunnel) patient models to quantify the HFD that corresponded to patient ages of 3, 8, and 15 years, respectively.

RESULTS

SVC:IVC flow ratio inverted at ≈8 years of age, indicating a clear shift to lower body flow predominance. Our data showed that variation of HFD in response to age-related changes in caval inflows (SVC:IVC, 2, 1, and 0.5 corresponded to ages, 3, 8, and 15+, respectively) was not significant for extracardiac but statistically significant for lateral tunnel cohorts. For all 3 caval inflow ratios, a positive correlation existed between the IVC flow distribution to both the lungs and the HFD. However, as the SVC:IVC ratio changed from 2 to 0.5 (age, 3-15+) years, the correlation's strength decreased from 0.87 to 0.64, due to potential flow perturbation as IVC flow momentum increased.

CONCLUSIONS

Our analysis provided quantitative insights into the impact of the changing caval inflows on Fontan's long-term HFD, highlighting the importance of SVC:IVC variations over time on Fontan's long-term hemodynamics. These findings broaden our understanding of Fontan hemodynamics and patient outcomes.

Impact of Age-related change in Caval Flow Ratio on Hepatic Flow Distribution in Fontan

Background

The Fontan operation is a palliative technique for patients born with single ventricle heart disease. The superior vena cava (SVC), inferior vena cava (IVC), and hepatic veins are connected to the pulmonary arteries in a total cavopulmonary connection by an extracardiac (EC) conduit or a lateral tunnel (LT) connection. A balanced hepatic flow distribution (HFD) to both lungs is essential to prevent pulmonary arteriovenous malformations and cyanosis. HFD is highly dependent on the local hemodynamics.

Objective

The effect of age-related changes in caval inflows on HFD was evaluated using cardiac MRI (CMR) data and patient-specific computational fluid dynamics (CFD) modeling.

Methods

SVC and IVC flow from 414 Fontan patients were collected to establish a relationship between SVC:IVC flow ratio and age. CFD modeling was performed in 60 (30 EC and 30 LT) patient models to quantify the HFD that corresponded to patient ages of 3, 8, and 15 years, respectively.

Results

SVC:IVC flow ratio inverted at ∼8 years of age, indicating a clear shift to lower body flow predominance. Our data showed that variation of HFD in response to age-related changes in caval inflows (SVC:IVC = 2,1, and 0.5 corresponded to ages 3, 8, and 15+ respectively) was not significant for EC but statistically significant for LT cohorts. For all three caval inflow ratios, a positive correlation existed between the IVC flow distribution to both the lungs and the HFD. However, as the SVC:IVC ratio changed from 2→0.5 (age 3→15+), the correlation's strength decreased from 0.87→0.64, due to potential flow perturbation as IVC flow momentum increased.

Conclusion

Our analysis provided quantitative insights into the impact of the changing caval inflows on Fontan's long-term HFD, highlighting the importance of including SVC:IVC variations over time to understand Fontan's long-term hemodynamics. These findings broaden our understanding of Fontan hemodynamics and patient outcomes.

Clinical Perspective

With improvement in standard of care and management of single ventricle patients with Fontan physiology, the population of adults with Fontan circulation is increasing. Consequently, there is a clinical need to comprehend the impact of patient growth on Fontan hemodynamics. Using CMR data, we were able to quantify the relationship between changing caval inflows and somatic growth. We then used patient-specific computational flow modeling to quantify how this relationship affected the distribution of long-term hepatic flow in extracardiac and lateral tunnel Fontan types. Our findings demonstrated the significance of including SVC:IVC changes over time in CFD modeling to learn more about the long-term hemodynamics of Fontan. Fontan surgical approaches are increasingly planned and optimized using computational flow modeling. For a patient undergoing a Fontan procedure, the workflow presented in this study that takes into account the variations in Caval inflows over time can aid in predicting the long-term hemodynamics in a planned Fontan pathway.

Passive performance evaluation and validation of a viscous impeller pump for subpulmonary fontan circulatory support

Patients with single ventricle defects undergoing the Fontan procedure eventually face Fontan failure. Long-term cavopulmonary assist devices using rotary pump technologies are currently being developed as a subpulmonary power source to prevent and treat Fontan failure. Low hydraulic resistance is a critical safety requirement in the event of pump failure (0 RPM) as a modest 2 mmHg cavopulmonary pressure drop can compromise patient hemodynamics. The goal of this study is therefore to assess the passive performance of a viscous impeller pump (VIP) we are developing for Fontan patients, and validate flow simulations against in-vitro data. Two different blade heights (1.09 mm vs 1.62 mm) and a blank housing model were tested using a mock circulatory loop (MCL) with cardiac output ranging from 3 to 11 L/min. Three-dimensional flow simulations were performed and compared against MCL data. In-silico and MCL results demonstrated a pressure drop of < 2 mmHg at a cardiac output of 7 L/min for both blade heights. There was good agreement between simulation and MCL results for pressure loss (mean difference - 0.23 mmHg 95% CI [0.24-0.71]). Compared to the blank housing model, low wall shear stress area and oscillatory shear index on the pump surface were low, and mean washout times were within 2 s. This study demonstrated the low resistance characteristic of current VIP designs in the failed condition that results in clinically acceptable minimal pressure loss without increased washout time as compared to a blank housing model under normal cardiac output in Fontan 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.

Computational Fontan Analysis: Preserving Accuracy While Expediting Workflow

Background: Postoperative outcomes of the Fontan operation have been linked to geometry of the cavopulmonary pathway, including graft shape after implantation. Computational fluid dynamics (CFD) simulations are used to explore different surgical options. The objective of this study is to perform a systematic in vitro validation for investigating the accuracy and efficiency of CFD simulation to predict Fontan hemodynamics. Methods: CFD simulations were performed to measure indexed power loss (iPL) and hepatic flow distribution (HFD) in 10 patient-specific Fontan models, with varying mesh and numerical solvers. The results were compared with a novel in vitro flow loop setup with 3D printed Fontan models. A high-resolution differential pressure sensor was used to measure the pressure drop for validating iPL predictions. Microparticles with particle filtering system were used to measure HFD. The computational time was measured for a representative Fontan model with different mesh sizes and numerical solvers. Results: When compared to in vitro setup, variations in CFD mesh sizes had significant effect on HFD (P  =  .0002) but no significant impact on iPL (P  =  .069). Numerical solvers had no significant impact in both iPL (P  =  .50) and HFD (P  =  .55). A transient solver with 0.5 mm mesh size requires computational time 100 times more than a steady solver with 2.5 mm mesh size to generate similar results. Conclusions: The predictive value of CFD for Fontan planning can be validated against an in vitro flow loop. The prediction accuracy can be affected by the mesh size, model shape complexity, and flow competition.

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.

Parametric investigation of an injection-jet self-powered Fontan circulation

Approximately \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/2500$$\end{document}1/2500 babies are born with only one functioning ventricle and the Fontan is the third and, ideally final staged palliative operation for these patients. This altered circulation is prone to failure with survival rates below \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50\%$$\end{document}50% into adulthood. Chronically elevated inferior vena cava (IVC) pressure is implicated as one cause of the mortality and morbidity in this population. An injection jet shunt (IJS) drawing blood-flow directly from the aortic arch to significantly lower IVC pressure is proposed. A computer-generated 3D model of a 2–4 year old patient with a fenestrated Fontan and a cardiac output of 2.3 L/min was generated. The detailed 3D pulsatile hemodynamics are resolved in a zero-dimensional lumped parameter network tightly-coupled to a 3D computational fluid dynamics model accounting for non-Newtonian blood rheology and resolving turbulence using large eddy simulation. IVC pressure and systemic oxygen saturation were tracked for various IJS-assisted Fontan configurations, altering design parameters such as shunt and fenestration diameters and locations. A baseline “failing” Fontan with a 4 mm fenestration was tuned to have an elevated IVC pressure (+ 17.8 mmHg). Enlargement of the fenestration to 8 mm resulted in a 3 mmHg IVC pressure drop but an unacceptable reduction in systemic oxygen saturation below 80%. Addition of an IJS with a 2 mm nozzle and minor volume load to the ventricle improved the IVC pressure drop to 3.2 mmHg while increasing systemic oxygen saturation above 80%. The salutary effects of the IJS to effectively lower IVC pressure while retaining acceptable levels of oxygen saturation are successfully demonstrated.

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.

An Efficient Assisted Bidirectional Glenn Design With Lowered Superior Vena Cava Pressure for Stage-One Single Ventricle Patients

Recently, the assisted bidirectional Glenn (ABG) procedure has been proposed as an alternative to the modified Blalock-Taussig shunt (mBTS) operation for neonates with single-ventricle physiology. Despite success in reducing heart workload and maintaining sufficient pulmonary flow, the ABG also raised the superior vena cava (SVC) pressure to a level that may not be tolerated by infants. To lower the SVC pressure, we propose a modified version of the ABG (mABG), in which a shunt with a slit-shaped nozzle exit is inserted at the junction of the right and left brachiocephalic veins. The proposed operation is compared against the ABG, the mBTS, and the bidirectional Glenn (BDG) operations using closed-loop multiscale simulations. Both normal (2.3 Wood units-m2) and high (7 Wood units-m2) pulmonary vascular resistance (PVR) values are simulated. The mABG provides the highest oxygen saturation, oxygen delivery, and pulmonary flow rate in comparison to the BDG and the ABG. At normal PVR, the SVC pressure is significantly reduced below that of the ABG and the BDG (mABG: 4; ABG: 8; BDG: 6; mBTS: 3 mmHg). However, the SVC pressure remains high at high PVR (mABG: 15; ABG: 16; BDG: 12; mBTS: 3 mmHg), motivating an optimization study to improve the ABG hemodynamics efficiency for a broader range of conditions in the future. Overall, the mABG preserves all advantages of the original ABG procedure while reducing the SVC pressure at normal PVR.

Engineering Perspective on Cardiovascular Simulations of Fontan Hemodynamics: Where Do We Stand with a Look Towards Clinical Application

BACKGROUND

Cardiovascular simulations for patients with single ventricles undergoing the Fontan procedure can assess patient-specific hemodynamics, explore surgical advances, and develop personalized strategies for surgery and patient care. These simulations have not yet been broadly accepted as a routine clinical tool owing to a number of limitations. Numerous approaches have been explored to seek innovative solutions for improving methodologies and eliminating these limitations.

PURPOSE

This article first reviews the current state of cardiovascular simulations of Fontan hemodynamics. Then, it will discuss the technical progress of Fontan simulations with the emphasis of its clinical impact, noting that substantial improvements have been made in the considerations of patient-specific anatomy, flow, and blood rheology. The article concludes with insights into potential future directions involving clinical validation, uncertainty quantification, and computational efficiency. The advancements in these aspects could promote the clinical usage of Fontan simulations, facilitating its integration into routine clinical practice.

Fluid-Structure Interaction Simulation of an Intra-Atrial Fontan Connection

Simple Summary

A fluid-structure interaction (FSI) simulation of an intra-atrial Fontan connection was performed. Power loss and pressure drop results fluctuated less during the FSI simulation than during the simulation run with rigid walls, but there were no observable differences in time-averaged pressure drop, connection power loss or hepatic flow distribution. These results suggested that employing a rigid wall is a reasonable assumption when evaluating time-averaged hemodynamic quantities of the Fontan connection under resting breath-held flow conditions.

Abstract

Total cavopulmonary connection (TCPC) hemodynamics has been hypothesized to be associated with long-term complications in single ventricle heart defect patients. Rigid wall assumption has been commonly used when evaluating TCPC hemodynamics using computational fluid dynamics (CFD) simulation. Previous study has evaluated impact of wall compliance on extra-cardiac TCPC hemodynamics using fluid-structure interaction (FSI) simulation. However, the impact of ignoring wall compliance on the presumably more compliant intra-atrial TCPC hemodynamics is not fully understood. To narrow this knowledge gap, this study aims to investigate impact of wall compliance on an intra-atrial TCPC hemodynamics. A patient-specific model of an intra-atrial TCPC is simulated with an FSI model. Patient-specific 3D TCPC anatomies were reconstructed from transverse cardiovascular magnetic resonance images. Patient-specific vessel flow rate from phase-contrast magnetic resonance imaging (MRI) at the Fontan pathway and the superior vena cava under resting condition were prescribed at the inlets. From the FSI simulation, the degree of wall deformation was compared with in vivo wall deformation from phase-contrast MRI data as validation of the FSI model. Then, TCPC flow structure, power loss and hepatic flow distribution (HFD) were compared between rigid wall and FSI simulation. There were differences in instantaneous pressure drop, power loss and HFD between rigid wall and FSI simulations, but no difference in the time-averaged quantities. The findings of this study support the use of a rigid wall assumption on evaluation of time-averaged intra-atrial TCPC hemodynamic metric under resting breath-held condition.

The impact of compliance on Stage 2 uni-ventricular heart circulation: An experimental assessment of the Bidirectional Glenn

The Bidirectional Glenn (BDG) or cavopulmonary connection is typically undertaken to volume unload the single ventricle in an effort to preserve ventricular and atrioventricular valve function. The geometry of this surgical palliation has been shown to influence the fluid energy loss as well as the distribution of flow that enters through the superior vena cava. In-vitro and in-silico studies to date have been performed on rigid wall models, while this investigation looks at the impact of flexible thin walled models versus rigid walls. Rigid and compliant models of two patient-specific Glenn geometries were fabricated and tested under various flow conditions, within a biosimulator capable of replicating patient specific flow conditions. It was found that the compliant models exhibit greater levels of energy loss compared to the rigid models. Along with these findings greater levels of turbulence was found in both compliant models compared to their rigid counterparts under ultrasound examinations. This shows that vessel compliance has a significant impact on the hemodynamics within hypoplastic left heart syndrome.

Comparison of Fontan Surgical Options for Patients with Apicocaval Juxtaposition

Apicocaval juxtaposition (ACJ) is a rare form of viscerocardiac malpositions in association with single-ventricle congenital heart defects. The Fontan surgery is the common palliation, and possible surgical options include ipsilateral, contralateral, and intra-atrial conduits. Concerns include lower hemodynamic performances or risks of conduit compression by the cardiac mass. This study investigates the hemodynamics and clinical outcomes of ACJ patients and potential surgical improvements. Ten consecutive ACJ patients were included, along with a reference cohort of ten non-ACJ patients. Magnetic resonance images were acquired at 6 ± 0.6 year follow-up for anatomical analysis and hemodynamic assessments using computational fluid dynamics. Metrics of interest are deformation index (DI), indexed power loss (iPL), and hepatic flow distribution (HFDoff). A "virtual" surgery was performed to explore potential hemodynamic improvements using a straightened conduit. DI for ACJ patients fell within the DI range of non-ACJ patients. Contralateral conduits had insignificantly higher iPL (0.070 [0.032,0.137]) than ipsilateral conduits (0.041 [0.013,0.095]) and non-ACJ conduits (0.034 [0.011,0.061]). HFDoff was similar for the ipsilateral (21 [12,35]), contralateral (26 [7,41]), and non-ACJ Fontan conduits (17 [0,48]). Virtual surgery demonstrated that a straightened conduit reduced HFDoff and iPL for the contralateral and ipsilateral conduits, potentially leading to improved clinical outcomes. In this limited sample, the hemodynamic performance of ACJ patients was not significantly different from their non-ACJ counterparts. The use of a straightened conduit option could potentially improve patient outcomes. Additionally, the fear of significant compression of conduits for ACJ patients was unsupported.

Non-Newtonian Effects on Patient-Specific Modeling of Fontan Hemodynamics

The Fontan procedure is a common palliative surgery for congenital single ventricle patients. In silico and in vitro patient-specific modeling approaches are widely utilized to investigate potential improvements of Fontan hemodynamics that are related to long-term complications. However, there is a lack of consensus regarding the use of non-Newtonian rheology, warranting a systematic investigation. This study conducted in silico patient-specific modeling for twelve Fontan patients, using a Newtonian and a non-Newtonian model for each patient. Differences were quantified by examining clinically relevant metrics: indexed power loss (iPL), indexed viscous dissipation rate (iVDR), hepatic flow distribution (HFD), and regions of low wall shear stress (A_WSS). Four sets of "non-Newtonian importance factors" were calculated to explore their effectiveness in identifying the non-Newtonian effect. No statistical differences were observed in iPL, iVDR, and HFD between the two models at the population-level, but large inter-patient variations exist. Significant differences were detected regarding A_WSS, and its correlations with non-Newtonian importance factors were discussed. Additionally, simulations using the non-Newtonian model were computationally faster than those using the Newtonian model. These findings distinguish good importance factors for identifying non-Newtonian rheology and encourage the use of a non-Newtonian model to assess Fontan hemodynamics.

Hemodynamic Effects of Additional Pulmonary Blood Flow on Glenn and Fontan Circulation

PURPOSE

Additional pulmonary blood flow (APBF) can provide better pulsating blood flow and systemic arterial oxygen saturation, while low blood pulsation and low oxygen saturation are defects of the Fontan and Glenn procedure. Studying the hemodynamic effect of APBF is beneficial for clinical decisions. This study aimed to explore the effect on particle washout, as well as the differences among the sensitivities of both different hemodynamic parameters and different procedures to APBF.

METHODS

The patient-specific clinical datasets of a patient who underwent bilateral bidirectional Glenn (BBDG) with APBF were enrolled in this study, and using these datasets, Glenn- and Fontan-type artery models were reconstructed. A series of parameters, including the total caval flow pulsatility index (TCPI), indexed energy loss (iPL), wall shear stress (WSS), systemic arterial oxygen saturation (Sat_art), particle washout time (WOT), pressure in the right superior vena cava (P_RSVC), pulmonary flow distribution (PFD) and hepatic flow distribution (HFD), were computed from computational fluid dynamic (CFD) simulation to evaluate the hemodynamic effect of APBF.

RESULTS

The result showed that APBF led to better iPL and Sat_art but worse P_RSVC and heart load accompanied by a great impact on HFD, making hepatic flow easier to perfuse the side without MPA and APBF. The increase in the APBF rate also effectively results in larger flow pulsation, region velocity, and wall shear stress and lower WOT, and this effect may be more effective for patients with persistent left superior vena cava (PLSVC). However, APBF might have little effect on PFD. Furthermore, APBF might affect WOT, iPL and HFD more significantly than P_RSVC and has a greater improvement effect in patients with poorer iPL and WOT.

CONCLUSIONS

Moderate APBF is not only a measure to promote pulmonary artery growth and systemic arterial oxygen saturation but also an effective method against endothelial dysfunction and thrombosis. However, moderate APBF is patient-specific and should be determined based on hemodynamic preference that leads to desired patient outcomes, and care should be taken to prevent P_RSVC and heart load from being too high as well as an imbalance in HFD.

Role of surgeon intuition and computer-aided design in Fontan optimization: A computational fluid dynamics simulation study

OBJECTIVE

Customized Fontan designs, generated by computer-aided design (CAD) and optimized by computational fluid dynamics simulations, can lead to novel, patient-specific Fontan conduits unconstrained by off-the-shelf grafts. The relative contributions of both surgical expertise and CAD to Fontan optimization have not been addressed. In this study, we assessed hemodynamic performance of Fontans designed by both surgeon's unconstrained modeling (SUM) and by CAD.

METHODS

Ten cardiac magnetic resonance imaging datasets were used to create 3-dimensional (3D) models of Fontans. Baseline computational fluid dynamics simulations assessed Fontan indexed power loss (iPL), hepatic flow distribution, and percentage of conduit surface area with abnormally low wall shear stress for venous flow (<1 dyne/cm²). Fontans not meeting thresholds were redesigned using 2 methods: SUM (ie, original venous anatomy without the Fontan was 3D printed and sent to surgeon for Fontan redesign with clay modeling) and CAD (ie, the same 3D geometry was sent to engineers for iterative Fontan redesign guided by computational fluid dynamics). Both groups were blinded to each other's results.

RESULTS

Eight Fontans were redesigned by SUM and CAD methods. Both SUM and CAD redesigns met iPL thresholds. SUM had lower iPL, whereas CAD demonstrated balanced hepatic flow distribution and lower wall shear stress percentage. Wall shear stress percentage shared an inverse relationship with iPL, preventing oversized Fontan designs.

CONCLUSIONS

Customized Fontan conduits with low iPL can be created by either a surgeon or CAD. CAD can also improve hepatic flow distribution and prevent oversized Fontan designs. Future studies should investigate workflows that combine SUM and CAD to optimize Fontan conduits.

Computational Fluid Dynamics of Vascular Disease in Animal Models

Recent applications of computational fluid dynamics (CFD) applied to the cardiovascular system have demonstrated its power in investigating the impact of hemodynamics on disease initiation, progression, and treatment outcomes. Flow metrics such as pressure distributions, wall shear stresses (WSS), and blood velocity profiles can be quantified to provide insight into observed pathologies, assist with surgical planning, or even predict disease progression. While numerous studies have performed simulations on clinical human patient data, it often lacks prediagnosis information and can be subject to large intersubject variability, limiting the generalizability of findings. Thus, animal models are often used to identify and manipulate specific factors contributing to vascular disease because they provide a more controlled environment. In this review, we explore the use of CFD in animal models in recent studies to investigate the initiating mechanisms, progression, and intervention effects of various vascular diseases. The first section provides a brief overview of the CFD theory and tools that are commonly used to study blood flow. The following sections are separated by anatomical region, with the abdominal, thoracic, and cerebral areas specifically highlighted. We discuss the associated benefits and obstacles to performing CFD modeling in each location. Finally, we highlight animal CFD studies focusing on common surgical treatments, including arteriovenous fistulas (AVF) and pulmonary artery grafts. The studies included in this review demonstrate the value of combining CFD with animal imaging and should encourage further research to optimize and expand upon these techniques for the study of vascular disease.

Modeling Physiological Flow Variation in Fontan Models with 4d Flow Mri, Particle Image Velocimetry, and Arterial Spin Labeling

The Fontan procedure is a successful palliation for single ventricle defect. Yet, a number of complications still occur in Fontan patients due to abnormal blood flow dynamics, necessitating improved flow analysis and treatment methods. Phase-contrast magnetic resonance imaging (MRI) has emerged as a suitable method for such flow analysis. However, limitations on altering physiological blood flow conditions in the patient while in the MRI bore inhibit experimental investigation of a variety of factors that contribute to impaired cardiovascular health in these patients. Furthermore, resolution and flow regime limitations in phase contrast MRI pose a challenge for accurate and consistent flow characterization. In this study, patient-specific physical models were created based on nine Fontan geometries and MRI experiments mimicking low and high flow conditions, as well as steady and pulsatile flow, were conducted. Additionally, an optically transparent Fontan model was created for flow analyses using a particle image velocimetry (PIV) system, arterial spin labeling (ASL), and four-dimensional (4D) flow MRI. Differences, though non-statistically significant, were observed between flow conditions and between patient-specific models. Large between-model variation supported the need for further improvement for patient-specific modeling on each unique Fontan anatomical configuration. Furthermore, high resolution PIV and flow tracking ASL data provided flow information that was not obtainable with 4D flow MRI alone.

Influence of coupled hemodynamics-arterial wall interaction on compliance in a realistic pulmonary artery with variable intravascular wall properties

Pulmonary hypertension is characterized by elevation of pulmonary artery (PA) pressure (p) and structural remodeling of the PA wall, leading to reduction in arterial compliance (c). As a step towards improving diagnosis of pulmonary disease, we use the PA branch geometry (main pulmonary artery (MPA) branching into left (LPA) and right (RPA) pulmonary arteries) obtained from MRI in conjunction with an inverse algorithm to obtain the pre-stress level in the artery walls. Next, a coupled blood-wall interaction (BWI) calculation provides hemodynamic information as well as compliance of the PA walls. We show that the computed load-free geometry from the inverse algorithm exhibits a 27.8% lower inner diameter (d) and 18.5% lower outer d compared to the in vivo geometry from MRI. Further, the mean p computed from the BWI computation in the main PA (p_MPA-n) is within 4% of the mean p_MPA-e (n-numerical; e-experimental). Also, the mean Q computed in the left PA (Q_LPA-n) is within 10% of the mean Q_LPA-e. Finally, the compliance c_MPA-n is computed to be 27% lower than c_MPA-e, while the c_LPA-n is computed to be 20.4% lower than c_LPA-e. Importantly, the PA shows significant intra-vascular variation in compliance, with the MPA showing higher overall compliance compared to the LPA (3.5-4 times).

Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics

Computational fluid dynamic (CFD) simulations are widely utilized to assess Fontan hemodynamics that are related to long-term complications. No previous studies have systemically investigated the effects of using different inlet velocity profiles in Fontan simulations. This study implements real, patient-specific velocity profiles for numerical assessment of Fontan hemodynamics using CFD simulations. Four additional, artificial velocity profiles were used for comparison: (1) flat, (2) parabolic, (3) Womersley, and (4) parabolic with inlet extensions [to develop flow before entering the total cavopulmonary connection (TCPC)]. The differences arising from the five velocity profiles, as well as discrepancies between the real and each of the artificial velocity profiles, were quantified by examining clinically important metrics in TCPC hemodynamics: power loss (PL), viscous dissipation rate (VDR), hepatic flow distribution, and regions of low wall shear stress. Statistically significant differences were observed in PL and VDR between simulations using real and flat velocity profiles, but differences between those using real velocity profiles and the other three artificial profiles did not reach statistical significance. These conclusions suggest that the artificial velocity profiles (2)-(4) are acceptable surrogates for real velocity profiles in Fontan simulations, but parabolic profiles are recommended because of their low computational demands and prevalent applicability.

The effect of respiration-driven flow waveforms on hemodynamic metrics used in Fontan surgical planning

OBJECTIVE

Poor total cavopulmonary connection (TCPC) hemodynamics have been hypothesized to be associated with long-term complications in Fontan patients. Image-based Fontan surgical planning has shown great potential as a clinical tool because it can pre-operatively evaluate patient-specific hemodynamics. Current surgical planning paradigms commonly utilize cardiac-gated phase contrast magnetic resonance (MR) imaging to acquire vessel flows. These acquisitions are often taken under breath-held (BH) conditions and ignore the effect of respiration on blood flow waveforms. This study investigates the effect of respiration-driven flow waveforms on patient-specific hemodynamics using real-time MR acquisitions.

METHODS

Patient-specific TCPCs were reconstructed from cardiovascular MR images. Real-time phase contrast MR images were acquired under both free-breathing (FB) and breath-held conditions for 9 patients. Numerical simulations were employed to assess flow structures and hemodynamics used in Fontan surgical planning including hepatic flow distribution (HFD) and indexed power loss (iPL), which were then compared between FB and BH conditions.

RESULTS

Differences in TCPC flow structures between FB and BH conditions were observed throughout the respiratory cycle. However, the average differences (BH - FB values for each patient, which are then averaged) in iPL and HFD between these conditions were 0.002 ± 0.011 (p = 0.40) and 1 ± 3% (p = 0.28), respectively, indicating no significant difference in clinically important hemodynamic metrics.

CONCLUSIONS

Respiration affects blood flow waveforms and flow structures, but might not significantly influence the values of iPL or HFD. Therefore, breath-held MR acquisition can be adequate for Fontan surgical planning when focusing on iPL and HFD.

A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction

We develop a unified continuum modeling framework using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear elasticity. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-α method is applied for temporal discretization. A segregated algorithm for the nonlinear solver, based on the original idea introduced in [107], is carefully analyzed. Second, we apply the new formulation to construct a novel unified formulation for fluid-solid coupled problems. The variational multiscale formulation is utilized for spatial discretization in both fluid and solid subdomains. The generalized-α method is applied for the whole continuum body, and optimal high-frequency dissipation is achieved in both fluid and solid subproblems. A new predictor multi-corrector algorithm is developed based on the segregated algorithm. The efficacy of the new formulations is examined in several benchmark problems. The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Computational Investigation of a Self-Powered Fontan Circulation

Children born with anatomic or functional "single ventricle" must progress through two or more major operations to sustain life. This management sequence culminates in the total cavopulmonary connection, or "Fontan" operation. A consequence of the "Fontan circulation", however, is elevated central venous pressure and inadequate ventricular preload, which contribute to continued morbidity. We propose a solution to these problems by increasing pulmonary blood flow using an "injection jet" (IJS) in which the source of blood flow and energy is the ventricle itself. The IJS has the unique property of lowering venous pressure while enhancing pulmonary blood flow and ventricular preload. We report preliminary results of an analysis of this circulation using a tightly-coupled, multi-scale computational fluid dynamics model. Our calculations show that, constraining the excess volume load to the ventricle at 50% (pulmonary to systemic flow ratio of 1.5), an optimally configured IJS can lower venous pressure by 3 mmHg while increasing systemic oxygen delivery. Even this small decrease in venous pressure may have substantial clinical impact on the Fontan patient. These findings support the potential for a straightforward surgical modification to decrease venous pressure, and perhaps improve clinical outcome in selected patients.

Numerical Investigation of the Effect of Additional Pulmonary Blood Flow on Patient-Specific Bilateral Bidirectional Glenn Hemodynamics

The effect of additional pulmonary blood flow (APBF) on the hemodynamics of bilateral bidirectional Glenn (BBDG) connection was marginally discussed in previous studies. This study assessed this effect using patient-specific numerical simulation. A 15-year-old female patient who underwent BBDG was enrolled in this study. Patient-specific anatomy, flow waveforms, and pressure tracings were obtained using computed tomography, Doppler ultrasound technology, and catheterization, respectively. Computational fluid dynamic simulations were performed to assess flow field and derived hemodynamic metrics of the BBDG connection with various APBF. APBF showed noticeable effects on the hemodynamics of the BBDG connection. It suppressed flow mixing in the connection, which resulted in a more antegrade flow structure. Also, as the APBF rate increases, both power loss and reflux in superior venae cavae (SVCs) monotonically increases while the flow ratio of the right to the left pulmonary artery (RPA/LPA) monotonically decreases. However, a non-monotonic relationship was observed between the APBF rate and indexed power loss. A high APBF rate may result in a good flow ratio of RPA/LPA but with the side effect of bad power loss and remarkable reflux in SVCs, and vice versa. A moderate APBF rate could be favourable because it leads to an optimal indexed power loss and achieves the acceptable flow ratio of RPA/LPA without causing severe power loss and reflux in SVCs. These findings suggest that patient-specific numerical simulation should be used to assist clinicians in determining an appropriate APBF rate based on desired outcomes on a patient-specific basis.

The Advantages of Viscous Dissipation Rate over Simplified Power Loss as a Fontan Hemodynamic Metric

Flow efficiency through the Fontan connection is an important factor related to patient outcomes. It can be quantified using either a simplified power loss or a viscous dissipation rate metric. Though practically equivalent in simplified Fontan circulation models, these metrics are not identical. Investigation is needed to evaluate the advantages and disadvantages of these metrics for their use in in vivo or more physiologically-accurate Fontan modeling. Thus, simplified power loss and viscous dissipation rate are compared theoretically, computationally, and statistically in this study. Theoretical analysis was employed to assess the assumptions made for each metric and its clinical calculability. Computational simulations were then performed to obtain these two metrics. The results showed that apparent simplified power loss was always greater than the viscous dissipation rate for each patient. This discrepancy can be attributed to the assumptions derived in theoretical analysis. Their effects were also deliberately quantified in this study. Furthermore, statistical analysis was conducted to assess the correlation between the two metrics. Viscous dissipation rate and its indexed quantity show significant, strong, linear correlation to simplified power loss and its indexed quantity (p < 0.001, r > 0.99) under certain assumptions. In conclusion, viscous dissipation rate was found to be more advantageous than simplified power loss as a hemodynamic metric because of its lack of limiting assumptions and calculability in the clinic. Moreover, in addition to providing a time-averaged bulk measurement like simplified power loss, viscous dissipation rate has spatial distribution contours and time-resolved values that may provide additional clinical insight. Finally, viscous dissipation rate could maintain the relationship between Fontan connection flow efficiency and patient outcomes found in previous studies. Consequently, future Fontan hemodynamic studies should calculate both simplified power loss and viscous dissipation rate to maintain ties to previous studies, but also provide the most accurate measure of flow efficiency. Additional attention should be paid to the assumptions required for each metric.

A method to quantify mechanobiologic forces during zebrafish cardiac development using 4-D light sheet imaging and computational modeling

Blood flow and mechanical forces in the ventricle are implicated in cardiac development and trabeculation. However, the mechanisms of mechanotransduction remain elusive. This is due in part to the challenges associated with accurately quantifying mechanical forces in the developing heart. We present a novel computational framework to simulate cardiac hemodynamics in developing zebrafish embryos by coupling 4-D light sheet imaging with a stabilized finite element flow solver, and extract time-dependent mechanical stimuli data. We employ deformable image registration methods to segment the motion of the ventricle from high resolution 4-D light sheet image data. This results in a robust and efficient workflow, as segmentation need only be performed at one cardiac phase, while wall position in the other cardiac phases is found by image registration. Ventricular hemodynamics are then quantified by numerically solving the Navier-Stokes equations in the moving wall domain with our validated flow solver. We demonstrate the applicability of the workflow in wild type zebrafish and three treated fish types that disrupt trabeculation: (a) chemical treatment using AG1478, an ErbB2 signaling inhibitor that inhibits proliferation and differentiation of cardiac trabeculation; (b) injection of gata1a morpholino oligomer (gata1aMO) suppressing hematopoiesis and resulting in attenuated trabeculation; (c) weak-atriumm58 mutant (wea) with inhibited atrial contraction leading to a highly undeveloped ventricle and poor cardiac function. Our simulations reveal elevated wall shear stress (WSS) in wild type and AG1478 compared to gata1aMO and wea. High oscillatory shear index (OSI) in the grooves between trabeculae, compared to lower values on the ridges, in the wild type suggest oscillatory forces as a possible regulatory mechanism of cardiac trabeculation development. The framework has broad applicability for future cardiac developmental studies focused on quantitatively investigating the role of hemodynamic forces and mechanotransduction during morphogenesis.

Experimental Study of Anisotropic Stress/Strain Relationships of Aortic and Pulmonary Artery Homografts and Synthetic Vascular Grafts

Homografts and synthetic grafts are used in surgery for congenital heart disease (CHD). Determining these materials' mechanical properties will aid in understanding tissue behavior when subjected to abnormal CHD hemodynamics. Homograft tissue samples from anterior/posterior aspects, of ascending/descending aorta (AA, DA), innominate artery (IA), left subclavian artery (LScA), left common carotid artery (LCCA), main/left/right pulmonary artery (MPA, LPA, RPA), and synthetic vascular grafts, were obtained in three orientations: circumferential, diagonal (45 deg relative to circumferential direction), and longitudinal. Samples were subjected to uniaxial tensile testing (UTT). True strain-Cauchy stress curves were individually fitted for each orientation to calibrate Fung model. Then, they were used to calibrate anisotropic Holzapfel–Gasser model (R2 > 0.95). Most samples demonstrated a nonlinear hyperelastic strain–stress response to UTT. Stiffness (measured by tangent modulus at different strains) in all orientations were compared and shown as contour plots. For each vessel segment at all strain levels, stiffness was not significantly different among aspects and orientations. For synthetic grafts, stiffness was significantly different among orientations (p < 0.042). Aorta is significantly stiffer than pulmonary artery at 10% strain, comparing all orientations, aspects, and regions (p = 0.0001). Synthetic grafts are significantly stiffer than aortic and pulmonary homografts at all strain levels (p < 0.046). Aortic, pulmonary artery, and synthetic grafts exhibit hyperelastic biomechanical behavior with anisotropic effect. Differences in mechanical properties among vascular grafts may affect native tissue behavior and ventricular/arterial mechanical coupling, and increase the risk of deformation due to abnormal CHD hemodynamics.

A Method for In Vitro TCPC Compliance Verification

The Fontan procedure is a common palliative intervention for sufferers of single ventricle congenital heart defects that results in an anastomosis of the venous return to the pulmonary arteries called the total cavopulmonary connection (TCPC). Local TCPC and global Fontan circulation hemodynamics are studied with in vitro circulatory models because of hemodynamic ties to Fontan patient long-term complications. The majority of in vitro studies, to date, employ a rigid TCPC model. Recently, a few studies have incorporated flexible TCPC models, but provide no justification for the model material properties. The method set forth in this study successfully utilizes patient-specific flow and pressure data from phase contrast magnetic resonance images (PCMRI) (n = 1) and retrospective pulse-pressure data from an age-matched patient cohort (n = 10) to verify the compliance of an in vitro TCPC model. These data were analyzed, and the target compliance was determined as 1.36 ± 0.78 mL/mm Hg. A method of in vitro compliance testing and computational simulations was employed to determine the in vitro flexible TCPC model material properties and then use those material properties to estimate the wall thickness necessary to match the patient-specific target compliance. The resulting in vitro TCPC model compliance was 1.37 ± 0.1 mL/mm Hg—a value within 1% of the patient-specific compliance. The presented method is useful to verify in vitro model accuracy of patient-specific TCPC compliance and thus improve patient-specific hemodynamic modeling.

Computational modeling and engineering in pediatric and congenital heart disease

PURPOSE OF REVIEW

Recent methodological advances in computational simulations are enabling increasingly realistic simulations of hemodynamics and physiology, driving increased clinical utility. We review recent developments in the use of computational simulations in pediatric and congenital heart disease, describe the clinical impact in modeling in single-ventricle patients, and provide an overview of emerging areas.

RECENT FINDINGS

Multiscale modeling combining patient-specific hemodynamics with reduced order (i.e., mathematically and computationally simplified) circulatory models has become the de-facto standard for modeling local hemodynamics and 'global' circulatory physiology. We review recent advances that have enabled faster solutions, discuss new methods (e.g., fluid structure interaction and uncertainty quantification), which lend realism both computationally and clinically to results, highlight novel computationally derived surgical methods for single-ventricle patients, and discuss areas in which modeling has begun to exert its influence including Kawasaki disease, fetal circulation, tetralogy of Fallot (and pulmonary tree), and circulatory support.

SUMMARY

Computational modeling is emerging as a crucial tool for clinical decision-making and evaluation of novel surgical methods and interventions in pediatric cardiology and beyond. Continued development of modeling methods, with an eye towards clinical needs, will enable clinical adoption in a wide range of pediatric and congenital heart diseases.

Patient-Specific Surgical Planning, Where Do We Stand? The Example of the Fontan Procedure

The Fontan surgery for single ventricle heart defects is a typical example of a clinical intervention in which patient-specific computational modeling can improve patient outcome: with the functional heterogeneity of the presenting patients, which precludes generic solutions, and the clear influence of the surgically-created Fontan connection on hemodynamics, it is acknowledged that individualized computational optimization of the post-operative hemodynamics can be of clinical value. A large body of literature has thus emerged seeking to provide clinically relevant answers and innovative solutions, with an increasing emphasis on patient-specific approaches. In this review we discuss the benefits and challenges of patient-specific simulations for the Fontan surgery, reviewing state of the art solutions and avenues for future development. We first discuss the clinical impact of patient-specific simulations, notably how they have contributed to our understanding of the link between Fontan hemodynamics and patient outcome. This is followed by a survey of methodologies for capturing patient-specific hemodynamics, with an emphasis on the challenges of defining patient-specific boundary conditions and their extension for prediction of post-operative outcome. We conclude with insights into potential future directions, noting that one of the most pressing issues might be the validation of the predictive capabilities of the developed framework.

An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves

In this paper, we develop a geometrically flexible technique for computational fluid-structure interaction (FSI). The motivating application is the simulation of tri-leaflet bioprosthetic heart valve function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including changes of topology. The proposed method directly analyzes a spline-based surface representation of the structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain. This places our method within an emerging class of computational techniques that aim to capture geometry on non-boundary-fitted analysis meshes. We introduce the term "immersogeometric analysis" to identify this paradigm. The framework starts with an augmented Lagrangian formulation for FSI that enforces kinematic constraints with a combination of Lagrange multipliers and penalty forces. For immersed volumetric objects, we formally eliminate the multiplier field by substituting a fluid-structure interface traction, arriving at Nitsche's method for enforcing Dirichlet boundary conditions on object surfaces. For immersed thin shell structures modeled geometrically as surfaces, the tractions from opposite sides cancel due to the continuity of the background fluid solution space, leaving a penalty method. Application to a bioprosthetic heart valve, where there is a large pressure jump across the leaflets, reveals shortcomings of the penalty approach. To counteract steep pressure gradients through the structure without the conditioning problems that accompany strong penalty forces, we resurrect the Lagrange multiplier field. Further, since the fluid discretization is not tailored to the structure geometry, there is a significant error in the approximation of pressure discontinuities across the shell. This error becomes especially troublesome in residual-based stabilized methods for incompressible flow, leading to problematic compressibility at practical levels of refinement. We modify existing stabilized methods to improve performance. To evaluate the accuracy of the proposed methods, we test them on benchmark problems and compare the results with those of established boundary-fitted techniques. Finally, we simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions, demonstrating the effectiveness of the proposed techniques in practical computations.

Simulations reveal adverse hemodynamics in patients with multiple systemic to pulmonary shunts

For newborns diagnosed with pulmonary atresia or severe pulmonary stenosis leading to insufficient pulmonary blood flow, cyanosis can be mitigated with placement of a modified Blalock-Taussig shunt (MBTS) between the innominate and pulmonary arteries. In some clinical scenarios, patients receive two systemic-to-pulmonary connections, either by leaving the patent ductus arteriosus (PDA) open or by adding an additional central shunt (CS) in conjunction with the MBTS. This practice has been motivated by the thinking that an additional source of pulmonary blood flow could beneficially increase pulmonary flow and provide the security of an alternate pathway in case of thrombosis. However, there have been clinical reports of premature shunt occlusion when more than one shunt is employed, leading to speculation that multiple shunts may in fact lead to unfavorable hemodynamics and increased mortality. In this study, we hypothesize that multiple shunts may lead to undesirable flow competition, resulting in increased residence time (RT) and elevated risk of thrombosis, as well as pulmonary overcirculation. Computational fluid dynamics-based multiscale simulations were performed to compare a range of shunt configurations and systematically quantify flow competition, pulmonary circulation, and other clinically relevant parameters. In total, 23 cases were evaluated by systematically changing the PDA/CS diameter, pulmonary vascular resistance (PVR), and MBTS position and compared by quantifying oxygen delivery (OD) to the systemic and coronary beds, wall shear stress (WSS), oscillatory shear index (OSI), WSS gradient (WSSG), and RT in the pulmonary artery (PA), and MBTS. Results showed that smaller PDA/CS diameters can lead to flow conditions consistent with increased thrombus formation due to flow competition in the PA, and larger PDA/CS diameters can lead to insufficient OD due to pulmonary hyperfusion. In the worst case scenario, it was found that multiple shunts can lead to a 160% increase in RT and a 10% decrease in OD. Based on the simulation results presented in this study, clinical outcomes for patients receiving multiple shunts should be critically investigated, as this practice appears to provide no benefit in terms of OD and may actually increase thrombotic risk.

The assisted bidirectional Glenn: a novel surgical approach for first-stage single-ventricle heart palliation

BACKGROUND

Outcomes after a modified Blalock-Taussig shunt (mBTS) in neonates with single-ventricle physiology remain unsatisfactory. However, initial palliation with a superior cavopulmonary connection, such as a bidirectional Glenn (BDG), is discouraged, owing to potential for inadequate pulmonary blood flow (PBF). We tested the feasibility of a novel surgical approach, adopting the engineering concept of an ejector pump, whereby the flow in the BDG is "assisted" by injection of a high-energy flow stream from the systemic circulation.

METHODS

Realistic 3-dimensional models of the neonatal mBTS and BDG circulations were created. The "assisted" bidirectional Glenn (ABG) consisted of a shunt between the right innominate artery and the superior vena cava (SVC), with a 1.5-mm clip near the SVC anastomosis to create a Venturi effect. The 3 models were coupled to a validated hydraulic circulation model, and 2 pulmonary vascular resistance (PVR) values (7 and 2.3 Wood units) were simulated.

RESULTS

The ABG provided the highest systemic oxygen saturation and oxygen delivery at both PVR levels. In addition to achieving higher PBF than the BDG, the ABG produced a lower single-ventricular workload than mBTS. SVC pressure was highest in the ABG model (ABG: 15; Glenn: 11; mBTS: 3 mm Hg; PVR = 7 Wood units), but at low PVR, the SVC pressure was significantly lower (ABG: 8; Glenn: 6; mBTS: <3 mm Hg).

CONCLUSIONS

Adopting the principle of an ejector pump, with additional flow directed into the SVC in a BDG, the ABG appears to increase PBF with a modest increase in SVC and pulmonary arterial pressure. Although multiscale modeling results demonstrate the conceptual feasibility of the ABG circulation, further technical refinement and investigations are necessary, especially in an appropriate animal model.

Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease

Kawasaki disease (KD) is the leading cause of acquired heart disease in children and can result in life-threatening coronary artery aneurysms in up to 25 % of patients. These aneurysms put patients at risk of thrombus formation, myocardial infarction, and sudden death. Clinicians must therefore decide which patients should be treated with anticoagulant medication, and/or surgical or percutaneous intervention. Current recommendations regarding initiation of anticoagulant therapy are based on anatomy alone with historical data suggesting that patients with aneurysms [Formula: see text]8 mm are at greatest risk of thrombosis. Given the multitude of variables that influence thrombus formation, we postulated that hemodynamic data derived from patient-specific simulations would more accurately predict risk of thrombosis than maximum diameter alone. Patient-specific blood flow simulations were performed on five KD patients with aneurysms and one KD patient with normal coronary arteries. Key hemodynamic and geometric parameters, including wall shear stress, particle residence time, and shape indices, were extracted from the models and simulations and compared with clinical outcomes. Preliminary fluid structure interaction simulations with radial expansion were performed, revealing modest differences in wall shear stress compared to the rigid wall case. Simulations provide compelling evidence that hemodynamic parameters may be a more accurate predictor of thrombotic risk than aneurysm diameter alone and motivate the need for follow-up studies with a larger cohort. These results suggest that a clinical index incorporating hemodynamic information be used in the future to select patients for anticoagulant therapy.

Computational fluid dynamics in Fontan patients to evaluate power loss during simulated exercise

OBJECTIVE

Exercise intolerance is common in total cavopulmonary connection (TCPC) patients. It has been suggested that power loss (Ploss) inside the TCPC plays a role in reduced exercise performance. Our objective is to establish the role of Ploss inside the TCPC during increased flow, simulating exercise in a patient-specific way.

METHODS

Cardiac MRI (CMR) was used to obtain flow rates from the caval veins during rest and increased flow, simulating exercise with dobutamine. A 3D reconstruction of the TCPC was created using CMR data. Computational fluid dynamics (CFD) simulations were performed to calculate Ploss inside the TCPC structure for rest and stress conditions. To reflect the flow distribution during exercise, a condition where inferior caval vein (IVC) flow was increased twofold compared with rest was added. 29 TCPC patients (15 intra-atrial lateral tunnel (ILT) and 14 extracardiac conduit (ECC)) were included.

RESULTS

Mean Ploss at rest was 1.36 ± 0.94 (ILT) and 3.20 ± 1.26 (ECC) mW/m(2) (p<0.001), 2.84 ±1.95 (ILT) and 8.41 ± 3.77 (ECC) mW/m(2) (p<0.001) during dobutamine and 5.21 ± 3.50 (ILT) and 15.28 ± 8.30 (ECC) mW/m(2) (p=0.001) with twofold IVC flow. The correlation between cardiac index and Ploss was exponential (ILT: R(2)=0.811, p<0.001; ECC: R(2)=0.690, p<0.001).

CONCLUSIONS

Ploss inside the TCPC structure is limited but increases with simulated exercise. This relates to the anatomy of TCPC and the surgical technique used. In all flow conditions, ILT patients have lower Ploss than ECC patients. We did not find a relationship between Ploss and exercise capacity.

Flow-induced ATP release in patient-specific arterial geometries--a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.

Simulation based planning of surgical interventions in pediatric cardiology

Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.

Hemodynamic effects of implanting a unidirectional valve in the inferior vena cava of the Fontan circulation pathway: an in vitro investigation

The Fontan surgical procedure used for treating patients with single ventricle congenital heart disorders results in a total cavopulmonary connection (TCPC) of the vena cavae to the pulmonary arteries (PAs). Sluggish TCPC flow and elevated hepatic venous pressures are commonly observed in this altered physiology, which in turn can lead to long-term complications including liver congestion and cirrhosis. The hypothesis of this study is that placement of a unidirectional valve within the inferior vena cava (IVC) will improve hemodynamics of the Fontan circulation by preventing retrograde flow and lowering hepatic venous pressure. An in vitro experimental setup consisting of an idealized TCPC model with flexible walls was used for investigation, and a bovine venous valve was inserted in the IVC below the TCPC. Pressure fluctuations were introduced in the flow through the model to simulate venous pulsatility. Hemodynamics of baseline and valve-implanted conditions were compared across total caval flows ranging from 1.0 to 2.5 l/min with varying caval flow distributions. The results indicated that valve closure occurred for 15-20% of the total cycle, with consequent reduction in the upstream hepatic venous pressure by 5 to 10 mmHg. Energy loss (EL) through the TCPC was lowered with valve implantation to 20-50% of baseline, occurring across all flow conditions considered with mean caval and PA pressures greater than 10 mmHg. The results of this in vitro modeling suggest that IVC valve placement has the potential to improve hemodynamics in the Fontan circulation by decreasing hepatic venous hypertension and EL.

Lagrangian analysis of hemodynamics data from FSI simulation

We present the computation of lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid-structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in lagrangian measures of the flow between deformable and rigid-vessel models was observed.

Treatment planning for a TCPC test case: a numerical investigation under rigid and moving wall assumptions

The hemodynamics in patients with total cavopulmonary connections (TCPC) is generally very complex and characterized by patient-to-patient variability. To better understand its effect on patients' outcome, CFD models are widely used, also to test and optimize surgical options before their implementation. These models often assume rigid geometries, despite the motion experienced by thoracic vessels that could influence the hemodynamics predictions. By improving their accuracy and expanding the range of simulated interventions, the benefit of treatment planning for patients is expected to increase. We simulate three types of intervention on a patient-specific 3D model, and compare their predicted outcome with baseline condition: a decrease in pulmonary vascular resistance obtainable with medications; a surgical revision of the connection design; the introduction of a fenestration in the TCPC wall. The simulations are performed both with rigid wall assumption and including patient-specific TCPC wall motion, reconstructed from a 4DMRI dataset. The results show the effect of each option on clinically important metrics and highlight the impact of patient-specific wall motion. The largest differences between rigid and moving wall models are observed in measures of energetic efficiency of TCPC as well as in hepatic flow distribution and transit time of seeded particles through the connection.

Predictive modeling of the virtual Hemi-Fontan operation for second stage single ventricle palliation: two patient-specific cases

Single ventricle hearts are congenital cardiovascular defects in which the heart has only one functional pumping chamber. The treatment for these conditions typically requires a three-staged operative process where Stage 1 is typically achieved by a shunt between the systemic and pulmonary arteries, and Stage 2 by connecting the superior venous return to the pulmonary circulation. Surgically, the Stage 2 circulation can be achieved through a procedure called the Hemi-Fontan, which reconstructs the right atrium and pulmonary artery to allow for an enlarged confluence with the superior vena cava. Based on pre-operative data obtained from two patients prior to Stage 2 surgery, we developed two patient-specific multi-scale computational models, each including the 3D geometrical model of the surgical junction constructed from magnetic resonance imaging, and a closed-loop systemic lumped-parameter network derived from clinical measurements. "Virtual" Hemi-Fontan surgery was performed on the 3D model with guidance from clinical surgeons, and a corresponding multi-scale simulation predicts the patient's post-operative hemodynamic and physiologic conditions. For each patient, a post-operative active scenario with an increase in the heart rate (HR) and a decrease in the pulmonary and systemic vascular resistance (PVR and SVR) was also performed. Results between the baseline and this "active" state were compared to evaluate the hemodynamic and physiologic implications of changing conditions. Simulation results revealed a characteristic swirling vortex in the Hemi-Fontan in both patients, with flow hugging the wall along the SVC to Hemi-Fontan confluence. One patient model had higher levels of swirling, recirculation, and flow stagnation. However, in both models, the power loss within the surgical junction was less than 13% of the total power loss in the pulmonary circulation, and less than 2% of the total ventricular power. This implies little impact of the surgical junction geometry on the SVC pressure, cardiac output, and other systemic parameters. In contrast, varying HR, PVR, and SVR led to significant changes in theses clinically relevant global parameters. Adopting a work-flow of customized virtual planning of the Hemi-Fontan procedure with patient-specific data, this study demonstrates the ability of multi-scale modeling to reproduce patient specific flow conditions under differing physiological states. Results demonstrate that the same operation performed in two different patients can lead to different hemodynamic characteristics, and that modeling can be used to uncover physiologic changes associated with different clinical conditions.

Modeling hemodynamics in vascular networks using a geometrical multiscale approach: numerical aspects

On the one hand the heterogeneity of the circulatory system requires the use of different models in its different compartments, featuring different assumptions on the spatial degrees of freedom. On the other hand, the mutual interactions between its compartments imply that these models should preferably not be considered separately. These requirements have led to the concept of geometrical multiscale modeling, where the main idea is to couple 3D models with reduced 1D and/or 0D models. As such detailed information on the flow field in a specific region of interest can be obtained while accounting for the global circulation. However, the combination of models with different mathematical features gives rise to many difficulties such as the assignment of boundary conditions at the interface between two models and the development of robust coupling algorithms, as the subproblems are usually solved in a partitioned way. This review aims to give an overview of the most important aspects concerning 3D-1D-0D coupled models. In addition, some applications are presented in order to illustrate the potentialities of these coupled models.