Computational Modeling of Right Ventricular Motion and Intracardiac Flow in Repaired Tetralogy of Fallot

Pressure boundary conditions for immersed-boundary methods

Immersed boundary methods have seen an enormous increase in popularity over the past two decades, especially for problems involving complex moving/deforming boundaries. In most cases, the boundary conditions on the immersed body are enforced via forcing functions in the momentum equations, which in the case of fractional step methods may be problematic due to: i) creation of slip-errors resulting from the lack of explicitly enforcing boundary conditions on the (pseudo-)pressure on the immersed body; ii) coupling of the solution in the fluid and solid domains via the Poisson equation. Examples of fractional-step formulations that simultaneously enforce velocity and pressure boundary conditions have also been developed, but in most cases the standard Poisson equation is replaced by a more complex system which requires expensive iterative solvers. In this work we propose a new formulation to enforce appropriate boundary conditions on the pseudo-pressure as part of a fractional-step approach. The overall treatment is inspired by the ghost-fluid method typically utilized in two-phase flows. The main advantage of the algorithm is that a standard Poisson equation is solved, with all the modifications needed to enforce the boundary conditions being incorporated within the right-hand side. As a result, fast solvers based on trigonometric transformations can be utilized. We demonstrate the accuracy and robustness of the formulation for a series of problems with increasing complexity.

Computational fluid dynamics in cardiac surgery and perfusion: A review

Cardiovascular diseases persist as a leading cause of mortality and morbidity, despite significant advances in diagnostic and surgical approaches. Computational Fluid Dynamics (CFD) represents a branch of fluid mechanics widely used in industrial engineering but is increasingly applied to the cardiovascular system. This review delves into the transformative potential for simulating cardiac surgery procedures and perfusion systems, providing an in-depth examination of the state-of-the-art in cardiovascular CFD modeling. The study first describes the rationale for CFD modeling and later focuses on the latest advances in heart valve surgery, transcatheter heart valve replacement, aortic aneurysms, and extracorporeal membrane oxygenation. The review underscores the role of CFD in better understanding physiopathology and its clinical relevance, as well as the profound impact of hemodynamic stimuli on patient outcomes. By integrating computational methods with advanced imaging techniques, CFD establishes a quantitative framework for understanding the intricacies of the cardiac field, providing valuable insights into disease progression and treatment strategies. As technology advances, the evolving synergy between computational simulations and clinical interventions is poised to revolutionize cardiovascular care. This collaboration sets the stage for more personalized and effective therapeutic strategies. With its potential to enhance our understanding of cardiac pathologies, CFD stands as a promising tool for improving patient outcomes in the dynamic landscape of cardiovascular medicine.

Tetralogy of Fallot regurgitation energetics and kinetics: an intracardiac flow analysis of the right ventricle using computational fluid dynamics

Repaired Tetralogy of Fallot (rTOF) patients suffer from pulmonary regurgitation and may require pulmonary valve replacement (PVR). Cardiac magnetic resonance imaging (cMRI) guides therapy, but conventional measurements do not quantify the intracardiac flow effects from pulmonary regurgitation or PVR. This study investigates intracardiac flow parameters of the right ventricle (RV) of rTOF by computational fluid dynamics (CFD). cMRI of rTOF patients and controls were retrospectively included. Feature-tracking captured RV endocardial contours from long-axis/short-axis cine. Ventricular motion was reconstructed via diffeomorphic mapping, serving as domain boundary for CFD simulations. Vorticity (1/s), viscous energy loss (ELoss, mJ/L) and turbulent kinetic energy (TKE, mJ/L) were quantified in RV outflow tract (RVOT) and RV inflow. These parameters were normalized against total RV kinetic energy (KE) and RV inflow vorticity to derive dimensionless metrics. Vorticity contours by Q-criterion were qualitatively compared. rTOF patients (n = 15) had mean regurgitant fraction 38 ± 12% and RV size 162 ± 35 mL/m2. Compared to controls (n = 12), rTOF had increased RVOT vorticity (142.6 ± 75.6/s vs. 40.4 ± 11.8/s, p < 0.0001), Eloss (55.6 ± 42.5 vs. 5.2 ± 4.4 mJ/L, p = 0.0004), and TKE (5.7 ± 5.9 vs. 0.84 ± 0.46 mJ/L, p = 0.0003). After PVR, there was decrease in normalized RVOT Eloss/TKE (p = 0.0009, p = 0.029) and increase in normalized tricuspid inflow vorticity/KE (p = 0.0136, p = 0.043), corresponding to reorganization of the "donut"-shaped tricuspid ring-vortex. The intracardiac flow in rTOF patients can be simulated to determine the impact of PVR and improve the clinical indications guided by cardiac imaging.

A Computational Model of Ventricular Dimensions and Hemodynamics in Growing Infants

Previous computer models have successfully predicted cardiac growth and remodeling in adults with pathologies. However, applying these models to infants is complicated by the fact that they also undergo normal, somatic cardiac growth and remodeling. Therefore, we designed a computational model to predict ventricular dimensions and hemodynamics in healthy, growing infants by modifying an adult canine left ventricular growth model. The heart chambers were modeled as time-varying elastances coupled to a circuit model of the circulation. Circulation parameters were allometrically scaled and adjusted for maturation to simulate birth through 3 yrs of age. Ventricular growth was driven by perturbations in myocyte strain. The model successfully matched clinical measurements of pressures, ventricular and atrial volumes, and ventricular thicknesses within two standard deviations of multiple infant studies. To test the model, we input 10th and 90th percentile infant weights. Predicted volumes and thicknesses decreased and increased within normal ranges and pressures were unchanged. When we simulated coarctation of the aorta, systemic blood pressure, left ventricular thickness, and left ventricular volume all increased, following trends in clinical data. Our model enables a greater understanding of somatic and pathological growth in infants with congenital heart defects. Its flexibility and computational efficiency when compared to models employing more complex geometries allow for rapid analysis of pathological mechanisms affecting cardiac growth and hemodynamics.

Intracardiac Flow Analysis of the Right Ventricle in Pediatric Patients With Repaired Tetralogy of Fallot Using a Novel Color Doppler Velocity Reconstruction

BACKGROUND

Repaired tetralogy of Fallot (RTOF) patients will develop right ventricular (RV) dysfunction from chronic pulmonary regurgitation (PR). Cardiac magnetic resonance sequences such as four-dimensional flow can demonstrate altered vorticity and flow energy loss (FEL); however, they are not as available as conventional echocardiography (echo). The study determined whether a novel, vendor-independent Doppler velocity reconstruction (DoVeR) could measure RV intracardiac flow in conventional echo of RTOF patients. The primary hypothesis was that DoVeR could detect increased vorticity and diastolic FEL in RTOF patients.

METHODS

Repaired tetralogy of Fallot patients with echo were retrospectively paired with age-/size-matched controls. Doppler velocity reconstruction employed the stream function-vorticity equation to approximate intracardiac flow fields from color Doppler. A velocity field of the right ventricle was reconstructed from the apical 4-chamber view. Vortex strength (VS, area integral of vorticity) and FEL were derived from DoVeR. Cardiac magnetic resonance and exercise stress parameters (performed within 1 year of echo) were collected for analysis.

RESULTS

Twenty RTOF patients and age-matched controls were included in the study. Mean regurgitant fraction was 40.5% ± 7.6%, and indexed RV end-diastolic volume was 158 ± 36 mL/m2. Repaired tetralogy of Fallot patients had higher total, mean diastolic, and peak diastolic VS (P = .0013, P = .0012, P = .0032, respectively) and higher total, mean diastolic, and peak diastolic body surface area-indexed FEL (P = .0016, P = .0022, P < .001, respectively). Peak diastolic indexed FEL and peak diastolic VS had weak-to-moderate negative correlation with RV ejection fraction (r = -0.52 [P = .019] and r = -0.49 [P = .030], respectively) and left ventricular ejection fraction (r = -0.47 [P = .034] and r = -0.64 [P = .002], respectively). Mean diastolic indexed FEL and VS had moderate-to-strong negative correlation with percent predicted maximal oxygen consumption (r = -0.69 [P = .012] and r = -0.75 [P = .006], respectively).

CONCLUSIONS

DoVeR can detect alterations to intracardiac flow in RTOF patients from conventional color Doppler imaging. Echo-based measures of diastolic VS and FEL correlated with ventricular function. DoVeR has the potential to provide serial evaluation of abnormal flow dynamics in RTOF patients.

Effect of pulmonary regurgitation on cardiac functions based on a human bi-ventricle model

BACKGROUND AND OBJECTIVE

Assessing the severity of pulmonary regurgitation (PR) and identifying optimal clinically relevant indicators for its treatment is crucial, yet standards for quantifying PR remain unclear in clinical practice. Computational modelling of the heart is in the process of providing valuable insights and information for cardiovascular physiology research. However, the advancements of finite element computational models have not been widely applied to simulate cardiac outputs in patients with PR. Furthermore, a computational model that incorporates both the left ventricle (LV) and right ventricle (RV) can be valuable in assessing the relationship between left and right ventricular morphometry and septal motion in PR patients. To enhance our understanding of the effect of PR on cardiac functions and mechanical behaviour, we developed a human bi-ventricle model to simulate five cases with varying degrees of PR severity.

METHODS

This bi-ventricle model was built using a patient-specific geometry and a widely used myofibre architecture. The myocardial material properties were described by a hyperelastic passive constitutive law and a modified time-varying elastance active tension model. To simulate realistic cardiac functions and the dysfunction of the pulmonary valve in PR disease cases, open-loop lumped parameter models representing systemic and pulmonary circulatory systems were designed.

RESULTS

In the baseline case, pressures in the aorta and main pulmonary artery and ejection fractions of both the LV and RV were within normal physiological ranges reported in the literature. The end-diastolic volume (EDV) of the RV under varying degrees of PR was comparable to the reported cardiac magnetic resonance imaging data. Moreover, RV dilation and interventricular septum motion from the baseline to the PR cases were clearly observed through the long-axis and short-axis views of the bi-ventricle geometry. The RV EDV in the severe PR case increased by 50.3% compared to the baseline case, while the LV EDV decreased by 18.1%. The motion of the interventricular septum was consistent with the literature. Furthermore, ejection fractions of both the LV and RV decreased as PR became severe, with LV ejection fraction decreasing from 60.5% at baseline to 56.3% in the severe case and RV ejection fraction decreasing from 51.8% to 46.8%. Additionally, the average myofibre stress of the RV wall at end-diastole significantly increased due to PR, from 2.7±12.1 kPa at baseline to 10.9±26.5 kPa in the severe case. The average myofibre stress of the LV wall at end-diastole increased from 3.7±18.1 kPa to 4.3±20.3 kPa.

CONCLUSIONS

This study established a foundation for the computational modelling of PR. The simulated results showed that severe PR leads to reduced cardiac outputs in both the LV and RV, clearly observable septum motion, and a significant increase in the average myofibre stress in the RV wall. These findings demonstrate the potential of the model for further exploration of PR.

Statistical shape modeling reveals the link between right ventricular shape, hemodynamic force, and myocardial function in patients with repaired tetralogy of Fallot

Patients with repaired tetralogy of Fallot (rTOF) can develop chronic pulmonary insufficiency (PI) with right ventricular (RV) dilation, progressive RV dysfunction, and decreased exercise capacity. Pulmonary valve replacement (PVR) can help reduce the amount of PI and RV dilation; however, optimal timing remains controversial; a better understanding of rTOF pathophysiology is of fundamental importance to inform clinical management of patients with rTOF and optimal timing of PVR. In this study, we hypothesize a tight interplay between RV shape, intracardiac biomechanics, and ventricular function in patients with rTOF. To explore this hypothesis and derive quantitative measures, we combined statistical shape modeling with physics-based analysis of in vivo 4D flow data in 36 patients with rTOF. Our study demonstrated for the first time a correlation between regional RV shape variations, hemodynamic forces (HDF), and clinical dysfunction in patients with rTOF. The main findings of this work include 1) general increase in RV size, due to both volume overload and physiological growth, correlated with decrease in strain magnitude in the respective directions, and with increased QRS; 2) regional PI-induced remodeling accounted for ∼10% of the shape variability of the population, and was associated with increased diastolic HDF along the diaphragm-to-right ventricular outflow tract (RVOT) direction, resulting in a net RV deformation along the same direction and decreased tricuspid annular plane systolic excursion (TAPSE); and 3) three shape modes independently correlated with systolic HDF and exercise capacity. Identification of patients based on the shape variations described in this study could help identify those at risk for irreversible dysfunction and guide optimal timing of PVR.NEW & NOTEWORTHY We combine statistical shape modeling with physics-based analysis of 4D flow data to elucidate the interplay between RV shape, hemodynamic forces, and clinical dysfunction in repaired tetralogy of Fallot. We are the first to show that ventricular remodeling is related to hemodynamic force magnitude and direction, global and regional functional parameters, and exercise intolerance. Identification of patients based on the shape variations described in this study could help identify those at risk for irreversible dysfunction.

Abnormal Diastolic Hemodynamic Forces: A Link Between Right Ventricular Wall Motion, Intracardiac Flow, and Pulmonary Regurgitation in Repaired Tetralogy of Fallot

Background and Objective

The effect of chronic pulmonary regurgitation (PR) on right ventricular (RV) dysfunction in repaired Tetralogy of Fallot (RTOF) patients is well recognized by cardiac magnetic resonance (CMR). However, the link between RV wall motion, intracardiac flow and PR has not been established. Hemodynamic force (HDF) represents the global force exchanged between intracardiac blood volume and endocardium, measurable by 4D flow or by a novel mathematical model of wall motion. In our study, we used this novel methodology to derive HDF in a cohort of RTOF patients, exclusively using routine CMR imaging.

Methods

RTOF patients and controls with CMR imaging were retrospectively included. Three-dimensional (3D) models of RV were segmented, including RV outflow tract (RVOT). Feature-tracking software (QStrain 2.0, Medis Medical Imaging Systems, Leiden, Netherlands) captured endocardial contours from long/short-axis cine and used to reconstruct RV wall motion. A global HDF vector was computed from the moving surface, then decomposed into amplitude/impulse of three directional components based on reference (Apical-to-Basal, Septal-to-Free Wall and Diaphragm-to-RVOT direction). HDF were compared and correlated against CMR and exercise stress test parameters. A subset of RTOF patients had 4D flow that was used to derive vorticity (for correlation) and HDF (for comparison against cine method).

Results

68 RTOF patients and 20 controls were included. RTOF patients had increased diastolic HDF amplitude in all three directions (p<0.05). PR% correlated with Diaphragm-RVOT HDF amplitude/impulse (r = 0.578, p<0.0001, r = 0.508, p < 0.0001, respectively). RV ejection fraction modestly correlated with global HDF amplitude (r = 0.2916, p = 0.031). VO2-max correlated with Septal-to-Free Wall HDF impulse (r = 0.536, p = 0.007). Diaphragm-to-RVOT HDF correlated with RVOT vorticity (r = 0.4997, p = 0.001). There was no significant measurement bias between Cine-derived HDF and 4D flow-derived HDF by Bland-Altman analysis.

Conclusion

RTOF patients have abnormal diastolic HDF that is correlated to PR, RV function, exercise capacity and vorticity. HDF can be derived from conventional cine, and is a potential link between RV wall motion and intracardiac flow from PR in RTOF patients.

Clinical Impact of Computational Heart Valve Models

This paper provides a review of engineering applications and computational methods used to analyze the dynamics of heart valve closures in healthy and diseased states. Computational methods are a cost-effective tool that can be used to evaluate the flow parameters of heart valves. Valve repair and replacement have long-term stability and biocompatibility issues, highlighting the need for a more robust method for resolving valvular disease. For example, while fluid-structure interaction analyses are still scarcely utilized to study aortic valves, computational fluid dynamics is used to assess the effect of different aortic valve morphologies on velocity profiles, flow patterns, helicity, wall shear stress, and oscillatory shear index in the thoracic aorta. It has been analyzed that computational flow dynamic analyses can be integrated with other methods to create a superior, more compatible method of understanding risk and compatibility.

Ventricular flow analysis and its association with exertional capacity in repaired tetralogy of Fallot: 4D flow cardiovascular magnetic resonance study

BACKGROUND

Four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) allows quantification of biventricular blood flow by flow components and kinetic energy (KE) analyses. However, it remains unclear whether 4D flow parameters can predict cardiopulmonary exercise testing (CPET) as a clinical outcome in repaired tetralogy of Fallot (rTOF). Current study aimed to (1) compare 4D flow CMR parameters in rTOF with age- and gender-matched healthy controls, (2) investigate associations of 4D flow parameters with functional and volumetric right ventricular (RV) remodelling markers, and CPET outcome.

METHODS

Sixty-three rTOF patients (14 paediatric, 49 adult; 30 ± 15 years; 29 M) and 63 age- and gender-matched healthy controls (14 paediatric, 49 adult; 31 ± 15 years) were prospectively recruited at four centers. All underwent cine and 4D flow CMR, and all adults performed standardized CPET same day or within one week of CMR. RV remodelling index was calculated as the ratio of RV to left ventricular (LV) end-diastolic volumes. Four flow components were analyzed: direct flow, retained inflow, delayed ejection flow and residual volume. Additionally, three phasic KE parameters normalized to end-diastolic volume (KEiEDV), were analyzed for both LV and RV: peak systolic, average systolic and peak E-wave.

RESULTS

In comparisons of rTOF vs. healthy controls, median LV retained inflow (18% vs. 16%, P = 0.005) and median peak E-wave KEiEDV (34.9 µJ/ml vs. 29.2 µJ/ml, P = 0.006) were higher in rTOF; median RV direct flow was lower in rTOF (25% vs. 35%, P < 0.001); median RV delayed ejection flow (21% vs. 17%, P < 0.001) and residual volume (39% vs. 31%, P < 0.001) were both greater in rTOF. RV KEiEDV parameters were all higher in rTOF than healthy controls (all P < 0.001). On multivariate analysis, RV direct flow was an independent predictor of RV function and CPET outcome. RV direct flow and RV peak E-wave KEiEDV were independent predictors of RV remodelling index.

CONCLUSIONS

In this multi-scanner multicenter 4D flow CMR study, reduced RV direct flow was independently associated with RV dysfunction, remodelling and, to a lesser extent, exercise intolerance in rTOF patients. This supports its utility as an imaging parameter for monitoring disease progression and therapeutic response in rTOF. Clinical Trial Registration https://www.clinicaltrials.gov . Unique identifier: NCT03217240.

Moving beyond size: vorticity and energy loss are correlated with right ventricular dysfunction and exercise intolerance in repaired Tetralogy of Fallot

BACKGROUND

The global effect of chronic pulmonary regurgitation (PR) on right ventricular (RV) dilation and dysfunction in repaired Tetralogy of Fallot (rTOF) patients is well studied by cardiovascular magnetic resonance (CMR). However, the links between PR in the RV outflow tract (RVOT), RV dysfunction and exercise intolerance are not clarified by conventional measurements. Not all patients with RV dilation share the same intracardiac flow characteristics, now measurable by time resolved three-dimensional phase contrast imaging (4D flow). In our study, we quantified regional vorticity and energy loss in rTOF patients and correlated these parameters with RV dysfunction and exercise capacity.

METHODS

rTOF patients with 4D flow datasets were retrospectively analyzed, including those with transannular/infundibular repair and conduit repair. Normal controls and RV dilation patients with atrial-level shunts (Qp:Qs > 1.2:1) were included for comparison. 4D flow was post-processed using IT Flow (Cardioflow, Japan). Systolic/diastolic vorticity (ω, 1/s) and viscous energy loss (VEL, mW) in the RVOT and RV inflow were measured. To characterize the relative influence of diastolic vorticity in the two regions, an RV Diastolic Vorticity Quotient (ωRVOT-Diastole/ωRV Inflow-Diastole, RV-DVQ) was calculated. Additionally, RVOT Vorticity Quotient (ωRVOT-Diastole/ωRVOT-Systole, RVOT-VQ) and RVOT Energy Quotient (VELRVOT-Diastole/VELRVOT-Systole, RVOT-EQ) was calculated. In rTOF, measurements were correlated against conventional CMR and exercise stress test results.

RESULTS

58 rTOF patients, 28 RV dilation patients and 12 controls were included. RV-DVQ, RVOT-VQ, and RVOT-EQ were highest in rTOF patients with severe PR compared to rTOF patients with non-severe PR, RV dilation and controls (p < 0.001). RV-DVQ positively correlated with RV end-diastolic volume (0.683, p < 0.001), PR fraction (0.774, p < 0.001) and negatively with RV ejection fraction (- 0.521, p = 0.003). Both RVOT-VQ, RVOT-EQ negatively correlated with VO2-max (- 0.587, p = 0.008 and - 0.617, p = 0.005) and % predicted VO2-max (- 0.678, p = 0.016 and - 0.690, p = 0.001).

CONCLUSIONS

In rTOF patients, vorticity and energy loss dominate the RVOT compared to tricuspid inflow, correlating with RV dysfunction and exercise intolerance. These 4D flow-based measurements may be sensitive biomarkers to guide surgical management of rTOF patients.