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.

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.