Alison L. Marsden

Hypoplastic Left Heart Syndrome : Current Considerations and Expectations

In the recent era, no congenital heart defect has undergone a more dramatic change in diagnostic approach, management, and outcomes than hypoplastic left heart syndrome (HLHS). During this time, survival to the age of 5 years (including Fontan) has ranged from 50% to 69%, but current expectations are that 70% of newborns born today with HLHS may reach adulthood. Although the 3-stage treatment approach to HLHS is now well founded, there is significant variation among centers. In this white paper, we present the current state of the art in our understanding and treatment of HLHS during the stages of care: 1) pre-Stage I: fetal and neonatal assessment and management; 2) Stage I: perioperative care, interstage monitoring, and management strategies; 3) Stage II: surgeries; 4) Stage III: Fontan surgery; and 5) long-term follow-up. Issues surrounding the genetics of HLHS, developmental outcomes, and quality of life are addressed in addition to the many other considerations for caring for this group of complex patients.

Effects of Exercise and Respiration on Hemodynamic Efficiency in CFD Simulations of the Total Cavopulmonary Connection

Congenital heart defects with a single functional ventricle, such as hypoplastic left heart syndrome and tricuspid atresia, require a staged surgical approach to separate the systemic and pulmonary circulations. Ultimately, the venous or pulmonary side of the heart is bypassed by directly connecting the vena cava to the pulmonary arteries with a modified t-shaped junction. The Fontan procedure (total cavopulmonary connection, TCPC) completes this process of separation. To date, computational fluid dynamics (CFD) simulations in this low pressure, passive flow, intrathoracic system have neglected the presumed important effects of respiration on physiology and higher “stress” states such as with exercise have never been considered. We hypothesize that incorporating effects of respiration and exercise would provide more realistic estimates of TCPC performance. Time-dependent, 3D blood flow simulations are performed by a custom finite element solver for two patient-specific Fontan models with a novel respiration model, developed to generate physiologic time-varying flow conditions. Blood flow features, pressure, and energy efficiency are analyzed at rest and with increasing flow rates to simulate exercise conditions. The simulations produce realistic pressure and flow data, comparable to that measured by catheterization and echocardiography, and demonstrate substantial increases in energy dissipation (i.e. decreased performance) with exercise and respiration due to increasing intensity of small scale vortices in the flow. As would be expected, these changes are highly dependent on patient-specific anatomy and Fontan geometry. We propose that respiration and exercise should be incorporated into TCPC CFD simulations to provide increasingly realistic evaluations of TCPC performance.

Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework

Shape optimization is applied to time-dependent trailing-edge flow in order to minimize aerodynamic noise. Optimization is performed using the surrogate management framework (SMF), a non-gradient based pattern search method chosen for its efficiency and rigorous convergence properties. Using SMF, design space exploration is performed not with the expensive actual function but with an inexpensive surrogate function. The use of a polling step in the SMF guarantees that the algorithm generates a convergent subsequence of mesh points in the parameter space. Each term of this subsequence is a weak local minimizer of the cost function on the mesh in a sense to be made precise later. We will discuss necessary optimality conditions for the design problem that are satisfied by the limit of this subsequence. Results are presented for an unsteady laminar flow past an acoustically compact airfoil. Constraints on lift and drag are handled within SMF by applying the filter pattern search method of Audet and Dennis, within which a penalty function is used to form and optimize a surrogate function. Optimal shapes that minimize noise have been identified for the trailing-edge problem in constrained and unconstrained cases. Results show a significant reduction (as much as 80%) in acoustic power with reasonable computational cost using several shape parameters. Physical mechanisms for noise reduction are discussed.

Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation

Derivative-free optimization techniques are applied in conjunction with large-eddy simulation (LES) to reduce the noise generated by turbulent flow over a hydrofoil trailing edge. A cost function proportional to the radiated acoustic power is derived based on the Ffowcs Williams and Hall solution to Lighthills equation. Optimization is performed using the surrogate-management framework with filter-based constraints for lift and drag. To make the optimization more efficient, a novel method has been developed to incorporate Reynolds-averaged Navier–Stokes (RANS) calculations for constraint evaluation. Separation of the constraint and cost-function computations using this method results in fewer expensive LES computations. This work demonstrates the ability to fully couple optimization to large-eddy simulation for time-accurate turbulent flow. The results demonstrate an 89% reduction in noise power, which comes about primarily by the elimination of low-frequency vortex shedding. The higher-frequency broadband noise is reduced as well, by a subtle change in the lower surface near the trailing edge.

A Stochastic Collocation Method for Uncertainty Quantification and Propagation in Cardiovascular Simulations

Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input parameters. In this work, we develop a general set of tools to evaluate the sensitivity of output parameters to input uncertainties in cardiovascular simulations. Uncertainties can arise from boundary conditions, geometrical parameters, or clinical data. These uncertainties result in a range of possible outputs which are quantified using probability density functions (PDFs). The objective is to systemically model the input uncertainties and quantify the confidence in the output of hemodynamic simulations. Input uncertainties are quantified and mapped to the stochastic space using the stochastic collocation technique. We develop an adaptive collocation algorithm for Gauss-Lobatto-Chebyshev grid points that significantly reduces computational cost. This analysis is performed on two idealized problems--an abdominal aortic aneurysm and a carotid artery bifurcation, and one patient specific problem--a Fontan procedure for congenital heart defects. In each case, relevant hemodynamic features are extracted and their uncertainty is quantified. Uncertainty quantification of the hemodynamic simulations is done using (a) stochastic space representations, (b) PDFs, and (c) the confidence intervals for a specified level of confidence in each problem.

Patient-Specific Multiscale Modeling of Blood Flow for Coronary Artery Bypass Graft Surgery

We present a computational framework for multiscale modeling and simulation of blood flow in coronary artery bypass graft (CABG) patients. Using this framework, only CT and non-invasive clinical measurements are required without the need to assume pressure and/or flow waveforms in the coronaries and we can capture global circulatory dynamics. We demonstrate this methodology in a case study of a patient with multiple CABGs. A patient-specific model of the blood vessels is constructed from CT image data to include the aorta, aortic branch vessels (brachiocephalic artery and carotids), the coronary arteries and multiple bypass grafts. The rest of the circulatory system is modeled using a lumped parameter network (LPN) 0 dimensional (0D) system comprised of resistances, capacitors (compliance), inductors (inertance), elastance and diodes (valves) that are tuned to match patient-specific clinical data. A finite element solver is used to compute blood flow and pressure in the 3D (3 dimensional) model, and this solver is implicitly coupled to the 0D LPN code at all inlets and outlets. By systematically parameterizing the graft geometry, we evaluate the influence of graft shape on the local hemodynamics, and global circulatory dynamics. Virtual manipulation of graft geometry is automated using Bezier splines and control points along the pathlines. Using this framework, we quantify wall shear stress, wall shear stress gradients and oscillatory shear index for different surgical geometries. We also compare pressures, flow rates and ventricular pressure–volume loops pre- and post-bypass graft surgery. We observe that PV loops do not change significantly after CABG but that both coronary perfusion and local hemodynamic parameters near the anastomosis region change substantially. Implications for future patient-specific optimization of CABG are discussed.

Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations

Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of backflow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D-0D interface.

Virtual surgeries in patients with congenital heart disease: a multi-scale modelling test case

The objective of this work is to perform a virtual planning of surgical repairs in patients with congenital heart diseases—to test the predictive capability of a closed-loop multi-scale model. As a first step, we reproduced the pre-operative state of a specific patient with a univentricular circulation and a bidirectional cavopulmonary anastomosis (BCPA), starting from the patients clinical data. Namely, by adopting a closed-loop multi-scale approach, the boundary conditions at the inlet and outlet sections of the three-dimensional model were automatically calculated by a lumped parameter network. Successively, we simulated three alternative surgical designs of the total cavopulmonary connection (TCPC). In particular, a T-junction of the venae cavae to the pulmonary arteries (T-TCPC), a design with an offset between the venae cavae (O-TCPC) and a Y-graft design (Y-TCPC) were compared. A multi-scale closed-loop model consisting of a lumped parameter network representing the whole circulation and a patient-specific three-dimensional finite volume model of the BCPA with detailed pulmonary anatomy was built. The three TCPC alternatives were investigated in terms of energetics and haemodynamics. Effects of exercise were also investigated. Results showed that the pre-operative caval flows should not be used as boundary conditions in post-operative simulations owing to changes in the flow waveforms post-operatively. The multi-scale approach is a possible solution to overcome this incongruence. Power losses of the Y-TCPC were lower than all other TCPC models both at rest and under exercise conditions and it distributed the inferior vena cava flow evenly to both lungs. Further work is needed to correlate results from these simulations with clinical outcomes.

Optimization of Cardiovascular Stent Design Using Computational Fluid Dynamics

Coronary stent design affects the spatial distribution of wall shear stress (WSS), which can influence the progression of endothelialization, neointimal hyperplasia, and restenosis. Previous computational fluid dynamics (CFD) studies have only examined a small number of possible geometries to identify stent designs that reduce alterations in near-wall hemodynamics. Based on a previously described framework for optimizing cardiovascular geometries, we developed a methodology that couples CFD and three-dimensional shape-optimization for use in stent design. The optimization procedure was fully-automated, such that solid model construction, anisotropic mesh generation, CFD simulation, and WSS quantification did not require user intervention. We applied the method to determine the optimal number of circumferentially repeating stent cells (N(C)) for slotted-tube stents with various diameters and intrastrut areas. Optimal stent designs were defined as those minimizing the area of low intrastrut time-averaged WSS. Interestingly, we determined that the optimal value of N(C) was dependent on the intrastrut angle with respect to the primary flow direction. Further investigation indicated that stent designs with an intrastrut angle of approximately 40 deg minimized the area of low time-averaged WSS regardless of vessel size or intrastrut area. Future application of this optimization method to commercially available stent designs may lead to stents with superior hemodynamic performance and the potential for improved clinical outcomes.