Moving Domain Computational Fluid Dynamics to Interface with an Embryonic Model of Cardiac Morphogenesis

Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP)y1 transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis. © 2013 Lee et al

Development of multiscale modeling methods for clinical decision making in single ventricle heart patients /

Infants with single ventricle physiology generally undergo three palliative surgeries starting with stage-one, in which a systemic-to-pulmonary connection is established via a shunt. Mortality is the highest among stage-one patients (up to 23%) due to sub-optimal oxygen delivery, ventricle volume overload, myocardial ischemia, and high risk of shunt blockage. The clinical objective of the present study is to simulate the stage-one circulation, analyze possible surgical options, optimize current surgical methods, and explore a novel alternative surgical option. Simulating the stage-one circulation in single ventricle repair requires a set of numerical tools that are developed in the first part of this dissertation. First, an implicit and modular multidomain framework with excellent stability and convergence properties is introduced that allows multiscale simulation of the circulatory system. Second, a stabilized formulation is presented for treating backflow at Neumann boundaries that is inexpensive, stable, simple, and minimally intrusive, and offers a promising alternative to previous methods. Third, an efficient pre-conditioner for coupled boundary conditions and an efficient iterative algorithm for solving system of equations governing incompressible flows are introduced. Fourth, a scalable parallel data structure is introduced for performing algebraic operations in iterative solvers efficiently. Fifth, an Eulerian formulation is proposed for calculating residence time that lacks mesh dependency and avoids the high computational cost of Lagrangian particle-based approaches. These tools are applicable to other cardiac mechanics and CFD simulations as well. In second part of this dissertation, single ventricle physiology is studied using the tools presented in the first part. First, a multiscale model of single ventricle physiology is simulated and the shunt geometry is optimized to maximize oxygen delivery and improve performance. Second, surgical scenarios single and multiple systemic-to-pulmonary connections are compared, revealing higher thrombotic risk and lower oxygen delivery in the presence of multiple connections. Third, a novel stage one palliative surgery, which provides an alternative source of blood flow in case of shunt blockage and may ultimately reduce the number of open chest surgeries from three to two, is proposed and tested using multiscale modeling. Results reveal the proposed surgical method, the Assisted Bidirectional Glenn, can deliver more oxygen at a reduced heart load with only a modest increase in venous return pressur

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

Investigators for the Modeling Of Congenital Hearts Alliance (MOCHA) : Edward Bove MD and Adam Dorfman MD (University of Michigan, USA); Andrew Taylor MD, Alessandro Giardini MD, Sachin Khambadkone MD, Marc de Leval MD, Silvia Schievano PhD, and T-Y Hsia MD (Institute of Child Health, UK); G. Hamilton Baker MD and Anthony Hlavacek (Medical University of South Carolina, USA); Francesco Migliavacca PhD, Giancarlo Pennati PhD, and Gabriele Dubini PhD (Politecnico di Milano, Italy); Richard Figliola PhD and John McGregor PhD (Clemson University, USA); Alison Marsden PhD (University of California, San Diego, USA); Irene Vignon-Clementel PhD (INRIA, France), Jeffrey A. Feinstein (Stanford University, USA).International audienceImplementation 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

Multi-scale geometrical Lagrangian statistics: Extensions and applications to particle-laden turbulent flows

We present multi-scale statistics of particle trajectories in isotropic turbulence and compare the behavior of fluid and inertial particles. The directional change of inertial particles is quantified by considering the curvature angle for different time increments. Distinct scaling behaviors of the mean angle are observed for short, intermediate and long time lags. We also introduce the scale-dependent torsion angle, which quantifies the directional change of particles moving out of a reference plane. The influence of the Stokes number on the mean angles and on the probability distributions are analyzed. Finally, we assess the impact of LES and particle SGS modeling on these statistics

Multi-scale geometrical Lagrangian statistics: Extensions and applications to particle-laden turbulent flows

We present multi-scale statistics of particle trajectories in isotropic turbulence and compare the behavior of fluid and inertial particles. The directional change of inertial particles is quantified by considering the curvature angle for different time increments. Distinct scaling behaviors of the mean angle are observed for short, intermediate and long time lags. We also introduce the scale-dependent torsion angle, which quantifies the directional change of particles moving out of a reference plane. The influence of the Stokes number on the mean angles and on the probability distributions are analyzed. Finally, we assess the impact of LES and particle SGS modeling on these statistics

Multi-scale geometrical Lagrangian statistics: Extensions and applications to particle-laden turbulent flows

We present multi-scale statistics of particle trajectories in isotropic turbulence and compare the behavior of fluid and inertial particles. The directional change of inertial particles is quantified by considering the curvature angle for different time increments. Distinct scaling behaviors of the mean angle are observed for short, intermediate and long time lags. We also introduce the scale-dependent torsion angle, which quantifies the directional change of particles moving out of a reference plane. The influence of the Stokes number on the mean angles and on the probability distributions are analyzed. Finally, we assess the impact of LES and particle SGS modeling on these statistics