Mahdi Esmaily-Moghadam

A non-discrete method for computation of residence time in fluid mechanics simulations

Cardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the advection-diffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a point-wise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease.

Multiscale Modeling of Cardiovascular Flows for Clinical Decision Support

Patient-specific cardiovascular simulations can provide clinicians with predictive tools, fill current gaps in clinical imaging capabilities, and contribute to the fundamental understanding of disease progression. However, clinically relevant simulations must provide not only local hemodynamics, but also global physiologic response. This necessitates a dynamic coupling between the Navier–Stokes solver and reduced-order models of circulatory physiology, resulting in numerical stability and efficiency challenges. In this review, we discuss approaches to handling the coupled systems that arise from cardiovascular simulations, including recent algorithms that enable efficient large-scale simulations of the vascular system. We maintain particular focus on multiscale modeling algorithms for finite element simulations. Because these algorithms give rise to an ill-conditioned system of equations dominated by the coupled boundaries, we also discuss recent methods for solving the linear system of equations arising from these systems. We then review applications that illustrate the potential impact of these tools for clinical decision support in adult and pediatric cardiology. Finally, we offer an outlook on future directions in the field for both modeling and clinical application.

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.

Low entropy data mapping for sparse iterative linear solvers

An efficient parallel data structure implementation is presented to modify the permutation on the residual vector to achieve optimized memory layout of partitioned meshes for solving sparse linear systems. This novel algorithm is proposed to sort the data on each processor with respect to a set of rules. This simplifies implementation of parallel iterative solver algorithms and allows an overlap between non-blocking MPI communication and computations in matrix-vector product operations.