Shawn C. Shadden

Collision avoidance for multiple agent systems

Techniques using gyroscopic forces and scalar potentials are used to create swarming behaviors for multiple agent systems. The methods result in collision avoidance between the agents as well as with obstacles.

Lagrangian analysis of fluid transport in empirical vortex ring flows

In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested.

Lagrangian coherent structures in n-dimensional systems

Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring is to identify the dynamic boundaries between these almost-invariant regions. Recently, ridges in finite-time Lyapunov exponent fields have been used to define such hyperbolic, almost material, Lagrangian coherent structures in two-dimensional systems. The objective of this paper is to develop and apply a similar theory in higher dimensional spaces. While the separatrix nature of these structures is their most important property, a necessary condition is their almost material nature. This property is addressed in this paper. These results are applied to a model of Rayleigh-Benard convection based on a three-dimensional extension of the model of Solomon and Gollub.

Characterization of Coherent Structures in the Cardiovascular System

Recent advances in blood flow modeling have provided highly resolved, four-dimensional data of fluid mechanics in large vessels. The motivation for such modeling is often to better understand how flow conditions relate to health and disease, or to evaluate interventions that affect, or are affected by, blood flow mechanics. Vessel geometry and the pulsatile pumping of blood leads to complex flow, which is often difficult to characterize. This article discusses a computational method to better characterize blood flow kinematics. In particular, we compute Lagrangian coherent structures (LCS) to study flow in large vessels. We demonstrate that LCS can be used to characterize flow stagnation, flow separation, partitioning of fluid to downstream vasculature, and mechanisms governing stirring and mixing in vascular models. This perspective allows valuable understanding of flow features in large vessels beyond methods traditionally considered.

Study of blood flow impact on growth of thrombi using a multiscale model

An extended multiscale model is introduced for studying the formation of platelet thrombi in blood vessels. The model describes the interplay between viscous, incompressible blood plasma, activated and non-activated platelets, as well as other blood cells, activating chemicals, fibrinogen and vessel walls. The macroscale dynamics of the blood flow is represented by the continuous submodel in the form of the Navier–Stokes equations. The microscale cell-cell interactions are described by the stochastic Cellular Potts Model (CPM). Simulations indicate that increase in flow rates leads to greater structural heterogeneity of the clot. As heterogeneous structural domains within the clot affect thrombus stability, understanding the factors influencing thrombus structure is of significant biomedical importance.

Optimal trajectory generation in ocean flows

In this paper it is shown that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater gliders in a dynamic ocean environment. This opens the opportunity for optimal path planning of autonomous underwater vehicles by studying the global flow geometry via dynamical systems methods. Optimal glider paths were computed for a 2-dimensionaI kinematic model of an end-point glider problem. Numerical solutions to the optimal control problem were obtained using Nonlinear Trajectory Generation (NTG) software. The resulting solution is compared to corresponding results on LCS obtained using the Direct Lyapunov Exponent method. The velocity data used for these computations was obtained from measurements taken in August, 2000, by HF-Radar stations located around Monterey Bay, CA, USA.

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.

Transport and stirring induced by vortex formation

The purpose of this study is to analyse the transport and stirring of fluid that occurs owing to the formation and growth of a laminar vortex ring. Experimental data was collected upstream and downstream of the exit plane of a piston-cylinder apparatus by particle-image velocimetry. This data was used to compute Lagrangian coherent structures to demonstrate how fluid is advected during the transient process of vortex ring formation. Similar computations were performed from computational fluid dynamics (CFD) data, which showed qualitative agreement with the experimental results, although the CFD data provides better resolution in the boundary layer of the cylinder. A parametric study is performed to demonstrate how varying the piston-stroke length-to-diameter ratio affects fluid entrainment during formation. Additionally, we study how regions of fluid are stirred together during vortex formation to help establish a quantitative understanding of the role of vortical flows in mixing. We show that identification of the flow geometry during vortex formation can aid in the determination of efficient stirring. We compare this framework with a traditional stirring metric and show that the framework presented in this paper is better suited for understanding stirring/mixing in transient flow problems. A movie is available with the online version of the paper.

Computational analysis of an aortic valve jet with Lagrangian coherent structures.

Important progress has been achieved in recent years in simulating the fluid-structure interaction around cardiac valves. An important step in making these computational tools useful to clinical practice is the development of postprocessing techniques to extract clinically relevant information from these simulations. This work focuses on flow through the aortic valve and illustrates how the computation of Lagrangian coherent structures can be used to improve insight into the transport mechanics of the flow downstream of the valve, toward the goal of aiding clinical decision making and the understanding of pathophysiology.

Topology of Blood Transport in the Human Left Ventricle by Novel Processing of Doppler Echocardiography

Novel processing of Doppler-echocardiography data was used to study blood transport in the left ventricle (LV) of six patients with dilated cardiomyopathy and six healthy volunteers. Bi-directional velocity field maps in the apical long axis of the LV were reconstructed from color-Doppler echocardiography. Resulting velocity field data were used to perform trajectory-based computation of Lagrangian coherent structures (LCS). LCS were shown to reveal the boundaries of blood injected and ejected from the heart over multiple beats. This enabled qualitative and quantitative assessments of blood transport patterns and residence times in the LV. Quantitative assessments of stasis in the LV are reported, as well as characterization of LV vortex formations from E-wave and A-wave filling.