Lisa Fauci

A computational model of aquatic animal locomotion

Abstract A computational model of the swimming of a neutrally buoyant organism undergoing deformations within a region of fluid is presented. The fluid is regarded as viscous and incompressible and the organism as a massless, elastic boundary immersed in this fluid. Fluid quantities are represented on a grid (Eulerian description), and the immersed boundary is represented by a discrete collection of moving points (Lagrangian description). Computed results are presented, along with comparisons with previous asymptotic analysis.

The method of regularized Stokeslets in three dimensions: Analysis, validation, and application to helical swimming

The method of regularized Stokeslets is a Lagrangian method for computing Stokes flow driven by forces distributed at material points in a fluid. It is based on the superposition of exact solutions of the Stokes equations when forces are given by a cutoff function. We present this method in three dimensions, along with an analysis of its accuracy and performance on the model problems of flow past a sphere and the steady state rotation of rigid helical tubes. Predicted swimming speeds for various helical geometries are compared with experimental data for motile spirochetes. In addition, the regularized Stokeslet method is readily implemented in conjunction with an immersed boundary representation of an elastic helix that incorporates passive elastic properties as well as mechanisms of internal force generation.

SPERM MOTILITY IN THE PRESENCE OF BOUNDARIES

The fluid dynamics of sperm motility near both rigid and elastic walls is studied using the immersed boundary method. Simulations of both single and interacting organisms are presented. In particular, we find that nearby organisms originally undulating with a 90 degree phase shift may adjust their relative swimming velocities and phase-lock. Comparisons with previous analytical results are also discussed. The tendency of a near-wall to attract organisms is demonstrated.

Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming

Animal movements result from a complex balance of many different forces. Muscles produce force to move the body; the body has inertial, elastic, and damping properties that may aid or oppose the muscle force; and the environment produces reaction forces back on the body. The actual motion is an emergent property of these interactions. To examine the roles of body stiffness, muscle activation, and fluid environment for swimming animals, a computational model of a lamprey was developed. The model uses an immersed boundary framework that fully couples the Navier–Stokes equations of fluid dynamics with an actuated, elastic body model. This is the first model at a Reynolds number appropriate for a swimming fish that captures the complete fluid-structure interaction, in which the body deforms according to both internal muscular forces and external fluid forces. Results indicate that identical muscle activation patterns can produce different kinematics depending on body stiffness, and the optimal value of stiffness for maximum acceleration is different from that for maximum steady swimming speed. Additionally, negative muscle work, observed in many fishes, emerges at higher tail beat frequencies without sensory input and may contribute to energy efficiency. Swimming fishes that can tune their body stiffness by appropriately timed muscle contractions may therefore be able to optimize the passive dynamics of their bodies to maximize peak acceleration or swimming speed.

Interaction of oscillating filaments: a computational study

Abstract The immersed boundary technique is used to model the interaction of swimming filaments in a viscous, incompressible fluid. Fluid quantities are represented on a grid, and the immersed filaments are each represented by a discrete collection of moving points. The effects of phase differences and proximity of the filaments on energy dissipation and swimming speeds are studied. The computed results are compared with previous asymptotic analysis. Furthermore, we present case studies which exhibit phase-(un)locking phenomena undetectable using previous asymptotic analysis.

Simulation of swimming organisms: coupling internal mechanics with external fluid dynamics

Problems in biological fluid dynamics typically involve the interaction of an elastic structure with its surrounding fluid. A unified computational approach, based on an immersed boundary framework, couples the internal force-generating mechanisms of organisms and cells with an external, viscous, incompressible fluid. Computational simulation, in conjunction with laboratory experiment, can provide valuable insight into complex biological systems that involve the interaction of an elastic structure with a viscous, incompressible fluid. This biological fluid-dynamics setting presents several more challenges than those traditionally faced in computational fluid dynamics - specifically, dynamic flow situations dominate, and capturing time-dependent geometries with large structural deformations is necessary. In addition, the shape of the elastic structures is not preset: fluid dynamics determines it. This article presents our recent progress on coupling the internal molecular motor mechanisms of beating cilia and flagella with an external fluid, as well as the three-dimensional (3D) undulatory swimming of nematodes and leeches. We expect these computational models to provide a testbed for examining different theories of internal force-generation mechanisms.

A computational model of ameboid deformation and locomotion

Abstract Traditional continuum models of ameboid deformation and locomotion are limited by the computational difficulties intrinsic in free boundary conditions. A new model using the immersed boundary method overcomes these difficulties by representing the cell as a force field immersed in fluid domain. The forces can be derived from a direct mechanical interpretation of such cell components as the cell membrane, the actin cortex, and the transmembrane adhesions between the cytoskeleton and the substratum. The numerical cytoskeleton, modeled as a dynamic network of immersed springs, is able to qualitatively model the passive mechanical behavior of a shear-thinning viscoelastic fluid (Bottino 1997). The same network is used to generate active protrusive and contractile forces. When coordinated with the attachment-detachment cycle of the cells adhesions to the substratum, these forces produce directed locomotion of the model ameba. With this model it is possible to study the effects of altering the numerical parameters upon the motility of the model cell in a manner suggestive of genetic deletion experiments. In the context of this ameboid cell model and its numerical implementation, simulations involving multicellular interaction, detailed internal signaling, and complex substrate geometries are tractable.

Fluid Dynamic Models of Flagellar and Ciliary Beating

Abstract:  We have developed a fluid–mechanical model of a eucaryotic axoneme that couples the internal force generation of dynein molecular motors, the passive elastic mechanics of microtubules, and forces due to nexin links with a surrounding incompressible fluid. This model has been used to examine both ciliary beating and flagellar motility. In this article, we show preliminary simulation results for sperm motility in both viscous and viscoelastic fluids, as well as multiciliary interaction with a mucus layer.

Peristaltic pumping and irreversibility of a Stokesian viscoelastic fluid

Peristaltic pumping by wavelike contractions is a fundamental biomechanical mechanism for fluid and material transport and is used in the esophagus, intestine, oviduct, and ureter. While peristaltic pumping of a Newtonian fluid is well understood, in many important settings, as in the fluid dynamics of reproduction, the fluids have non-Newtonian responses. Here, we present a numerical method for simulating an Oldroyd-B fluid coupled to contractile, moving walls. A marker and cell grid-based projection method is used for the fluid equations and an immersed boundary method is used for coupling to a Lagrangian representation of the deforming walls. We examine numerically the peristaltic transport of a highly viscous Oldroyd-B fluid over a range of Weissenberg numbers and peristalsis wavelengths and amplitudes.

A microscale model of bacterial and biofilm dynamics in porous media.

A microscale model for the transport and coupled reaction of microbes and chemicals in an idealized two‐dimensional porous media has been developed. This model includes the flow, transport, and bioreaction of nutrients, electron acceptors, and microbial cells in a saturated granular porous media. The fluid and chemicals are represented as a continuum, but the bacterial cells and solid granular particles are represented discretely. Bacterial cells can attach to the particle surfaces or be advected in the bulk fluid. The bacterial cells can also be motile and move preferentially via a run and tumble mechanism toward a chemoattractant. The bacteria consume oxygen and nutrients and alter the profiles of these chemicals. Attachment of bacterial cells to the soil matrix and growth of bacteria can change the local permeability. The coupling of mass transport and bioreaction can produce spatial gradients of nutrients and electron acceptor concentrations. We describe a numerical method for the microscale model, show results of a convergence study, and present example simulations of the model system.