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Fish schools can make frequent accelerations that are almost simultaneous. While schooling at constant speed is well studied, far less is known for accelerating fish school across various body caudal fin swimming styles. The present study investigates the effects of swimming styles and schooling on two accelerating wavy hydrofoils in a free stream flow at various wavelengths λ = 0.5 − 8, Strouhal number St = 0.2 − 0.7, front-back distance D = 0, 0.25, 0.5, 0.75, phase difference ϕ/π = 0, 0.5, 1, 1.5, and lateral gap distance G = 0.25, 0.3, 0.35 with fixed Reynolds number Re = 5000 and maximum amplitude Amax = 0.1. In total, 591 cases were simulated by open-source software IBAMR based on immersed boundary method. Low and high wavelength corresponds to advantageous propulsive efficiency and thrust force, respectively. The highest group propulsive efficiency is obtained at low wavelength λ < 1.2. At side-by-side arrangement, the thrust force upon the two foils can be equivalent across various wavelengths, indicating a synchronised acceleration. At staggered arrangement, the follower can take significant advantage of the leader in locomotion performance by tuning phase difference, especially at high wavelength and close distances. Frontback distance is a key factor affecting the follower’s propulsive efficiency for short wavelength swimmers, but not for long wavelength ones. Various combinations of wavelength and relative distance can lead to distinct flow structures, indicating a tunable stealth capacity of the accelerating fish schools. more...

Objective Bioprosthetic heart valves (BHVs) are commonly used in surgical and percutaneous valve replacement. The durability of percutaneous valve replacement is unknown, but surgical valves have been shown to require reintervention after 10 to 15 years. Further, smaller-diameter surgical BHVs generally experience higher rates of prosthesis–patient mismatch, which leads to higher rates of failure. Bioprosthetic aortic valves can flutter in systole, and fluttering is associated with fatigue and failure in flexible structures. The determinants of flutter in BHVs have not been well characterized, despite their potential to influence durability. Methods We use an experimental pulse duplicator and a computational fluid-structure interaction model of this system to study the role of device geometry on BHV dynamics. The experimental system mimics physiological conditions, and the computational model enables precise control of leaflet biomechanics and flow conditions to isolate the effects of variations in BHV geometry on leaflet dynamics. Results Both experimental and computational models demonstrate that smaller-diameter BHVs yield markedly higher leaflet fluttering frequencies across a range of conditions. The computational model also predicts that fluttering frequency is directly related to leaflet thickness. A scaling model is introduced that rationalizes these findings. Conclusions We systematically characterize the influence of BHV diameter and leaflet thickness on fluttering dynamics. Although this study does not determine how flutter influences device durability, increased flutter in smaller-diameter BHVs may explain how prosthesis–patient mismatch could induce BHV leaflet fatigue and failure. Ultimately, understanding the effects of device geometry on leaflet kinematics may lead to more durable valve replacements. more...

Current clinical practice for aneurysmatic interventions is often based on the maximum diameter of the vessel and/or on the growth rate, although rupture can occur at any diameter and growth rate, leading to fatality. For 27 medial samples obtained from 12 non-aneurysmatic (control) and 9 aneurysmatic human descending thoracic aortas we examined: the mechanical responses up to rupture using uniaxial extension tests of circumferential and longitudinal specimens; the structure of these tissues using second-harmonic imaging and histology, in particular, the content proportions of collagen, elastic fibers and smooth muscle cells in the media. It was found that the mean failure stresses were higher in the circumferential directions (Control-C 1474 kPa; Aneurysmatic-C 1446 kPa), than in the longitudinal directions (Aneurysmatic-L 735 kPa; Control-L 579 kPa). This trend was the opposite to that observed for the mean collagen fiber directions measured from the loading axis (Control-L > Aneurysmatic-L > Aneurysmatic-C > Control-C), thus suggesting that the trend in the failure stress can in part be attributed to the collagen architecture. The difference in the mean values of the out-of-plane dispersion in the radial/longitudinal plane between the control and aneurysmatic groups was significant. The difference in the mean values of the mean fiber angle from the circumferential direction was also significantly different between the two groups. Most specimens showed delamination zones near the ruptured region in addition to ruptured collagen and elastic fibers. This study provides a basis for further studies on the microstructure and the uniaxial failure properties of (aneurysmatic) arterial walls towards realistic modeling and prediction of tissue failure. Statement of Significance A data set relating uniaxial failure properties to the microstructure of non-aneurysmatic and aneurysmatic human thoracic aortic medias under uniaxial extension tests is presented for the first time. It was found that the mean failure stresses were higher in the circumferential directions, than in the longitudinal directions. The general trend for the failure stresses was Control-C > Aneurysmatic-C > Aneurysmatic-L > Control-L, which was the opposite of that observed for the mean collagen fiber direction relative to the loading axis (Control-L > Aneurysmatic-L > Aneurysmatic-C > Control-C) suggesting that the trend in the failure stress can in part be attributed to the collagen architecture. This study provides a first step towards more realistic modeling and prediction of tissue failure. more...

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The algorithm combines the interface capturing level set method with a variable-coefficient incompressible Navier-Stokes solver that is demonstrated to stably resolve material contrast ratios of up to six orders of magnitude. The discretization approach ensures second-order pointwise accuracy for both velocity and pressure with several physical boundary treatments, including velocity and traction boundary conditions. The paper includes several test cases that demonstrate the order of accuracy and algorithmic scalability of the flow solver. To ensure the stability of the numerical scheme in the presence of high density and viscosity ratios, we employ a consistent treatment of mass and momentum transport in the conservative form of discrete equations. This consistency is achieved by solving an additional mass balance equation, which we approximate via a strong stability preserving Runga-Kutta time integrator and by employing the same mass flux (obtained from the mass equation) in the discrete momentum equation. The scheme uses higher-order total variation diminishing (TVD) and convection-boundedness criterion (CBC) satisfying limiter to avoid numerical fluctuations in the transported density field. The high-order bounded convective transport is done on a dimension-by-dimension basis, which makes the scheme simple to implement. We also demonstrate through several test cases that the lack of consistent mass and momentum transport in non-conservative formulations, which are commonly used in practice, or the use of non-CBC satisfying limiters can yield very large numerical error and very poor accuracy for convection-dominant high density ratio flows., Comment: Figures are compressed to comply with arXiv size requirements more...

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava. more...

Cardiac Pacemaker Cells (CPCs) rhythmically initiate the electrical impulses that drive heart contraction. CPCs display the highest rate of spontaneous depolarization in the heart despite being subjected to inhibitory electrochemical conditions that should theoretically suppress their activity. While several models have been proposed to explain this apparent paradox, the actual molecular mechanisms that allow CPCs to overcome electronic barriers to their function remain largely unexplored. Here we have traced CPC development at single cell resolution and uncovered a series of cytoarchitectural patterning events that are critical for proper pacemaking. Specifically, our data reveal that CPCs dynamically modulate adherens junction (AJ) engagement to control characteristics including surface area, volume, and gap junctional coupling. This allows CPCs to adopt a structural configuration that supports their overall excitability. Thus, our data have identified a previously unrecognized role for local cellular mechanics in patterning critical morphological features that are necessary for CPC electrical activity. more...

High-order numerical methods for solving elliptic equations over arbitrary domains typically require specialized machinery, such as high-quality conforming grids for finite elements method, and quadrature rules for boundary integral methods. These tools make it difficult to apply these techniques to higher dimensions. In contrast, fixed Cartesian grid methods, such as the immersed boundary (IB) method, are easy to apply and generalize, but typically are low-order accurate. In this study, we introduce the Smooth Forcing Extension (SFE) method, a fixed Cartesian grid technique that builds on the insights of the IB method, and allows one to obtain arbitrary orders of accuracy. Our approach relies on a novel Fourier continuation method to compute extensions of the inhomogeneous terms to any desired regularity. This is combined with the highly accurate Non-Uniform Fast Fourier Transform for interpolation operations to yield a fast and robust method. Numerical tests confirm that the technique performs precisely as expected on one-dimensional test problems. In higher dimensions, the performance is even better, in some cases yielding sub-geometric convergence. We also demonstrate how this technique can be applied to solving parabolic problems and for computing the eigenvalues of elliptic operators on general domains, in the process illustrating its stability and amenability to generalization. more...

The immersed boundary–finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are generally discontinuities in the pressure and viscous stress at fluid–structure interfaces. The standard immersed boundary approach, which connects the Lagrangian and Eulerian variables via integral transforms with regularized Dirac delta function kernels, smooths out these discontinuities, which generally leads to low order accuracy. This paper describes an approach to accurately resolve pressure discontinuities for these types of formulations, in which the solid may undergo large deformations. Our strategy is to decompose the physical pressure field into a sum of two pressure–like fields, one defined on the entire computational domain, which includes both the fluid and solid subregions, and one defined only on the solid subregion. Each of these fields is continuous on its domain of definition, which enables high accuracy via standard discretization methods without sacrificing sharp resolution of the pressure discontinuity. Numerical tests demonstrate that this method improves rates of convergence for displacements, velocities, stresses, and pressures as compared to the conventional IBFE method. Further, it produces much smaller errors at reasonable numbers of degrees of freedom. The performance of this method is tested on several cases with analytic solutions, a nontrivial benchmark problem of incompressible solid mechanics, and an example involving a thick, actively contracting torus. more...

Simulating the electric field-driven motion of rigid or deformable bodies in fluid media requires the solution of coupled equations of electrodynamics and hydrodynamics. In this work, we present a numerical method for treating such equations of electrohydrodynamics in an immersed body framework. In our approach, the electric field and fluid equations are solved on an Eulerian grid, and the immersed structures are modeled by meshless collections of Lagrangian nodes that move freely through the background Eulerian grid. Fluid-structure interaction is handled by an efficient distributed Lagrange multiplier approach, whereas the body force induced by the electric field is calculated using the Maxwell stress tensor. In addition, we adopt an adaptive mesh refinement (AMR) approach to discretizing the equations that permits us to resolve localized electric field gradients and fluid boundary layers with relatively low computational cost. Using this framework, we address a broad range of problems, including the dielectrophoretic motion of particles in microfluidic channels, three-dimensional nanowire assembly, and the effects of rotating electric fields to orient particles and to separate cells using their dielectric properties in a lab-on-a-chip device. We also simulate the phenomenon of electrolocation, whereby an animal uses distortions of a self-generated electric field to locate objects. Specifically, we perform simulations of a black ghost knifefish that tracks and captures prey using electrolocation. Although the proposed tracking algorithm is not intended to correspond to the physiological tracking mechanisms used by the real knifefish, extensions of this algorithm could be used to develop artificial ''electrosense'' for underwater vehicles. To our knowledge, these dynamic simulations of electrolocation are the first of their kind. more...

Many problems of interest in biological fluid mechanics involve interactions between fluids and solids that require the coupled solution of momentum equations for both the fluid and the solid. In this work, we develop a mathematical framework and an adaptive numerical method for such fluid-structure interaction (FSI) problems in which the structure may be rigid, deforming, or elastic. We employ an immersed boundary (IB) formulation of the problem that permits us to avoid body conforming discretizations and to use fast Cartesian grid solvers. Rigidity and deformational kinematic constraints are imposed using a formulation based on distributed Lagrange multipliers, and a conventional IB method is used to describe the elasticity of the immersed body. We use Cartesian grid adaptive mesh refinement (AMR) to discretize the equations of motion and thereby obtain a solution methodology that efficiently captures thin boundary layers at fluid-solid interfaces as well as flow structures shed from such interfaces. This adaptive methodology is validated for several benchmark problems in two and three spatial dimensions. In addition, we use this scheme to simulate free swimming, including the maneuvering of a two-dimensional model eel and a three-dimensional model of the weakly electric black ghost knifefish. more...

The mitral valve (MV) is one of the four cardiac valves. It consists of two leaflets that are connected to the left ventricular papillary muscles via multiple fibrous chordae tendinae. The primary functions of the MV are to allow for the free flow of blood into the left ventricle (LV) of the heart from the left atrium (LA) during the diastolic and early systolic phases of the cardiac cycle, and to prevent regurgitant flow from the LV to the LA in deep systole. MV disorders such as mitral stenosis and regurgitation cause significant morbidity and mortality, and an improved understanding of MV biomechanics could lead to improved medical and surgical procedures to restore normal MV function in patients with such disorders. Computational models can realistically capture the anatomical and functional features of the MV and hence can provide detailed spatial and temporal data that may not be easily obtained clinically or experimentally. In this study, an anatomical model of a human MV is derived from in vivo magnetic resonance imaging (MRI) data. Using this clinical imaging-derived model, fluid–structure interaction (FSI) simulations are performed using the immersed boundary (IB) method under physiological, dynamic transvalvular pressure loads. Computational analyses show that the subject-specific MV geometry has a significant influence on the simulation results. An initial validation of the model is achieved by comparing the opening height and flow rates to clinical measurements. more...

The projection method is a widely used fractional-step algorithm for solving the incompressible Navier-Stokes equations. Despite numerous improvements to the methodology, however, imposing physical boundary conditions with projection-based fluid solvers remains difficult, and obtaining high-order accuracy may not be possible for some choices of boundary conditions. In this work, we present an unsplit, linearly-implicit discretization of the incompressible Navier-Stokes equations on a staggered grid along with an efficient solution method for the resulting system of linear equations. Since our scheme is not a fractional-step algorithm, it is straightforward to specify general physical boundary conditions accurately; however, this capability comes at the price of having to solve the time-dependent incompressible Stokes equations at each timestep. To solve this linear system efficiently, we employ a Krylov subspace method preconditioned by the projection method. In our implementation, the subdomain solvers required by the projection preconditioner employ the conjugate gradient method with geometric multigrid preconditioning. The accuracy of the scheme is demonstrated for several problems, including forced and unforced analytic test cases and lid-driven cavity flows. These tests consider a variety of physical boundary conditions with Reynolds numbers ranging from 1 to 30000. The effectiveness of the projection preconditioner is compared to an alternative preconditioning strategy based on an approximation to the Schur complement for the time-dependent incompressible Stokes operator. The projection method is found to be a more efficient preconditioner in most cases considered in the present work. more...

Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-)elastic structure (the muscular walls and the valves of the heart). The immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves, and extensions of this work have yielded a three-dimensional model of the heart and great vessels. In the present work, we introduce a new adaptive version of the immersed boundary method. This adaptive scheme employs the same hierarchical structured grid approach (but a different numerical scheme) as the two-dimensional adaptive immersed boundary method of Roma et al. [A multilevel self adaptive version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1996; An adaptive version of the immersed boundary method, J. Comput. Phys. 153 (2) (1999) 509–534] and is based on a formally second order accurate (i.e., second order accurate for problems with sufficiently smooth solutions) version of the immersed boundary method that we have recently described [B.E. Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput. Phys. 208 (1) (2005) 75–105]. Actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell. We also present initial results from the application of this methodology to the three-dimensional simulation of blood flow in the heart and great vessels. The results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution. Differences are also observed in the flow about the mitral valve leaflets. more...

The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M.-C. Lai, C.S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys. 160 (2000) 705-719], Lai and Peskin introduced a formally second order accurate immersed boundary method, but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions. Consequently, in practice only first order convergence rates have been observed. In the present work, we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid-structure interaction problem, involving an immersed viscoelastic shell of finite thickness, studied over a broad range of Reynolds numbers. We consider two sets of material properties for the viscoelastic structure, including a case where the material properties of the coupled system are discontinuous at the fluid-structure interface. For both sets of material properties, the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations. more...