Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies

Simulating cardiac fluid dynamics in the human heart

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions (FSIs). However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the valves are limited in their abilities to predict valve performance, capture fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac FSI in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart's microstructure. Further, it is the first FSI model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and that its responses to changes in loading conditions are consistent with the Frank-Starling mechanism. These complex relationships emerge intrinsically from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical interventions. They also can provide platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients.

Fluid-structure interaction simulation of mechanical aortic valves: a narrative review exploring its role in total product life cycle

Over the last years computer modelling and simulation has emerged as an effective tool to support the total product life cycle of cardiovascular devices, particularly in the device preclinical evaluation and post-market assessment. Computational modelling is particularly relevant for heart valve prostheses, which require an extensive assessment of their hydrodynamic performance and of risks of hemolysis and thromboembolic complications associated with mechanically-induced blood damage. These biomechanical aspects are typically evaluated through a fluid-structure interaction (FSI) approach, which enables valve fluid dynamics evaluation accounting for leaflets movement. In this context, the present narrative review focuses on the computational modelling of bileaflet mechanical aortic valves through FSI approach, aiming to foster and guide the use of simulations in device total product life cycle. The state of the art of FSI simulation of heart valve prostheses is reviewed to highlight the variety of modelling strategies adopted in the literature. Furthermore, the integration of FSI simulations in the total product life cycle of bileaflet aortic valves is discussed, with particular emphasis on the role of simulations in complementing and potentially replacing the experimental tests suggested by international standards. Simulations credibility assessment is also discussed in the light of recently published guidelines, thus paving the way for a broader inclusion of in silico evidence in regulatory submissions. The present narrative review highlights that FSI simulations can be successfully framed within the total product life cycle of bileaflet mechanical aortic valves, emphasizing that credible in silico models evaluating the performance of implantable devices can (at least) partially replace preclinical in vitro experimentation and support post-market biomechanical evaluation, leading to a reduction in both time and cost required for device development.

Overset meshing in combination with novel blended weak-strong fluid-structure interactions for simulations of a translating valve in series with a second valve

Mechanical circulatory support (MCS) devices can bridge the gap to transplant whilst awaiting a viable donor heart. The Realheart Total Artificial Heart is a novel positive-displacement MCS that generates pulsatile flow via bileaflet mechanical valves. This study developed a combined computational fluid dynamics and fluid-structure interaction (FSI) methodology for simulating positive displacement bileaflet valves. Overset meshing discretised the fluid domain, and a blended weak-strong coupling FSI algorithm was combined with variable time-stepping. Four operating conditions of relevant stroke lengths and rates were assessed. The results demonstrated this modelling strategy is stable and efficient for modelling positive-displacement artificial hearts.

Smoothed particle hydrodynamics based FSI simulation of the native and mechanical heart valves in a patient-specific aortic model

The failure of the aortic heart valve is common, resulting in deterioration of the pumping function of the heart. For the end stage valve failure, bi-leaflet mechanical valve (most popular artificial valve) is implanted. However, due to its non-physiological behaviour, a significant alteration is observed in the normal haemodynamics of the aorta. While in-vivo experimentation of a human heart valve (native and artificial) is a formidable task, in-silico study using computational fluid dynamics (CFD) with fluid structure interaction (FSI) is an effective and economic tool for investigating the haemodynamics of natural and artificial heart valves. In the present work, a haemodynamic model of a natural and mechanical heart valve has been developed using meshless particle-based smoothed particle hydrodynamics (SPH). In order to further enhance its clinical relevance, this study employs a patient-specific vascular geometry and presents a successful validation against traditional finite volume method and 4D magnetic resonance imaging (MRI) data. The results have demonstrated that SPH is ideally suited to simulate the heart valve function due to its Lagrangian description of motion, which is a favourable feature for FSI. In addition, a novel methodology for the estimation of the wall shear stress (WSS) and other related haemodynamic parameters have been proposed from the SPH perspective. Finally, a detailed comparison of the haemodynamic parameters has been carried out for both native and mechanical aortic valve, with a particular emphasis on the clinical risks associated with the mechanical valve.

A contact model based on the coefficient of restitution for simulations of bio-prosthetic heart valves

A new general contact model is proposed for preventing inter-leaflet penetration of bio-prosthetic heart valves (BHV) at the end of the systole, which has the advantage of applying kinematic constraints directly and creating smooth free edges. At the end of each time step, the impenetrability constraints and momentum exchange between the impacting bodies are applied separately based on the coefficient of restitution. The contact method is implemented in a rotation-free, large deformation, and thin shell finite-element (FE) framework based on loop's subdivision surfaces. A nonlinear, anisotropic material model for a BHV is employed which uses Fung-elastic constitutive laws for in-plane and bending responses, respectively. The contact model is verified and validated against several benchmark problems. For a BHV-specific validation, the computed strains on different regions of a BHV under constant pressure are compared with experimentally measured data. Finally, dynamic simulations of BHV under physiological pressure waveform are performed for symmetrical and asymmetrical fiber orientations incorporating the new contact model and compared with the penalty contact method. The proposed contact model provides the coaptation area of a functioning BHV during the closing phase for both of the fiber orientations. Our results show that fiber orientation affects the dynamic of leaflets during the opening and closing phases. A swirling motion for the BHV with asymmetrical fiber orientation is observed, similar to experimental data. To include the fluid effects, fluid-structure interaction (FSI) simulation of the BHV is performed and compared to the dynamic results.

[Experimental and numerical investigation of fluid-particle-interactions in water]

For the development of improved sediment transport models, the basic understanding of the interaction between the solid particle and the moving fluid (water) is important. In this article, current developments in the field of fluid-particle interaction are presented based on two research articles by Gold et al. (2023) and Worf et al. (2022). One presented in this article uses state of the art measurement methods to investigate the flow around spheres of different densities that oscillate in initially resting body of water. For the spherical pendulum a similar vortex shedding characteristic was observed for all investigated fluid density ratios (m * = ρ S / ρ F = 1.14 , 14.95 , density ratio between solid and fluid). A new object tracking method (DOT) is also presented, which enables temporally and spatially resolved analysis of flow structures in the fluid field. The experimental results of Gold et al. (2023) show, that vortex shedding occurs during the first period. This vortex propagates downward and eventually dissipates. Furthermore, a damping optimum of the spherical pendulum in the range of m * = 2.50 was observed. Additionally, an experiment with a cylindrical pendulum with m ∗ = 4 . 98 was investigated numerically utilizing an immersed boundary method. The process of creation and separation up to the dissipation of a vortex ring was described. Furthermore, this investigation by Worf et al. (2022) described the creation of tip vortices. These were connected with the development of the three-dimensional flow and added mass coefficient.

Multiscale model for blood flow after a bileaflet artificial aortic valve implantation

Cardiovascular diseases are the leading cause of mortality in the world, mainly due to atherosclerosis and its consequences. The article presents the numerical model of the blood flow through artificial aortic valve. The overset mesh approach was applied to simulate the valve leaflets motion and to realize the moving mesh, in the aortic arch and the main branches of cardiovascular system. To capture the cardiac system's response and the effect of vessel compliance on the outlet pressure, the lumped parameter model has been also included within the solution procedure. Three different turbulence modeling approaches were used and compared - the laminar, k-ϵ and k-ω model. The simulation results were also compared with the model excluding the moving valve geometry and the importance of the lumped parameter model for the outlet boundary condition was analyzed. Proposed numerical model and protocol was found as suitable for performing the virtual operations on the real patient vasculature geometry. The time-efficient turbulence model and overall solving procedure allows to support the clinicians in making decisions about the patient treatment and to predict the results of the future surgery.

Lagrangian dynamics of contaminant particles released from a point source in New York City

In this study, we investigated the transport of contaminants in the southern tip of Manhattan, New York City, under prevailing wind conditions. We considered a hypothetical contaminant particle release on the East side of the New York Stock Exchange at 50 m above the ground level. The transport of individual particles due to the wind flow in the city was simulated by coupling large-eddy simulations (Eulerian) with a Lagrangian model. The simulation results of our coupled Eulerian and Lagrangian approach showed that immediately after the contaminant particles are released, they propagate downwind and expand in the spanwise direction by ∼0.5 km. Specifically, approximately 15 min after the release, the contaminant particles reach the end of the 2.5-km-long study area with a mean velocity of 1.8 m/s, which is approximately 50% of the dominant wind velocity. With the cessation of the particle release, the contaminant particles start to recede from the urban area, mainly owing to their outflux from the study area and the settling of some particles on solid surfaces in the metropolitan area. More specifically, the study area becomes clear of particles in approximately 48.5 min. It was observed that some particles propagate with a mean velocity of 0.6 m/s, i.e., ∼17% of the dominant wind velocity. We also conducted a detailed investigation of the nature of particle transport patterns using finite-time Lyapunov exponents, which showed that dynamically rich Lagrangian coherent structures are formed around the buildings and off the tops of the skyscrapers.

Fluid-Structure Interaction Analysis on the Influence of the Aortic Valve Stent Leaflet Structure in Hemodynamics

Transcatheter aortic valve replacement (TAVR) is a minimally invasive surgical treatment for heart valve disease. At present, personalized TAVR valves are not available for some patients. This study adopts the fluid-structure interaction (FSI) model of the research object that has a three-disc leaflet form and structural design in the valve leaflet area. The valve opening shape, orifice area, stress-strain, and distribution of hemodynamic flow and pressure were compared under the condition of equal contact area between valve and blood. The FSI method was used to simulate the complex three dimensional characteristics of the flow field more accurately around the valve after TAVR stent implantation. Three personalized stent systems were established to study the performance of the leaflet design based on computational fluid dynamics. By comparing the different leaflet geometries, the maximum stress on leaflets and stents of model B was relatively reduced, which effectively improved the reliability of the stent design. Such valve design also causes the opening area of the valve leaflet to increase and the low-velocity area of the flow field to decrease during the working process of the valve, thus reducing the possibility of thrombosis. These findings can underpin breakthroughs in product design, and provide important theoretical support and technical guidance for clinical research.

The Effects of Implantation Orientation of a Bileaflet Mechanical Heart Valve in an Anatomic Left Ventricle-Aorta Configuration

We have performed three-dimensional high-resolution numerical simulations of a bi-leaflet mechanical heart valve (BMHV) implanted at different orientations in an anatomic left ventricle-aorta obtained from magnetic resonance imaging (MRI) of a volunteer. The thoroughly validated overset curvilinear-immersed boundary (overset-CURVIB) fluid-structure interaction (FSI) flow solver is used in which the aorta and LV are discretized with boundary-conforming and non-conforming curvilinear grids, respectively. The motion of the LV wall is prescribed based on a lumped parameter model while the motion of the leaflets are calculated using a strong coupled FSI algorithm enhanced with Aitken convergence technique. We carried out simulations for three valve orientations, which differ from each other by 45 degrees and compared the leaflet motion and flow field for multiple cycles. Our results show reproducible and relatively symmetrical opening for all valve orientations. The presence of small-scale vortical structures after peak systole, cause significant cycle-to-cycle variations in valve kinematics during the closing phase for all valve orientations. Furthermore, our results show that valve orientation does not have a significant effect on the distribution of viscous shear stress in the ascending aorta. Additionally, two different mathematical activation models including linear level of activation and Soares model are used to quantify the platelet activation in the ascending aorta. The results show that the valve orientation does not significantly affect (less than 8%) the total platelet activation in the ascending aorta.

Computational Methods for Fluid-Structure Interaction Simulation of Heart Valves in Patient-Specific Left Heart Anatomies

Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.

Ramifications of Vorticity on Aggregation and Activation of Platelets in Bi-Leaflet Mechanical Heart Valve: Fluid-Structure-Interaction Study

Bileaflet Mechanical Heart Valves (BMHV) are widely implanted to replace diseased heart valves. Despite many improvements in design, these valves still suffer from various complications, such as valve dysfunction, tissue overgrowth, hemolysis, and thromboembolism. Thrombosis and thromboembolism are believed to be initiated by platelet activation due to contact with foreign surfaces and non-physiological flow patterns. The implantation of the valve causes non-physiological patterns of vortex shedding behind the leaflets. The present study signifies the importance of vorticity in platelet activation and aggregation in BMHV implants. A two-phase model with the first Eulerian phase for blood and the second Discrete phase for platelets are used here. The generalized cross model of viscosity has been used to simulate the non-Newtonian viscosity of blood. A Fluid-Structure-Interaction model has been used to simulate the motion of leaflets. The present study has also estimated Platelet Activation State (PAS), which is the mathematical estimation of the degree of activation of platelets due to flow-induced shear stresses that cause thrombus formation. The regions in the fluid domain with a higher vorticity field have been found to contain platelets with relatively higher PAS than regions with relatively lower vorticity fields. Also, this study has quantitatively reported the effect of vorticity on platelet aggregation. The densities of platelets in the fluid areas with higher vorticity fields are higher than densities in the fluid regions with relatively lower vorticity fields, which indicate aggregation of highly activated platelets in areas with somewhat higher vorticity.

Computational Analysis of Active and Passive Flow Control for Backward Facing Step

The internal steady and unsteady flows with a frequency and amplitude are examined through a backward facing step (expansion ratio 2), for low Reynolds numbers (Re=400, Re=800), using the immersed boundary method. A lower part of the backward facing step is oscillating with the same frequency as the unsteady flow. The effect of the frequency, the amplitude, and the length of this oscillation is investigated. By suitable active control regulation, the recirculation lengths are reduced, and, for a percentage of the time period, no upper wall, negative velocity, region occurs. Moreover, substituting the prescriptively moving surface by a pressure responsive homogeneous membrane, the fluid–structure interaction is examined. We show that, by selecting proper values for the membrane parameters, such as membrane tension and applied external pressure, the upper wall flow separation bubble vanishes, while the lower one diminishes significantly in both the steady and the unsteady cases. Furthermore, for the time varying case, the length fluctuation of the lower wall reversed flow region is fairly contracted. The findings of the study have applications at the control of confined and external flows where separation occurs.

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

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 the computational tests indicate that the methodology introduced here remains stable for selected test cases across a range of solid-fluid 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.

A distributed lumped parameter model of blood flow with fluid-structure interaction

A distributed lumped parameter (DLP) model of blood flow was recently developed that can be simulated in minutes while still incorporating complex sources of energy dissipation in blood vessels. The aim of this work was to extend the previous DLP modeling framework to include fluid-structure interactions (DLP-FSI). This was done by using a simple compliance term to calculate pressure that does not increase the simulation complexity of the original DLP models. Verification and validation studies found DLP-FSI simulations had good agreement compared to analytical solutions of the wave equations, experimental measurements of pulsatile flow in elastic tubes, and in vivo MRI measurements of thoracic aortic flow. This new development of DLP-FSI allows for significantly improved computational efficiency of FSI simulations compared to FSI approaches that solve the full 3D conservation of mass and momentum equations while also including the complex sources of energy dissipation occurring in cardiovascular flows that other simplified models neglect.

A kinematics-based model for the settling of gravity-driven arbitrary-shaped particles on a surface

A discrete model is proposed for settling of an arbitrary-shaped particle onto a flat surface under the gravitational field. In this method, the particle dynamics is calculated such that (a) the particle does not create an overlap with the wall and (b) reaches a realistic equilibrium state, which are not guaranteed in the conventional discrete element methods that add a repulsive force (torque) based on the amount of overlap between the particle and the wall. Instead, upon the detection of collision, the particle’s kinematics is modified depending on the type of contact, i.e., point, line, and surface types, by assuming the contact point/line as the instantaneous center/line of rotation for calculating the rigid body dynamics. Two different stability conditions are implemented by comparing the location of the projection of the center of mass on the wall along gravity direction against the contact points to identify the equilibrium (stable) state on the wall for particles with multiple contact points. A variety of simulations are presented, including smooth surface particles (ellipsoids), regular particles with sharp edges (cylinders and pyramids) and irregular-shaped particles, to show that the method can provide the analytically-known equilibrium state.

A numerical study of fish adaption behaviors in complex environments with a deep reinforcement learning and immersed boundary-lattice Boltzmann method

Fish adaption behaviors in complex environments are of great importance in improving the performance of underwater vehicles. This work presents a numerical study of the adaption behaviors of self-propelled fish in complex environments by developing a numerical framework of deep learning and immersed boundary-lattice Boltzmann method (IB-LBM). In this framework, the fish swimming in a viscous incompressible flow is simulated with an IB-LBM which is validated by conducting two benchmark problems including a uniform flow over a stationary cylinder and a self-propelled anguilliform swimming in a quiescent flow. Furthermore, a deep recurrent Q-network (DRQN) is incorporated with the IB-LBM to train the fish model to adapt its motion to optimally achieve a specific task, such as prey capture, rheotaxis and Kármán gaiting. Compared to existing learning models for fish, this work incorporates the fish position, velocity and acceleration into the state space in the DRQN; and it considers the amplitude and frequency action spaces as well as the historical effects. This framework makes use of the high computational efficiency of the IB-LBM which is of crucial importance for the effective coupling with learning algorithms. Applications of the proposed numerical framework in point-to-point swimming in quiescent flow and position holding both in a uniform stream and a Kármán vortex street demonstrate the strategies used to adapt to different situations.

A hybrid echocardiography-CFD framework for ventricular flow simulations

Image-based CFD is a powerful tool to study cardiovascular flows while 2D echocardiography (echo) is the most widely used noninvasive imaging modality for the diagnosis of heart disease. Here, echo is combined with CFD, that is, an echo-CFD framework, to study ventricular flows. To achieve this, the previous 3D reconstruction from multiple 2D echo at standard cross sections is extended by: (a) reconstructing aortic and mitral valves from 2D echo and closing the left-ventricle (LV) geometry by approximating a superior wall; (b) incorporating the physiological assumption of the fixed apex as a reference (fixed) point in the 3D reconstruction; and (c) incorporating several smoothing algorithms to remove the nonphysical oscillations (ringing) near the basal section. The method is applied to echo from a baseline LV and one after inducing acute myocardial ischemia (AMI). The 3D reconstruction is validated by comparing it against a reference reconstruction from many echo sections while flow simulations are validated against the Doppler ultrasound velocity measurements. The sensitivity study shows that the choice of the smoothing algorithm does not change the flow pattern inside the LV. However, the presence of the mitral valve can significantly change the flow pattern during the diastole phase. In addition, the abnormal shape of a LV with AMI can drastically change the flow during diastole. Furthermore, the hemodynamic energy loss, as an indicator of the LV pumping performance, for different test cases is calculated, which shows a larger energy loss for a LV with AMI compared to the baseline one.

Effects of pannus formation on the flow around a bileaflet mechanical heart valve

Some patients with a bileaflet mechanical heart valve (BMHV) show significant increases in the transvalvular pressure drop and abnormal leaflet motion due to a pannus (an abnormal fibrovascular tissue) formed on the ventricular side, even in the absence of physical contact between the pannus and leaflets. We investigate the effects of the pannus shape (circular or semi-circular ring), implantation location and height on the leaflet motion, flow structure and transvalvular pressure drop using numerical simulations. The valve model considered resembles a 25 mm masters HP valve. The mean systolic pressure drop is significantly increased with increasing pannus height, irrespective of its implantation orientation. Near the peak inflow rate, the flow behind the pannus becomes highly turbulent, and the transvalvular pressure drop is markedly increased by the pannus. At the end of valve opening and the start of valve closing, oscillatory motions of the leaflets occur due to periodic shedding of vortex rings behind the pannus, and their amplitudes become large with increasing pannus height. When the pannus shape is asymmetric (e.g., a semi-circular ring) and its height reaches about 0.1D (D (= 25 mm) is the diameter of an aorta), abnormal leaflet motions occur: two leaflets move asymmetrically, and valve closing is delayed in time or incomplete, which increases the regurgitation volume. The peak energy loss coefficients due to panni are obtained from simulation data and compared with those predicted by a one-dimensional model. The comparison indicates that the one-dimensional model is applicable for the BMHV with and without pannus.

Numerical Simulations of Flow around Copepods: Challenges and Future Directions

Copepods are small aquatic creatures which are abundant in oceans as a major food source for fish, thereby playing a vital role in marine ecology. Because of their role in the food chain, copepods have been subject to intense research through different perspectives from anatomy, form-function biology, to ecology. Numerical simulations can uniquely support such investigations by quantifying: (i) the force and flow generated by different parts of the body, thereby clarify the form-function relation of each part; (ii) the relation between the small-scale flow around animal and the large-scale (e.g., oceanic) flow of its surroundings; and (iii) the flow and its energetics, thereby answering ecological questions, particularly, the three major survival tasks, i.e., feeding, predator avoidance, and mate-finding. Nevertheless, such numerical simulations need to overcome challenges involving complex anatomic shape of copepods, multiple moving appendages, resolving different scales (appendage-, animal- to large-scale). The numerical methods capable of handling such problems and some recent simulations are reviewed. At the end, future developments necessary to simulate copepods from animal- to surrounding-scale are discussed.

The Ground Effect in Anguilliform Swimming

Some anguilliform swimmers such as eels and lampreys swim near the ground, which has been hypothesized to have hydrodynamic benefits. To investigate whether swimming near ground has hydrodynamics benefits, two large-eddy simulations of a self-propelled anguilliform swimmer are carried out-one swimming far away from the ground (free swimming) and the other near the ground, that is, midline at 0 . 07 of fish length (L) from the ground creating a gap of 0 . 04 L . Simulations are carried out under similar conditions with both fish starting from rest in a quiescent flow and reaching steady swimming (constant average speed). The numerical results show that both swimmers have similar speed, power consumption, efficiency, and wake structure during steady swimming. This indicates that swimming near the ground with a gap larger than 0 . 04 L does not improve the swimming performance of anguilliform swimmers when there is no incoming flow, that is, the interaction of the wake with the ground does not improve swimming performance. When there is incoming flow, however, swimming near the ground may help because the flow has lower velocities near the ground.

An Immersed Interface Method for Discrete Surfaces

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C 0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.

Alternative mechanical heart valves for the developing world

Due to the prevalence of rheumatic heart disease in the developing world, mechanical heart valves in the younger patient population remain the prostheses of choice if repair is not feasible. Despite their durability, mechanical valves are burdened by coagulation and thromboembolism. Modern design tools can be utilized during the design process of mechanical valves, which allow a more systematic design approach and more detailed analysis of the blood flow through and around valves. These tools include computer-aided design, manufacturing, and engineering, such as computational fluid dynamics and finite element analysis, modern manufacturing techniques such as additive manufacturing, and sophisticated in-vitro and in-vivo tests. Following this systematic approach, a poppet valve was redesigned and the results demonstrate the benefits of the method. More organized flow patterns and fewer complex fluid structures were observed. The alternative trileaflet valve design has also been identified as a potential solution and, if a similar design approach is adopted, it could lead to the development of an improved mechanical heart valve in the future. It is imperative that researchers in developing countries continue their search for a mechanical heart valve with a reduced thromboembolic risk, requiring less or no anticoagulation.

Flow-Structure Interaction Simulations of the Aortic Heart Valve at Physiologic Conditions: The Role of Tissue Constitutive Model

The blood flow patterns in the region around the aortic valve depend on the geometry of the aorta and on the complex flow-structure interaction between the pulsatile flow and the valve leaflets. Consequently, the flow depends strongly on the constitutive properties of the tissue, which can be expected to vary between healthy and diseased heart valves or native and prosthetic valves. The main goal of this work is to qualitatively demonstrate that the choice of the constitutive model of the aortic valve is critical in analysis of heart hemodynamics. To accomplish that two different constitutive models were used in curvilinear immersed boundary-finite element-fluid-structure interaction (CURVIB-FE-FSI) method developed by Gilmanov et al. (2015, "A Numerical Approach for Simulating Fluid Structure Interaction of Flexible Thin Shells Undergoing Arbitrarily Large Deformations in Complex Domains," J. Comput. Phys., 300, pp. 814-843.) to simulate an aortic valve in an anatomic aorta at physiologic conditions. The two constitutive models are: (1) the Saint-Venant (StV) model and (2) the modified May-Newman&Yin (MNY) model. The MNY model is more general and includes nonlinear, anisotropic effects. It is appropriate to model the behavior of both prosthetic and biological tissue including native valves. Both models are employed to carry out FSI simulations of the same valve in the same aorta anatomy. The computed results reveal dramatic differences in both the vorticity dynamics in the aortic sinus and the wall shear-stress patterns on the aortic valve leaflets and underscore the importance of tissue constitutive models for clinically relevant simulations of aortic valves.

Immersed Methods for Fluid-Structure Interaction

Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

Image-Guided Fluid-Structure Interaction Simulation of Transvalvular Hemodynamics: Quantifying the Effects of Varying Aortic Valve Leaflet Thickness

When flow-induced forces are altered at the blood vessel, maladaptive remodeling can occur. One reason such remodeling may occur has to do with the abnormal functioning of the aortic heart valve due to disease, calcification, injury, or an improperly-designed prosthetic valve, which restricts the opening of the valve leaflets and drastically alters the hemodynamics in the ascending aorta. While the specifics underlying the fundamental mechanisms leading to changes in heart valve function may differ from one cause to another, one common and important change is in leaflet stiffness and/or mass. Here, we examine the link between valve stiffness and mass and the hemodynamic environment in aorta by coupling magnetic resonance imaging (MRI) with high-resolution fluid–structure interaction (FSI) computational fluid dynamics to simulate blood flow in a patient-specific model. The thoracic aorta and a native aortic valve were re-constructed in the FSI model from the MRI data and used for the simulations. The effect of valve stiffness and mass is parametrically investigated by varying the thickness (h) of the leaflets (h = 0.6, 2, 4 mm). The FSI simulations were designed to investigate systematically progressively higher levels of valve stiffness by increasing valve thickness and quantifying hemodynamic parameters known to be linked to aortopathy and valve disease. The computed results reveal dramatic differences in all hemodynamic parameters: (1) the geometric orifice area (GOA), (2) the maximum velocity V max of the jet passing through the aortic orifice area, (3) the rate of energy dissipation E ˙ diss ( t ) , (4) the total loss of energy E diss , (5) the kinetic energy of the blood flow E kin ( t ) , and (6) the average magnitude of vorticity Ω a ( t ) , illustrating the change in hemodynamics that occur due to the presence of aortic valve stenosis.

Diffuse-interface immersed-boundary framework for conjugate-heat-transfer problems

A monolithic solver based on a diffuse-interface immersed-boundary (IB) approach for conjugate-heat-transfer (CHT) problems is presented. The IB strategy assumes that the solid which is "immersed" into the computational grid is occupied by a "virtual" fluid to facilitate construction of "unified" governing equations that are solved everywhere in the domain. A unified momentum equation is devised using the solid volume fraction that reduces to the Navier-Stokes equation outside of the solid and to the no-slip boundary condition inside of it. The "unified" energy equation is constructed in an analogous fashion reducing to a convective-diffusive equation in the fluid domain and a fully diffusive equation in the solid domain with different thermal conductivities (or diffusivities) for both domains. The resulting equations are solved in both domains simultaneously using a hybrid staggered and nonstaggered finite-volume (FV) framework for incompressible flows. The second-order accurate IB-FV solver is employed to carry out investigations for CHT problems in natural and forced convective regimes. Numerical studies for different fluid-to-solid conductivity ratios show that the monolithic IB-CHT solver is a fast, simple, and accurate framework for simulations of CHT problems for Boussinesq flows.

A non-dimensional parameter for classification of the flow in intracranial aneurysms. I. Simplified geometries

Non-dimensional parameters are routinely used to classify different flow regimes. We propose a non-dimensional parameter, called Aneurysm number (An), which depends on both geometric and flow characteristics, to classify the flow inside aneurysm-like geometries (sidewalls and bifurcations). The flow inside aneurysm-like geometries can be widely classified into (i) the vortex mode in which a vortex ring is formed and (ii) the cavity mode in which a stationary shear layer acts similar to a moving lid of a lid-driven cavity. In these modes, two competing time scales exist: (a) a transport time scale, T t , which is the time scale to develop a shear layer by transporting a fluid particle across the expansion region, and (b) the vortex formation time scale,T v . Consequently, a relevant non-dimensional parameter is the ratio of these two time scales, which is called Aneurysm number: An = T t /T v . It is hypothesized, based on this definition, that the flow is in the vortex mode if the time required for vortex ring formationT v is less than the transport time T t (An ≳ 1). Otherwise, the flow is in the cavity mode (An ≲ 1). This hypothesis is systematically tested through numerical simulations on simplified geometries and shown to be true through flow visualizations and identification of the main vortex and shear layer. The main vortex is shown to evolve when An ≳ 1 but stationary when An ≲ 1. In fact, it is shown that the flows with An ≲ 1 (cavity mode) are characterized by much smaller fluctuations of wall shear stress and oscillatory shear index relative to flows with An ≳ 1 (vortex mode) because of their quasi-stationary flow pattern (cavity mode) compared to the evolution and breakdown of the formed vortex ring (vortex mode).

A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries

A simple parameter, called the Aneurysm number (An) which is defined as the ratio of transport to vortex time scales, has been shown to classify the flow mode in simplified aneurysm geometries. Our objective is to test the hypothesis that An can classify the flow in patient-specific intracranial aneurysms (IA). Therefore, the definition of this parameter is extended to anatomic geometries by using hydraulic diameter and the length of expansion area in the approximate direction of the flow. The hypothesis is tested using image-based flow simulations in five sidewall and four bifurcation geometries, i.e., if An ≲ 1 (shorter transport time scale), then the fluid is transported across the neck before the vortex could be formed, creating a quasi-stationary shear layer (cavity mode). By contrast, if An ≳ 1 (shorter vortex time scale), a vortex is formed. The results show that if An switches from An ≲ 1 to An ≳ 1, then the flow mode switches from the cavity mode to the vortex mode. However, if An does not switch, then the IAs stay in the same mode. It is also shown that IAs in the cavity mode have significantly lower An, temporal fluctuations of wall shear stress and oscillatory shear index (OSI) compared to the vortex mode (p < 0.01). In addition, OSI correlates with An in each flow mode and with pulsatility index in each IA. This suggests An to be a viable hemodynamic parameter which can be easily calculated without the need for detailed flow measurements/ simulations.

Methods for determination of stagnation in pneumatic ventricular assist devices

Background:

A pneumatic paediatric ventricular assist device developed at the Foundation of Cardiac Surgery Development, Zabrze, equipped with valves based on J. Moll’s design, with later modifications introduced at the Institute of Turbomachinery, Lodz University of Technology, was tested numerically and experimentally. The main aim of those investigations was to detect stagnation zones within the ventricular assist device and indicate advantages and limitations of both approaches.

Methods:

In the numerical transient test, a motion of the diaphragm and discs was simulated. Two different methods were used to illustrate stagnation zones in the ventricular assist device. The flow pattern inside the chamber was represented by velocity contours and vectors to validate the results using images obtained in the laser particle image velocimetry experiment.

Results:

The experimental light-based method implied problems with proper illumination of regions in the wall vicinity. High-resolution flow data and other important parameters as stagnation regions or flow patterns in regions not accessible for light in the particle image velocimetry method are derived in the numerical solution. However, computations of a single case are much more time-consuming if compared to a single experiment conducted on a well-calibrated stand.

Conclusion:

The resulting main vortexes in the central part of the pump chamber and the velocity magnitudes are correlated in both methods, which are complementary and when used together offer better insight into the flow structure inside the ventricular assist device and enable a deeper analysis of the results.

3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE FEM Model

Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.

Fluid-structure interaction with the entropic lattice Boltzmann method

We propose a fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show the validity of the proposed scheme for various challenging setups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with a finite element method (FEM) solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic surfaces.

Computational methods for the aortic heart valve and its replacements

INTRODUCTION

Replacement with a prosthetic device remains a major treatment option for the patients suffering from heart valve disease, with prevalence growing resulting from an ageing population. While the most popular replacement heart valve continues to be the bioprosthetic heart valve (BHV), its durability remains limited. There is thus a continued need to develop a general understanding of the underlying mechanisms limiting BHV durability to facilitate development of a more durable prosthesis. In this regard, computational models can play a pivotal role as they can evaluate our understanding of the underlying mechanisms and be used to optimize designs that may not always be intuitive. Areas covered: This review covers recent progress in computational models for the simulation of BHV, with a focus on aortic valve (AV) replacement. Recent contributions in valve geometry, leaflet material models, novel methods for numerical simulation, and applications to BHV optimization are discussed. This information should serve not only to infer reliable and dependable BHV function, but also to establish guidelines and insight for the design of future prosthetic valves by analyzing the influence of design, hemodynamics and tissue mechanics. Expert commentary: The paradigm of predictive modeling of heart valve prosthesis are becoming a reality which can simultaneously improve clinical outcomes and reduce costs. It can also lead to patient-specific valve design.

Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion

Numerical simulations are employed to study the hydrodynamics of self-propelled thunniform swimming. The swimmer is modeled as a tuna-like flexible body undulating with kinematics of thunniform type. The wake evolution follows the vortex structures arranged nearly vertical to the forward direction, vortex dipole formation resulting in the propulsion motion, and finally a reverse Kármán vortex street. We also carry out a systematic parametric study of various aspects of the fluid dynamics behind the freely swimming behavior, including the swimming speed, hydrodynamic forces, power requirement and wake vortices. The present results show that the fin thrust as well as swimming velocity is an increasing function of both tail undulating amplitude Ap and oscillating amplitude of the caudal fin θm. Whereas change on the propulsive performance with Ap is associated with the strength of wake vortices and the area of suction region on the fin, the swimming performance improves with θm due to the favorable tilting of the fin that make the pressure difference force more oriented toward the thrust direction. Moreover, the energy loss in the transverse direction and the power requirement increase with Ap but decrease with θm, and this indicates that for achieving a desired swimming speed increasing θm seems more efficiently than increasing Ap. Furthermore, we have compared the current simulations with the published experimental studies on undulatory swimming. Comparisons show that our work tackles the flow regime of natural thunniform swimmers and follows the principal scaling law of undulatory locomotion reported. Finally, this study enables a detailed quantitative analysis, which is difficult to obtain by experiments, of the force production of the thunniform mode as well as its connection to the self-propelled swimming kinematics and vortex wake structure. The current findings help provide insights into the swimming performance and mechanisms of self-propelled thunniform locomotion.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Non-Newtonian Blood Flow Simulation of Diastolic Phase in Bileaflet Mechanical Heart Valve Implanted in a Realistic Aortic Root Containing Coronary Arteries

Coronary arteries, which are branched from the sinuses, have tangible effects on the hemodynamic performance of the bileaflet mechanical heart valve (BMHV), especially in the diastolic phase. To better understand this issue, a computer model of ascending aorta including realistic sinus shapes and coronary arteries has been generated in this study in order to investigate the BMHV performance during diastole. Three-dimensional transient numerical analysis is conducted to simulate the diastolic blood flow through the hinges and in coronary arteries under the assumption of non-Newtonian behavior. Results indicate that as blood flows to the coronary arteries mainly during diastole, leakage flow from the hinge and other gaps will change considering the influence of coronary arteries. In addition, BMHV in the case of aortic replacement will increase blood flow rate into the coronary arteries about 100% as the mechanical valve resistance is higher than a native heart valve. Also, it will change the wall shear stress (WSS) distribution and increase coronary artery disease (CAD) potential. It is found out that although less leakage flow reduces the velocity magnitudes through the gaps, the shear stress acting on blood elements with non-Newtonian assumption will be detrimental in the hinge corner at the ventricular side. High WSS of 1800 Pa is observed at beginning of diastole at this region.

Effects of Reynolds and Womersley Numbers on the Hemodynamics of Intracranial Aneurysms

The effects of Reynolds and Womersley numbers on the hemodynamics of two simplified intracranial aneurysms (IAs), that is, sidewall and bifurcation IAs, and a patient-specific IA are investigated using computational fluid dynamics. For this purpose, we carried out three numerical experiments for each IA with various Reynolds (Re = 145.45 to 378.79) and Womersley (Wo = 7.4 to 9.96) numbers. Although the dominant flow feature, which is the vortex ring formation, is similar for all test cases here, the propagation of the vortex ring is controlled by both Re and Wo in both simplified IAs (bifurcation and sidewall) and the patient-specific IA. The location of the vortex ring in all tested IAs is shown to be proportional to Re/Wo² which is in agreement with empirical formulations for the location of a vortex ring in a tank. In sidewall IAs, the oscillatory shear index is shown to increase with Wo and 1/Re because the vortex reached the distal wall later in the cycle (higher resident time). However, this trend was not observed in the bifurcation IA because the stresses were dominated by particle trapping structures, which were absent at low Re = 151.51 in contrast to higher Re = 378.79.

Automated Three-Dimensional Reconstruction of the Left Ventricle From Multiple-Axis Echocardiography

Two-dimensional echocardiography (echo) is the method of choice for noninvasive evaluation of the left ventricle (LV) function owing to its low cost, fast acquisition time, and high temporal resolution. However, it only provides the LV boundaries in discrete 2D planes, and the 3D LV geometry needs to be reconstructed from those planes to quantify LV wall motion, acceleration, and strain, or to carry out flow simulations. An automated method is developed for the reconstruction of the 3D LV endocardial surface using echo from a few standard cross sections, in contrast with the previous work that has used a series of 2D scans in a linear or rotational manner for 3D reconstruction. The concept is based on a generalized approach so that the number or type (long-axis (LA) or short-axis (SA)) of sectional data is not constrained. The location of the cross sections is optimized to minimize the difference between the reconstructed and measured cross sections, and the reconstructed LV surface is meshed in a standard format. Temporal smoothing is implemented to smooth the motion of the LV and the flow rate. This software tool can be used with existing clinical 2D echo systems to reconstruct the 3D LV geometry and motion to quantify the regional akinesis/dyskinesis, 3D strain, acceleration, and velocities, or to be used in ventricular flow simulations.

Biomechanical Behavior of Bioprosthetic Heart Valve Heterograft Tissues: Characterization, Simulation, and Performance

The use of replacement heart valves continues to grow due to the increased prevalence of valvular heart disease resulting from an ageing population. Since bioprosthetic heart valves (BHVs) continue to be the preferred replacement valve, there continues to be a strong need to develop better and more reliable BHVs through and improved the general understanding of BHV failure mechanisms. The major technological hurdle for the lifespan of the BHV implant continues to be the durability of the constituent leaflet biomaterials, which if improved can lead to substantial clinical impact. In order to develop improved solutions for BHV biomaterials, it is critical to have a better understanding of the inherent biomechanical behaviors of the leaflet biomaterials, including chemical treatment technologies, the impact of repetitive mechanical loading, and the inherent failure modes. This review seeks to provide a comprehensive overview of these issues, with a focus on developing insight on the mechanisms of BHV function and failure. Additionally, this review provides a detailed summary of the computational biomechanical simulations that have been used to inform and develop a higher level of understanding of BHV tissues and their failure modes. Collectively, this information should serve as a tool not only to infer reliable and dependable prosthesis function, but also to instigate and facilitate the design of future bioprosthetic valves and clinically impact cardiology.

Self-propelled swimming simulations of bio-inspired smart structures

This paper presents self-propelled swimming simulations of a foldable structure, whose folded configuration is a box. For self-locomotion through water the structure unfolds and undulates. To guide the design of the structure and understand how it should undulate to achieve either highest speed or maximize efficiency during locomotion, several kinematic parameters were systematically varied in the simulations: the wave type (standing wave versus traveling wave), the smoothness of undulations (smooth undulations versus undulations of rigid links), the mode of undulations (carangiform: mackerel-like versus anguilliform: eel-like undulations), and the maximum amplitude of undulations. We show that the swimmers with standing wave are slow and inefficient because they are not able to produce thrust using the added-mass mechanism. Among the tested types of undulation at low Reynolds number (Re) regime of [Formula: see text] (Strouhal number of about 1.0), structures that employ carangiform undulations can swim faster, whereas anguilliform swimmers are more economic, i.e., using less power they can swim a longer distance. Another finding of our simulations is that structures which are made of rigid links are typically less efficient (lower propulsive and power efficiencies and also lower swimming speed) compared with smoothly undulating ones because a higher added-mass force is generated by smooth undulations. The wake of all the swimmers bifurcated at the low Re regime because of the higher lateral relative to the axial velocity (high Strouhal number) that advects the vortices laterally creating a double row of vortices in the wake. In addition, we show that the wake cannot be used to predict the performance of the swimmers because the net force in each cycle is zero for self-propelled bodies and the pressure term is not negligible compared to the other terms.

Immersed boundary-finite element model of fluid-structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to e-volve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinsuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configurations of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high-Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left ventricular fluid dynamics.

The impact of valve simplifications on left ventricular hemodynamics in a three dimensional simulation based on in vivo MRI data

Left ventricle (LV) fluid dynamics and the function of its valves have a crucial impact on clinical diagnosis, treatment and prosthesis design. In this paper, we simulated left ventricular flow using 3D computational fluid dynamics (CFD) based on geometrical and deformational information obtained from MRI. Time variant smoothed LV shapes were extracted from MR images. Corresponding deformation data was interpolated using a cubic-spline interpolation. To evaluate valve influence on LV flow, we compared two planar valve models: physiologically corrected gradually opening/closing model and a simple on/off model. Endocardial displacement was applied to fluid boundary using fluid-structure interaction (FSI) approach. Arbitrary Lagrangian-Eulerian (ALE) formulation was used for unsteady incompressible viscous Newtonian blood flow in the fluid domain. Comparison of results for LV flow with two valve models demonstrated a clear distinction between pressure distribution, velocity distribution, vortex formation/growth/vanishing and energy dissipation especially in the filling phase. Consequently, LV flow simulation by ignoring geometrical details of valves׳ model may lead to non-realistic results in some aspects.

Blood damage through a bileaflet mechanical heart valve: a quantitative computational study using a multiscale suspension flow solver

Bileaflet mechanical heart valves (BMHVs) are among the most popular prostheses to replace defective native valves. However, complex flow phenomena caused by the prosthesis are thought to induce serious thromboembolic complications. This study aims at employing a novel multiscale numerical method that models realistic sized suspended platelets for assessing blood damage potential in flow through BMHVs. A previously validated lattice-Boltzmann method (LBM) is used to simulate pulsatile flow through a 23 mm St. Jude Medical (SJM) Regent™ valve in the aortic position at very high spatiotemporal resolution with the presence of thousands of suspended platelets. Platelet damage is modeled for both the systolic and diastolic phases of the cardiac cycle. No platelets exceed activation thresholds for any of the simulations. Platelet damage is determined to be particularly high for suspended elements trapped in recirculation zones, which suggests a shift of focus in blood damage studies away from instantaneous flow fields and toward high flow mixing regions. In the diastolic phase, leakage flow through the b-datum gap is shown to cause highest damage to platelets. This multiscale numerical method may be used as a generic solver for evaluating blood damage in other cardiovascular flows and devices.

The hydrodynamic advantages of synchronized swimming in a rectangular pattern

Fish schooling is a remarkable biological behavior that is thought to provide hydrodynamic advantages. Theoretical models have predicted significant reduction in swimming cost due to two physical mechanisms: vortex hypothesis, which reduces the relative velocity between fish and the flow through the induced velocity of the organized vortex structure of the incoming wake; and the channeling effect, which reduces the relative velocity by enhancing the flow between the swimmers in the direction of swimming. Although experimental observations confirm hydrodynamic advantages, there is still debate regarding the two mechanisms. We provide, to our knowledge, the first three-dimensional simulations at realistic Reynolds numbers to investigate these physical mechanisms. Using large-eddy simulations of self-propelled synchronized swimmers in various rectangular patterns, we find evidence in support of the channeling effect, which enhances the flow velocity between swimmers in the direction of swimming as the lateral distance between swimmers decreases. Our simulations show that the coherent structures, in contrast to the wake of a single swimmer, break down into small, disorganized vortical structures, which have a low chance for constructive vortex interaction. Therefore, the vortex hypothesis, which is relevant for diamond patterns, was not found for rectangular patterns, but needs to be further studied for diamond patterns in the future. Exploiting the channeling mechanism, a fish in a rectangular school swims faster as the lateral distance decreases, while consuming similar amounts of energy. The fish in the rectangular school with the smallest lateral distance (0.3 fish lengths) swims 20% faster than a solitary swimmer while consuming similar amount of energy.