Breaking the symmetry of a wavy channel alters the route to chaotic flow.

We numerically explore the two-dimensional, incompressible, isothermal flow through a wavy channel, with a focus on how the channel geometry affects the routes to chaos at Reynolds numbers between 150 and 1000. We find that (i) the period-doubling route arises in a symmetric channel, (ii) the Ruelle-Takens-Newhouse route arises in an asymmetric channel, and (iii) the type-II intermittency route arises in both asymmetric and semiwavy channels. We also find that the flow through the semiwavy channel evolves from a quasiperiodic torus to an unstable invariant set (chaotic saddle), before eventually settling on a period-1 limit-cycle attractor. This study reveals that laminar channel flow at elevated Reynolds numbers can exhibit a variety of nonlinear dynamics. Specifically, it highlights how breaking the symmetry of a wavy channel can not only influence the critical Reynolds number at which chaos emerges, but also diversify the types of bifurcation encountered en route to chaos itself.

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.

A learning-based, region of interest-tracking algorithm for catheter detection in echocardiography.

Echocardiography (echo) is gaining popularity to guide the catheter during surgical procedures. However, it is difficult to discern the catheter tip in echo even with an acoustically active catheter. An acoustically active catheter is detected for the first time in cardiac echo images using two methods. First, a convolutional neural network (CNN) model was trained to detect the region of interest (ROI), the interior of the left ventricle, containing the catheter tip. Color intensity difference detection technique was implemented on the ROI to detect the catheter. This method succeeded in detecting the catheter without any manual input on 94% and 57% of long- and short-axis projections, respectively. Second, several tracking methods were implemented and tested. Given the manually identified initial positions of the catheter, the tracking methods could distinguish between the target (catheter tip) and the surrounding on the rest of the frames. Combining the two techniques, for the first time, resulted in an automatic, robust, and fast method for catheter detection in echo images.

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 implanted at different orientations in an anatomic left ventricle-aorta obtained from magnetic resonance imaging of a volunteer. The thoroughly validated overset curvilinear-immersed boundary fluid-structure interaction flow solver is used in which the aorta and left ventricle (LV) are discretized with boundary-conforming and nonconforming curvilinear grids, respectively. The motion of the left ventricle wall is prescribed based on a lumped parameter model while the motion of the leaflets is calculated using a strongly coupled fluid-structure interaction algorithm enhanced with Aitken convergence technique. We carried out simulations for three valve orientations, which differ from each other by 45 deg, 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 causes 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.

Automatic segmentation of the left ventricle in echocardiographic images using convolutional neural networks.

BACKGROUND: Two-dimensional echocardiography (2D echo) is the most widely used non-invasive imaging modality due to its fast acquisition time, low cost, and high temporal resolution. Boundary identification of left ventricle (LV) in 2D echo, i.e., image segmentation, is the first step to calculate relevant clinical parameters. Currently, LV segmentation in 2D echo is primarily conducted semi-manually. A fully-automatic segmentation of the LV wall needs further development. METHODS: We evaluated the performance of the state-of-the-art convolutional neural networks (CNNs) for the segmentation of 2D echo images from 6 standard projections of the LV. We used two segmentation algorithms: U-net and segAN. The models were trained using an in-house dataset, which consists of 1,649 porcine images from 6 to 8 different pigs. In addition, a transfer learning approach was used for the segmentation of long-axis projections by training models with our database based on the previously trained weights obtained from Cardiac Acquisitions for Multi-structure Ultrasound Segmentation (CAMUS) dataset. The models were tested on a separate set of images from two other pigs by computing several metrics. The segmentation process was combined with a 3D reconstruction framework to quantify the physiological indices such as LV volumes and ejection fraction (EF). RESULTS: The average dice metric for the LV cavity was 0.90 and 0.91 for the U-net and segAN, respectively, which was higher than 0.82 for the level-set (P value: 3.31×10-25). The average Hausdorff distance for the LV cavity was 2.71 mm and 2.82 mm for the U-net and segAN, respectively, which was lower than 3.64 mm for the level-set (P value: 4.86×10-16). The LV shapes and volumes obtained using the CNN segmentation models were in good agreement with the results segmented by the experts. In addition, the differences of the calculated physiological parameters between two 3D reconstruction models segmented by the experts and CNNs were less than 15%. CONCLUSIONS: The results showed that both CNN models achieve higher performance on LV segmentation than the level-set method. The error of the reconstruction from automatic segmentation compared to the expert segmentation is less than 15%, which is within the 20% error of echo compared to the gold standard.

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.

Fluid-structure coupled biotransport processes in aortic valve disease.

Biological transport processes near the aortic valve play a crucial role in calcific aortic valve disease initiation and bioprosthetic aortic valve thrombosis. Hemodynamics coupled with the dynamics of the leaflets regulate these transport patterns. Herein, two-way coupled fluid-structure interaction (FSI) simulations of a 2D bicuspid aortic valve and a 3D mechanical heart valve were performed and coupled with various convective mass transport models that represent some of the transport processes in calcification and thrombosis. Namely, five different continuum transport models were developed to study biochemicals that originate from the blood and the leaflets, as well as residence-time and flow stagnation. Low-density lipoprotein (LDL) and platelet activation were studied for their role in calcification and thrombosis, respectively. Coherent structures were identified using vorticity and Lagrangian coherent structures (LCS) for the 2D and 3D models, respectively. A very close connection between vortex structures and biochemical concentration patterns was shown where different vortices controlled the concentration patterns depending on the transport mechanism. Additionally, the relationship between leaflet concentration and wall shear stress was revealed. Our work shows that blood flow physics and coherent structures regulate the flow-mediated biological processes that are involved in aortic valve calcification and thrombosis, and therefore could be used in the design process to optimize heart valve replacement durability.

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.

A Simple Flow Classification Parameter Can Discriminate Rupture Status in Intracranial Aneurysms.

BACKGROUND: A simple dimensionless aneurysm number ($An$), which depends on geometry and flow pulsatility, was previously shown to distinguish the flow mode in intracranial aneurysms (IA): vortex mode with a dynamic vortex formation/evolution if $An > 1$, and cavity mode with a steady shear layer if $An < 1$. OBJECTIVE: To hypothesize that $An\ > \ 1$ can distinguish rupture status because vortex mode is associated with high oscillatory shear index, which, in turn, is statistically associated with rupture. METHODS: The above hypothesis is tested on a retrospective, consecutively collected database of 204 patient-specific IAs. The first 119 cases are assigned to training and the remainder to testing dataset. $An$ is calculated based on the pulsatility index (PI) approximated either from the literature or solving an optimization problem (denoted as$\ \widehat {PI}$). Student's t-test and logistic regression (LR) are used for hypothesis testing and data fitting, respectively. RESULTS: $An$ can significantly discriminate ruptured and unruptured status with 95% confidence level (P < .0001). $An$ (using PI) and $\widehat {An}$ (using $\widehat {PI}$) significantly predict the ruptured IAs (for training dataset $An\!:\ $AUC = 0.85, $\widehat {An}\!:\ $AUC = 0.90, and for testing dataset $An\!:\ $sensitivity = 94%, specificity = 33%, $\widehat {An}\!:\ $sensitivity = 93.1%, specificity = 52.85%). CONCLUSION: $An > 1$ predicts ruptured status. Unlike traditional hemodynamic parameters such as wall shear stress and oscillatory shear index, $An$ has a physical threshold of one (does not depend on statistical analysis) and does not require time-consuming flow simulations. Therefore, $An$ is a simple, practical discriminator of IA rupture status.

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.

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 formation T 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.

Comparison of platelet activation through hinge vs bulk flow in bileaflet mechanical heart valves.

Bileaflet mechanical heart valves (BMHVs) are prone to thromboembolic complications which are believed to be initiated by platelet activation. Platelets are activated by non-physiologic shear stresses in the bulk flow or the leakage/hinge flow, whose contributions has yet to be quantified. Here, the contribution of bulk and hinge flows to the activation of platelets in BMHVs is quantified for the first time by performing simulations of the flow through a BMHV and resolving the hinge by overset grids (one grid for the bulk flow and two for the hinge regions coupled together using one-way and two-way interpolation). It was found that two-way coupling is essential to obtain correct hinge flow features. The platelet activation through the hinge for two gap sizes (250 and 150 µm) is compared to the activation in the bulk flow using two platelet activation models to ensure the consistency of the observed trends. The larger gap has a higher total activation, but a better washout ability due to higher velocities. The maximum shear stress observed in the bulk flow (∼320dyne/cm2) is much smaller than the hinge (∼1000dyne/cm2). However, the total activation by the bulk flow is found to be several folds higher than by the hinge/leakage flow. This is mainly due to the higher flow rate of the bulk flow which exposes much more platelets to shear stress than the leakage flow.

Platelet activation of mechanical versus bioprosthetic heart valves during systole.

Thrombus formation is a major concern for recipients of mechanical heart valves (MHVs), which requires them to take anticoagulant drugs for the rest of their lives. Bioprosthetic heart valves (BHVs) do not require life-long anticoagulant therapy but deteriorate after 10-15years. The thrombus formation is initiated by the platelet activation which is thought to be mainly generated in MHVs by the flow through the hinge and the leakage flow during the diastole. However, our results show that the activation in the bulk flow during the systole phase might play an essential role as well. This is based on our results obtained by comparing the thrombogenic performance of a MHV and a BHV (as control) in terms of shear induced platelet activation under exactly the same conditions. Three different mathematical activation models including linear level of activation, damage accumulation, and Soares model are tested to quantify the platelet activation during systole using the previous simulations of the flow through MHV and BHV in a straight aorta under the same physiologic flow conditions. Results indicate that the platelet activation in the MHV at the beginning of the systole phase is slightly less than the BHV. However, at the end of the systole phase the platelet activation by the bulk flow for the MHV is several folds (1.41, 5.12, and 2.81 for linear level of activation, damage accumulation, and Soares model, respectively) higher than the BHV for all tested platelet activation models.

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.

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.

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.

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.

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.

The Role of Shape and Heart Rate on the Performance of the Left Ventricle.

The left ventricle function is to pump the oxygenated blood through the circulatory system. Ejection fraction is the main noninvasive parameter for detecting heart disease (healthy >55%), and it is thought to be the main parameter affecting efficiency. However, the effects of other parameters on efficiency have yet to be investigated. We investigate the effect of heart rate and left ventricle shape by carrying out 3D numerical simulations of a left ventricle at different heart rates and perturbed geometries under constant, normal ejection fraction. The simulation using the immersed boundary method provide the 3D flow and pressure fields, which enable direct calculation of a new hemodynamic efficiency (H-efficiency) parameter, which does not depend on any reference pressure. The H-efficiency is defined as the ratio of flux of kinetic energy (useful power) to the total cardiac power into the left ventricle control volume. Our simulations show that H-efficiency is not that sensitive to heart rate but is maximized at around normal heart rate (72 bpm). Nevertheless, it is more sensitive to the shape of the left ventricle, which affects the H-efficiency by as much as 15% under constant ejection fraction.