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.

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 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.

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.

The fish tail motion forms an attached leading edge vortex.

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail's delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.

The functional role of caudal and anal/dorsal fins during the C-start of a bluegill sunfish.

Fast starts are crucial in the survival of aquatic swimmers to capture prey or avoid predators. Currently, it is widely accepted that during C-starts: (1) the caudal fin generates a considerable hydrodynamic force; and (2) anal/dorsal fins are erected to significantly increase the hydrodynamic force. In this work, the above hypotheses on the role of fins during C-starts are studied using experimentally guided numerical simulations of four bluegill sunfish, whose fins are removed or erected. The amount of force created by the body and fins at each time instant was not constant and varied during the C-start. Nevertheless, in agreement with hypothesis (1), up to 70% of the instantaneous hydrodynamic force was generated by the tail during Stage 2 of the C-start, when the sunfish rapidly bends out of the C-shape. Additionally, the contribution in Stage 1, when the sunfish bends into a C-shape, is less than 20% at each instant. Most of the force in Stage 1 was produced by the body of the sunfish. In contrast to hypothesis (2), the effect of erection/removal of the fins was less than 5% of the instantaneous force in both Stages 1 and 2, except for a short period of time (2 ms) just before Stage 2. However, it is known that the anal/dorsal fins are actively controlled during the C-start from muscle activity measurements. Based on the results presented here, it is suggested that the active control of the anal/dorsal fins can be related to retaining the stability of the sunfish against roll and pitch movements during the C-start. Furthermore, the erection of the fins increases the moment of inertia to make the roll and pitch movements more difficult.

A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows.

We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position.

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.

Hydrodynamics of the bluegill sunfish C-start escape response: three-dimensional simulations and comparison with experimental data.

In this work we study the hydrodynamics of a bluegill sunfish performing a C-start maneuver in unprecedented detail using 3-D numerical simulations guided by previous laboratory experiments with live fish. The 3-D fish body geometry and kinematics are reconstructed from the experiments using high-speed video and prescribed as input to the numerical simulation. The calculated instantaneous flow fields at various stages of the C-start maneuver are compared with the two-dimensional particle image velocimetry measurements, and are shown to capture essentially all flow features observed in the measurements with good quantitative accuracy; the simulations reveal the experimentally observed three primary jet flow patterns whose momentum time series are in very good agreement with the measured flow field. The simulations elucidate for the first time the complex 3-D structure of the wake during C-starts, revealing an intricate vortical structure consisting of multiple connected vortex loops at the end of the C-start. We also find that the force calculated based on the 3-D flow field has higher magnitudes than that implied by the jet momentum on the midplane, and it exhibits large and rapid fluctuations during the two stages of the C-start. These fluctuations are physical and are related to the change in the direction of the acceleration of the fish body, which changes the location of the high and low pressure pockets around the fish.

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.

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.

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.

On the role of copepod antennae in the production of hydrodynamic force during hopping.

We integrate high-resolution experimental observations of a freely hopping copepod with three-dimensional numerical simulations to investigate the role of the copepod antennae in production of hydrodynamic force during hopping. The experimental observations revealed a distinctive asymmetrical deformation of the antennae during the power and return strokes, which lead us to the hypothesis that the antennae are active contributors to the production of propulsive force with kinematics selected in nature in order to maximize net thrust. To examine the validity of this hypothesis we carried out numerical experiments using an anatomically realistic, tethered, virtual copepod, by prescribing two sets of antenna kinematics. In the first set, each antenna moves as a rigid, oar-like structure in a reversible manner, whereas in the second set, the antenna is made to move asymmetrically as a deformable structure as revealed by the experiments. The computed results show that for both cases the antennae are major contributors to the net thrust force during hopping, and the results also clearly demonstrate the significant hydrodynamic benefit in terms of thrust enhancement and drag reduction derived from the biologically realistic, asymmetric antenna motion. This finding is not surprising given the low local Reynolds number environment within which the antenna operates, and points to striking similarities between the copepod antenna motion and ciliary propulsion. Finally, the simulations provide the first glimpse into the complex, highly 3-D structure of copepod wakes.

The effect of implantation orientation of a bileaflet mechanical heart valve on kinematics and hemodynamics in an anatomic aorta.

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.

Pulsatile flow effects on the hemodynamics of intracranial aneurysms.

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number (α), and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.

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 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.

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.