Metachronal Coordination of Multiple Appendages for Swimming and Pumping.

As a strategy for creating fluid flow, metachronal motion is widespread across sizes and species, including a broad array of morphologies, length scales, and coordination patterns. Because of this great diversity, it has not generally been viewed holistically: The study of metachrony for swimming and pumping has historically been taxonomically siloed, in spite of many commonalities between seemingly disparate organisms. The goal of the present symposium was to bring together individuals from different backgrounds, all of whom have made substantial individual contributions to our understanding of the fluid dynamics of metachronal motion. Because these problems share a common physical-mathematical basis, intentionally connecting this community is likely to yield future collaborations and significant scientific discovery. Here, we briefly introduce the concept of metachronal motion, present the benefits of creating a research network based on the common aspects of metachrony across biological systems, and outline the contributions to the symposium.

Interspecific variation in bristle number on forewings of tiny insects does not influence clap-and-fling aerodynamics.

Miniature insects must overcome significant viscous resistance in order to fly. They typically possess wings with long bristles on the fringes and use a clap-and-fling mechanism to augment lift. These unique solutions to the extreme conditions of flight at tiny sizes (<2 mm body length) suggest that natural selection has optimized wing design for better aerodynamic performance. However, species vary in wingspan, number of bristles (n) and bristle gap (G) to diameter (D) ratio (G/D). How this variation relates to body length (BL) and its effects on aerodynamics remain unknown. We measured forewing images of 38 species of thrips and 21 species of fairyflies. Our phylogenetic comparative analyses showed that n and wingspan scaled positively and similarly with BL across both groups, whereas G/D decreased with BL, with a sharper decline in thrips. We next measured aerodynamic forces and visualized flow on physical models of bristled wings performing clap-and-fling kinematics at a chord-based Reynolds number of 10 using a dynamically scaled robotic platform. We examined the effects of dimensional (G, D, wingspan) and non-dimensional (n, G/D) geometric variables on dimensionless lift and drag. We found that: (1) increasing G reduced drag more than decreasing D; (2) changing n had minimal impact on lift generation; and (3) varying G/D minimally affected aerodynamic forces. These aerodynamic results suggest little pressure to functionally optimize n and G/D. Combined with the scaling relationships between wing variables and BL, much wing variation in tiny flying insects might be best explained by underlying shared growth factors.

Hybrid Metachronal Rowing Augments Swimming Speed and Acceleration via Increased Stroke Amplitude.

Numerous aquatic invertebrates use drag-based metachronal rowing for swimming, in which closely spaced appendages are oscillated starting from the posterior, with each appendage phase-shifted in time relative to its neighbor. Continuously swimming species such as Antarctic krill generally use "pure metachronal rowing" consisting of a metachronal power stroke and a metachronal recovery stroke, while burst swimming species such as many copepods and mantis shrimp typically use "hybrid metachronal rowing" consisting of a metachronal power stroke followed by a synchronous or nearly synchronous recovery stroke. Burst swimming organisms need to rapidly accelerate in order to capture prey and/or escape predation, and it is unknown whether hybrid metachronal rowing can augment acceleration and swimming speed compared to pure metachronal rowing. Simulations of rigid paddles undergoing simple harmonic motion showed that collisions between adjacent paddles restrict the maximum stroke amplitude for pure metachronal rowing. Hybrid metachronal rowing similar to that observed in mantis shrimp (Neogonodactylus bredini) permits oscillation at larger stroke amplitude while avoiding these collisions. We comparatively examined swimming speed, acceleration, and wake structure of pure and hybrid metachronal rowing strategies by using a self-propelling robot. Both swimming speed and peak acceleration of the robot increased with increasing stroke amplitude. Hybrid metachronal rowing permitted operation at larger stroke amplitude without collision of adjacent paddles on the robot, augmenting swimming speed and peak acceleration. Hybrid metachronal rowing generated a dispersed wake unlike narrower, downward-angled jets generated by pure metachronal rowing. Our findings suggest that burst swimming animals with small appendage spacing, such as copepods and mantis shrimp, can use hybrid metachronal rowing to generate large accelerations via increasing stroke amplitude without concern of appendage collision.

Closer Appendage Spacing Augments Metachronal Swimming Speed by Promoting Tip Vortex Interactions.

Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as "metachronal paddling," has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at nonzero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L <1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from the metachronal motion only when the stroke amplitude is large.

Pausing after clap reduces power required to fling wings apart at low Reynolds number.

The smallest flying insects, such as thrips (body length < 2 mm), are challenged with needing to move in air at a chord-based Reynolds number (Rec) of the order of 10. Pronounced viscous dissipation at such a low Recrequires considerable energetic expenditure for tiny insects to stay aloft. Thrips flap their densely bristled wings at large stroke amplitudes, bringing both wings in close proximity to each other at the end of upstroke ('clap') and moving their wings apart at the start of downstroke ('fling'). From high-speed videos of free take-off flights of thrips, we observed that their forewings remain clapped for approximately 10% of the wingbeat cycle before the start of downstroke (fling stroke). We sought to examine if there are aerodynamic advantages associated with pausing wing motion after upstroke (clap stroke) and before downstroke (fling stroke) at Rec= 10. A dynamically scaled robotic clap and fling platform was used to measure lift and drag forces generated by physical models of solid (non-bristled) and bristled wings in single wing and wing pair configurations, for pause times ranging between 0% to 41% of the cycle. For solid and bristled wing pairs, pausing before the start of downstroke (fling stroke) dissipated vorticity generated at the end of upstroke (clap stroke). This resulted in a decrease in the drag coefficient averaged across downstroke (fling stroke) and in turn reduced power requirements. Also, increasing the pause time resulted in a larger decrease in the dimensionless power coefficient for the wing-pair configurations compared to the single-wing configurations. Our findings show that wing-wing interaction observed in the clap and fling motion of tiny insect wings is necessary to realize the aerodynamic benefits of pausing before fling, by reducing the power required to clap and fling for a small compromise in lift.

Metachronal Motion across Scales: Current Challenges and Future Directions.

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Finally, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

On the role of phase lag in multi-appendage metachronal swimming of euphausiids.

Metachronal paddling is a common method of drag-based aquatic propulsion, in which a series of swimming appendages are oscillated, with the motion of each appendage phase-shifted relative to the neighboring appendages. Ecologically and economically important euphausiid species such as Antarctic krill (Euphausia superba) swim constantly by stroking their paddling appendages (pleopods), with locomotion accounting for the bulk of their metabolic expenditure. They tailor their swimming gaits for behavioral and energetic needs by changing pleopod kinematics. The functional importance of inter-pleopod phase lag (ϕ) to metachronal swimming performance and wake structure is unknown. To examine this relation, we developed a geometrically and dynamically scaled robot ('krillbot') capable of self-propulsion. Krillbot pleopods were prescribed to mimic published kinematics of fast-forward swimming (FFW) and hovering (HOV) gaits ofE. superba, and the Reynolds number and Strouhal number of the krillbot matched well with those calculated for freely-swimmingE. superba. In addition to examining published kinematics with unevenϕbetween pleopod pairs, we modifiedE. superbakinematics to uniformly varyϕfrom 0% to 50% of the cycle. Swimming speed and thrust were largest for FFW withϕbetween 15%-25%, coincident withϕrange observed in FFW gait ofE. superba. In contrast to synchronous rowing (ϕ= 0%) where distances between hinged joints of adjacent pleopods were nearly constant throughout the cycle, metachronal rowing (ϕ> 0%) brought adjacent pleopods closer together and moved them farther apart. This factor minimized body position fluctuation and augmented metachronal swimming speed. Though swimming speed was lowest for HOV, a ventrally angled downward jet was generated that can assist with weight support during feeding. In summary, our findings show that inter-appendage phase lag can drastically alter both metachronal swimming speed and the large-scale wake structure.

Diastolic Vortex Alterations With Reducing Left Ventricular Volume: An In Vitro Study.

Despite the large number of studies of intraventricular filling dynamics for potential clinical applications, little is known as to how the diastolic vortex ring properties are altered with reduction in internal volume of the cardiac left ventricle (LV). The latter is of particular importance in LV diastolic dysfunction (LVDD) and in congenital diseases such as hypertrophic cardiomyopathy (HCM), where LV hypertrophy (LVH) can reduce LV internal volume. We hypothesized that peak circulation and the rate of decay of circulation of the diastolic vortex would be altered with reducing end diastolic volume (EDV) due to increasing confinement. We tested this hypothesis on physical models of normal LV and HCM geometries, under identical prescribed inflow profiles and for multiple EDVs, using time-resolved particle image velocimetry (TR-PIV) measurements on a left heart simulator. Formation and pinch-off of the vortex ring were nearly unaffected with changes to geometry and EDV. Pinch-off occurred before the end of early filling (E-wave) in all test conditions. Peak circulation of the vortex core near the LV outflow tract (LVOT) increased with lowering EDV and was lowest for the HCM model. The rate of decay of normalized circulation in dimensionless formation time (T*) increased with decreasing EDV. When using a modified version of T* that included average LV cross-sectional area and EDV, normalized circulation of all tested EDVs collapsed closely in the normal LV model (10% maximum difference between EDVs). Collectively, our results show that LV shape and internal volume play a critical role in diastolic vortex ring dynamics.

Hydrodynamics of metachronal paddling: effects of varying Reynolds number and phase lag.

Negatively buoyant freely swimming crustaceans such as krill must generate downward momentum in order to maintain their position in the water column. These animals use a drag-based propulsion strategy, where pairs of closely spaced swimming limbs are oscillated rhythmically from the tail to head. Each pair is oscillated with a phase delay relative to the neighbouring pair, resulting in a metachronal wave travelling in the direction of animal motion. It remains unclear how oscillations of limbs in the horizontal plane can generate vertical momentum. Using particle image velocimetry measurements on a robotic model, we observed that metachronal paddling with non-zero phase lag created geometries of adjacent paddles that promote the formation of counter-rotating vortices. The interaction of these vortices resulted in generating large-scale angled downward jets. Increasing phase lag resulted in more vertical orientation of the jet, and phase lags in the range used by Antarctic krill produced the most total momentum. Synchronous paddling produced lower total momentum when compared with metachronal paddling. Lowering Reynolds number by an order of magnitude below the range of adult krill (250-1000) showed diminished downward propagation of the jet and lower vertical momentum. Our findings show that metachronal paddling is capable of producing flows that can generate both lift (vertical) and thrust (horizontal) forces needed for fast forward swimming and hovering.

Aerodynamic effects of varying solid surface area of bristled wings performing clap and fling.

The smallest flying insects with body lengths under 2 mm show a marked preference for wings consisting of a thin membrane with long bristles, and the use of clap and fling kinematics to augment lift at Reynolds numbers (Re) of approximately 10. Bristled wings have been shown to reduce drag forces in clap and fling, but the aerodynamic roles of several bristled wing geometric variables remain unclear. This study examines the effects of varying the ratio of membrane area (A M) to total wing area (A T) on aerodynamic forces and flow structures generated during clap and fling at Re on the order of 10. We also examine the aerodynamic consequences of scaling bristled wings to Re = 120, relevant to flight of fruit flies. We analyzed published forewing images of 25 species of thrips (Thysanoptera) and found that A M/A T ranged from 14% to 27%, as compared to 11% to 88% previously reported for smaller-sized fairyflies (Hymenoptera). These data were used to develop physical bristled wing models with A M/A T ranging from 15% to 100%, which were tested in a dynamically scaled robotic clap and fling model. At all Re, bristled wings produced slightly lower lift coefficients (C L) when compared to solid wings, but provided significant drag reduction. At Re = 10, largest values of peak lift over peak drag ratios were generated by wing models with A M/A T similar to thrips forewings (15% to 30%). Circulation of the leading edge vortex and trailing edge vortex decreased with decreasing A M/A T during clap and fling at Re = 10. Decreased chordwise circulation near the wing tip, vortex shedding, and interaction between flow structures from clap with those from fling resulted in lowering C L generated via clap and fling at Re = 120 as compared to Re = 10. Clap and fling becomes less beneficial at Re = 120, regardless of the drag reduction provided by bristled wings.

Atrial systole enhances intraventricular filling flow propagation during increasing heart rate.

Diastolic fluid dynamics in the left ventricle (LV) has been examined in multiple clinical studies for understanding cardiac function in healthy humans and developing diagnostic measures in disease conditions. The question of how intraventricular filling vortex flow pattern is affected by increasing heart rate (HR) is still unanswered. Previous studies on healthy subjects have shown a correlation between increasing HR and diminished E/A ratio of transmitral peak velocities during early filling (E-wave) to atrial systole (A-wave). We hypothesize that with increasing HR under constant E/A ratio, E-wave contribution to intraventricular vortex propagation is diminished. A physiologic in vitro flow phantom consisting of a LV physical model was used for this study. HR was varied across 70, 100 and 120 beats per minute (bpm) with E/A of 1.1-1.2. Intraventricular flow patterns were characterized using 2D particle image velocimetry measured across three parallel longitudinal (apical-basal) planes in the LV. A pair of counter-rotating vortices was observed during E-wave across all HRs. With increasing HR, diminished vortex propagation occurred during E-wave and atrial systole was found to amplify secondary vorticity production. The diastolic time point where peak vortex circulation occurred was delayed with increasing HR, with peak circulation for 120bpm occurring as late as 90% into diastole near the end of A-wave. The role of atrial systole is elevated for higher HR due to the limited time available for filling. Our baseline findings and analysis approach can be applied to studies of clinical conditions where impaired exercise tolerance is observed.

Role of Mitral Annulus Diastolic Geometry on Intraventricular Filling Dynamics.

The mitral valve (MV) is a bileaflet valve positioned between the left atrium and ventricle of the heart. The annulus of the MV has been observed to undergo geometric changes during the cardiac cycle, transforming from a saddle D-shape during systole to a flat (and less eccentric) D-shape during diastole. Prosthetic MV devices, including heart valves and annuloplasty rings, are designed based on these two configurations, with the circular design of some prosthetic heart valves (PHVs) being an approximation of the less eccentric, flat D-shape. Characterizing the effects of these geometrical variations on the filling efficiency of the left ventricle (LV) is required to understand why the flat D-shaped annulus is observed in the native MV during diastole in addition to optimizing the design of prosthetic devices. We hypothesize that the D-shaped annulus reduces energy loss during ventricular filling. An experimental left heart simulator (LHS) consisting of a flexible-walled LV physical model was used to characterize the filling efficiency of the two mitral annular geometries. The strength of the dominant vortical structure formed and the energy dissipation rate (EDR) of the measured fields, during the diastolic period of the cardiac cycle, were used as metrics to quantify the filling efficiency. Our results indicated that the O-shaped annulus generates a stronger (25% relative to the D-shaped annulus) vortical structure than that of the D-shaped annulus. It was also found that the O-shaped annulus resulted in higher EDR values throughout the diastolic period of the cardiac cycle. The results support the hypothesis that a D-shaped mitral annulus reduces dissipative energy losses in ventricular filling during diastole and in turn suggests that a symmetric stent design does not provide lower filling efficiency than an equivalent asymmetric design.

Cardiovascular magnetic resonance compatible physical model of the left ventricle for multi-modality characterization of wall motion and hemodynamics.

BACKGROUND: The development of clinically applicable fluid-structure interaction (FSI) models of the left heart is inherently challenging when using in vivo cardiovascular magnetic resonance (CMR) data for validation, due to the lack of a well-controlled system where detailed measurements of the ventricular wall motion and flow field are available a priori. The purpose of this study was to (a) develop a clinically relevant, CMR-compatible left heart physical model; and (b) compare the left ventricular (LV) volume reconstructions and hemodynamic data obtained using CMR to laboratory-based experimental modalities. METHODS: The LV was constructed from optically clear flexible silicone rubber. The geometry was based off a healthy patient's LV geometry during peak systole. The LV phantom was attached to a left heart simulator consisting of an aorta, atrium, and systemic resistance and compliance elements. Experiments were conducted for heart rate of 70 bpm. Wall motion measurements were obtained using high speed stereo-photogrammetry (SP) and cine-CMR, while flow field measurements were obtained using digital particle image velocimetry (DPIV) and phase-contrast magnetic resonance (PC-CMR). RESULTS: The model reproduced physiologically accurate hemodynamics (aortic pressure = 120/80 mmHg; cardiac output = 3.5 L/min). DPIV and PC-CMR results of the center plane flow within the ventricle matched, both qualitatively and quantitatively, with flow from the atrium into the LV having a velocity of about 1.15 m/s for both modalities. The normalized LV volume through the cardiac cycle computed from CMR data matched closely to that from SP. The mean difference between CMR and SP was 5.5 ± 3.7%. CONCLUSIONS: The model presented here can thus be used for the purposes of: (a) acquiring CMR data for validation of FSI simulations, (b) determining accuracy of cine-CMR reconstruction methods, and

Clap and fling mechanism with interacting porous wings in tiny insect flight.

The aerodynamics of flapping flight for the smallest insects such as thrips is often characterized by a 'clap and fling' of the wings at the end of the upstroke and the beginning of the downstroke. These insects fly at Reynolds numbers (Re) of the order of 10 or less where viscous effects are significant. Although this wing motion is known to augment the lift generated during flight, the drag required to fling the wings apart at this scale is an order of magnitude larger than the corresponding force acting on a single wing. As the opposing forces acting normal to each wing nearly cancel during the fling, these large forces do not have a clear aerodynamic benefit. If flight efficiency is defined as the ratio of lift to drag, the clap and fling motion dramatically reduces efficiency relative to the case of wings that do not aerodynamically interact. In this paper, the effect of a bristled wing characteristic of many of these insects was investigated using computational fluid dynamics. We performed 2D numerical simulations using a porous version of the immersed boundary method. Given the computational complexity involved in modeling flow through exact descriptions of bristled wings, the wing was modeled as a homogeneous porous layer as a first approximation. High-speed video recordings of free-flying thrips in take-off flight were captured in the laboratory, and an analysis of the wing kinematics was performed. This information was used for the estimation of input parameters for the simulations. Compared with a solid wing (without bristles), the results of the study show that the porous nature of the wings contributes largely to drag reduction across the Re range explored. The aerodynamic efficiency, calculated as the ratio of lift to drag coefficients, was larger for some porosities when compared with solid wings.

Design and validation of a diaphragm pump for pediatric CRRT during ECMO.

PURPOSE: Children requiring artificial heart-lung support through extracorporeal membrane oxygenation (ECMO) are at increased risk of developing acute kidney injury (AKI). Continuous renal replacement therapy (CRRT) is the preferred method of treatment in pediatric AKI patients. CRRT devices are noted to provide inaccurate fluid balance (FB) when operated under low flow rates seen in children. We present the design and validation of a novel pump concept to provide accurate pediatric CRRT during ECMO. METHODS: A diaphragm pump was prototyped with a working stroke volume (SV) of 7 mL. Fluid transport occurs by periodic expansion and contraction of a flexible membrane due to pressure fluctuations of hydraulic fluid contained below its surface. Comparison of intravenous (IV) pumps to the diaphragm pump was conducted in vitro across the range of pressures observed during CRRT in ECMO. The pump was integrated into a CRRT circuit parallel with ECMO and FB accuracy was evaluated. RESULTS: The pump design improved efficiency of fluid transport, with flow rate errors as low as 1-5 ml/hr as compared to IV pumps (15-50 ml/hr). The SV of IV pumps increased with source pressure in a nearly linear manner compared to the minimal variation produced by the diaphragm pump. Inclusion of the diaphragm pump in a conventional CRRT circuit with ECMO improved the FB accuracy. CONCLUSIONS: A novel diaphragm pump concept has been presented for providing CRRT during ECMO in the pediatric population. Improvement of the pump accuracy compared to currently used CRRT pumps was demonstrated via in vitro testing.

Hemodynamic effects of implanting a unidirectional valve in the inferior vena cava of the Fontan circulation pathway: an in vitro investigation.

The Fontan surgical procedure used for treating patients with single ventricle congenital heart disorders results in a total cavopulmonary connection (TCPC) of the vena cavae to the pulmonary arteries (PAs). Sluggish TCPC flow and elevated hepatic venous pressures are commonly observed in this altered physiology, which in turn can lead to long-term complications including liver congestion and cirrhosis. The hypothesis of this study is that placement of a unidirectional valve within the inferior vena cava (IVC) will improve hemodynamics of the Fontan circulation by preventing retrograde flow and lowering hepatic venous pressure. An in vitro experimental setup consisting of an idealized TCPC model with flexible walls was used for investigation, and a bovine venous valve was inserted in the IVC below the TCPC. Pressure fluctuations were introduced in the flow through the model to simulate venous pulsatility. Hemodynamics of baseline and valve-implanted conditions were compared across total caval flows ranging from 1.0 to 2.5 l/min with varying caval flow distributions. The results indicated that valve closure occurred for 15-20% of the total cycle, with consequent reduction in the upstream hepatic venous pressure by 5 to 10 mmHg. Energy loss (EL) through the TCPC was lowered with valve implantation to 20-50% of baseline, occurring across all flow conditions considered with mean caval and PA pressures greater than 10 mmHg. The results of this in vitro modeling suggest that IVC valve placement has the potential to improve hemodynamics in the Fontan circulation by decreasing hepatic venous hypertension and EL.

Development of an accurate fluid management system for a pediatric continuous renal replacement therapy device.

Acute kidney injury is common in critically ill children, and renal replacement therapies provide a life-saving therapy to a subset of these children. However, there is no Food and Drug Administration-approved device to provide pediatric continuous renal replacement therapy (CRRT). Consequently, clinicians adapt approved adult CRRT devices for use in children because of lack of safer alternatives. Complications occur using adult CRRT devices in children because of inaccurate fluid balance (FB) between the volumes of ultrafiltrate (UF) removed and replacement fluid (RF) delivered. We demonstrate the design and validation of a pediatric fluid management system for obtaining accurate instantaneous and cumulative FB. Fluid transport was achieved via multiple novel pulsatile diaphragm pumps. The conservation of volume principle leveraging the physical property of fluid incompressibility along with mechanical coupling via a crankshaft was used for FB. Accuracy testing was conducted in vitro for 8 hour long continuous operation of the coupled UF and RF pumps. The mean cumulative FB error was <1% across filtration flows from 300 to 3000 ml/hour. This approach of FB control in a pediatric-specific CRRT device would represent a significant accuracy improvement over currently used clinical implementations.

Mechanics of healthy and functionally diseased mitral valves: a critical review.

The mitral valve is a complex apparatus with multiple constituents that work cohesively to ensure unidirectional flow between the left atrium and ventricle. Disruption to any or all of the components-the annulus, leaflets, chordae, and papillary muscles-can lead to backflow of blood, or regurgitation, into the left atrium, which deleteriously effects patient health. Through the years, a myriad of surgical repairs have been proposed; however, a careful appreciation for the underlying structural mechanics can help optimize long-term repair durability and inform medical device design. In this review, we aim to present the experimental methods and significant results that have shaped the current understanding of mitral valve mechanics. Data will be presented for all components of the mitral valve apparatus in control, pathological, and repaired conditions from human, animal, and in vitro studies. Finally, current strategies of patient specific and noninvasive surgical planning will be critically outlined.

Novel method of measuring valvular regurgitation using three-dimensional nonlinear curve fitting of Doppler signals within the flow convergence zone.

Mitral valve regurgitation (MR) is among the most prevalent and significant valve problems in the Western world. Echocardiography plays a significant role in the diagnosis of degenerative valve disease. However, a simple and accurate means of quantifying MR has eluded both the technical and clinical ultrasound communities. Perhaps the best clinically accepted method used today is the 2-D proximal isovelocity surface area (PISA) method. In this study, a new quantification method using 3-D color Doppler ultrasound, called the field optimization method (FOM), is described. For each 3-D color flow volume, this method iterates on a simple fluid dynamics model that, when processed by a model of ultrasound physics, attempts to agree with the observed velocities in a least-squares sense. The output of this model is an estimate of the regurgitant flow and the location of its associated orifice. To validate the new method, in vitro experiments were performed using a pulsatile flow loop and different geometric orifices. Measurements from the FOM and from 2-D PISA were compared with measurements made with a calibrated ultrasonic flow probe. Results show that the new method has a higher correlation to the truth data and has lower inter- and intra-observer variability than the 2-D PISA method.

Reconfiguration and the reduction of vortex-induced vibrations in broad leaves.

Flexible plants, fungi and sessile animals reconfigure in wind and water to reduce the drag acting upon them. In strong winds and flood waters, for example, leaves roll up into cone shapes that reduce drag compared with rigid objects of similar surface area. Less understood is how a leaf attached to a flexible leaf stalk will roll up stably in an unsteady flow. Previous mathematical and physical models have only considered the case of a flexible sheet attached to a rigid tether in steady flow. In this paper, the dynamics of the flow around the leaf of the wild ginger Hexastylis arifolia and the wild violet Viola papilionacea are described using particle image velocimetry. The flows around the leaves are compared with those of simplified physical and numerical models of flexible sheets attached to both rigid and flexible beams. In the actual leaf, a stable recirculation zone is formed within the wake of the reconfigured cone. In the physical model, a similar recirculation zone is observed within sheets constructed to roll up into cones with both rigid and flexible tethers. Numerical simulations and experiments show that flexible rectangular sheets that reconfigure into U-shapes, however, are less stable when attached to flexible tethers. In these cases, larger forces and oscillations due to strong vortex shedding are measured. These results suggest that the three-dimensional cone structure in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced by the leaf.