Coriolis and centrifugal forces drive haltere deformations and influence spike timing.

The halteres of flies are mechanosensory organs that serve a crucial role in the control of agile flight, providing sensory input for rapid course corrections to perturbations. Derived from hind wings, halteres are actively flapped and are thus subject to a variety of inertial forces as the fly undergoes complex flight trajectories. Previous analyses of halteres modelled them as a point mass, showing that Coriolis forces lead to subtle deflections orthogonal to the plane of flapping. By design, these models could not consider the effects of force gradients associated with a mass distribution, nor could they reveal three-dimensional spatio-temporal patterns of strain that result from those forces. In addition, diversity in the geometry of halteres, such as shape and asymmetries, could not be simply modelled with a point mass on a massless rod. To study the effects of mass distributions and asymmetries, we examine the haltere subject to both flapping and body rotations using three-dimensional finite-element simulations. We focus on a set of simplified geometries, in which we vary the stalk and bulb shape. We find that haltere mass distribution gives rise to two unreported deformation modes: (i) halteres twist with a magnitude that strongly depends on stalk and bulb geometry and (ii) halteres with an asymmetric mass distribution experience out-of-plane bending due to centrifugal forces, independent of body rotation. Since local strains at the base of the haltere drive deformations of mechanosensory neurons, we combined measured neural encoding mechanisms with our structural analyses to predict the spatial and temporal patterns of neural activity. This activity depends on both the flapping and rotation dynamics, and we show how the timing of neural activity is a viable mechanism for rotation-rate encoding. Our results provide new insights in haltere dynamics and show the viability for timing-based encoding of fly body rotations by halteres.

A new twist on gyroscopic sensing: body rotations lead to torsion in flapping, flexing insect wings.

Insects perform fast rotational manoeuvres during flight. While two insect orders use flapping halteres (specialized organs evolved from wings) to detect body dynamics, it is unknown how other insects detect rotational motions. Like halteres, insect wings experience gyroscopic forces when they are flapped and rotated and recent evidence suggests that wings might indeed mediate reflexes to body rotations. But, can gyroscopic forces be detected using only changes in the structural dynamics of a flapping, flexing insect wing? We built computational and robotic models to rotate a flapping wing about an axis orthogonal to flapping. We recorded high-speed video of the model wing, which had a flexural stiffness similar to the wing of the Manduca sexta hawkmoth, while flapping it at the wingbeat frequency of Manduca (25 Hz). We compared the three-dimensional structural dynamics of the wing with and without a 3 Hz, 10° rotation about the yaw axis. Our computational model revealed that body rotation induces a new dynamic mode: torsion. We verified our result by measuring wing tip displacement, shear strain and normal strain of the robotic wing. The strains we observed could stimulate an insect's mechanoreceptors and trigger reflexive responses to body rotations.

Fluid-structure interaction in compliant insect wings.

Insect wings deform significantly during flight. As a result, wings act as aeroelastic structures wherein both the driving motion of the structure and the aerodynamic loading of the surrounding fluid potentially interact to modify wing shape. We explore two key issues associated with the design of compliant wings: over a range of driving frequencies and phases of pitch-heave actuation, how does wing stiffness influence (1) the lift and thrust generated and (2) the relative importance of fluid loading on the shape of the wing? In order to examine a wide range of parameters relevant to insect flight, we develop a computationally efficient, two-dimensional model that couples point vortex methods for fluid force computations with structural finite element methods to model the fluid-structure interaction of a wing in air. We vary the actuation frequency, phase of actuation, and flexural stiffness over a range that encompasses values measured for a number of insect taxa (10-90 Hz; 0-π rad; 10(-7)-10(-5) N m(2)). We show that the coefficients of lift and thrust are maximized at the first and second structural resonant frequencies of the system. We also show that even in regions of structural resonance, fluid loading never contributes more than 20% to the development of flight forces.

Haemodynamic determinants of the mitral valve closure sound: a finite element study.

Automatic acoustic classification and diagnosis of mitral valve disease remain outstanding biomedical problems. Although considerable attention has been given to the evolution of signal processing techniques, the mechanics of the first heart sound generation has been largely overlooked. In this study, the haemodynamic determinants of the first heart sound were examined in a computational model. Specifically, the relationship of the transvalvular pressure and its maximum derivative to the time-frequency content of the acoustic pressure was examined. To model the transient vibrations of the mitral valve apparatus bathed in a blood medium, a dynamic, non-linear, fluid-coupled finite element model of the mitral valve leaflets and chordae tendinae was constructed. It was found that the root mean squared (RMS) acoustic pressure varied linearly (r2= 0.99) from 0.010 to 0.259 mmHg, following an increase in maximum dP/dt from 415 to 12470 mm Hg s(-1). Over that same range, peak frequency varied non-linearly from 59.6 to 88.1 Hz. An increase in left-ventricular pressure at coaptation from 22.5 to 58.5mm Hg resulted in a linear (r2= 0.91) rise in RMS acoustic pressure from 0.017 to 1.41mm Hg. This rise in transmitral pressure was accompanied by a non-linear rise in peak frequency from 63.5 to 74.1 Hz. The relationship between the transvalvular pressure and its derivative and the time-frequency content of the first heart sound has been examined comprehensively in a computational model for the first time. Results suggest that classification schemes should embed both of these variables for more accurate classification.

Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes.

We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function.

Mechanisms of aortic valve incompetence: finite-element modeling of Marfan syndrome.

OBJECTIVES: Progressive aortic root dilatation and an increased aortic root elastic modulus have been documented in persons with Marfan syndrome. To examine the effect of aortic root dilatation and increased elastic modulus on leaflet stress, strain, and coaptation, we used a finite-element model. METHODS: The normal model incorporated the geometry, tissue thickness, and anisotropic elastic moduli of normal human roots and valves. Four Marfan models were evaluated, in which the diameter of the aortic root was dilated by 5%, 15%, 30%, and 50%. Aortic root elastic modulus in the 4 Marfan models was doubled. Under diastolic pressure, regional stresses and strains were evaluated, and the percentage of leaflet coaptation was calculated. RESULTS: Root dilatation and stiffening significantly increased regional leaflet stress and strain compared with normal levels. Stress increases ranged from 80% to 360% and strain increases ranged from 60% to 200% in the 50% dilated Marfan model. Leaflet stresses and strains were disproportionately high at the attachment edge and coaptation area. Leaflet coaptation was decreased by approximately 20% in the 50% root dilatation model. CONCLUSIONS: Increasing root dilatation and root elastic modulus to simulate Marfan syndrome significantly increases leaflet stress and strain and reduces coaptation in an otherwise normal aortic valve. These alterations may influence the decision to use valve-sparing aortic root replacement procedures in patients with Marfan syndrome.

Inertial range determination for aerothermal turbulence using fractionally differenced processes and wavelets.

A fractionally differenced (FD) process is used to model aerothermal turbulence data, and the model parameters are estimated via wavelet techniques. Theory and results are presented for three estimators of the FD parameter: an "instantaneous" block-independent least squares estimator and block-dependent weighted least squares and maximum likelihood estimators. Confidence intervals are developed for the block-dependent estimators. We show that for a majority of the aerothermal turbulence data studied herein, there is a strong departure from the theoretical Kolmogorov turbulence over finite ranges of scale. A time-scale-dependent inertial range statistic is developed to quantify this departure.

Finite-element analysis of aortic valve-sparing: influence of graft shape and stiffness.

Aortic valve incompetence due to aortic root dilation may be surgically corrected by resuspension of the native valve within a vascular graft. This study was designed to examine the effect of graft shape and material properties on aortic valve function, using a three-dimensional finite-element model of the human aortic valve and root. First, the normal root elements in the model were replaced with graft elements, in either a cylindrical or a "pseudosinus" shape. Next, the elements were assigned the material properties of either polyethylene terephthalate, expanded polytetrafluoroethylene, or polyurethane. Diastolic pressures were applied, and stresses, strains, and coaptation were recorded for the valve, root, and graft. Regarding shape, the cylindrical graft models increased the valve stresses by up to 173%, whereas the root-shaped graft model increased valve stresses by up to 40% as compared to normal. Regarding material properties, the polyurethane models demonstrated valve stress, strain, and coaptation values closest to normal, for either root shape. Graft shape had a greater effect on the simulated valve function than did the material property of the graft. Optimizing the shape and material design of the graft may result in improved longevity of the spared valve if a normal environment is restored.

Mechanisms of aortic valve incompetence: finite element modeling of aortic root dilatation.

BACKGROUND: Idiopathic root dilatation often results in dysfunction of an otherwise normal aortic valve. To examine the effect of root dilatation on leaflet stress, strain, and coaptation, we utilized a finite element model. METHODS: The normal model incorporated the geometry, tissue thickness, stiffness, and collagen fiber alignment of normal human roots and valves. We evaluated four dilatation models in which diameters of the aortic root were dilated by 5%, 15%, 30%, and 50%. Regional stress and strain were evaluated and leaflet coaptation percent was calculated under diastolic pressure. RESULTS: Root dilatation significantly increased regional leaflet stress and strain beyond that found in the normal model. Stress increases ranged from 57% to 399% and strain increases ranged from 39% to 189% in the 50% dilatation model. Leaflet stress and strain were disproportionately high at the attachment edge and coaptation area. Leaflet coaptation was decreased by 18% in the 50% root dilatation model. CONCLUSIONS: Idiopathic root dilatation significantly increases leaflet stress and strain and reduces coaptation in an otherwise normal aortic valve. These alterations may affect valve-sparing aortic root replacement procedures.

Re-creation of sinuses is important for sparing the aortic valve: a finite element study.

OBJECTIVE: The treatment of choice for aortic valve insufficiency due to root dilatation has become root replacement with aortic valve sparing. However, root replacement with a synthetic graft may result in altered valve stresses. The purpose of this study was to compare the stress/strain patterns in the spared aortic valve in different root replacement procedures by means of finite element modeling. METHODS: Our finite element model of the normal human root and valve was modified to simulate and evaluate three surgical techniques: (1) "cylindrical" graft sutured below the valve at the anulus, (2) "tailored" graft sutured just above the valve, and (3) "pseudosinus" graft, tailored and sutured below the valve at the anulus. Simulated diastolic pressures were applied, and stresses and strains were calculated for the valve, root, and graft. Leaflet coaptation was also quantified. RESULTS: All three root replacement models demonstrated significantly altered leaflet stress patterns as compared with normal patterns. The cylindrical model showed the greatest increases in stress (16%-173%) and strain (10%-98%), followed by the tailored model (stress +10%-157%, strain +9%-36%). The pseudosinus model showed the smallest increase in stress (9%-28%) and strain (2%-31%), and leaflet coaptation was closest to normal. CONCLUSION: Valve-sparing techniques that allow the potential for sinus space formation (tailored, pseudosinus) result in simulated leaflet stresses that are closer to normal than the cylindrical technique. Normalized leaflet stresses in the clinical setting may result in improved longevity of the spared valve.

Mechanisms of aortic valve incompetence in aging: a finite element model.

BACKGROUND AND AIM OF THE STUDY: The effect of aging on aortic valve and root function was examined using a three-dimensional finite element model of the aortic root and valve. METHODS: Three models representing normal (< 35 years), middle (35-55 years) and older (> 55 years) age groups, were created by assigning tissue thickness and stiffness that increased with age (using ANSYS software). Diastolic pressure was applied; stresses and strains were then evaluated for the valve and root, and percent leaflet coaptation was calculated. RESULTS: Leaflet stresses were increased with aging, whereas leaflet strain and coaptation were decreased with aging. Specifically, leaflet stresses were increased by 6-14% in the middle-age model, and by 2-11% in the older-age model, as compared with normal in specified leaflet regions. Conversely, leaflet strains were decreased by 27-41% and 42-50% in the middle-age and older-age models, respectively. This reduced strain resulted in markedly decreased coaptation (9% and 30% reduction for middle- and older-age models). In the root, stress remained fairly constant with age, but strain in the root was progressively reduced with age (11% and 35% reduction for the middle and older-age models, respectively). CONCLUSIONS: In these models, increased stiffness and thickness due to aging reduces leaflet deformation and restricts coaptation. Clinically, valvular regurgitation may result due to leaflet thickening and stiffening with normal aging. Our model can now be utilized to evaluate the root-valve relationship in the presence of bioprosthetic valves or root replacements.

Stress variations in the human aortic root and valve: the role of anatomic asymmetry.

The asymmetry of the aortic valve and aortic root may influence their biomechanics, yet was not considered in previous valve models. This study developed an anatomically representative model to evaluate the regional stresses of the valve within the root environment. A finite-element model was created from magnetic-resonance images of nine human valve-root specimens, carefully preserving their asymmetry. Regional thicknesses and anisotropic material properties were assigned to higher-order elastic shell elements representing the valve and root. After diastolic pressurization, peak principal stresses were evaluated for the right, left, and noncoronary leaflets and root walls. Valve stresses were highest in the noncoronary leaflet (538 kPa vs right 473 kPa vs left 410 kPa); peak stresses were located at the free margin and belly near the coaptation surfaces (averages 537 and 482 kPa for all leaflets, respectively). Right and noncoronary sinus stresses were 21% and 10% greater than the left sinus. In all sinuses, stresses near the annulus were higher than near the sinotubular junction. Stresses vary across the valve and root, likely due to their inherent morphologic asymmetry and stress sharing. These factors may influence bioprosthetic valve durability and the incidence of isolated sinus dilatation.