Per G. Reinhall

Stress Variations in the Human Aortic Root and Valve: The Role of Anatomic Asymmetry

AbstractThe 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.

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.

Underwater Mach wave radiation from impact pile driving: theory and observation.

The underwater noise from impact pile driving is studied using a finite element model for the sound generation and parabolic equation model for propagation. Results are compared with measurements using a vertical line array deployed at a marine construction site in Puget Sound. It is shown that the dominant underwater noise from impact driving is from the Mach wave associated with the radial expansion of the pile that propagates down the pile after impact at supersonic speed. The predictions of vertical arrival angle associated with the Mach cone, peak pressure level as function of depth, and dominant features of the pressure time series compare well with corresponding field observations.

54.3: Modeling and Control of the Resonant Fiber Scanner for Laser Scanning Display or Acquisition

The resonant fiber scanner produces a flying laser spot scan for display or image acquisition purposes. Dynamic nonlinearities during large amplitude vibrations of the resonant fiber scanner result in distortions in the two-dimensional scan pattern and the acquired images. A dynamic model which includes the fibers dynamic nonlinearities has been developed to understand the nonlinear behavior and as the basis of a controller to remove the scan distortion. A robust state-space controller has been implemented to force the resonant fiber scanner to follow a spiral scan pattern. Acquired images at 250×250 pixel resolution demonstrate improved image fidelity over previous images taken with open-loop scanning.

Single-fiber flexible endoscope: general design for small size, high resolution, and wide field of view

Flexible endoscopes currently used in medicine have a fundamental tradeoff. Either resolution or field of view (FOV) is sacrificed when the scope diameter is less than 3 mm, since the minimum pixel size is usually greater than 4 microns in a pixel-array such as a camera or fiber bundle. Thus, the number of pixels within the image plane determines the minimum size of a conventional scope. However, an image plane is not required for image acquisition using a scanning single-fiber scope. Both high resolution and wide FOV are possible in a scanning single-fiber scope of 1 to 2 mm in diameter. The technical challenge is to produce a two- dimensional scanned beam of light at the distal tip of the scope. By manipulating a resonant fiberoptic cantilever as the optical scanner, various 2-D scan patterns can be produced. The general design concepts and analyses of the fiberoptic scanner for scaling to small size and high resolution/FOV are reviewed. In our initial experimental tests, the size of the photon detector in a fiberoptic scanning scope is demonstrated to not affect image resolution, unlike existing endoscopes with pixel-based detector systems.

A shear and plantar pressure sensor based on fiber-optic bend loss.

Lower-limb complications associated with diabetes include the development of plantar ulcers that can lead to infection and subsequent amputation. While we know from force-plate analyses that medial/lateral and anterior/posterior shear components of ground-reaction forces exist, little is known about the actual distribution of these stresses during daily activities or about the role that shear stresses play in causing plantar ulceration. Furthermore, one critical reason why these data have not been obtained previously is the lack of a validated, widely used, commercially available shear sensor, partly because of the various technical issues associated with measuring shear. In this study, we present a novel means of transducing plantar pressure and shear stress with a fiber-optic sensor. The pressure/shear sensor consists of an array of optical fibers lying in perpendicular rows and columns separated by elastomeric pads. We constructed a map of normal and shear stresses based on observed macrobending through the intensity attenuation from the physical deformation of two adjacent perpendicular fibers. Initial results show that this sensor exhibits low noise and responds to applied normal and shear loads with good repeatability.

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 mm Hg, 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 58.5 mm Hg resulted in a linear (r2=0.91) rise in RMS acoustic pressure from 0.017 to 1.41 mm 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.

The Relationship of Normal and Abnormal Microstructural Proliferation to the Mitral Valve Closure Sound

BACKGROUND Many diseases that affect the mitral valve are accompanied by the proliferation or degradation of tissue microstructure. The early acoustic detection of these changes may lead to the better management of mitral valve disease. In this study, we examine the nonstationary acoustic effects of perturbing material parameters that characterize mitral valve tissue in terms of its microstructural components. Specifically, we examine the influence of the volume fraction, stiffness and splay of collagen fibers as well as the stiffness of the nonlinear matrix in which they are embedded. METHODS AND RESULTS To model the transient vibrations of the mitral valve apparatus bathed in a blood medium, we have constructed a dynamic nonlinear fluid-coupled finite element model of the valve leaflets and chordae tendinae. The material behavior for the leaflets is based on an experimentally derived structural constitutive equation. The gross movement and small-scale acoustic vibrations of the valvular structures result from the application of physiologic pressure loads. Material changes that preserved the anisotropy of the valve leaflets were found to preserve valvular function. By contrast, material changes that altered the anisotropy of the valve were found to profoundly alter valvular function. These changes were manifest in the acoustic signatures of the valve closure sounds. Abnormally, stiffened valves closed more slowly and were accompanied by lower peak frequencies. CONCLUSION The relationship between stiffness and frequency, though never documented in a native mitral valve, has been an axiom of heart sounds research. We find that the relationship is more subtle and that increases in stiffness may lead to either increases or decreases in peak frequency depending on their relationship to valvular function.

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.

Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope

Scanning fiber optical endoscopy shows promise as a small, inexpensive imaging tool. Using this method of image acquisition, a scanning fiber is actuated at mechanical resonance, projecting a light spot across an imaged surface. Light backscattered from scanned spots is measured to form an image. The acquired image field of view, resolv- able pixels, and frame rate are dependent on the dynamics of the optical fiber used as a resonant scanner. A finite-element analysis FEA model was constructed to predict scanning fiber dynamics, and compared with experimental results. A scanning fiber microfabrication process was de- veloped that allows for the controlled manufacture of fiber scanners. Ex- perimental results confirm that the theoretical model was accurate in predicting the system transfer function with less than 6% error in ampli- tude and less than 10% error in resonant frequency at the first two reso- nant modes of a cylindrical and a microfabricated fiber. The scanning fiber microfabrication process proved to be capable of repeatably etching notches in optical fibers as small as 2.00±0.05 mm in length and 15±2 m in diameter. FEA was used to predict the effect of geometry change on microfabricated fiber scan dynamics, yielding candidate de- signs chosen for enhanced performance of future scanning endoscopes.