Separating Fluid Shear Stress from Acceleration during Vibrations in Vitro: Identification of Mechanical Signals Modulating the Cellular Response

The identification of the physical mechanism(s) by which cells can sense vibrations requires the determination of the cellular mechanical environment. Here, we quantified vibration-induced fluid shear stresses in vitro and tested whether this system allows for the separation of two mechanical parameters previously proposed to drive the cellular response to vibration - fluid shear and peak accelerations. When peak accelerations of the oscillatory horizontal motions were set at 1g and 60Hz, peak fluid shear stresses acting on the cell layer reached 0.5Pa. A 3.5-fold increase in fluid viscosity increased peak fluid shear stresses 2.6-fold while doubling fluid volume in the well caused a 2-fold decrease in fluid shear. Fluid shear was positively related to peak acceleration magnitude and inversely related to vibration frequency. These data demonstrated that peak shear stress can be effectively separated from peak acceleration by controlling specific levels of vibration frequency, acceleration, and/or fluid viscosity. As an example for exploiting these relations, we tested the relevance of shear stress in promoting COX-2 expression in osteoblast like cells. Across different vibration frequencies and fluid viscosities, neither the level of generated fluid shear nor the frequency of the signal were able to consistently account for differences in the relative increase in COX-2 expression between groups, emphasizing that the eventual identification of the physical mechanism(s) requires a detailed quantification of the cellular mechanical environment.

Brief daily exposure to low-intensity vibration mitigates the degradation of the intervertebral disc in a frequency-specific manner

Hindlimb unloading of the rat causes rapid hypotrophy of the intervertebral disc (IVD) as well as reduced IVD height and glycosaminoglycan content. Here we tested the hypothesis that low-intensity mechanical vibrations (0.2 g), as a surrogate for exercise, will mitigate this degradation. Four groups of Sprague-Dawley rats (4.5 mo, n = 11/group) were hindlimb unloaded (HU) for 4 wk. In two of the HU groups, unloading was interrupted for 15 min/day by placing rats in an upright posture on a platform that was vertically oscillating at 45 or 90 Hz (HU+45, HU+90). Sham control rats stood upright on an inactive plate for 15 min/day (HU+SC). These three experimental groups were compared with HU uninterrupted by weightbearing (HU) and to normally ambulating age-matched controls. In the HU and HU+SC rats, 4 wk of unloading resulted in a 10% smaller IVD height, as well as less glycosaminoglycan in the whole IVD (7%) and nucleus pulposus (17%) and a greater collagen-to-glycosaminoglycan ratio in the whole IVD (17%). Brief daily exposure to 90 Hz mechanical oscillations mitigated this degradation; compared with HU ± SC, the IVD of HU+90 had an 8% larger height and greater glycosaminoglycan content in the whole IVD (12%) and nucleus pulposus (24%). In contrast, the 45 Hz signal failed to mitigate changes in height or glycosaminoglycan content brought with altered spinal loading, but normalized the collagen-to-glycosaminoglycan ratio to levels observed in age-matched controls. In summary, unloading caused marked phenotypic and biochemical changes in the IVD, a deterioration that was not slowed by brief weightbearing. However, low-intensity 90 Hz vibrations superimposed on weightbearing largely preserved the morphology and biochemistry of the IVD and suggest that these biomechanically based signals may help protect the IVD during long bouts of nonambulation.

High resolution mechanical function in the intact porcine heart: mechanical effects of pacemaker location

The necessity to quantify the mechanical function with high spatial resolution stemmed from the advancement of myocardial salvaging techniques. Since these therapies are localized interventions, a whole field technique with high spatial resolution was needed to differentiate the normal, diseased, and treated myocardium. We developed a phase correlation algorithm for measuring myocardial displacement at high spatial resolution and to determine the regional mechanical function in the intact heart. Porcine hearts were exposed and high contrast microparticles were placed on the myocardium. A pressure transducer, inserted into the left ventricle, synchronized the pressure (LVP) with image acquisition using a charge-coupled device camera. The deformation of the myocardium was measured with a resolution of 0.58+/-0.04 mm. Within the region of interest (ROI), regional stroke work (RSW), defined as the integral of LVP with respect to regional area, was determined on average at 21 locations with a resolution of 27.1+/-2.7 mm2. To alter regional mechanical function, the heart was paced at three different locations around the ROI. Independent of the pacemaker location, RSW decreased in the ROI. In addition, a gradient of increasing RSW in the outward direction radiating from the pacemaker was observed in all pacing protocols. These data demonstrated the ability to determine regional whole field mechanical function with high spatial resolution, and the significant alterations induced by electrical pacing.

Effects of Ischemia on Epicardial Deformation in the Passive Rabbit Heart

BACKGROUND

Surgically induced ischemia in the arrested heart can result in changes in the mechanical properties of the myocardium. Regions of ischemia may be characterized based on the amount of epicardial deformation for a given load. Computer aided speckle interferometry (CASI), which tracks the movement of clusters of particles, is developed as a technique for measuring epicardial deformation, thereby determining the perfusion status of the passive heart.

MATERIALS AND METHODS

Silicone carbide particles and retroreflective beads were dispersed randomly onto the epicardial surface of 11 isolated rabbit hearts to form speckle images. The hearts were arrested with hyperkalemic Krebs-Henseleit buffered solution. Each heart was then exposed to a series of intracavitary pressures, and at each pressure speckle images were acquired with a charge-coupled device (CCD) camera. Nine hearts were exposed to global ischemia, and two hearts were exposed to regional ischemia by occluding the second diagonal branch of the left anterior descending artery (LAD). The hearts were again loaded and the speckle images were acquired. CASI was used to determine the distribution of deformation field.

RESULTS

CASI was able to determine displacements with a spatial resolution of about 50 microns. Global ischemia resulted in a significant increase in the maximum principle strain and the first invariant of the 2-D strain tensor. In the regionally ischemic heart, a large difference in deformation between the ischemic and perfused regions was clearly observed.

CONCLUSION

Based on epicardial deformation, CASI is able to distinguish between perfused and ischemic myocardium, with a spatial resolution of 50 microns.

Microscopic phase-shifting profilometry based on digital micromirror device technology

A microscopic three-dimensional (3-D) shape measurement system based on digital fringe projection has been developed and experimentally investigated. A Digital Micromirror Device along with its illumination optics is integrated into a stereomicroscope, which projects computer-generated fringe patterns with a sinusoidal intensity profile through the microscope objective onto the object surface being measured. The fringe patterns deformed by the object surface are recorded by a CCD camera. The microscopic 3-D shape of the object surface is measured and reconstructed by use of a phase-shifting technique. We discuss design considerations and error analysis of the system. Experimental results successfully demonstrate the capability of this technique for surface profile measurement of rough surfaces at the micrometer level.

Double three-step phase-shifting algorithm

We describe what we believe is a new phase-shifting algorithm called a double three-step algorithm developed to reduce the measurement error of a three-dimensional shape-measurement system, which is based on digital fringe-projection and phase-shifting techniques. After comparing the performance of different existing phase-shifting algorithms, we present the new double three-step algorithm based on the error analysis of the standard three-step algorithm. In this algorithm, three-step phase shifting is done twice with an initial phase offset of 60 degrees between them, and the two obtained phase maps are averaged to generate the final phase map. Both theoretical and experimental results showed that this new algorithm worked well in significantly reducing the measurement error.

Computer aided speckle interferometry: a technique for measuring deformation of the surface of the heart

An investigation of the inhomogeneous and anisotropic properties of myocardium necessitates a whole field measurement technique with high spatial resolution. Computer aided speckle interferometry (CASI) may be applied to measuring deformation on the epicardial surface of the heart. Silicone carbide particles (approximately 40 microm in diameter) were sprinkled randomly onto the epicardial surface of isolated rabbit hearts. When illuminated with white light, speckles may be observed with a charge coupled device (CCD) camera. A balloon was placed in the left ventricle to control the intracavitary load on the arrested heart. To compare CASI to the "gold" standard technique of sonomicrometry, two ultrasonic transducers were implanted into the wall of the myocardium. Three hearts were exposed to various loading conditions, and at each condition speckle images were recorded. CASI was used to determine the distribution of displacement vectors (both direction and magnitude) in the region imaged by the CCD camera. Strain along the axis of the implanted transducers was determined with CASI and compared to that obtained with sonomicrometry. Strain determined from CASI and sonomicrometry produced equivalent results. Unlike sonomicrometry, whereby the displacement between two points with a relatively large gauge length is obtained, CASI is able to determine displacement vectors for hundreds of "points" within the same region. In conclusion, CASI produced equivalent results to those obtained from sonomicrometry (although not with the same temporal resolution), but it is a whole field deformation mapping technique that has a spatial resolution three orders of magnitude higher than that of sonomicrometry.

Correlation of bony ingrowth to the distribution of stress and strain parameters surrounding a porous-coated implant

The ability of shear strains to inhibit bony ingrowth was investigated by use of a transcortical porous-coated cylindrical plug implant in a functionally isolated turkey ulna model in which the mechanical loading environment could be accurately controlled and rigorously defined. The distribution of ingrowth at the bone-implant interface was quantified following 8 weeks of in vivo loading consisting of 100 seconds per day of a 20 Hz sinusoidal stimulus sufficient to cause a local peak strain of approximately 100 microstrain in the cortex at the bone-implant interface in four turkeys. A nonuniform but repeatable pattern of bony ingrowth, from 33 +/- 6 to 72 +/- 6% (mean +/- SE), was observed. The mechanical environment in the vicinity of the bone-implant interface was calculated using a three-dimensional elastic orthotropic finite element model. The general stress-strain state of the bone as predicted by the finite element model was validated in two additional turkeys using four three-element rosette strain gauges, while high resolution moiré interferometry was used to determine the mechanical state of the region immediately adjacent to the implant itself. Shear strains and stresses were evaluated at the interface and correlated to the pattern of bony ingrowth circumscribing the implant interface. Linear regressions between ingrowth and both shear strain and shear stress were negative, with the values of R = -0.75 and R = -0.78 (p < 0.001), respectively, indicating significant inhibition of ingrowth where shear components were maximal. These results suggest that the minimization of shear stress and strain components is a major determinant in achieving successful ingrowth of bone into a prosthesis.

Digital speckle-displacement measurement using a complex spectrum method

An alternative approach to fully automatic speckle-displacement measurement is described. Two speckle patterns of a specimen, one before and one after deformation, are captured by a CCD camera and registered by a frame grabber. Two series of small subimages are obtained by segmenting the two speckle patterns. The corresponding subimage pairs extracted from both series are analyzed pointwise. The interrogation of each subimage pair involves a two-step fast-Fourier transform. While the first-step fast-Fourier transform achieves a complex spectrum characterized by the local displacement information, the second-step one generates a signal peak in the second spectral domain that resolves the local displacement vector. A rough estimate of the displacement vector is achieved by detecting the maximum pixel of the discrete spectrum. A more accurate determination is attained by a subpixel-maximum determination through a biparabolic fitting near the signal peak. The u- and v-displacement fields are deduced by analyzing all subimage pairs. A large rigid-body displacement can be overcome by introducing an artificial rigid shift of the two speckle patterns toward each other before the numerical process. The technique retains all the advantages of optical speckle photography and provides an extended range of measurement. Dynamic incremental deformations can be inspected by registering more speckle patterns at many consecutive deformation stages by using a high-speed CCD camera. The system was applied successfully to the study of crack-tip deformation fields.

Computer-aided speckle interferometry using spectral amplitude fringes

A fully automatic speckle metrology technique is developed. Two speckle patterns of a specimen, one before and one after the specimen deformation, are captured by a video camera. An equivalent double-exposure speckle pattern is obtained by superimposing the two digital images. The superimposed speckle pattern is then segmented into a series of small subimages. For each subimage a fast-Fourier transform is applied and a computer-generated Young's fringe pattern is obtained. The fringe pattern, which characterizes the local displacement vector, is analyzed by a second fast-Fourier transform. The local displacement vector is determined by a cardinal interpolation and a crest searching around a signal peak in the second spectral domain. An artificial rigid shift between the two images is introduced in the cases of extremely large or small displacements. From analysis of all subimage pairs of the whole superimposed speckle pattern a complete two-dimensional displacement field is deduced. Experimental results using laser as well as white-light speckle patterns are demonstrated.

Three-dimensional dimension of laser speckle

It is well known that the three-dimensional dimension of laser speckle is a critical parameter in laser holographic interferometry, laser speckle photography, and holospeckle interferometry. In this paper a statistical analysis for computing the three-dimensional dimension of laser speckle is presented. Explicit formulas have been derived for laser speckle in a free space from a circular scattering area along with some supporting results from an experimental investigation.

Analysis of combined moire and laser speckle grating methods used in 3-D crack tip deformation measurements

The paper provides analyses for two optical schemes developed for mapping 3-D crack tip fields in ductile materials. The first scheme combines the in-plane moire method with the projection moire method to determine all three displacement components simultaneously. In the second method, we combined onebeam laser speckle photography with the projection moire method to measure 3-D deformation fields. The experimental results obtained using these methods are presented.

Resolution of resultant displacement into components in double exposure speckle photography

An equation to resolve the resultant displacement, recorded using double exposure laser speckle photography, at the surface of a cylinder suffering radial expansion, axial twist, and transverse displacement, into these three components is presented.

Effects of low-modulus coatings on pin-bone contact stresses in external fixation

The intent of this study was to investigate the stress distribution in cortical bone around fracture fixation pins and around pins coated with various polymeric and elastomeric materials. Since these interface stresses cannot be measured directly, a photoelastic technique was employed and stresses were measured in two-dimensional bone models fabricated from sheets of epoxy resin. Our results showed that when a fixation pin was loaded in compression, the compressive stress measured in the model was greatest at the pin-model interface. The magnitude of the compressive stress was found to diminish steeply away from the hole in a log decrement distribution which was asymptotic to the value of the average stress in the model. When polymeric and elastomeric materials were applied as pin coatings and the performance of the coated pins was compared to that of uncoated pins of the same overall diameter, a reduction of the maximum stress in the bone model was demonstrated. Among the coatings tested, we found that of the polymeric materials ultrahigh molecular weight polyethylene (UHMWPE) was most effective at reducing the peak cortical stress magnitude. The most effective coating material overall was found to be silicon elastomer. Computation of stress values in models loaded through stainless-steel pins and through pins coated with 1-mm silicon elastomer showed that the presence of the elastomer layer caused a reduction of about 50% in the maximum compressive stress in the model.

Objective white-light speckles and their application to stress-intensity factor determination

A new technique using objective white-light speckles for displacement and deformation measurement is introduced that has an application to fracture mechanics.

Contouring by laser speckle

A technique is presented to determine surface contours of 3-D objects by laser speckle interferometry. A double exposure specklegram is recorded by giving the object a small tilt between exposures. Surface contours are obtained by Fourier filtering of the specklegram.

Thermal strain measurement by one-beam laser speckle interferometry

A method of one-beam laser speckle interferometry was applied to the measurement of transient thermal strain fields in an aluminum plate heated at a small region. A ruby pulse laser minimized the effect of thermal air turbulence on speckle correlation. High quality isothetic fringe patterns were obtained. The result compares well with available existing data.

Stress analysis Of in-plane vibration Of 2-D structures by A laser speckle method

By time-average recording of laser speckles formed on the surface of a structure under sinusoidal oscillation, isothetics along any direction can be obtained by Fourier filtering the resulting specklegram. Principal strains and stresses can then be calculated through the use of strain-rosette equations and the stress-strain law, respectively.

White light projection speckle method for generating deflection contours

By projecting a random speckle pattern with a simple slide projector onto a plate and recording the speckle shift by double exposure before and after the deflection of the plate, deflection contour fringes of various sensitivities can be obtained by optical Fourier filtering.

Time-average reflection-moiré method for vibration analysis of plates

A moiré method is described whereby time-average slope contours are obtained from vibrating plates. It has an advantage over deflection contouring methods in that only first-order differentiation of experimental data is needed for stress calculations.

Laser speckle interferometry for plate bending problems

A method is proposed whereby the spatial speckles created in front of a plate with an optically rough surface when illuminated by a coherent laser beam is used to generate slope contour fringes. This is done by photographing the speckles contained in a parallel plane in front of the plate before and after deformation via double exposure. The resulting speckle interferogram is then optically Fourier transformed to yield the fringe pattern of slope contours. It is shown that the method is analogous to the Ligtenberg reflection moiré method with a grating of continuously variable pitch and orientation. The method can be applied to plates made of almost any material.

Strain analysis by one-beam laser speckle interferometry. 1: Single aperture method

A two-dimensional analysis of a double-exposed speckle pattern as created by illuminating a plane surface with a beam of laser light is presented with the role played by the aperture illumination function described in detail. Between exposures, the surface is to undergo in-plane general deformation. Two approaches (one whole field and one pointwise) are presented to delineate from the speckle pattern the three Cartesian components of strain at each point in the field. An analogy is drawn between the whole field approach and the classical in-plane moiré method. Quantitative examples are included to demonstrate the validity of the methods.