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Numerical conversion of transient to harmonic response functions for linear viscoelastic materials.

Viscoelastic material behavior is often characterized using one of the three measurements: creep, stress-relaxation or dynamic sinusoidal tests. A two-stage numerical method was developed to allow representation of data from creep and stress-relaxation tests on the Fourier axis in the Laplace domain. The method assumes linear behavior and is theoretically applicable to any transient test which attains an equilibrium state. The first stage numerically resolves the Laplace integral to convert temporal stress and strain data, from creep or stress-relaxation, to the stiffness function, G(s), evaluated on the positive real axis in the Laplace domain. This numerical integration alone allows the direct comparison of data from transient experiments which attain a final equilibrium state, such as creep and stress relaxation, and allows such data to be fitted to models expressed in the Laplace domain. The second stage of this numerical procedure maps the stiffness function, G(s), from the positive real axis to the positive imaginary axis to reveal the harmonic response function, or dynamic stiffness, G(j omega). The mapping for each angular frequency, s, is accomplished by fitting a polynomial to a subset of G(s) centered around a particular value of s, substituting js for s and thereby evaluating G(j omega). This two-stage transformation circumvents previous numerical difficulties associated with obtaining Fourier transforms of the stress and strain time domain signals. The accuracy of these transforms is verified using model functions from poroelasticity, corresponding to uniaxial confined compression of an isotropic material and uniaxial unconfined compression of a transversely isotropic material. The addition of noise to the model data does not significantly deteriorate the transformed results and data points need not be equally spaced in time. To exemplify its potential utility, this two-stage transform is applied to experimental stress relaxation data to obtain the dynamic stiffness which is then compared to direct measurements of dynamic stiffness using steady-state sinusoidal tests of the same cartilage disk in confined compression. In addition to allowing calculation of the dynamic stiffness from transient tests and the direct comparison of experimental data from different tests, these numerical methods should aid in the experimental analysis of linear and nonlinear material behavior, and increase the speed of curve-fitting routines by fitting creep or stress relaxation data to models expressed in the Laplace domain.

Algorithms↗

Analysis of cementless implants using interface nonlinear friction--experimental and finite element studies.

Measured interface nonlinear friction properties are used to develop models to study the short-term fixation response of smooth- and porous-surfaced posts, bone screws, and plates fixed with and without posts/screws. Experimental studies are carried out to validate the model predictions and identify the relative role of posts and screws in fixation of a plate on a polyurethane block under symmetric/eccentric axial compression loads. The idealized Coulomb's friction is also used for the sake of comparison. The incorporation of measured nonlinear, rather than the idealized Coulomb, friction is essential to compute realistic results. For plate fixation, the experimental and finite element results show that the screw fixation yields the stiffest response followed by the smooth- and then porous-coated post fixation. For example, under 1000 N eccentric axial compression, the edge of the plate opposite the loaded edge is measured to lift by 1147 +/- 72, 244 +/- 38, or 112 +/- 28 microns, respectively, for the cases with no fixation, with smooth-surfaced posts, or with screws. The corresponding models predict, respectively, values of 1538, 347, or 259 microns and also 556 microns for the plate fixed with porous coated posts. The satisfactory agreement between numerical and experimental results confirms the importance of proper interface modelling for the analysis of posts, screws, and complex fixation systems. This becomes further evident when considering cementless implants in which the bone-implant interface exhibits relatively large displacements as the maximum resistance force is reached. The developed models can be used to investigate the post-operative short-term stability of various cementless implant designs.

Bone Cements↗

Artifactual nonlinearity due to wear grooves and friction in four-point bending experiments of cortical bone.

Experiments and analyses were performed to determine the cause of a nonlinear force-deflection response observed in four-point flexural fatigue of beams of cortical bone machined from the mid-diaphysis of the equine third metacarpus. Observable grooves which formed on the beam surface at supports and load noses were found to be the primary cause of the nonlinearity. An additional geometric nonlinearity at large deflections revealed by finite element modeling may be minimized by using the smallest diameter supports and load noses recommended in ASTM 790. However, frictional constraint of the beams at the load noses and supports can occur at low load levels and should be avoided by using roller-bearing supports and load noses, or some equivalent method.

Animals↗

Spinal ligament transducer based on a hall effect sensor.

A spinal ligament transducer (SLT) was developed to measure in situ spinal ligament elongation during the simulation of whiplash trauma with a cadaveric spine specimen. The SLT was designed to be affixed to two K-wires drilled into the bone at the approximate points of ligament origin and insertion. The transducer is low cost and is capable of measuring the linear distance between the K-wires in the range 4-12 mm with the root mean square (RMS) accuracy of 0.025 mm.

Bone Wires↗

A high-frequency shear device for testing soft biological tissues.

Accurate mechanical property data obtained at large shear deformations and high frequencies are a fundamental component of realistic numerical simulations of soft tissue injury. Although many commercial systems exist for testing shear properties of viscoelastic materials with properties similar to soft biological tissue, none are capable of determining properties at high loading rates necessary for modeling soft tissue injury. Previous custom shear testing systems, though capable of high-frequency loading, indirectly measure tissue properties by using analytical corrections for inertial effects. To address these limitations, a new custom designed oscillatory shear testing apparatus (STA) capable of testing soft biological tissues in simple shear has been constructed and validated. Through a proper selection of sample thickness, direct measurement of material properties at high frequencies is achieved mechanically without analytical inertial adjustments. The complex shear modulus of three mixtures of silicone gel with viscoelastic properties in a range similar to soft biological tissue was characterized in the STA over a dynamic frequency range of 20-200 Hz and validated with a commercially available solids rheometer. The frequency-dependent complex shear modulus measurements of the STA were within 10% of the rheometer measurements for all mixtures over the entire frequency range tested. The STA represents substantive improvement over current shear testing methods by providing direct measurement of the shear behavior of soft viscoelastic material at high frequencies. Mechanical property data gained from this device will provide a more realistic basis for numerical simulations of biological structures.

Brain↗

Placing a bone graft more posteriorly may reduce the risk of pedicle screw breakage: analysis of an unexpected case of pedicle screw breakage.

Telemeterized internal spinal fixation devices were implanted in a patient with degenerative instability and a narrow spinal canal in order to measure the fixator loads during daily activities. Anterior interbody fusion was performed three weeks later. During walking, the typical maximum flexion bending moments were 10 N m in the left and 5 N m in the right fixator. On removal of the implants three months later, a fatigue fracture was found not on the high loaded left side but in the upper right pedicle screw. The crack started on the caudal side of the cross-sectional area and progressed cranially. Upper vertebral tilting in the sagittal plane must have caused the screw breakage. This would probably have been prevented by a more posteriorly placed bone graft.

Activities of Daily Living↗

Imposing thermodynamic restrictions on the elastic constant-fabric tensor relationship.

Zysset and Curnier (1995) rederive the general representation for the fourth rank elasticity tensor in terms of the fabric tensor given originally by Cowin (1985). Zysset and Curnier (1995) then obtain a form of the representation that is sufficiently restricted to satisfy the thermodynamic constraint that the compliance tensor be positive definite. Zysset and Curnier (1995, 1996) argue that their representation has an advantage over that of Cowin (1985) because it has, a priori, been sufficiently restricted to satisfy the thermodynamic constraint that the compliance tensor be positive definite. The purpose of this note is to point out that the limitations of the Zysset and Curnier (1995, 1996) sufficiency representation are quite severe, restricting the flexibility of the model by allowing only five of the nine normally independent orthotropic elastic coefficients to be independent. Potential users should consider employing the Cowin (1985) representation and subsequently imposing the condition that the elasticity tensor be positive definite.

Algorithms↗

Circumferentially flexible vascular grafts.

An arterial graft with a corrugated cylindrical cross-section has been proposed as a partial solution to the problem of elastic stiffness mismatch between conventional grafts and arterial tissue (Trescony et al., 1994, US Patent 5,282, 847 (granted February 1 1994)). A two-dimensional ring theory model and a finite element shell theory model are used to study the inflation under uniform interior pressure of grafts with noncircular cross-sections as a first approximation to their behavior in vivo. For the physically relevant range of area expansions (typically 7-10%) and pressures (8-18 kPa), corrugations can significantly reduce the graft stiffness in comparison to conventional circular cross-section grafts.

Algorithms↗

Repetitive lifting tasks fatigue the back muscles and increase the bending moment acting on the lumbar spine.

During manual handling, the back muscles protect the spine from excessive flexion, but in doing so impose a high compressive force on it. Epidemiological links between back pain and repetitive lifting suggest that fatigued muscles may adversely affect the balance between bending and compression. Fifteen volunteers lifted and lowered a 10 kg weight from floor to waist height 100 times. Throughout this task, the bending moment acting on the osteoligamentous lumbar spine was estimated from continuous measurements of lumbar flexion, obtained using the 3-Space Isotrak. Spinal compression was estimated from the electromyographic (EMG) activity of the erector spinae muscles, recorded from skin-surface electrodes at the levels of T10 and L3. EMG signals were calibrated against force when subjects pulled up on a load cell, and correction factors were applied to account for changes in muscle length and contraction velocity. Fatigue in the erector spinae muscles was quantified by comparing the frequency content of their EMG signal during static contractions performed before, and immediately after, the 100 lifts. Results showed that peak lumbar flexion increased during the 100 lifts from 83.3 +/- 14.8% to 90.4 +/- 14.3%, resulting in a 36% increase in estimated peak bending moment acting on the lumbar spine (P = 0.008). Peak spinal compression fell by 11% (p = 0.007). The median frequency of the EMG signal at L3 decreased by 5.5% following the 100 lifts (p = 0.042) confirming that the erector spinae were fatigued, but measures of fatigue showed no significant correlation with increased bending. We conclude that repetitive lifting induces measurable fatigue in the erector spinae muscles, and substantially increases the bending moment acting on the lumbar spine.

Adult↗

Bone size and mechanics at the femoral diaphysis across age and sex.

The reasons for the increase in fracture rates with age are not fully understood. It is known that there is a decrease in bone mass with a presumed loss of strength. This decrease may possibly be compensated for by changes in cross-sectional geometry. Previous studies, which have been limited by lack of information on subjects' heights and weights, were not able to resolve this issue. In this study, measurements of cross-sectional geometry (area and second moments of area) from 107 specimens of human femoral diaphysis from subjects aged 21-92 years were analysed. Mathematical models of the variation in bone geometry with age were developed. These models included the effects of sex, height and weight. Values of parameters from these models were then used in a biomechanical analysis of the static stresses at the mid-shaft of the femur. Results indicate that although there was a reduction in cortical area in old age, bone tissue was redistributed so that neither bending stresses in the coronal plane nor torsional stresses were higher in old age than in young adulthood. An additional finding was that at any age women had smaller bones, less cortical bone area and higher bone stresses than men. This finding may have some bearing on the higher fracture incidence seen in older women.

Adult↗

A methodology for studying the effects of various types of prosthetic feet on the biomechanics of trans-femoral amputee gait.

This paper reports on a methodology developed for studying the effects of various types of prosthetic feet on the gait of trans-femoral amputees. It is shown that an analysis in three planes of motion of not only the prosthetic, but also the sound limb provides important information on the performance of prosthetic feet. Two male trans-femoral amputees were tested with four different prosthetic feet; the Springlite II, Carbon Copy III, Seattle LightFoot and the Multiflex foot. A detailed analysis of the results of one amputee and a summary of the most important results of a second subject is presented. The tests were carried out at normal (1.16 m s(-1)) and fast (1.56 m s(-1)) walking speeds. Three dimensional gait analysis was carried out to derive the time curves of the joint angles, intersegmental moments and power at the ankle, knee and hip joints at both the prosthetic and sound sides. A higher first peak of the ground reaction force at the sound side with the Seattle LightFoot compared to that with the Springlite II, may be the result of the lower late stance dorsiflexion angle with the former. Compared to the other two feet, the Carbon Copy III and the Springlite II showed higher prosthetic dorsiflexing moments and positive power at late stance, which could assist in the push-off. The 3D intersegmental loads at the ankle and knee can be used as a guide for design and for compilation of standards for testing of lower limb prostheses incorporating flexible feet.

Adult↗

The effects of damage and microcracking on the impact strength of bone.

Microcracking has been shown to occur when bone is 'damaged' as shown by a loss of stiffness. The effect on bone's toughness of the types of damage produced at low losses of stiffness are not known. We loaded bovine bone specimens in bending and tension to stiffness losses of up to 27%, and examined the microcracking produced. The tensile specimens had diffuse arrays of microcracks of 2-20 microm in length, characteristic of tensile loading, on all surfaces. The bending specimens showed tensile microcracking on the tensile surface and characteristic long, straight, cross-hatched compression cracks on the compressive surface. Specimens were then broken in impact. Those that had been damaged in bending were divided into two groups, in one group the part of the specimen which had undergone compression damage was placed in tension, and in the other group the tensile damage was placed in tension. Tensile damage loaded in tension did not reduce the bone's energy-absorbing ability in impact until a modulus reduction of over 20%. However compression damage loaded in tension did severely reduce the bone's energy absorption capabilities (by an average of about 40%).

Animals↗

Mechanical validation of whole bone composite tibia models.

Composite synthetic models of the human tibia have recently become commercially available as substitutes for cadaveric specimens. Their use is justified by the advantages they offer as a substitute for real tibias. The present investigation concentrated on an extensive experimental validation of the mechanical behaviour of the whole bone composite model, compared to human specimens for different loading conditions. The stiffness of the tibias was measured with a torsional load applied along the long axis, and with a bending load applied both in the latero-medial and in the antero-posterior direction. The bending stiffness of the composite tibias matched well with that of the cadaveric specimens. This was not true for the torsional stiffness. In fact, the composite tibias were much stiffer than the cadaveric specimens, possibly due to the structure of the reinforcement material. The inter-specimen variability for the composite tibias was much lower than that for the cadaveric specimens. Thus, it seems that the composite tibias are suitable to replace cadaveric specimens for certain types of test, whereas they might be unsuitable for others, depending on the loading regimen.

Biomechanical Phenomena↗

Mechanical effects of continuous passive motion on the lumbar spine in seating.

The aim of this study was to develop a model which describes the mechanical spinal response to small alternating pelvic stimulation induced by an active rotational movement of a normal chair. The rotary continuous passive motion (RCPM) of the seat about a vertical axis of only 0.6 degrees resulted in an increased in spinal length as opposed to the normal daily shrinkage, and back patients experienced pain relief. Passive and active exercies have been broadly applied for treating and healing spinal disorders. A rigid body package (ADAMS Android) was used to translate the stimulation of the ischial tubersoity in caudo-cranial handing-over visualisation. The parameters of the model were set so that the values of the global stiffness and geometry of the intervertebral discs could be changed. In vivo validation of the model was based on force and moment measurements using an internal AO fixator. The predicitons of the model concerning natural frequency (4.5Hz) in vertical direction and the axial torsion response on small pelvic torsion are comparable with experimental data.

Algorithms↗

On the role of the conformational flexibility of the active-site lid on the allosteric kinetics of glucosamine-6-phosphate deaminase.

The active site of glucosamine-6-phosphate deaminase from Escherichia coli (GlcN6P deaminase, EC 3.5.99.6) has a complex lid formed by two antiparallel beta-strands connected by a helix-loop segment (158-187). This motif contains Arg172, which is a residue involved in binding the substrate in the active-site, and three residues that are part of the allosteric site, Arg158, Lys160 and Thr161. This dual binding role of the motif forming the lid suggests that it plays a key role in the functional coupling between active and allosteric sites. Previous crystallographic work showed that the temperature coefficients of the active-site lid are very large when the enzyme is in its T allosteric state. These coefficients decrease in the R state, thus suggesting that this motif changes its conformational flexibility as a consequence of the allosteric transition. In order to explore the possible connection between the conformational flexibility of the lid and the function of the deaminase, we constructed the site-directed mutant Phe174-Ala. Phe174 is located at the C-end of the lid helix and its side-chain establishes hydrophobic interactions with the remainder of the enzyme. The crystallographic structure of the T state of Phe174-Ala deaminase, determined at 2.02 A resolution, shows no density for the segment 162-181, which is part of the active-site lid (PDB 1JT9). This mutant form of the enzyme is essentially inactive in the absence of the allosteric activator, N-acetylglucosamine-6-P although it recovers its activity up to the wild-type level in the presence of this ligand. Spectrometric and binding studies show that inactivity is due to the inability of the active-site to bind ligands when the allosteric site is empty. These data indicate that the conformational flexibility of the active-site lid critically alters the binding properties of the active site, and that the occupation of the allosteric site restores the lid conformational flexibility to a functional state.

Alanine↗

Measuring dynamic flexibility of the coil state of a helix-forming peptide.

To investigate the dynamic flexibility of the coil state of a helix-forming peptide the end-to-end contact rate was determined. Nanosecond optical excitation of tryptophan at one end of a 22 residue, alanine peptide populates a long-lived triplet state which is quenched upon close contact with a cyclic disulfide attached to the opposite end. Analysis of the decay of the triplet population using a two-state model for helix formation yields the diffusion-limited end-to-end contact rate of the coil state of the peptide as well as the helix-->coil and coil-->helix rates. The helix-coil rates are very similar to those previously measured in laser temperature-jump experiments. The end-to-end contact rate of 1.1 x 10(7) s(-1) in the coil state is tenfold faster than the rate for a disordered peptide with threonine substituted for alanine and, somewhat surprisingly, is about twice the rate for a disordered glycine-containing peptide. These differences are discussed in terms of the theory of Szabo, Schulten and Schulten. The rates should provide important new benchmarks for testing the accuracy of atomistic molecular dynamics simulations.

Disulfides↗

Contrasting IgG structures reveal extreme asymmetry and flexibility.

The crystal structure of IgG1 b12 represents the first visualization of an intact human IgG with a full-length hinge that has all domains ordered and visible. In comparison to intact murine antibodies and hinge-deletant human antibodies, b12 reveals extreme asymmetry, indicative of the extraordinary interdomain flexibility within an antibody. In addition, the structure provides an illustration of the human IgG1 hinge in its entirety and of asymmetry in the composition of the carbohydrate attached to each C(H)2 domain of the Fc. The two separate hinges assume different conformations in order to accommodate the vastly different placements of the two Fab domains relative to the Fc domain. Interestingly, only one of two possible intra-hinge disulfides is formed.

Animals↗

Crystal structure of the C. perfringens alpha-toxin with the active site closed by a flexible loop region.

Clostridium perfringens biotype A strains are the causative agents of gas-gangrene in man and are also implicated as etiological agents in sudden death syndrome in young domestic livestock. The main virulence factor produced by these strains is a zinc-dependent, phosphatidylcholine-preferring phospholipase C (alpha-toxin). The crystal structure of alpha-toxin, at pH 7.5, with the active site open and therefore accessible to substrate has previously been reported, as has calcium-binding to the C-terminal domain of the enzyme at pH 4.7. Here we focus on conformation changes in the N-terminal domain of alpha-toxin in crystals grown at acidic pH. These changes result in both the obscuring of the toxin active site and the loss of one of three zinc ions from it. Additionally, this "closed" form contains a small alpha helix, not present in the open structure, which hydrogen bonds to both the N and C-terminal domains. In conjunction with the previously reported findings that alpha-toxin can exist in active and inactive forms and that Thr74Ile and Phe69Cys substitutions markedly reduced the haemolytic activity of the enzyme, our work suggests that these loop conformations play a critical role in the activity of the toxin.

Binding Sites↗