Determining effective centroid position in biomechanical testing: a technique for simplifying whole bone analysis

BACKGROUND: Whole bone in vitro biomechanical compressive testing can be complicated by three factors: sample asymmetry, heterogeneous material properties, and unknown effective centroid location. METHOD OF APPROACH: The technique presented here facilitates the calculation of effective centroid position, modulus of elasticity and equivalent uniform strain magnitude for a cross section of bone from a simple whole bone compressive test. Simplification of section response to load is achieved through a combination of linear beam and simple planer geometry theory. The technique requires three longitudinal strain gauges be affixed around the test specimen cross section of interest, gauge position need not be determined. Sample loading is then accomplished using a simple four point loading jig. RESULTS: Results of the technique are presented on an object with known elasticity and geometry, an aluminium tube, and seven pairs of equine third metacarpal whole bones. CONCLUSIONS: Average cross section modulus of elasticity, equivalent uniform cross section strain, and effective centroid locations were all predicted to within the range of published values. Employing the testing setup and analysis technique presented in this paper resulted in a significant savings in both implementation complexity and cost over previously available techniques.     

Novel Pedicle Screw and Plate System Provides Superior Stability in Unilateral Fixation for Minimally Invasive Transforaminal Lumbar Interbody Fusion: An In Vitro Biomechanical Study

Purpose

This study aims to compare the biomechanical properties of the novel pedicle screw and plate system with the traditional rod system in asymmetrical posterior stabilization for minimally invasive transforaminal lumbar interbody fusion (MI-TLIF). We compared the immediate stabilizing effects of fusion segment and the strain distribution on the vertebral body.

Methods

Seven fresh calf lumbar spines (L3-L6) were tested. Flexion/extension, lateral bending, and axial rotation were induced by pure moments of ± 5.0 Nm and the range of motion (ROM) was recorded. Strain gauges were instrumented at L4 and L5 vertebral body to record the strain distribution under flexion and lateral bending (LB). After intact kinematic analysis, a right sided TLIF was performed at L4-L5. Then each specimen was tested for the following constructs: unilateral pedicle screw and rod (UR); unilateral pedicle screw and plate (UP); UR and transfacet pedicle screw (TFS); UP and TFS; UP and UR.

Results

All instrumented constructs significantly reduced ROM in all motion compared with the intact specimen, except the UR construct in axial rotation. Unilateral fixation (UR or UP) reduced ROM less compared with the bilateral fixation (UP/UR+TFS, UP+UR). The plate system resulted in more reduction in ROM compared with the rod system, especially in axial rotation. UP construct provided more stability in axial rotation compared with UR construct. The strain distribution on the left and right side of L4 vertebral body was significantly different from UR and UR+TFS construct under flexion motion. The strain distribution on L4 vertebral body was significantly influenced by different fixation constructs.

Conclusions

The novel plate could provide sufficient segmental stability in axial rotation. The UR construct exhibits weak stability and asymmetrical strain distribution in fusion segment, while the UP construct is a good alternative choice for unilateral posterior fixation of MI-TLIF.     

A comparison of bone strain measurements at anatomically relevant sites using surface gauges versus strain gauged bone staples

Instrumented bone staples were first introduced as an alternative to surface-mounted strain gauges for use in human in vivo bone strain measurements because their fixation to bone is secure and requires not only minimally invasive surgery. Bench-top bone bending models have shown that the output from strain gauged bone staples compares favorably to that of traditional mounted gauges. However their within- and across-subject performance at sites typically instrumented in vivo has never been examined. This study used seven human cadaver lower extremities with an age range of 23-81 years old and a dynamic gait simulator to examine and compare axial strains in the mid tibial diaphysis and on the dorsal surface of the second metatarsal as measured simultaneously with strain gauged bone staples and with traditional surface-mounted gauges. Rosette configurations were used at the tibial site for deriving principal compression and tension, and shear strains. Axial outputs from the two gauge types demonstrated strong linear relationships for the tibia (r(2)=0.78-0.94) and the second metatarsal (r(2)=0.96-0.99), but coefficients (slopes) for the relationship were variable (range 7-20), across subjects and across sites. The apparent low reliability of strain gauged staples may be explained by the fact that both strain gauged staples and surface strain gauges are inexact to some degree, do not measure strains from exactly the same areas and strain gauged staples reflect surface strains as well as deformations within the cortex. There were no relationships for the principal tibia compression, tension or shear strain measurements derived from the two rosette gauge types, reflecting the very different anatomical areas measured by each of the constructs in this study. Strain gauged bone staples may be most useful in comparing relative axial intra-subject differences between activities, but inter-subject variability may require larger sample sizes to detect differences between populations.     

Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry

Finite element analysis is a powerful tool for predicting the mechanical behaviour of complex biological structures like bones, but to be confident in the results of an analysis, the model should be validated against experimental data. In such validation experiments, the strains in the loaded bones are usually measured with strain gauges glued to the bone surface, but the use of strain gauges on bone can be difficult and provides only very limited data regarding surface strain distributions. This study applies the full-field strain measurement technique of digital speckle pattern interferometry to measure strains in a loaded human mandible and compares the results with the predictions of voxel-based finite element models of the same specimen. It is found that this novel strain measurement technique yields consistent, reliable measurements. Further, strains predicted by the finite element analysis correspond well with the experimental data. These results not only confirm the usefulness of this technique for future validation studies in the field of bone mechanics, but also show that the modelling approach used in this study is able to predict the experimental results very accurately.     

The effect of the density-modulus relationship selected to apply material properties in a finite element model of long bone

Material property assignment is a critical step in developing subject-specific finite element models of bone. Inhomogeneous material properties are often applied using an equation relating density and elastic modulus, with the density information coming from CT scans of the bone. Very few previous studies have investigated which density-elastic modulus relationships from the literature are most suitable for application in long bone. No such studies have been completed for the ulna. The purpose of this study was to investigate six such density-modulus relationships and compare the results to experimental strains from eight cadaveric ulnae. Subject-specific finite element models were developed for each bone using micro-CT scans. Six density-modulus equations were trialed in each bone, resulting in a total of 48 models. Data from a previously completed experimental study in which each bone was instrumented with twelve strain gauges were used for comparison. Although the relationship that best matched experimental strains was somewhat specimen and location dependent, there were two relations which consistently matched the experimental strains most closely. One of these under-estimated and one over-estimated the experimental strain values, by averages of 15% and 31%, respectively. The results of this study suggest that the ideal relationship for the ulna may lie somewhere in between these two relations.     

Effect of a pedicle-screw-based motion preservation system on lumbar spine biomechanics: A probabilistic finite element study with subsequent sensitivity analysis

Pedicle-screw-based motion preservation systems are often used to support a slightly degenerated disc. Such implants are intended to reduce intradiscal pressure and facet joints forces, while having a minimal effect on the motion patterns.In a probabilistic finite element study with subsequent sensitivity analysis, the effects of 10 input parameters, such as elastic modulus and diameter of the elastic rod, distraction of the segment, level of bridged segments, etc. on the output parameters intervertebral rotations, intradiscal pressures, and facet joint forces were determined. A validated finite element model of the lumbar spine was employed. Probabilistic studies were performed for seven loading cases: upright standing, flexion, extension, left and right lateral bending and left and right axial rotation.The simulations show that intervertebral rotation angles, intradiscal pressures and facet joint forces are in most cases reduced by a motion preservation system. The influence on intradiscal pressure is small, except in extension. For many input parameter combinations, the values for intervertebral rotations and facet joint forces are very low, which indicates that the implant is too stiff in these cases. The output parameters are affected most by the following input parameters: loading case, elastic modulus and diameter of the elastic rod, distraction of the segment, and angular rigidity of the connection between screws and rod.The designated functions of a motion preservation system can best be achieved when the longitudinal rod has a low stiffness, and when the connection between rod and pedicle screws is rigid.     

Specimen dimensions influence the measurement of material properties in tendon fascicles

Stress, strain and modulus are regularly used to characterize material properties of tissue samples. However, when comparing results from different studies it is evident the reported material properties, particularly failure strains, vary hugely. The aim of our study was to characterize how and why specimen length and cross-sectional area (CSA) appear to influence failure stress, strain and modulus in fascicles from two functionally different tendons. Fascicles were dissected from five rat tails and five bovine foot extensors, their diameters determined by a laser micrometer, and loaded to failure at a range of grip-to-grip lengths. Strain to failure significantly decreased with increasing in specimen length in both rat and bovine fascicles, while modulus increased. Specimen length did not influence failure stress in rat tail fascicles, although in bovine fascicles it was significantly lower in the longer 40 mm specimens compared to 5 and 10 mm specimens. The variations in failure strain and modulus with sample length could be predominantly explained by end-effects. However, it was also evident that strain fields along the sample length were highly variable and notably larger towards the ends of the sample than the mid-section even at distances in excess of 5 mm from the gripping points. Failure strain, stress and modulus correlated significantly with CSA at certain specimen lengths. Our findings have implications for the mechanical testing of tendon tissue: while it is not always possible to control for fascicle length and/or CSA, these parameters have to be taken into account when comparing samples of different dimensions.     

The effect of axial compression and distraction on cervical facet mechanics during anterior shear,flexion, axial rotation,and lateral bending motions

The subaxial cervical facets are important load-bearing structures, yet little is known about their mechanical response during physiological or traumatic intervertebral motion. Facet loading likely increases when intervertebral motions are superimposed with axial compression forces, increasing the risk of facet fracture. The aim of this study was to measure the mechanical response of the facets when intervertebral axial compression or distraction is superimposed on constrained, non-destructive shear, bending and rotation motions. Twelve C6/C7 motion segments (70 ± 13 yr, nine male) were subjected to constrained quasi-static anterior shear (1 mm), axial rotation (4°), flexion (10°), and lateral bending (5°) motions. Each motion was superimposed with three axial conditions: (1) 50 N compression; (2) 300 N compression (simulating neck muscle contraction); and, (3) 2.5 mm distraction. Angular deflections, and principal and shear surface strains, of the bilateral C6 inferior facets were calculated from motion-capture data and rosette strain gauges, respectively. Linear mixed-effects models (α = 0.05) assessed the effect of axial condition. Minimum principal and maximum shear strains were largest in the compressed condition for all motions except for maximum principal strains during axial rotation. For right axial rotation, maximum principal strains were larger for the contralateral facets, and minimum principal strains were larger for the left facets, regardless of axial condition. Sagittal deflections were largest in the compressed conditions during anterior shear and lateral bending motions, when adjusted for facet side.     

Pipette aspiration technique for the measurement of nonlinear and anisotropic mechanical properties of blood vessel walls under biaxial stretch

A pipette aspiration technique was proposed for the measurement of nonlinear mechanical properties of arteries under biaxial stretching. A cross-shaped specimen of porcine thoracic aorta whose principal axes corresponded with the axial and circumferential directions of the aortic walls was excised. The intraluminal surface of the specimen was aspirated with a circular cross-sectioned glass pipette while the specimen was stretching in the axial and circumferential directions in 10% increments. The elastic modulus agreed with the incremental elastic modulus obtained through a conventional pressure-diameter test of the same specimen to within an error of 30% at a circumferential stretch ratio below 1.3 and an axial stretch ratio of 1.0, 1.1 or 1.2, which represent lower range of physiological stretch ratios for the porcine aorta. A rectangular cross-sectioned pipette was utilized to measure anisotropic properties of the specimen under biaxial stretching. When aspirated with such a pipette, the specimens' elastic properties along the length of the rectangular pipette cross section can be neglected. The elastic modulus was found to increase rapidly when the specimen was stretched in the direction of the pipette's width. Thus, pipette aspiration should have many advantages such as well measurement of the local nonlinear and anisotropic mechanical properties of blood vessel walls.     

Sensitivity of multiple damage parameters to compressive overload in cortical bone

Damage accumulation plays a key role in weakening bones prior to complete fracture and in stimulating bone remodeling. The goal of this study was to characterize the degradation in the mechanical properties of cortical bone following a compressive overload. Longitudinally oriented, low-aspect ratio specimens (n=24) of bovine cortical bone were mechanically tested using an overload-hold-reload protocol. No modulus reductions greater than 5% were observed following overload magnitudes less than 0.73% strain. For each specimen, changes in strength and Poisson's ratio were greater (p=0.02) than that in modulus by 10.8- and 26.6-fold, respectively, indicating that, for the specimen configuration used in this study, longitudinal elastic modulus is one of the least sensitive properties to a compressive overload. Residual strains were also proportionately greater by 6.4-fold (p=0.01) in the transverse than axial direction. These results suggest that efforts to relate microcrack density and morphology to changes in compressive mechanical properties of cortical bone may benefit from considering alternative parameters to modulus reductions.     

Stepwise reduction of functional spinal structures increase disc bulge and surface strains

Previous studies postulated that an axial compression of lumbar intervertebral discs causes a complex strain pattern on the annulus. This pattern is not fully understood, since most studies measured only the uniaxial ultimate tensile strain of the annulus. The aim of this study was to investigate surface strains and their relation to disc bulging. This work was extended to study some defects that are relevant for the intermediate process of finite element modeling. Six specimens (L2-3) with a median age of 51 years were utilized for this in vitro study. Specimens were loaded with pure moments (2.5-7.5Nm) in the principal directions. The anatomy was subsequently reduced in three steps: (1) ligamentous and bony posterior structures, (2) anterior and posterior ligaments and (3) nucleus. Measured were ranges of motion, three-dimensional disc bulging and surface strains of the outer annulus. Lateral bending showed the largest axial strains (9.7%) for intact specimens, which increased to 15.1% after the removal of posterior structures. Disc bulging was largest in flexion with 1.56mm, which increased to 2.06mm after step (1). Defect (2) caused that flexion yielded the largest axial strains with 22.6% and 2.17mm of bulging. We could also determine a constriction effect of these ligaments. Nucleotomy did not essentially increase anterior disc bulging in flexion, but inward disc bulging increased by 0.55mm, in extension. Due to the increase in the complexity of finite element models, it is difficult to obtain data from the literature for validation purposes. This study presents new data, which assist in the development of such models.     

Animation of in vitro biomechanical tests.

Interdisciplinary communication of three-dimensional kinematic data arising from in vitro biomechanical tests is challenging. Complex kinematic representations such as the helical axes of motion (HAM) add to the challenge. The difficulty increases further when other quantities (i.e. load or tissue strain data) are combined with the kinematic data. The objectives of this study were to develop a method to graphically replay and animate in vitro biomechanical tests including HAM data. This will allow intuitive interpretation of kinematic and other data independent of the viewer's area of expertise. The value of this method was verified with a biomechanical test investigating load-sharing of the cervical spine. Three 3.0 mm aluminium spheres were glued to each of the two vertebrae from a C2-3 segment of a human cervical spine. Before the biomechanical tests, CT scans were made of the specimen (slice thickness=1.0 mm and slice spacing=1.5 mm). The specimens were subjected to right axial torsion moments (2.0 Nm). Strain rosettes mounted to the anterior surface of the C3 vertebral body and bilaterally beneath the facet joints on C3 were used to estimate the force flow through the specimen. The locations of the aluminium spheres were digitised using a space pointer and the motion analysis system. Kinematics were measured using an optoelectronic motion analysis system. HAMs were calculated to describe the specimen kinematics. The digitised aluminium sphere locations were used to match the CT and biomechanical test data (RMS errors between the CT and experimental points were less than 1.0 mm). The biomechanical tests were "replayed" by animating reconstructed CT models in accordance with the recorded experimental kinematics, using custom software. The animated test replays allowed intuitive analysis of the kinematic data in relation to the strain data. This technique improves the ability of experts from disparate backgrounds to interpret and discuss this type of biomechanical data.     

A method on strain measurement of HAP in cortical bone from diffusive profile of X-ray diffraction

Bone tissue is a composite material composed of hydroxyapatite (HAp) and collagen matrix. As HAp is a crystalline structure, an X-ray diffraction method is available to measure the lattice strain of HAp crystals. However, mineral particles of HAp in bone have much lower crystallinity than usual crystalline materials, which show a diffusive intensity profile of X-ray diffraction. It is not easy to determine quantitatively an infinitesimal strain of HAp from the peak position of diffusive profile. In order to improve the accuracy of strain measurement of HAp in bone tissue and to obtain reproducible results, this paper proposes an X-ray diffraction method applied to a diffusive profile for low crystallinity. This method is to estimate the lattice strain of HAp using not a peak position but a whole diffraction profile. In this experiment, a strip specimen of 28 x 8 x 2 mm was made from bone axial, outside circumferential and cross-sectional circumferential region in the cortical bone of bovine femur. The X-ray diffraction measurements were carried out before and after applying an external load. As a result, the precision of strain measurement was much improved by this method. Although a constant value of macroscopic strain was applied in the specimen, the lattice strain had a lower value than the macroscopic strain and had a different value in each specimen.     

The measurement of the variation in the surface strains of Achilles tendon grafts using imaging techniques

Uniaxial tensile tests are commonly used to characterize the structural and material properties of tendons and ligaments. During these tests, the stress and strain distributions applied to the specimen are assumed to be uniform. However, few studies have investigated the strain distributions throughout the tissue. The purpose of this study was to use imaging techniques to measure the strains around the circumference of 11 mm wide Achilles tendon grafts during a uniaxial tensile test. Pairs of radiopaque beads with a diameter of 2mm were affixed around the mid-substance of the tendon in four different locations. The motion of the beads was recorded using a cine fluoroscope. This system was shown to measure the displacement of the beads with an accuracy of 0.02 mm. During the uniaxial tensile test, large variations in local tissue strains were observed. At 10 MPa of applied stress, the local tissue strain varied from an average of 2.5-8.7%, an increase in strain of more than three times. As a result of these large variations, the modulus calculated from the stress-strain data varied from an average of 217 to 897 MPa, an increase of approximately 4 times. Furthermore, these data suggest that underestimates of the elastic modulus may result if a uniform strain distribution is assumed. These results indicate that during uniaxial tensile tests, the assumption of uniform stress and strain distributions should be carefully considered and small, uniform specimens should be used when measuring the material properties of soft tissues.     

Development of a model based method for investigating facet articulation

Reported investigations of facet articulation in the human spine have often been conducted through the insertion of pressure sensitive film into the joint space, which requires incision of the facet capsule and may alter the characteristics of interaction between the facet surfaces. Load transmission through the facet has also been measured using strain gauges bonded to the articular processes. While this method allows for preservation of the facet capsule, it requires extensive instrumentation of the spine, as well as strain-gauge calibration, and is highly sensitive to placement and location of the strain gauges. The inherently invasive nature of these techniques makes it difficult to translate them into medical practice. A method has been developed to investigate facet articulation through the application of test kinematics to a specimen-specific rigid-body model of each vertebra within a lumbar spine segment. Rigid-body models of each vertebral body were developed from CT scans of each specimen. The distances between nearest-neighboring points on each facet surface were calculated for specific time frames of each specimen's flexion/extension test. A metric describing the proportion of each facet surface within a distance (2 mm) from the neighboring surface, the contact area ratio (CAR), was calculated at each of these time frames. A statistically significant difference (p<0.037) was found in the CAR between the time frames corresponding to full flexion and full extension in every level of the lumbar spine (L1-L5) using the data obtained from the seven specimens evaluated in this study. The finding that the contact area of the facet is greater in extension than flexion corresponds to other findings in the literature, as well as the generally accepted role of the facets in extension. Thus, a biomechanical method with a sufficiently sensitive metric is presented as a means to evaluate differences in facet articulation between intact and treated or between healthy and pathologic spines.     

Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion

Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.     

Axial-shear interaction effects on microdamage in bovine tibial trabecular bone

Because many osteoporotic fractures occur during a fall, understanding the effect of off-axis loads on initiation and propagation of microdamage in trabecular bone should provide further insight into the biomechanics of age-related fractures. Fourteen on-axis cylindrical specimens were prepared from 12 bovine tibiae. Fluorescent stains were used to label the microdamage due to a sequence of compressive and torsional damaging loads. The mean decrease in Young's modulus was over four times greater than that in the shear modulus after the compressive overload, while there was no difference between the decrease in the axial and torsional stiffnesses after the torsional overload. The total microcrack density due to compression was uniform across the radius of the cylindrical specimens, while the mean density of microcracks due to torsional overloading increased from the axis of the cylindrical specimen to the circumference. The high density of microcracks near the axis of the specimen following torsional overloading was unexpected because of the low strains. Nearly 40% of the microcracks due to torsion propagated from pre-existing microcracks caused by axial compression, indicating that existing microcracks may extend at relatively low strain if the loading mode changes. The propagating microcracks were, on average, longer than the initiating microcracks due to either compressive or torsional loading. Damage due to axial compression appears to increase the susceptibility of trabecular bone to damage propagation during subsequent torsional loads, but it has little effect on the elastic properties in shear.     

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens.

The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens was studied by non-destructive uniaxial compression to 0.4% strain using cylindrical specimens with different sizes and length-to-diameter ratios, and by comparing cubic and cylindrical specimens with the same cross-sectional area. Both the length and the cross-sectional area of the specimen had a highly significant influence on the mechanical behaviour (p less than 0.0001). Within the actual range of length (2.75-11.0 mm) the normalized stiffness (Young's modulus) was related nearly linearly to the specimen length. This dependency on specimen length is suggested to be caused mainly by structural disintegrity of the trabecular specimens near the surface. The normalized stiffness (Young's modulus) was also positively correlated to the cross-sectional area. This dependency on cross-sectional area is probably due to friction-induced stress inhomogeneity at the platen-specimen interface. A cube with side length 6.5 mm or a cylindrical specimen with 7.5 mm diameter and 6.5 mm length are suggested as standard specimens for comparative studies on trabecular bone mechanics.     

Mapping the depth dependence of shear properties in articular cartilage

Determining the depth dependence of the shear properties of articular cartilage is essential for understanding the structure-function relation in this tissue. Here, we measured spatial variations in the shear modulus G of bovine articular cartilage using a novel technique that combines shear testing, confocal imaging and force measurement. We found that G varied by up to two orders of magnitude across a single sample, exhibited a global minimum 50-250 microm below the articular surface in a region just below the superficial zone and was roughly constant at depths > 1000 microm (the "plateau region"). For plateau strains gamma(plateau) approximately 0.75% and overall compressive strains epsilon approximately 5%, G(min) and G(plateau) were approximately 70 and approximately 650 kPa, respectively. In addition, we found that the shear modulus profile depended strongly on the applied shear and axial strains. The greatest change in G occurred at the global minimum where the tissue was highly nonlinear, stiffening under increased shear strain, and weakening under increased compressive strain. Our results can be explained through a simple thought model describing the observed nonlinear behavior in terms of localized buckling of collagen fibers and suggest that compression may decrease the vulnerability of articular cartilage to shear-induced damage by lowering the effective strain on individual collagen fibrils.