An automated approach for direct measurement of two-dimensional strain distributions within articular cartilage under unconfined compression

An automated approachfor measuring in situ two-dimensional strain fields was developed and validated for its application to cartilage mechanics. This approach combines video microscopy, optimized digital image correlation (DIC), thin-plate spline smoothing (TPSS) and generalized cross-validation (GCV) techniques to achieve the desired efficiency and accuracy. Results demonstrate that sub-pixel accuracies can be achieved for measuring tissue displacements with this methodology with a measurement uncertainty ranging from 0.25 to 0.30 pixels. The deformational gradients (from which the strains are determined) can be evaluated directly using the optimized DIC, with a measurement uncertainty of 0.017 to approximately 0.032. In actual measurements of strain in cartilage, TPSS and differentiation can be used to achieve a more accurate measurement of the gradients from the displacement data. Using this automated approach, the two-dimensional strain fields inside immature bovine carpometacarpal joint cartilage specimens under unconfined compression were characterized (n=21). The depth-dependent apparent elastic modulus and Poisson's ratio were also determined and found to be smallest at the articular surface and increasing with depth. The apparent Poisson's ratio is found to decrease with increasing compressive strain, with values as low as 0.01 observed near the articular surface at 25% compression. The variation of the apparent Poisson's ratio with depth is found to be consistent with a theoretical model of cartilage which accounts for the disparity in its tensile and compressive moduli.     

Principles and methods of geometric morphometrics

The basic concepts, notions and methods of geometric morphometrics (GM) are considered. This approach implies multivariate analysis of landmark coordinates located following certain rules on the surface of a morphological object. The aim of GM is to reveal differences between morphological objects by their shapes as such, the "size factor" being excluded. The GM is based on the concept of Kendall's space (KS) defined as a hypersphere with points distributed on its surface. These points are the shapes defined as aligned landmark configurations. KS is a non-Euclidian space, its metrics called Procrustes is defined by landmark configuration of a reference shape relative to which other shapes are aligned and compared. The differences among shapes are measured as Procrustes distances between respective points. For the linear methods of multivariate statistics to be applied to comparison of shapes, the respective points are projected onto the tangent plane (tangent space), the tangent point being defined by the reference. There are two principal methods of shape comparisons in GM: the Procrustes superimposition (a version of the least squares analysis) and thin-plate spline analysis. In the first case, Procrustes residuals are the outcome shape variables which remain after isometric alignment of the shapes being compared. Their summation over all landmarks yields Procrustes distances among these shapes. The Procrustes distances can be used in multivariate analyses just as the Euclidian distances. In the second case, the shapes are fitted to the references by stretching/compressing and shearing until complete identity of their landmark configurations. Eigenvectors of resulting bending energy matrix are defined as new shape variables, principal warps which yield another shape space with the origin defined by the reference. Projections of the shapes being compared onto principal warps yield partial warps, and their covariance matrix decomposition into eigenvectors yields relative warps which are similar to principal components (in particular, they are mutually orthogonal). Both partial and relative warps can be used in many multivariate statistic analyses as quantitative shape variables. Results of thin-plate spline analysis can be represented graphically by transformation grid which displays type, amount and localization of the shape differences. Basis rules of sample composition and landmark positioning to be used in GM are considered. At present, rigid (with minimal degrees of freedom) 2D morphological objects are most suitable for GM applications. It is important to recognize three type of real landmarks, and additionally semi-landmarks and "virtual" landmarks. Some procedures of thin-plate spline analysis are considered exemplified by some study cases, as well as applications of some standard multivariate methods to GM results. They make it possible to evaluate correlation between different shapes, as well as between a shape and some non-shape variables (linear measurements etc); to evaluate the differences among organisms by shape of a morphological structure; to identify landmarks which most accounted for both correlation and differences between the shapes. An annotated list of most popular softwares for GM is provided.     

Non-uniform strain distribution within rat cartilaginous growth plate under uniaxial compression

Growth plates are highly inhomogeneous in morphology and composition. Mechanical loading can modulate longitudinal bone growth, though the mechanisms underlying this mechanobiology are poorly understood. The proximal tibial growth plates of six rats were tested in vitro under uniaxial compression to 5% strain, and confocal microscopy was used to track and capture images of fluorescently labeled cell nuclei with increasing applied strains. The local strain patterns through the growth plate thickness were quantified using texture correlation analysis. The technique of texture correlation analysis was first validated by comparing theoretical simulated strain maps generated from numerically distorted images. The texture correlation algorithm was sensitive to the grid size superimposed on the original image, but remained insensitive to parameters related to the size of the final image mask, which was searched by the correlation algorithm for each grid point of the original image. Within the growth plate, experimental strain distributions were non-uniform in all six specimens. Growth plates were mostly under compression strains. The strain distributions differed among the histomorphological zones of the growth plate, which was most obvious in specimens with regular growth plate shape: higher compressive strains (4-8 times higher than the applied 5% strain) were located mainly in regions overlapping the reserve and hypertrophic zones with lower compressive strains in the proliferative zone. This study documents the non-uniform mechanical behavior of growth plate across its three histological zones when exposed to compression. Further investigation is required to establish the significance of non-uniform strain fields during growth in vivo.     

Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation

The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split-line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stress-strain responses exhibited nonlinearity under finite strain, while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.     

The evolution of development: two portraits of skull ossification in pipoid frogs

Abstract.— Development creates morphology, and the study of developmental processes has repeatedly shed light on patterns of morphological evolution. However, development itself evolves as well, often concomitantly with changes in life history or in morphology. In this paper, two approaches are used to examine the evolution of skull development in pipoid frogs. Pipoids have highly unusual morphologies and life histories compared to other frogs, and their development also proves to be remarkable. First, a phylogenetic examination of skull bone ossification sequences reveals that jaw ossification occurs significantly earlier in pipoids than in other frogs; this represents a reversal to the primitive vertebrate condition. Early jaw ossification in pipoids is hypothesized to result from the absence of certain larval specializations possessed by other frogs, combined with unusual larval feeding behaviors. Second, thin-plate spline morphometric studies of ontogenetic shape change reveal important differences between pipoid skull development and that of other frogs. In the course of frog evolution, there has been a shift away from salamander-like patterns of ontogenetic shape change. The pipoids represent the culmination of this trend, and their morphologies are highly derived in numerous respects. This study represents the first detailed examination of the evolution of skull development in a diverse vertebrate clade within a phylogenetic framework. It is also the first study to examine ossification sequences across vertebrates, and the first to use thin-plate spline morphometrics to quantitatively describe ontogenetic trajectories.     

An analysis of the complete strain field within Flexercell membranes

The purpose of the current investigation was to use finite element analysis to quantify the complete strain field for the membranes of the Flexercell^TM apparatus, a device extensively used to study the effects of mechanical loading on cultured cells. Four vacuum pressure simulations were run for the membrane for both the uniaxial and biaxial loading post, yielding the distribution of longitudinal (E_xx) and transverse (E_yy) strain for the uniaxial post, and the radial (E_rr) and the circumferential (E_θθ) strain for the biaxial post. The discrete values of each strain were evaluated at the center of the loading post as well as the region off of the post. Experimental measurements were made for both types of loading posts in order to validate our simulations. The biaxial post simulation was found to provide a central circular region of equal and constant E_rr and E_θθ in the membrane on the post. Likewise, the uniaxial post simulation provided a definitive region of constant E_xx for a central rectangular region on the post. For the uniaxial simulation, the region on the post resulted in small compressive E_yy, while the region off the post resulted in tensile E_yy. The biaxial simulation resulted in large tensile E_rr and E_θθ on the post, while the region off the post resulted in large E_rr and smaller E_θθ. Our simulations were reasonably consistent with the experimental measurements made for both types of loading posts. We believe that the results of this study will allow scientists to more accurately describe the response of cells to known strains on all portions of the membrane, thus increasing the range of known strain regions for investigation in the Flexercell^TM apparatus.     

A geometric morphometric analysis of the shape of the first upper molar in mice of the genus Mus (Muridae, Rodentia)

Phenotypic variation in the shape of the first upper molar among 595 mice, representing nine extant and three extinct taxa of the genus Mus , was studied with thin-plate spline analysis. The reliability of classification of individual specimens into known groups based on their molars varied from 75 to 100%, depending on group and method used. Including 13 sliding semilandmarks to the analysis improved the detection of different kinds of size and shape variation as well as visualization of shape differences between studied groups. Correlation between phylogenetic and morphometric distances suggested about 80% contribution of phylogenetic inertia to the molar shape variation; moreover, the importance of localized versus global shape changes was similar in the detection of phylogenetic signals. Finally, shape changes along individual evolutionary lineages were revealed, suggesting a few cases of reversals, convergence and/or retention of ancestral shape. The evolution of mouse molars has thus been driven by random effects of drift together with stabilizing selection and convergence.     

Dynamic response of immature bovine articular cartilage in tension and compression, and nonlinear viscoelastic modeling of the tensile response

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with R2 = 0.970+/-0.019 at 1% strain and R2 = 0.992+/-0.007 at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at 10 Hz was approximately 2.3 times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was approximately 24. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of 16.7+/-7.4 deg versus 53.5+/-12.8 deg at 10(-3) Hz). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies (R2 = 0.908+/-0.100). The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.     

Personalised Mechanical Properties of Scoliotic Vertebrae Determined In Vivo Using Tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

Accuracy of respiratory inductive plethysmographic cross-sectional areas

The present study was undertaken to evaluate whether the respiratory inductive plethysmograph (RIP) 1) reflects changes of cross-sectional area enclosed by its transducer band in the presence of deformations of shape or whether it 2) has a stable base line. Testing of RIP was carried out with a device incorporating a thermally compensated oscillator and digital demodulatory circuitry. This system, introduced to commerce in 1983, superceded the nonthermal compensated oscillatory and analog demodulator circuitry first used in 1977. Testing the effects of changing cross-sectional area was accomplished by stretching a standard RIP transducer band around wooden dowels placed in holes on a peg board grid to form 23 curved and 5 rectangular shapes. The output voltage from RIP was linear for both the curved and rectangular shapes for changes of cross-sectional area within a physiological range. However, the regression line of voltage vs. cross-sectional area for the rectangular shapes was parallel and slightly displaced from the regression line for the curved shapes due to mutual coupling of inductance in the corners. Base-line drift from a RIP transducer band stretched to enclose an elliptical shape was less than 2.5 mV over a 12-h observation period. Current RIP technology accurately reflects changes of cross-sectional area of physiological shapes and has a stable base line.     

Form and performance: body shape and prey-capture success in four drift-feeding minnows

Identifying links between morphology and performance for ecologically relevant tasks will help elucidate the relationships between organismal design and fitness. We conducted a laboratory study to quantify the relationship between variation in body shape and prey-capture success in four drift-feeding minnow species. We offered drifting prey to individual fish in a test flume, counted successful strikes to measure prey-capture success and recorded the position (X, Y coordinates) of ten landmarks on each fish’s outline to delineate the specimen’s form. We then quantified shape variation among species and related it to capture performance through thin-plate spline analysis. Body shape varied significantly among species and with specimen size and was the major determinant of capture success, explaining 45–47% of its variability. Prey-capture success at differing velocities differed among species, but once the effects of shape and size were accounted for, those differences were no longer significant. Allometric shape changes appeared responsible for most of the ontogenetic variation in capture performance, although other size-related, non-shape factors also seemed relevant. Fishes with deeper, shorter bodies, more caudally placed median fins and larger, more upward-pointing mouths exhibited greater capture success than more fusiform fish, suggesting that streamlining, which is energetically advantageous for sustained swimming, entails a cost in terms of prey-capture ability. Our findings demonstrate a strong connection between organismal shape and performance and provide empirical evidence of the cost of morphological specialization for fishes in the drift-feeding functional guild.     

Personalised mechanical properties of scoliotic vertebrae determined in vivo using tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

Experimental and finite element analysis of the rat ulnar loading model-correlations between strain and bone formation following fatigue loading

The rat forelimb compression model has been used widely to study bone response to mechanical loading. We used strain gages to assess load sharing between the ulna and radius in the forelimb of adult Fisher rats. We used histology and peripheral quantitative computed tomography (pQCT) to quantify ulnar bone formation 12 days after in vivo fatigue loading. Lastly, we developed a finite element model of the ulna to predict the pattern of surface strains during compression. Our findings indicate that at the mid-shaft the ulna carries 65% of the applied compressive force on the forelimb. We observed large variations in fatigue-induced bone formation over the circumference and length of the ulna. Bone formation was greatest 1-2 mm distal to the mid-shaft. At the mid-shaft, we observed woven bone formation that was greatest medially. Finite element analysis indicated a strain pattern consistent with a compression-bending loading mode, with the greatest strains occurring in compression on the medial surface and lesser tensile strains occurring laterally. A peak strain of -5190 microepsilon (for 13.3N forelimb compression) occurred 1-2 mm distal to the mid-shaft. The pattern of bone formation in the longitudinal direction was highly correlated to the predicted peak compressive axial strains at seven cross-sections (r2 = 0.89, p = 0.014). The in-plane pattern of bone formation was poorly correlated to the predicted magnitude of axial strain at 51 periosteal locations (r2 = 0.21, p < 0.001), because the least bone formation was observed where tensile strains were highest. These findings indicate that the magnitude of bone formation after fatigue loading is greatest in regions of high compressive strain.     

Influence of tensile strain on smooth muscle cell orientation in rat blood vessels.

Blood vessels are subject to tensile stress and associated strain which may influence the structure and organization of smooth muscle cells (SMCs) during physiological development and pathological remodeling. This study focused on the influence of the major tensile strain on the SMC orientation in the blood vessel wall. Several blood vessels, including the aorta, the mesenteric artery and vein, and the jugular vein of the rat were used to observe the normal distribution of tensile strains and SMC orientation; and a vein graft model was used to observe the influence of altered strain direction on the SMC orientation. The circumferential and longitudinal strains in these blood vessels were measured by using a biomechanical technique, and the SMC orientation was examined by fluorescent microscopy at times of 10, 20, and 30 days. Results showed that the SMCs were mainly oriented in the circumferential direction of straight blood vessels with an average angle of approximately 85 deg between the SMC axis and the vessel axis in all observed cases. The SMC orientation coincided with the principal direction of the circumferential strain, a major tensile strain, in the blood vessel wall. In vein grafts, the major tensile strain direction changed from the circumferential to the longitudinal direction at observation times of 10, 20, and 30 days after graft surgery. This change was associated with a decrease in the angle between the axis of newly proliferated SMCs and that of the vessel at all observation times (43 +/- 11 deg, 42 +/- 10 deg, and 41 +/- 10 deg for days 10, 20, and 30, respectively), indicating a shift of the SMC orientation from the circumferential toward the longitudinal direction. These results suggested that the major tensile strain might play a role in the regulation of SMC orientation during the development of normal blood vessels as well as during remodeling of vein grafts.     

Assessing morphological differences in an adaptive trait: a landmark-based morphometric approach

East African cichlid fishes have evolved a stunning array of oral jaw morphologies. To better understand the adaptive evolution of this trait, we performed a morphological analysis of the jaws of two closely related species from Lake Malawi that have very different modes of feeding. Labeotropheus fuelleborni forages along the substrate with a "biting" mode of feeding, while Metriaclima zebra feeds in the water column with a "sucking" mode. We analyzed each of the four skeletal elements that make up the oral jaws: the dentary, articular, premaxilla, and maxilla. In addition, we performed the same analysis on the neurocranium, an element closely associated with the oral jaws. We used the thin-plate spline method to quantify morphological differences, which allowed us to relate our results to the functional biology of the species. We find many aspects of shape change that relate directly to the functional design of the cichlid head. The same series of measurements was made on hybrids between Labeotropheus and Metriaclima. For every character, hybrid progeny are statistically different from both parental species. These results suggest an additive mode of action of the alleles responsible for these phenotypes.     

Relations of the soft structures of the posterior mediastinum in the scoliotic spine

In 20 dissections of scoliotic cadavers, the changes of the structures in the posterior mediastinum in relation to the spine were found to be as follows. The aorta persistently followed and adhered to the abnormal curves of the spine. The azygos vein and the thoracic duct followed the aorta closely in its changes. The sympathetic trunk and the greater splanchnic nerves likewise followed the changes in the curvature of the scoliotic spine, but they were often disturbed in their course by vertebral osteophytes and by hyperostoses due to arthritis of the costovertebral joints. The esophagus preserved its normal straight course, unaffected by the scoliotic curves.     

Getting into Shape: An Empirical Comparison of Traditional Truss-Based Morphometric Methods with a Newer Geometric Method Applied to New World Cichlids

Body shape is a difficult, but important, trait to quantify. Researchers have traditionally used multivariate analysis of several linear measures ('trusses') across the body form to quantify shape. Newer geometric morphometric methods claim to better estimate shape because they analyze the geometry among the locations of all landmarks simultaneously rather than the linear distances between pairs of landmarks. We tested this claim by comparing the results of several traditional morphometric analyses against a newer geometric analysis involving thin-plate splines (TPS), all applied to a common data set of morphologically variable new world cichlids Amphilophus citrinellus and A. zaliosus. The TPS method yielded slightly stronger evidence of morphological differences among forms, although traditional methods also distinguished the two species. Perhaps our most important result was the idiosyncratic interpretation of shape variation among the traditional truss-based methods, whereas the generation of deformation grids using the TPS approach yielded clear and visually interpretable figures. Our results indicate that geometric morphometrics can be a more effective way to analyze and interpret body form, but also that traditional methods can be relied upon to provide statistical evidence of shape differences, although not necessarily accurate information about the nature of variation in shape.     

Phenotypic plasticity of the aedeagus of Drosophila mediopunctata: Effect of the temperature

In this study, we analyzed the phenotypic plasticity of the male intromittent organ (aedeagus) of Drosophila mediopunctata genitalia in response to temperature. Size and shape of the aedeagus were examined with univariate statistics and geometric morphometrics. The following results emerged: firstly, flies raised at 16.5 °C had bigger aedeagi than those raised at 20 °C; secondly, significant differences in shape were also found between the two groups of flies, mainly in the apical area, located using the thin-plate spline interpolating function; thirdly, the coefficients of variation for the traits of the aedeagus were comparable to other traits in Drosophila and likewise to genital traits in other organisms. These findings were analyzed in an evolutionary context.