Claudio Vergari

True stress and Poisson's ratio of tendons during loading

Excessive axial tension is very likely involved in the aetiology of tendon lesions, and the most appropriate indicator of tendon stress state is the true stress, the ratio of instantaneous load to instantaneous cross-sectional area (CSA). Difficulties to measure tendon CSA during tension often led to approximate true stress by assuming that CSA is constant during loading (i.e. by the engineering stress) or that tendon is incompressible, implying a Poissons ratio of 0.5, although these hypotheses have never been tested. The objective of this study was to measure tendon CSA variation during quasi-static tensile loading, in order to assess the true stress to which the tendon is subjected and its Poissons ratio. Eight equine superficial digital flexor tendons (SDFT, about 30cm long) were tested in tension until failure while the CSA of each tendon was measured in its metacarpal part by means of a linear laser scanner. Axial elongation and load were synchronously recorded during the test. CSA was found to linearly decrease with strain, with a mean decrease at failure of -10.7±2.8% (mean±standard deviation). True stress at failure was 7.1-13.6% higher than engineering stress, while stress estimation under the hypothesis of incompressibility differed from true stress of -6.6 to 2.3%. Average Poissons ratio was 0.55±0.12 and did not significantly vary with load. From these results on equine SDFT it was demonstrated that tendon in axial quasi-static tension can be considered, at first approximation, as an incompressible material.

Axial speed of sound is related to tendon's nonlinear elasticity

Axial speed of sound (SOS) measurements have been successfully applied to noninvasively evaluate tendon load, while preliminary studies showed that this technique also has a potential clinical interest in the follow up of tendon injuries. The ultrasound propagation theory predicts that the SOS is determined by the effective stiffness, mass density and Poissons ratio of the propagating medium. Tendon stiffness characterizes the tissues mechanical quality, but it is often measured in quasi-static condition and for entire tendon segments, so it might not be the same as the effective stiffness which determines the SOS. The objectives of the present study were to investigate the relationship between axial SOS and tendons nonlinear elasticity, measured in standard laboratory conditions, and to evaluate if tendons mass density and cross-sectional area (CSA) affect the SOS level. Axial SOS was measured during in vitro cycling of 9 equine superficial digital tendons. Each tendons stiffness was characterized with a tangent modulus (the continuous derivative of the true stress/true strain curve) and an elastic modulus (the slope of this curves linear region). Tendons SOS was found to linearly vary with the square root of the tangent modulus during loading; tendons SOS level was found correlated to the elastic moduluss square root and inversely correlated to the tendons CSA, but it was not affected by tendons mass density. These results confirm that tendons tangent and elastic moduli, measured in laboratory conditions, are related to axial SOS and they represent one of its primary determinants.

3D reconstruction of rib cage geometry from biplanar radiographs using a statistical parametric model approach

Rib cage 3D reconstruction is an important prerequisite for thoracic spine modelling, particularly for studies of the deformed thorax in adolescent idiopathic scoliosis. This study proposes a new method for rib cage 3D reconstruction from biplanar radiographs, using a statistical parametric model approach. Simplified parametric models were defined at the hierarchical levels of rib cage surface, rib midline and rib surface, and applied on a database of 86 trunks. The resulting parameter database served to train statistical models which were used to quickly provide a first estimate of the reconstruction from identifications on both radiographs. This solution was then refined by manual adjustments in order to improve the matching between model and image. Accuracy was assessed by comparison with 29 rib cages from CT scans in terms of geometrical parameter differences and in terms of line-to-line error distance between the rib midlines. Intra and inter-observer reproducibility was determined for 20 scoliotic patients. The first estimate (mean reconstruction time of 2 min 30 s) was sufficient to extract the main rib cage global parameters with a 95% confidence interval lower than 7%, 8%, 2% and 4° for rib cage volume, antero-posterior and lateral maximal diameters and maximal rib hump, respectively. The mean error distance was 5.4 mm (max 35 mm) down to 3.6 mm (max 24 mm) after the manual adjustment step (3 min 30 s). The proposed method will improve developments of rib cage finite element modelling and evaluation of clinical outcomes.

Lamellar and fibre bundle mechanics of the annulus fibrosus in bovine intervertebral disc

UNLABELLED The intervertebral disc is a multicomposite structure, with an outer fibrous ring, the annulus fibrosus, retaining a gel-like core, the nucleus pulposus. The disc presents complex mechanical behaviour, and it is of high importance for spine biomechanics. Advances in multiscale modelling and disc repair raised a need for new quantitative data on the finest details of annulus fibrosus mechanics. In this work we explored inter-lamella and inter-bundle behaviour of the outer annulus using micromechanical testing and second harmonic generation microscopy. Twenty-one intervertebral discs were dissected from cow tails; the nucleus and inner annulus were excised to leave a ring of outer annulus, which was tested in circumferential loading while imaging the tissues collagen fibres network with sub-micron resolution. Custom software was developed to determine local tissue strains through image analysis. Inter-bundle linear and shear strains were 5.5 and 2.8 times higher than intra-bundle strains. Bundles tended to remain parallel while rotating under loading, with large slipping between them. Inter-lamella linear strain was almost 3 times the intra-lamella one, but no slipping was observed at the junction between lamellae. This study confirms that outer annulus straining is mainly due to bundles slipping and rotating. Further development of disc multiscale modelling and repair techniques should take into account this modular behaviour of the lamella, rather than considering it as a homogeneous fibre-reinforced matrix. STATEMENT OF SIGNIFICANCE The intervertebral disc is an organ tucked between each couple of vertebrae in the spine. It is composed by an outer fibrous layer retaining a gel-like core. This organ undergoes severe and repeated loading during everyday life activities, since it is the compliant component that gives the spine its flexibility. Its properties are affected by pathologies such as disc degeneration, a major cause of back pain. In this article we explored the micromechanical behaviour of the discs outer layer using second harmonic generation, a technique which allowed us to visualize, with unprecedented detail, how bundles of collagen fibres slide relative to each other when loaded. Our results will help further the development of new multiscale numerical models and repairing techniques.

A Linear Laser Scanner to Measure Cross-Sectional Shape and Area of Biological Specimens During Mechanical Testing

Measure of the cross-sectional area (CSA) of biological specimens is a primary concern for many biomechanical tests. Different procedures are presented in literature but besides the fact that noncontact techniques are required during mechanical testing, most of these procedures lack accuracy or speed. Moreover, they often require a precise positioning of the specimen, which is not always feasible, and do not enable the measure of the same section during tension. The objective of this study was to design a noncontact, fast, and accurate device capable of acquiring CSA of specimens mounted on a testing machine. A system based on the horizontal linear displacement of two charge-coupled device reflectance laser devices next to the specimen, one for each side, was chosen. The whole measuring block is mounted on a vertical linear guide to allow following the measured zone during sample tension (or compression). The device was validated by measuring the CSA of metallic rods machined with geometrical shapes (circular, hexagonal, semicircular, and triangular) as well as an equine superficial digital flexor tendon (SDFT) in static condition. We also performed measurements during mechanical testing of three SDFTs, obtaining the CSA variations until tendon rupture. The system was revealed to be very fast with acquisition times in the order of 0.1 s and interacquisition time of about 1.5 s. Measurements of the geometrical shapes yielded mean errors lower than 1.4% (n=20 for each shape) while the tendon CSA at rest was 90.29 ± 1.69 mm(2) (n=20). As for the tendons that underwent tension, a mean of 60 measures were performed for each test, which lasted about 2 min until rupture (at 20 mm/min), finding CSA variations linear with stress (R(2)>0.85). The proposed device was revealed to be accurate and repeatable. It is easy to assemble and operate and capable of moving to follow a defined zone on the specimen during testing. The system does not need precise centering of the sample and can perform noncontact measures during mechanical testing; therefore, it can be used to measure variations of the specimen CSA during a tension (or compression) test in order to determine, for instance, the true stress and transverse deformations.

Intervertebral disc characterization by shear wave elastography: An in vitro preliminary study

Patient-specific numerical simulation of the spine is a useful tool both in clinic and research. While geometrical personalization of the spine is no more an issue, thanks to recent technological advances, non-invasive personalization of soft tissue’s mechanical properties remains a challenge. Ultrasound elastography is a relatively recent measurement technique allowing the evaluation of soft tissue’s elastic modulus through the measurement of shear wave speed. The aim of this study was to determine the feasibility of elastographic measurements in intervertebral disc. An in vitro approach was chosen to test the hypothesis that shear wave speed can be used to evaluate intervertebral disc mechanical properties and to assess measurement repeatability. In total, 11 oxtail intervertebral discs were tested in compression to determine their stiffness and apparent elastic modulus at rest and at 400 N. Elastographic measurements were performed in these two conditions and compared to these mechanical parameters. The protocol was repeated six times to determine elastographic measurement repeatability. Average shear wave speed over all samples was 5.3 ± 1.0 m/s, with a repeatability of 7% at rest and 4.6% at 400 N; stiffness and apparent elastic modulus were 266.3 ± 70.5 N/mm and 5.4 ± 1.1 MPa at rest, respectively, while at 400 N they were 781.0 ± 153.8 N/mm and 13.2 ± 2.4 MPa, respectively. Correlations were found between elastographic measurements and intervertebral disc mechanical properties; these preliminary results are promising for further in vivo application.

Discrimination of two equine racing surfaces based on forelimb dynamic and hoof kinematic variables at the canter

The type and condition of sport surfaces affect performance and can also be a risk factor for injury. Combining the use a 3-dimensional dynamometric horseshoe (DHS), an accelerometer and high-speed cameras, variables reflecting hoof-ground interaction and maximal limb loading can be measured. The aim of the present study was to compare the effects of two racing surfaces, turf and all-weather waxed (AWW), on the forelimbs of five horses at the canter. Vertical hoof velocity before impact was higher on AWW. Maximal deceleration at impact (vertical impact shock) was not significantly different between the two surfaces, whereas the corresponding vertical force peak at impact measured by the DHS was higher on turf. Low frequency (0-200 Hz) vibration energy was also higher on turf; however high frequency (>400 Hz) vibration energy tended to be higher on AWW. The maximal longitudinal force during braking and the maximal vertical force at mid-stance were lower on AWW and their times of occurrence were delayed. AWW was also characterised by larger slip distances and sink distances, both during braking and at maximal sink. On a given surface, no systematic association was found between maximal vertical force at mid-stance and either sink distance or vertical impact shock. This study confirms the damping properties of AWW, which appear to be more efficient for low frequency events. Given the biomechanical changes induced by equestrian surfaces, combining dynamic and kinematic approaches is strongly recommended for a reliable assessment of hoof-ground interaction and maximal limb loading.

Non-invasive assessment of human multifidus muscle stiffness using ultrasound shear wave elastography: A feasibility study.

There is a lack of numeric data for the mechanical characterization of spine muscles, especially in vivo data. The multifidus muscle is a major muscle for the stabilization of the spine and may be involved in the pathogenesis of chronic low back pain (LBP). Supersonic shear wave elastography (SWE) has not yet been used on back muscles. The purpose of this prospective study is to assess the feasibility of ultrasound SWE to measure the elastic modulus of lumbar multifidus muscle in a passive stretching posture and at rest with a repeatable and reproducible method. A total of 10 asymptotic subjects (aged 25.5 ± 2.2 years) participated, 4 females and 6 males. Three operators performed 6 measurements for each of the 2 postures on the right multifidus muscle at vertebral levels L2-L3 and L4-L5. Repeatability and reproducibility have been assessed according to ISO 5725 standard. Intra-class correlation coefficients (ICC) for intra- and inter-observer reliability were rated as both excellent [ICC=0.99 and ICC=0.95, respectively]. Reproducibility was 11% at L2-L3 level and 19% at L4-L5. In the passive stretching posture, shear modulus was significantly higher than at rest (µ < 0.05). This preliminary work enabled to validate the feasibility of measuring the shear modulus of the multifidus muscle with SWE. This kind of measurement could be easily introduces into clinical routine like for the medical follow-up of chronic LBP or scoliosis treatments.

Comparison of superficial digital flexor tendon loading on asphalt and sand in horses at the walk and trot

The incidence of superficial digital flexor tendon (SDFT) injuries is one of the highest of all equine musculoskeletal conditions. Horses with SDFT injuries commonly show no improvement of lameness on soft ground, unlike those suffering from distal bone or joint lesions. The aim of this study was to compare the SDFT loading in five horses at the walk and trot on asphalt and sand using a non-invasive ultrasonic tendon force measurement device. Three horses were equipped with the ultrasonic device, whereas the other two horses were equipped with the ultrasonic device and a dynamometric horseshoe (DHS); the DHS was used to calibrate the measured values of tendon speed of sound (SOS) converted to tendon force, while a previously established ground reaction force pattern was used to calibrate SOS measurements for the other three horses. Although the horses tended to be slower on S, maximal tendon force was higher on sand than on asphalt at the trot (+6%); there was no significant difference between the two surfaces at the walk. The duration of tendon loading was longer on S (+5%) and the area under the tendon force-time curve was larger on S (+10%) at both walk and trot. SDFT loading is significantly affected by the ground surface and the observed increase in SDFT loading on sand compared with asphalt is consistent with clinical observations in horses with SDFT injuries.

The hierarchical response of human corneal collagen to load

Graphical abstract