J. Martínez-Reina

Effect of porosity and mineral content on the elastic constants of cortical bone: a multiscale approach

A micromechanical multiscale model which estimates the elastic properties of cortical bone as a function of porosity and mineral content is presented. The steps of the model are divided into two main phases. In the first one, the elastic properties of the collagen fibril, collagen fiber and lamella are given. In the second phase, porosity is included in the lamella in the form of canaliculi, lacunae and Haversian canals, to provide the elastic properties of the osteonal tissue. Then, a symmetrization technique is used to estimate the transversely isotropic elasticity tensor of the osteon. Osteons are superimposed using a self-consistent scheme, and finally, the fluid filling the pores is included to estimate the elastic constants of the undrained cortical tissue. The main novelty of the model presented here is the possibility of varying the mineral content of bone, considering that mineralization begins from the inner levels, initially intrafibrillar and then interfibrillar. Correlations of the elastic properties of cortical bone obtained with this model on the one hand, and porosity and ash fraction on the other hand, are estimated.

A bone remodelling model including the directional activity of BMUs

Bone is able to adapt itself to the mechanical and biological environment by changing its porosity and/or orientation of its internal microstructure in a process known as bone remodelling. As a consequence, a change of bone mechanical properties is produced leading to an optimum structure, able to bear the external loads with the minimum weight. This adaptation is carried out by a temporal association of cells known as BMUs (basic multicellular units) that resorb old bone and sometimes produce new organic extracellular matrix (osteoid) that is later mineralized. This involves changes in porosity, damage level (density of microcracks accumulated by cyclic loads) and mineral content. All of these features were taken into account in a previous model, but the whole process and therefore the resulting bone constitutive behaviour was considered isotropic. The model proposed herein, recognizing that bone is actually anisotropic, tries to explain how BMUs modify the anisotropy by changing their progressing direction. We check the potential of the model to predict the alignment of the bone microstructure with the external loads in different situations. Then, the model is also applied to obtain the anisotropy and mechanical properties of the human proximal femur under physiological loads with initial conditions corresponding to a heterogeneous, but otherwise isotropic bone.

Percutaneous iliosacral fixation in external rotational pelvic fractures. A biomechanical analysis.

INTRODUCTION Although the gold standard in open book pelvic fractures remains the pubic symphysis (PS) plate fixation, the clinical outcomes are not satisfactory, despite the excellent anatomical reduction assessed radiologically. Some authors suggest that residual instability of the posterior pelvic elements may be responsible for the chronic pain and the early osteoarthritic changes in the sacroiliac joint (SIJ). OBJECTIVE To evaluate whether the isolated posterior fixation with one or two iliosacral screws (ISSs) is sufficient to provide adequate stability for the treatment of Burgess Young APC-II (YB APC-II) type of pelvic ring injuries. METHODS Biomechanical experimental study using 7 fresh human pelvises, where an YB APC-II pelvic injury was previously implemented. The isolated posterior fixation of the pelvic ring with 1 or 2 ISSs directed in the S1 vertebra body was analysed in each specimen following an axial load of 300N. The different displacement of the SIJ and of the PS were analysed in all three spatial axes, using the validated optical measurement system 3D PONTOS 5M. A multivariate version of Friedman test (non-parametric ANOVA for repeated measures) was performed. RESULTS The isolated fixation of the SIJ with 1 ISS did not show any differences with respect to the intact pelvis (p=0.851). Regarding the PS, both type of fixations (with 1 or 2 ISSs) confirmed an acceptable correction and adequate control of the PS even though with some differences compared to the intact pelvis (p=0.01). The presence of the second ISS found not to offer any significant additional benefit. The three-dimensional analysis of the behaviour of the pelvic elements, in these two different types of fixation, did not show any statistical significant differences (p=0.645). CONCLUSION The posterior fixation with ISS can represent an alternative option for treatment of pelvic injuries associated with rotational instability. Further prospective clinical studies are necessary to determine, the influence of the residual pubic symphysis mobility in the every day life, when the above-mentioned technique is applied.

A study of the temporomandibular joint during bruxism

A finite element model of the temporomandibular joint (TMJ) and the human mandible was fabricated to study the effect of abnormal loading, such as awake and asleep bruxism, on the articular disc. A quasilinear viscoelastic model was used to simulate the behaviour of the disc. The viscoelastic nature of this tissue is shown to be an important factor when sustained (awake bruxism) or cyclic loading (sleep bruxism) is simulated. From the comparison of the two types of bruxism, it was seen that sustained clenching is the most detrimental activity for the TMJ disc, producing an overload that could lead to severe damage of this tissue.

Biomechanical analysis of a new minimally invasive system for osteosynthesis of pubis symphysis disruption.

INTRODUCTION We analysed the effectiveness of a new percutaneous osteosynthesis system for the treatment of pelvis fractures with rotational instability. METHODS A pre-clinical cross-sectional experimental study wherein Tile type B1 injuries (open-book fractures) were produced in 10 specimens of fresh human cadavers, including the L4-5 vertebrae, pelvic ring, and proximal third of the femur, keeping intact the capsular and ligamentous structures, is presented in this paper. The physiological mobility of the intact pelvis in a standing position post-injury was compared to that following the performance of a minimally invasive osteosynthesis of the symphysis with two cannulated screws. A specially designed test rig capable of applying loads simulating different weights, coupled with a photogrammetry system, was employed to determine the 3D displacements and rotations in three test cases: intact, injured and fixed. RESULTS After applying an axial load of 300 N, no differences were observed in the average displacement (mm) of the facet joints of the intact pubic symphysis in comparison to those treated with screws (p >0.7). A statistical difference was observed between the average displacements of the sacroiliac facet joints and pelvises with symphyseal fractures treated with screws after the application of a load (p <0.05). CONCLUSION The symphyseal setting with two crossed screws appears to be an effective alternative to osteosynthesis in pelvic fractures with rotational instability.

Finite element analysis of the human mastication cycle

The aim of this paper is to propose a biomechanical model that could serve as a tool to overcome some difficulties encountered in experimental studies of the mandible. One of these difficulties is the inaccessibility of the temporomandibular joint (TMJ) and the lateral pterygoid muscle. The focus of this model is to study the stresses in the joint and the influence of the lateral pterygoid muscle on the mandible movement. A finite element model of the mandible, including the TMJ, was built to simulate the process of unilateral mastication. Different activation patterns of the left and right pterygoid muscles were tried. The maximum stresses in the articular disc and in the whole mandible during a complete mastication cycle were reached during the instant of centric occlusion. The simulations show a great influence of the coordination of the right and left lateral pterygoid muscles on the movement of the jaw during mastication. An asynchronous activation of the lateral pterygoid muscles is needed to achieve a normal movement of the jaw during mastication.

Numerical simulation of a relaxation test designed to fit a quasi-linear viscoelastic model for temporomandibular joint discs

The main objectives of this work are: (a) to introduce an algorithm for adjusting the quasi-linear viscoelastic model to fit a material using a stress relaxation test and (b) to validate a protocol for performing such tests in temporomandibular joint discs. This algorithm is intended for fitting the Prony series coefficients and the hyperelastic constants of the quasi-linear viscoelastic model by considering that the relaxation test is performed with an initial ramp loading at a certain rate. This algorithm was validated before being applied to achieve the second objective. Generally, the complete three-dimensional formulation of the quasi-linear viscoelastic model is very complex. Therefore, it is necessary to design an experimental test to ensure a simple stress state, such as uniaxial compression to facilitate obtaining the viscoelastic properties. This work provides some recommendations about the experimental setup, which are important to follow, as an inadequate setup could produce a stress state far from uniaxial, thus, distorting the material constants determined from the experiment. The test considered is a stress relaxation test using unconfined compression performed in cylindrical specimens extracted from temporomandibular joint discs. To validate the experimental protocol, the test was numerically simulated using finite-element modelling. The disc was arbitrarily assigned a set of quasi-linear viscoelastic constants (c1) in the finite-element model. Another set of constants (c2) was obtained by fitting the results of the simulated test with the proposed algorithm. The deviation of constants c2 from constants c1 measures how far the stresses are from the uniaxial state. The effects of the following features of the experimental setup on this deviation have been analysed: (a) the friction coefficient between the compression plates and the specimen (which should be as low as possible); (b) the portion of the specimen glued to the compression plates (smaller areas glued are better); and (c) the variation in the thickness of the specimen. The specimen’s faces should be parallel to ensure a uniaxial stress state. However, this is not possible in real specimens, and a criterion must be defined to accept the specimen in terms of the specimen’s thickness variation and the deviation of the fitted constants arising from such a variation.

On the role of bone damage in calcium homeostasis

Bone serves as the reservoir of some minerals including calcium. If calcium is needed anywhere in the body, it can be removed from the bone matrix by resorption and put back into the blood flow. During bone remodelling the resorbed tissue is replaced by osteoid which gets mineralized very slowly. Then, calcium homeostasis is controlled by bone remodelling, among other processes: the more intense is the remodelling activity, the lower is the mineral content of bone matrix. Bone remodelling is initiated by the presence of microstructural damage. Some experimental evidences show that the fatigue properties of bone are degraded and more microdamage is accumulated due to the external load as the mineral content increases. That damage initiates bone remodelling and the mineral content is so reduced. Therefore, this process prevents the mineral content of bone matrix to reach very high (non-physiological) values. A bone remodelling model has been used to simulate this regulatory process. In this model, damage is an initiation factor for bone remodelling and is estimated through a fatigue algorithm, depending on the macroscopic strain level. Mineral content depends on bone remodelling and mineralization rate. Finally, the bone fatigue properties are defined as dependent on the mineral content, closing the interconnection between damage and mineral content. The remodelling model was applied to a simplified example consisting of a bar under tension with an initially heterogeneous mineral distribution. Considering the fatigue properties as dependent on the mineral content, the mineral distribution tends to be homogeneous with an ash fraction within the physiological range. If such dependance is not considered and fatigue properties are assumed constant, the homogenization is not always achieved and the mineral content may rise up to high non-physiological values. Thus, the interconnection between mineral content and fatigue properties is essential for the maintenance of bones structural integrity as well as for the calcium homeostasis.

Effect of non-uniform thickness of samples in stress relaxation tests under unconfined compression of samples of articular discs.

A precise information of the biomechanical properties of soft tissues is required to develop a suitable simulation model, with which the distribution of stress and strain in the complex structures can be estimated. Many soft tissues have been mechanically characterized by stress relaxation tests under unconfined or confined compression. In general, full-thickness samples are extracted to reduce the damage in the tissue as much as possible. However, it is not guaranteed that these samples have a uniform thickness or, in other words, planar parallel faces. In particular, in the articular disc of the temporomandibular joint, many studies can be found testing full-thickness samples for which that thickness is known to be non-uniform, while making the assumption of uniaxial stress state to extract the mechanical properties from those tests. That inaccuracy may have a strong influence in some cases and needs a profound revision. The main goal of this work is to quantify the error committed in that assumption and the influence of the variation of thickness on that error in a particular test: stress relaxation tests under unconfined compression. Based on this error and defining an allowable tolerance, a criterion is established to reject samples depending on their aspect ratio.

Effect of freezing storage time on the elastic and viscous properties of the porcine TMJ disc

The correct characterisation of the articular disc of the temporomandibular joint (TMJ) is key to study the masticatory biomechanics. For the interval from extraction until testing, freezing is the most used preservation technique for biological tissues, but its influence on their behaviour is still unclear. An important error can be committed in the characterisation of such tissues if freezing has any effect on their mechanical properties. Thus, the aim of this study was to determine whether the freezing storage time causes any change in the mechanical properties of the TMJ discs. To check that, the specimens were stored in a -20°C freezer during different time intervals: 1 day, 1 week, 1 month and 3 months. Fresh specimens, tested right after extraction, were used as the control group. Compressive stress relaxation tests were carried out on the specimens and a quasi-linear viscoelastic (QLV) model was used to fit the experimental curves. A statistical analysis detected significant differences among the groups. Post-hoc tests determined that freezing the specimens more than 30 days may lead to changes in the viscoelastic properties of the tissue.