Trabecular bone remodelling under pathological conditions based on biochemical and mechanical processes involved in BMU activity.

In adulthood, bone tissue is continuously renewed by processes governed by basic multicellular units composed of osteocytes, osteoclasts and osteoblasts, which are subjected to local mechanical loads. Osteocytes are known to be integrated mechanosensors that regulate the activation of the osteoclasts and osteoblasts involved in bone resorption and apposition processes, respectively. After collagen tissue apposition, a process of collagen mineralisation takes place, gradually increasing the effective stiffness of bone. This study presents a new model based on physicochemical parameters involved in spongy bone remodelling under pathological conditions. Our model simulates the transient evolution of both geometry and effective Young's modulus of the trabeculae, also taking turnover into account. Various loads were applied on a trabecula in order to determine the evolution of bone volume fraction under pathological conditions. A parametric study performed on the model showed that one key parameter here is the kinetic constant of hydroxyapatite crystallisation. We subsequently tested our model on a pathological case approaching osteoporosis, involving a decrease in the number of viable osteocytes present in bone. The model converges to a lower value (- 5%) for bone volume fraction than with a normal quantity of osteocytes. This useful tool offers new perspectives for predicting bone remodelling deficits on a local scale in patients with pathological conditions such as osteoporosis and in bedridden patients, as well as for astronauts subjected to weightlessness in space.

Design parameters dependences on contact stress distribution in gait and jogging phases after total hip arthroplasty.

We have developed a mathematical model to calculate the contact stress distribution in total hip arthroplasty (THA) prosthesis between the articulating surfaces. The model uses the clearance between bearing surfaces as well as the inclination and thickness of the Ultra High Molecular Weight Poly-Ethylene (UHMWPE) cup to achieve this. We have used this mathematical model to contrast the maximal force during normal gait and during jogging. This is based on the assumption that the contact stress is proportional to the radial deformation of the cup. The results show that the magnitude of the maximal contact stress remains constant for inclination values in the range of [0-35 degrees ] and increase significantly with the cup clearance and liner thickness for inclination values in the range of [35-65 degrees ]. A major use for this model would be the calculation of spatial contact stress distribution during normal gait or jogging for different couples of bearing surfaces.

Divided medium-based model for analyzing the dynamic reorganization of the cytoskeleton during cell deformation.

Cell deformability and mechanical responses of living cells depend closely on the dynamic changes in the structural architecture of the cytoskeleton (CSK). To describe the dynamic reorganization and the heterogeneity of the prestressed multi-modular CSK, we developed a two-dimensional model for the CSK which was taken to be a system of tension and compression interactions between the nodes in a divided medium. The model gives the dynamic reorganization of the CSK consisting of fast changes in connectivity between nodes during medium deformation and the resulting mechanical behavior is consistent with the strain-hardening and prestress-induced stiffening observed in cells in vitro. In addition, the interaction force networks which occur and balance to each other in the model can serve to identify the main CSK substructures: cortex, stress fibers, intermediate filaments, microfilaments, microtubules and focal adhesions. Removing any of these substructures results in a loss of integrity in the model and a decrease in the prestress and stiffness, and suggests that the CSK substructures are highly interdependent. The present model may therefore provide a useful tool for understanding the cellular processes involving CSK reorganization, such as mechanotransduction, migration and adhesion processes.

Mechanisms governing the visco-elastic responses of living cells assessed by foam and tensegrity models.

The visco-elastic properties of living cells, measured to date by various authors, vary considerably, depending on the experimental methods and/or on the theoretical models used. In the present study, two mechanisms thought to be involved in cellular visco-elastic responses were analysed, based on the idea that the cytoskeleton plays a fundamental role in cellular mechanical responses. For this purpose, the predictions of an open unit-cell model and a 30-element visco-elastic tensegrity model were tested, taking into consideration similar properties of the constitutive F-actin. The quantitative predictions of the time constant and viscosity modulus obtained by both models were compared with previously published experimental data obtained from living cells. The small viscosity modulus values (10(0)-10(3) Pa x s) predicted by the tensegrity model may reflect the combined contributions of the spatially rearranged constitutive filaments and the internal tension to the overall cytoskeleton response to external loading. In contrast, the high viscosity modulus values (10(3)-10(5) Pa x s) predicted by the unit-cell model may rather reflect the mechanical response of the cytoskeleton to the bending of the constitutive filaments and/or to the deformation of internal components. The present results suggest the existence of a close link between the overall visco-elastic response of micromanipulated cells and the underlying architecture.