Sylvie Wendling-Mansuy

Frequency Response of a Viscoelastic Tensegrity Model: Structural Rearrangement Contribution to Cell Dynamics

In an attempt to understand the role of structural rearrangement onto the cell response during imposed cyclic stresses, we simulated numerically the frequency-dependent behavior of a viscoelastic tensegrity structure (VTS model) made of 24 elastic cables and 6 rigid bars. The VTS computational model was based on the nonsmooth contact dynamics (NSCD) method in which the constitutive elements of the tensegrity structure are considered as a set of material points that mutually interact. Low amplitude oscillatory loading conditions were applied and the frequency response of the overall structure was studied in terms of frequency dependence of mechanical properties. The latter were normalized by the homogeneous properties of constitutive elements in order to capture the essential feature of spatial rearrangement. The results reveal a specific frequency-dependent contribution of elastic and viscous effects which is responsible for significant changes in the VTS model dynamical properties. The mechanism behind is related to the variable contribution of spatial rearrangement of VTS elements which is decreased from low to high frequency as dominant effects are transferred from mainly elastic to mainly viscous. More precisely, the elasticity modulus increases with frequency while the viscosity modulus decreases, each evolution corresponding to a specific power-law dependency. The satisfactorily agreement found between present numerical results and the literature data issued from in vitro cell experiments suggests that the frequency-dependent mechanism of spatial rearrangement presently described could play a significant and predictable role during oscillatory cell dynamics.

Nutrient distribution and metabolism in the intervertebral disc in the unloaded state: A parametric study

A 2-D finite element model for the intervertebral disc in which quadriphasic theory is coupled to the transport of solutes involved in cellular nutrition was developed for investigating the main factors contributing to disc degeneration. Degeneration is generally considered to result from chronic disc cell nutrition insufficiency, which prevents the cells from renewing the extracellular matrix and thus leads to the loss of proteoglycans. Hence, the osmotic power of the disc is decreased, causing osmomechanical impairments. Cellular metabolism depends strongly on the oxygen, lactate and glucose concentrations and on pH in the disc. To study the diffusion of these solutes in a mechanically or osmotically loaded disc, the osmomechanical and diffusive effects have to be coupled. The intervertebral disc is modeled here using a plane strain formulation at the equilibrium state under physiological conditions after a long rest period (called unloaded state). The correlations between solute distribution and various properties of healthy and degenerated discs are investigated. The numerical simulation shows that solute distribution in the disc depends very little on the elastic modulus or the proteoglycan concentration but greatly on the porosity, diffusion coefficient and endplate diffusion area. This coupled model therefore opens new perspectives for investigating intervertebral disc degeneration mechanisms.

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.

A topology optimization based model of bone adaptation

A novel topology optimization model based on homogenization methods was developed for predicting bone density distribution and anisotropy, assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness. The feasibility and efficiency of this method were tested on a 2D model for a proximal femur under single and multiple loading conditions. The main aim was to compute homogenized optimal designs using an optimal laminated microstructure. The computational results showed that high bone density levels are distributed along the diaphysis and form arching struts within the femoral head. The pattern of bone density distribution and the anisotropic bone behavior predicted by the model in the multiple load case were both in good agreement with the structural architecture and bone density distribution occurring in natural femora. This approach provides a novel means of understanding the remodeling processes involved in fracture repair and the treatment of bone diseases.

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 (100–103 Pa.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 (103–105 Pa.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.

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 Youngs 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.

Numerical simulation of an osteoporotic femur: Before and after total hip arthroplasty

Bone remodelling adapts bone geometry and properties under supported loadings. This optimization process is deteriorated by metabolic diseases like osteoporosis which involves femoral neck fractures and implies Total Hip Arthroplasty. Two finite element models are developed to evaluate the stress distribution within osteoporotic human femur bone tissue, and its influence on the stem stability. The geometries of human femur and prosthesis are obtained by helicoid scanner acquisition. The cortical bone was separated from the trabecular bone by apparent density threshold. The results obtained for osteoporotic femur show that the degradation of trabecular architecture causes high stresses in the anteroinferior zone of the cortical bone. For the femur with hip prosthesis, high stresses weak the bone tissue in the lateral zone of the proximal dyaphisis and in the medial zone of the distal part at the end of the stem.

Assessment of the contact stress distribution dependent on functional and design parameters after total hip arthroplasty

A numerical model was developed to assess the contact stress distribution in total hip prosthesis as a function of geometrical parameters such as the clearance between the bearing surfaces, the inclination and thickness of the UHMWPE cup. The contact stress distribution model proposed is submitted to static loading considering the maximal force during gait and jogging. The results shows that the magnitude of the maximal contact stress remains constant for inclination values in the range of [0-35°] and increase significantly with the cup clearance and liner thickness for inclination values in the range of [35°-65°]. This model could be improved by considering other factors such as friction and dynamic loading conditions. This approach would permit to bring new perspectives for studying the long-term behaviour of total hip prostheses.

Spongy bone multicellular unit remodelling model: a parametric study

At adulthood, bone tissue is continuously renewed by processes governed by so-called basic multicellular units (BMU) composed of osteocytes, osteoclasts and osteoblasts submitted to local mechanical loading. Osteocytes are known to be integrated mechano sensors that regulate the activation of osteoclasts and osteoblasts involved, respectively, in bone resorption and apposition. After collagenic tissues the apposition of, a mineralisation process takes place in these areas which increases their effective stiffness progressively. Several BMU remodelling models have been developed considering that the osteocytes send a signal depending on the strain-energy C they record to inhibit osteoclast activity and/or bone formation (Mullender et al. 1994; Mullender and Huiskes 1995). The mechanism according to which BMU’s cells communicate with each other is fundamental to better understand bone remodelling dysfunctions that occur with ageing or diseases. The aim of the present study is to describe osteocyte signals and to analyse the resorption initiation that appears in spongy bone disuse. To do so, we have adapted an existing model of bone remodelling at the trabecular scale.

SPH-based numerical model of wear particles formation in total hip prosthesis

Ultra-high molecular weight polyethylene (UHMWPE) wear debris have been recognized as the cause of aseptic loosening in total hip replacement (Harris 1994). The transport of wear particles and the surface roughness (microscopic asperities) of the prosthetic rigid head generate severe damages at the UHMWPE acetabular component. The experimental work of Cooper et al. (1993) has confirmed the general theory of abrasive and adhesive wear for UHMWPE at a microscopic level in joint replacement. In addition to the different operating conditions, such as normal load and sliding velocity, abrasive wear mechanisms are related to the angularity of the abrasive wear particles or microscopic asperity. Our study consists in numerical simulation of a rigid asperity sliding against the UHMWPE surface using a smoothed particle hydrodynamics (SPH) method. The goal of this work is to analyze the effect of the asperity geometry on abrasive wear mechanisms as well as wear particle formation.