Christian Oddou

In vitro acoustic waves propagation in human and bovine cancellous bone.

The acoustic behavior of cancellous bone with regard to its complex poroelastic nature has been investigated. The existence of two longitudinal modes of propagation is demonstrated in both bovine and human cancellous bone. Failure to take into account the presence of these two waves may result in inaccurate material characterization.

Buckling of a Short Cylindrical Shell Surrounded by an Elastic Medium

The lateral surface of a cylindrical structure, which is composed of a thin tube embedded in a large outer medium, is submitted to a uniform external pressure. The buckling pressure of such a structure, corresponding to a low flexural state of the inner tube wall, is theoretically analyzed on the basis of the asymptotic method, The theoretical results are compared with experimental ones obtained from a compression test realized on an elastic tube inserted in a foam. It is found that the Euler pressure and the associated buckling mode index strongly depend upon the rheological and geometrical parameters of both the tube and the surrounding medium.

IN VITRO ACOUSTIC WAVE PROPAGATION IN HUMAN AND BOVINE CANCELLOUS BONE AS PREDICTED BY BIOT'S THEORY

Recent in vitro studies have provided evidence of the propagation of two different longitudinal wave modes at ultrasonic frequencies in cancellous bone. The genesis of these two plane waves in fluid-saturated porous media is predicted by the poroelastic approach to wave propagation originally developed by Biot. However, wave velocity is usually analyzed as a function of bone mass density only; therefore, the influence of the cancellous bone microstructure over the wave velocity is not taken into account. In the present study, a descriptor of the microstructure is considered in Biots theory. This model is used to evaluate the large experimental variability of both fast and slow wave velocities measured on randomly oriented human and bovine cancellous bone samples. The role of the anisotropic solid structure and fluid in the behavior of fast and slow wave velocities is examined. Experimental and theoretically predicted velocities are found in close agreement when analyzed as a function of both porosity and structural index. This model has the potential to be used to determine an acoustically derived structural index in cancellous bone.

Interrelations between elastic energy and strain in a tensegrity model: contribution to the analysis of the mechanical response in living cells.

Interactions between the physical and physiological properties of cellular sub-units result in changes in the shape and mechanical behaviour of living tissues. To understand the mechanotransmission processes, models are needed to describe the complex interrelations between the elements and the cytoskeletal structure. In this study, we used a 30-element tensegrity structure to analyse the influence of the type of loading on the mechanical response and shape changes of the cell. Our numerical results, expressed in terms of strain energy as a function of the overall deformation of the tensegrity structure, suggest that changes in cell functions during mechanical stimuli for a given potential energy are correlated to the type of loading applied, which determines the resultant changes in cell shape. The analysis of these cellular deformations may explain the large variability in the response of bone cells submitted to different types of mechanical loading.

Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport.

Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 μm in fibre diameter with approximately 60% porosity). A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis–Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab® 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant. Results show that within a few hours of culture process and for a perfusion velocity of the order of 10− 4 m s− 1, the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10− 3 Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 × 10− 5 m s− 1. But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant. Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.

Numerical determination of the lacuno-canalicular permeability of bone

A precise determination of the fluid velocity and the pressure fields surrounding the osteocytes (i.e. within the lacuno-canalicular porosity) is crucial when studying phenomena involving cell–fluid interactions such as bone remodelling (Fritton and Weinbaum 2009). Using the Biot poroelasticity theory – as the interstitial bone fluid flow is induced by skeleton strains – the bone hydro-mechanical behaviour can be mimicked to simulate its remodelling (Adachi et al. 2010). In this theory, the bone interstitial fluid transfer is quantified by a textural parameter only depending on the porous network geometry called the intrinsic permeability k (Vafai 2011). An accurate evaluation of k is then needed to model the interstitial cell–fluid interactions. Nevertheless, owing to the multiscale structure of the bone porosity, theoretical or experimental determinations of this parameter remain delicate, explaining the large range of values found in the literature (from 10 £ 10 to 10 £ 10 m) (Gardinier et al. 2010). The aim of this study was, therefore, to relate the permeability k to the lacuna-canalicular pore geometry using a numerical approach (finite element method). In this paper, the first naive step is presented, which allows us to determine a Kozeny-like expression for k.

A method for the determination of mechanical parameters in a porous elastically deformable medium : Applications to biological soft tissues

Abstract A further approach has been tentatively envisaged for the determination of the mechanical parameters characterizing the unsteady behaviour of soft biological tissues considered as porous, elastically deformable media, saturated with a viscous fluid. If the two solid and fluid phases are incompressible, the parameters to be determined are : the drained Young’s modulus and Poisson’s ratio, the permeability of the porous solid structure and the dynamic viscosity of the interstitial fluid. Standard ramp–relaxation tests have been performed in order to investigate the time evolution of the force acting upon tissular discoidal samples subjected to unconfined compressive strains, under controlled environmental conditions. For moderate compressive strains, such a response in resultant force, characterizing a stress diffusion phenomenon within the medium, can be analyzed using a spectral decomposition with orthogonal eigenvectors. Such an analysis reveals that the overall response is defined by its asymptotic behaviour during both compression and relaxation phases, leading to the evaluation of the Young’s modulus and Poisson’s ratio. Moreover, the determination of the relaxation time leads to the evaluation of the specific permeability of the structure—the dynamic viscosity of the fluid being already known. A few examples of experimental tests data, involving both rubber foam, myocardium tissue in passive state and fibroblastic biological collagenic gels, are presented here in order to illustrate and validate such a rheological methodology. Particular attention is paid to the relations between the poroelastic behaviour and microstructural parameters of the material, with an emphasis on possible nonlinear effects arising from these very deformable media.

MECHANICS OF ACTIVE POROUS MEDIA: BONE TISSUE ENGINEERING APPLICATION

In orthopedics, a currently developed technique for large graft hybrid implants consists of using porous and biocompatible scaffolds seeded with a patients bone cells. Successful culture in such large implants remains a challenge for biologists, and requires strict control of the physicochemical and mechanical environments achieved by perfusion within a bioreactor for several weeks. This perfusion, with a nutritive fluid carrying solute ingredients, is necessary for the active cells to grow, proliferate, differentiate, and produce extracellular matrices. An understanding and control of these processes, which lead to substrate degradation and extracellular matrix remodeling during the in vitro culture phase, depend widely on the success in the realization of new orthopedic biomaterials. Within this context, the analysis of the interactions between convective phenomena of hydrodynamic origin and chemical reactions of biological order which are associated to these processes is a fundamental challenge in the framework of bone tissue engineering. In order to better account for the different intricate processes taking place in such a sample and to design a relevant experimental protocol leading to the definition of an optimal tissue implant, we propose one- and two-dimensional theoretical models based on transport phenomena in porous active media.

Biomechanical Function in Regenerative Medicine

The essential aim of regenerative medicine is to obtain a sufficient mass of whatever specific type of cell, or more organised entity such as tissue or organ, needed to restore the normal physiology of a part of the body damaged by physical, chemical or ischaemic insult, or as a consequence of infectious or genetic disease. This is necessitated by the fact that the intrinsic regenerative capacity of most tissues and organs is very limited in mammals compared to many lower vertebrates. Even where damage does induce significant cellular proliferation, the newly formed cells often fail to differentiate appropriately to replace those that have been lost. The generation of autologous grafts then requires the development of procedures to quickly expand human mesenchymal stem cells (MSCs) in 3D systems and to promote their differentiation in a controlled way in order to maintain their tissue genesis potential.

Theoretical Analysis of Remodelling Processes in Bony Tissue Engineered Implants

In order to design adequate and performing artificial tissue implants, porous biocompatible and biodegradable substrates have to be cells seeded. Moreover they have to be submitted to perfusion inside a bioreactor, during few weeks, with a nutritive fluid carrying solute ingredients necessary for the active cells to grow, proliferate, differentiate and produce extra-cellular matrices. From the understanding and control of the processes leading to the substrate degradation and extra cellular matrix remodelling taking place during the in vitro culture phase, depends widely the success in the realization of new orthopaedic biomaterials. Within this context, the analysis of the interactions between convective phenomena of hydrodynamic origin and chemical reaction of biological order which are associated to these processes is a fundamental challenge in the framework of the bone tissue engineering. In order to better account for the different intricate processes taking place in such a sample and to design a relevant experimental protocol leading to the definition of an optimal tissue implant, we proposed a theoretical model based on transport phenomena in porous active media. For these “opened” systems in state of permanent imbalance created by the local convection induced in the medium, the analysis of such complex interactions remains relatively coarse. The adopted approach is based on a formulation similar to that of the active porous media in which all the biochemical processes related to the cellular metabolism are described in terms of the physicochemical processes taking place at the fluid-solid interface, leading to the degradation and remodelling of the solid matrix. The model includes the effects of the complex microscopic architecture of the substrate and the specificity of the biological processes such as extra cellular matrix production and resorption. This leads to a numerical solution of the coupled fluid dynamics, transport equations and biochemical reaction inside the porous medium. The fundamental parameters on which depends the evolution of the structure of the medium are thus put in evidence and evaluated in the framework of bone tissue engineering. One of the revealed outcomes is the fact that local and minor interaction can lead to long-range imbalance and substantial changes in the initial architecture of the substrate even to engender phenomena of chaotic instability..