Fulgence Razafimahery

Mechanical interaction between cells and fluid for bone tissue engineering scaffold: modulation of the interfacial shear stress

An analytical model of the fluid/cell mechanical interaction was developed. The interfacial shear stress, due to the coupling between the fluid and the cell deformation, was characterized by a new dimensionless number N(fs). For N(fs) above a critical value, the fluid/cell interaction had a damping effect on the interfacial shear stress. Conversely, for N(fs) below this critical value, interfacial shear stress was amplified. As illustration, the role of the dynamic fluid/cell mechanical coupling was studied in a specific biological situation involving cells seeded in a bone scaffold. For the particular bone scaffold chosen, the dimensionless number N(fs) was higher than the critical value. In this case, the dynamic shear stress at the fluid/cell interface is damped for increasing excitation frequency. Interestingly, this damping effect is correlated to the pore diameter of the scaffold, furnishing thus target values in the design of the scaffold. Correspondingly, an efficient cell stimulation might be achieved with a scaffold of pore size larger than 300 microm as no dynamic damping effect is likely to take place. The analytical model proposed in this study, while being a simplification of a fluid/cell mechanical interaction, brings complementary insights to numerical studies by analyzing the effect of different physical parameters.

Targeted Mechanical Properties for Optimal Fluid Motion Inside Artificial Bone Substitutes

Our goal was to develop a method to identify the optimal elastic modulus, Poissons ratio, porosity, and permeability values for a mechanically stressed bone substitute. We hypothesized that a porous bone substitute that favors the transport of nutriments, wastes, biochemical signals, and cells, while keeping the fluid‐induced shear stress within a range that stimulates osteoblasts, would likely promote osteointegration. Two optimization criteria were used: (i) the fluid volume exchange between the artificial bone substitute and its environment must be maximal and (ii) the fluid‐induced shear stress must be between 0.03 and 3 Pa. Biots poroelastic theory was used to compute the fluid motion due to mechanical stresses. The impact of the elastic modulus, Poissons ratio, porosity, and permeability on the fluid motion were determined in general and for three different bone substitute sizes used in high tibial osteotomy. We found that fluid motion was optimized in two independent steps. First, fluid transport was maximized by minimizing the elastic modulus, Poissons ratio, and porosity. Second, the fluid‐induced shear stress could be adjusted by tuning the bone substitute permeability so that it stayed within the favorable range of 0.03 to 3 Pa. Such method provides clear guidelines to bone substitute developers and to orthopedic surgeons for using bone substitute materials according to their mechanical environment.

2D dynamical efficiency of a swimfin: a fluid–structure interaction approach

Recent literature has shown a great interest in evaluating the propulsive efficiency in order to enhance performances in fin swimming or development of biomimetic systems. Such problems appear to be complex for two reasons. On the one hand, for realistic undulatory motion, there is a strong interaction between the fluid and the moving fin. On the other hand, the deformable feature of the structure plays an important role on the dynamical response during the locomotion. A coupled fluid–structure interaction model is therefore necessary to quantify the energy transfer between the fin and the water and to evaluate the accurate propulsive force generated.

Torsional Vibrations of Fluid-Filled Multilayered Transversely Isotropic Finite Circular Cylinder

An analytical and numerical study for the torsional vibrations of viscous fluid-filled three-layer transversely isotropic cylinder is presented in this paper. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equations of a viscous fluid. The analytical solution of the frequency equation is obtained using the boundary conditions at the free surface of the solid layer and the boundary conditions at the fluid–solid interface. The frequency equation is deduced and analytically solved using the symbolic Software Mathematica. The finite element method using Comsol Multiphysics Software results are compared with present method for validation and an acceptable match between them were obtained. It is shown that the results from the proposed method are in good agreement with numerical solutions. The influence of fluid dynamic viscosity is thoroughly analyzed and the effect of the isotropic properties on the natural frequencies is also investigated.

THEORETICAL AND NUMERICAL INVESTIGATIONS OF FREQUENCY ANALYSIS OF TWO CIRCULAR CYLINDERS OSCILLATING IN A INCOMPRESSIBLE VISCOUS FLUID

A potential flow is presented in this paper for the analysis of the fluid-structure interaction systems including, but not limited to, the idealized human head. The model considers a cerebro-spinal fluid (CSF) medium interacting with two solid domain. The fluid field is governed by the linearized Navier–Stokes equation. A potential technique is used to obtain a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier–Stokes equation. From the solution, modal shapes and stokes cells are shown. In the analysis, the elastic skull model and the rigid skull model are presented. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effects of the fluid thickness is also investigated.

Vibration Analysis of Euler-Bernoulli Beams Partially Immersed in a Viscous Fluid

The vibrational characteristics of a microbeam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical study of the modal analysis of microbeams partially immersed in a viscous fluid. A fixed-free microbeam vibrating in a viscous fluid is modeled using the Euler-Bernoulli equation for the beams. The unsteady Stokes equations are solved using a Helmholtz decomposition technique in a two-dimensional plane containing the microbeams cross sections. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results is compared with present method for validation and an acceptable match between them was obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.

Fluid-Structure Interaction Effects on the Propulsion of an Flexible Composite Monofin

Finite element method has been used to analyze the propulsive efficiency of a swimming fin. Fluid-structure interaction model can be used to study the effects of added mass on the natural frequencies of a multilayer anisotropic fin oscillating in a compressible fluid. Water by neglecting viscidity effects has been considered as a surrounding fluid and the frequency response of the fin has been compared with that of vacuum conditions. It has been shown that because of the added mass effects in water environment, the natural frequencies of the fin decrease.

Three-dimensional investigation of the stokes eigenmodes in hollow circular cylinder

This paper studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced.

Propulsive efficiency of a multilayer anisotropic fin in fluid–structure interaction

This study aims to evaluate the dynamic performances, in particular the drag and the lift forces, which are the two relevant parameters to quantify the propulsive efficiency of a fin. Some previous models are mostly either of discrete type or based on the behaviours of the organs of propulsion of certain marine cetaceans, and we use continuous models. Our work is mostly numerical and discusses the development of a continuous model in the framework of the fluid–structure interaction approach. To this end, we place ourselves in the frame reference attached to the foot of a swimmer. We use kinematics proposed by Read et al. (2003), including heaving and pitching. Indeed, the kinematics is expected to allow us, in the future, the development of new experimental protocol for measuring hydrodynamic parameters of a fin.

Parametric study of a spherical head model in fluid‐structure interaction

Impact loading of the head may lead to the damage of the skull–head–cerebrospinal fluid (CSF), either blunt trauma or diffusive trauma. Some recent works have pointed out the importance of some paths flow of the CSF (e.g. Zonga et al. 2006). In a recent work (El Baroudi 2010), attention has turned to a cylindrical head model, which has shown some drawbacks in terms of dynamic response. These observations led us to propose a model more closer to reality, which is not easily achieved experimentally (Hault-Dubrulle 2007). To compare the results with the previous model, we worked at constant volume, that is to say that the geometric and material characteristics were preserved. This allows to set different radii of the different layers. Using the above results, the skull is assumed rigid. Due to the thinness of CSF, we propose to use a viscous coupling associated with the model of Stokes. It is expected to highlight the existence or non-cell Stokes spherical geometry and some particular CSF flows.