Modelling the course of healing of a long bone subjected to loading has been the subject of several investigations. These have succeeded in predicting the differentiation of tissues in the callus in response to a static mechanical load and the diffusion of biological factors. In this paper an approach is presented which includes both mechanoregulation of tissue differentiation and the diffusion and proliferation of cell populations (mesenchymal stem cells, fibroblasts, chondrocytes, and osteoblasts). This is achieved in a three-dimensional poroelastic finite element model which, being poroelastic, can model the effect of the frequency of dynamic loading. Given the number of parameters involved in the simulation, a parameter variation study is reported, and final parameters are selected based on comparison with an in vivo experiment. The model predicts that asymmetric loading creates an asymmetric distribution of tissues in the callus, but only for high bending moments. Furthermore the frequency of loading is predicted to have an effect. In conclusion, a numerical algorithm is presented incorporating both mechanoregulation and evolution of cell populations, and it proves capable of predicting realistic difference in bone healing in a 3D fracture callus.
The geometry of an implant surface to best promote osseointegration has been the subject of several experimental studies, with porous beads and woven mesh surfaces being among the options available. Furthermore, it is unlikely that one surface geometry is optimal for all loading conditions. In this paper, a computational method is used to simulate tissue differentiation and osseointegration on a smooth surface, a surface covered with sintered beads (this simulated the experiment (Simmons, C., and Pilliar, R., 2000, Biomechanical Study of Early Tissue Formation Around Bone-Interface Implants: The Effects of Implant Surface Geometry," Bone Engineering, J. E. Davies, ed., Emsquared, Chap. A, pp. 369-379) and established that the method gives realistic results) and a surface covered by porous tantalum. The computational method assumes differentiation of mesenchymal stem cells in response to fluid flow and shear strain and models cell migration and proliferation as continuum processes. The results of the simulation show a higher rate of bone ingrowth into the surfaces with porous coatings as compared with the smooth surface. It is also shown that a thicker interface does not increase the chance of fixation failure.
SUMMARYWe present a finite element formulation for simulation of electromechanical coupling using a combination of fictitious domain and level set methods. The electric field is treated with a fixed (Eulerian-like) mesh, whereas the structure (taken as a perfect conductor) is modelled with a conventional Lagrangian approach. The compatibility between the potential of the conductor and of the electric domain is obtained by introducing a Lagrange multiplier function, defined on the boundary of the conductor. The electromechanical forces are obtained using a variational formulation for the coupled electromechanical domain. We use a Heaviside function on the level set to remove the electric energy in the conductor domain. Results are presented for an radio frequency switch and an element of a comb drive.
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