Biomechanical Model and Numerical Analysis of Tissue Regeneration within a Porous Scaffold

Abstract

The development of a mechanobiological concept of reparative regeneration of bone tissue determined by the cell differentiation law and the impact of an external periodic mechanical load is presented. A mathematical model of bone regeneration within a porous implant (scaffold) with a regular or chaotic internal structure is developed on the basis of finite-element analysis of the stress-strain state of a poroelastic medium. The analytical method for the estimation of effective elastic moduli of a composite object that describes the “bone-implant” system is presented; it enables the assessment of the poroelastic characteristics of the model of the changing continuous medium at each time step upon the computational simulation of bone tissue regeneration within the implant material. The computational algorithms developed are used for the study of a three-dimensional finite element model of osteosynthesis in a human tubular bone assisted by a porous implant. Parametric analysis of a computational model of bone tissue regeneration under the influence of an external stimulatory load that changes according to the harmonic law has been performed and the relationships between the regeneration characteristics, the parameters of external impact, and implant porosity have been determined.