Influence of different mechanical stimuli in a multi-scale mechanobiological isotropic model for bone remodelling

Abstract

This work represents a study of a mathematical model that describes the biological response to different mechanical stimuli in a cellular dynamics model for bone remodelling. The biological system discussed herein consists of three specialised cellular types, responsive osteoblasts, active osteoblasts and osteoclasts, three types of signalling molecules, transforming growth factor beta (TGF-β), receptor activator of nuclear factor kappa-b ligand (RANKL) and osteoprotegerin (OPG) and the parathyroid hormone (PTH). Three proposals for mechanical stimuli were tested: strain energy density (SED), hydrostatic and deviatoric parts of SED. The model was tested in a two-dimensional geometry of a standard human femur. The spatial discretization was performed by the finite element method while the temporal evolution of the variables was calculated by the 4th order Runge–Kutta method. The obtained results represent the temporal evolution of the apparent density distribution and the mean apparent density and thickness for the cortical bone after 600 days of remodelling simulation. The main contributions of this paper are the coupling of mechanical and biological models and the exploration of how the different mechanical stimuli affect the cellular activity in different types of physical activities. The results revealed that hydrostatic SED stimulus was able to form more cortical bone than deviatoric SED and total SED stimuli. The computational model confirms how different mechanical stimuli can impact in the balance of bone homeostasis.