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.

A novel mechanobiological model can predict how physiologically relevant dynamic loading causes proteoglycan loss in mechanically injured articular cartilage

“…Similar approaches for iterative tissue adaptation as applied here have been used to study cartilage mechanics 24 , 54 – 57 , bone remodeling 29 , 58 – 62 and tissue engineering characterization 63 , 64 . A critical factor in the model generation and simulation is the selection of the degeneration thresholds.…”

The Influence of Geometry of Implants for Direct Skeletal Attachment of Limb Prosthesis on Rehabilitation Program and Stress-Shielding Intensity

“…Poisson's coefficient was assumed to be constant for both bone tissues throughout the simulation. The threshold values for bone density were ρ max = 2.000 g/cm 3 and ρ min = 0.200 g/cm 3 [41].…”

A comparative analysis of internal bone remodelling concepts in a novel implant for direct skeletal attachment of limb prosthesis evaluation: A finite element analysis

“…The maximum and minimum bone density values were also established: ρ max = 2.000 g cm −3 and ρ min = 0.200 g cm −3 . 26 In the analyses, three different concepts of internal bone remodelling were used that include strain energy density as a stimulus for bone reconstruction: (1) without lazy (dead) zone; (2) with consideration of lazy (dead) zone; and (3) with the consideration of overloading the bone tissues, using the quadratic formula. 27–29 In order to continuously update the changes in mechanical properties and bone density during the calculation process, a properly prepared Fortran user-subroutine was used.…”