Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Abstract

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

Physiological loading-induced streaming potentials in osteogenesis imperfecta bone

“…Controlled electrical stimulation in combination with mechanical loads may effectively improve mechanical and electric stimuli in bone and thus can be potential therapeutics in enhancement of mechanobiological stimulus required for bone remodelling. This also affirms the computational results of Bansod et al 60 which suggest the application of combined electrical and mechanical stimulation to improve the bone mass in pathological situations. Therefore, electrical stimulation can be utilised in combination with prophylactic exercises such as mild walking to improve bone strength in OI patients having less mechanosensitivity to mechanical stimulations.…”

Computational Analysis of Bone Remodeling in the Proximal Tibia Under Electrical Stimulation Considering the Piezoelectric Properties

“…Within our implementation of the open-source framework ( Figure 2A ), the Python-based open-source software packages used were ITK-SNAP ( http://www.itksnap.org /, version 3.6.0, GNU-GPL) ( Yushkevich et al, 2006 ) for segmentation, Salome ( https://www.salome-platform.org/ , version 8.5.0, GNU-LGPL) ( Ribes and Caremoli, 2007 ) for designing and meshing, Gmsh ( http://gmsh.info/ , version 4.4.1, GNU-GPL) ( Geuzaine and Remacle, 2009 ) and command-line tool dolfin-convert (GNU-LGPL) for pre-processing, the finite element software FEniCS for solving and post-processing, and Paraview ( https://www.paraview.org/ , version 5.0.1, 3-Clause BSD License) ( Ahrens et al, 2005 ) for visualizing the simulation results. More details of the steps followed to set up the finite element model are published in ( Bansod et al, 2021 ; Bansod and van Rienen, 2019 ). Figure 2B outlines the implemented bone remodeling algorithm, where the material properties were updated in each iteration through the positive feedback loop.…”

“…An obvious drawback of this two-dimensional model is the lack of connection between the cortical diaphysis regions. As a solution to this problem, an additional side-plate was considered ( Figure 3B ) joining these regions similar to that of the two-dimensional femur ( Weinans et al, 1992 ; Fischer et al, 1997 ; Fernández et al, 2010 ; Garijo et al, 2014 ; Bansod et al, 2021 ). The cortical regions were joined only at medial and lateral nodes highlighted with black dots (see Figure 3C ).…”

Multi-Parametric Exploration of a Selection of Piezoceramic Materials for Bone Graft Substitute Applications

“…The generation of small electric charges induced by the piezoelectric effect under biomechanical stress is predicted to signal to osteoblast cells to orientate the efforts of remodelling and healing in the direction of the applied force, leading to new bone strengthening and rendering resistance [62][63][64][65]. This created the premises for defining a new generation of macro-porous bone graft substitutes utilizing the piezoelectrical triggers for boosting bone regeneration, a subject which only recently, although rarely, started being tackled (e.g., BT [66], barium strontium titanate/β-TCP blends [67], BCTZ-simple [68] or coated with bioactive glass [69], or (K,Na)NbO 3 [70]).…”