A meshless Local Boundary Integral Equation (LBIE) method for cell proliferation predictions in bone healing

Abstract

Bone healing involves a series of complicated cellular and molecular mechanisms that result in bone formation. Several mechanobiological models have been developed to simulate these cellular mechanisms via diffusive processes. In most cases solution to diffusion equations is accomplished using the Finite Element Method (FEM) which however requires global remeshing in problems with moving or new born surfaces or material phases. This limitation is addressed in meshless methods in which no background cells are needed for the numerical solution of the integrals. In this study a new meshless Local Boundary Integral Equation (LBIE) method is employed for deriving predictions of cell proliferation during bone healing. First a benchmark problem is presented to assess the accuracy of the method. Then the LBIE method is utilized for the solution of cell diffusion problem in a two-dimensional (2D) model of fractured model. Our findings indicate that the proposed here LBIE method can successfully predict cell distributions during fracture healing.

Finite-Element Modeling and Analysis in Nanomedicine and Dentistry

“…The main phases of fracture healing were predicted by the FE simulation and bone healing was simulated beyond the reparative phase by modeling the transition of the woven bone into lamellar bone. Grivas et al utilized a new meshless local boundary integral equation method that addresses the limitation of FEM for deriving predictions of cell proliferation during bone healing [26]. Numerical simulations of cell diffusion were performed in a 2D computational model.…”

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

“…Bone remodeling algorithm based on the NNRPIM meshless method (modified after[131]). Owing to the complexity involved in the bone healing process and the limitations of meshing and remeshing in the FEM, Grivas and his co-workers implemented a meshless Local Boundary Integral Equation (LBIE) method for cell proliferation predictions in bone healing by solving a cell diffusion problem[133]. They also analyzed the nonlinear Fisher transient diffusion equation[134] for the 2D modeling of a fractured bone by incorporating initial cell concentrations at the periosteum, the marrow, and between the bone and the callus (at the fractured end).…”