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

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.