Analysis of a bone remodeling model with myeloma disease arising in cellular dynamics. (24th March 2020) - Baldonedo, Jacobo; Fernández, José R.; Segade, Abraham
Abstract: In this work we study a bone remodeling model for the evolution of the myeloma disease. The biological problem is written as a coupled nonlinear system consisting of parabolic partial differential equations. They are written in terms of the concentrations of osteoblasts and osteoclasts, the density of the relative bone and the concentration of the tumor cells. Then, we deal with the numerical analysis of this variational problem, introducing a numerical approximation by using the finite element method and a hybrid combination of both implicit and explicit Euler schemes. We perform some a priori error estimates and show a few numerical simulations to demonstrate the accuracy of the approximation. Finally, we present the comparison with previous works and the behavior of the solution in two‐dimensional examples. Abstract : In this paper, we numerically studied a bone remodeling model for the evolution of the myeloma disease. It was written as a nonlinear system depending on the concentrations of osteoblasts and osteoclasts, the bone density and the concentration of the tumor cells. A fully discrete approximation was introduced by using the finite element method and Euler schemes, and an a priori analysis was provided. The numerical simulations show the accuracy of the approximation and a comparison with another work.