An Upstream Finite Volume Scheme for a Bone Healing Model

Abstract

This paper is devoted to the introduction of a numerical scheme for a bone healing model and simulation of skull fractures. The mathematical model describes the evolution of mesenchymal stem cells, osteoblasts, bone matrix and osteogenic growth factor. We propose a numerical scheme based on an implicit finite volume method constructed on an orthogonal mesh. The efficiency and robustness of the scheme are shown in simulating a skull fracture in rats.

Keywords

• bone growth
• finite volume method
• numerical simulation