Evolution of bone tissue based on angiogenesis as a crucial factor: New mathematical attempt

Abstract

In this paper, we present a novel theoretical model of bone evolution. The model takes into account growth of the blood vessels network as a real issue during the process. The stimulation of this growth is controlled by the signals from overloaded dying cells. A system of integro-differential equations describes changes in the density of blood vessels, bone cells and Young modulus, all of which define how the bone tissue evolves over time. The model considers several biomechanical signals such as changes in the density of elastic strain energy and nutrients. Two examples of changing bone tissue were examined to test the model: bone healing around a tooth implant and formation of osteophytes during osteoarthritis. In both cases, the effects of mechanical loading in the bone tissue evolution which are in agreement with the medical observations can be observed.