Modeling of an initial stage of bone fracture healing

Abstract

In case of the secondary bone fracture healing, four characteristic steps are often distinguished. The first stage, hematoma and clot formation, which is an object of our study, is important because it prepares the environment for the following stages. In this work, a new mathematical model describing basic effects present short after the injury is proposed. The main idea is based on the assumption that blood leaking from the ruptured blood vessels propagates into a poroelastic saturated tissue close to the fracture and mixes with the interstitial liquid present in pores. After certain time period from the first contact with surrounding tissue, the solidification of blood in the fluid mixture starts. This results in clot formation. By assuming the time necessary to initiate solidification and critical saturation of blood in the mixture, the shape and the structure of blood clot could be determined. In numerical example, proposed mathematical formulas were used to study the size of the gap between fractured parts and its effect in blood clot formation.