The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules

During secondary bone healing, different tissue types are formed within the fracture callus depending on the local mechanical and biological environment. Our aim was to understand the temporal succession of these tissue patterns for a normal bone healing progression by means of a basic mechanobiological model. The experimental data stemmed from an extensive, previously published animal experiment on sheep with a 3 mm tibial osteotomy. Using recent experimental data, the development of the hard callus was modelled as a porous material with increasing stiffness and decreasing porosity. A basic phenomenological model was employed with a small number of simulation parameters, which allowed comprehensive parameter studies. The model distinguished between the formation of new bone via endochondral and intramembranous ossification. To evaluate the outcome of the computer simulations, the tissue images of the simulations were compared with experimentally derived tissue images for a normal healing progression in sheep. Parameter studies of the threshold values for the regulation of tissue formation were performed, and the source of the biological stimulation (comprising e.g. stem cells) was varied. It was found that the formation of the hard callus could be reproduced in silico for a wide range of threshold values. However, the bridging of the fracture gap by cartilage on the periosteal side was observed only (i) for a rather specific choice of the threshold values for tissue differentiation and (ii) when assuming a strong source of biological stimulation at the periosteum.