Novel description of bone remodelling including finite memory effect, stimulation and signalling mechanisms

A new mathematical model is presented for bone remodelling that includes a finite memory effect. In this new model, stimulus resulting from mechanical loading is separated from the signalling to grow or absorb bone. Also, a signal decaying exponentially to the distance from the point produced as well as an effect of decaying signal in time are considered. In addition, the model presented correctly predicts the synthesis and resorption of the bone tissue in a normal healthy mandible and in cases when teeth are missing. The model presented could be implemented to study cases of bone diseases where the signalling between the cells is disrupted and to predict changes in bone caused by several anomalies, such as missing a tooth or the presence of a dental prosthesis.