Mathematical modelling of tendon healing process: blow-ups mean healing

Tendon injuries, although not directly threatening the lives of the affected person, can significantly lower their quality of life. For a long time, the main therapeutic approach was surgery followed by a arduous rehabilitation. Even so, after a year the structure and function of the healed tendon remains inferior to the healthy one. Only recently with the new advances in regenerative medicine new therapeutic methods become available. However better use of these methods requires deeper understanding the healing process itself, which is multiscale, complex and not fully understood. We present a new approach consisting of a new integro-differential equation. It describes the collagen remodelling during tendon healing process. We relate the possible blow-ups of solutions with the healing of injury without the scar formation.