A mathematical model of medial collateral ligament repair: migration, fibroblast proliferation and collagen formation

Abstract

The partial rupture of ligament fibres leads to an injury known as grade 2 sprain. Wound healing after injury consists of four general stages: swelling, release of platelet-derived growth factor (PDGF), fibroblast migration and proliferation and collagen production. The aim of this paper is to present a mathematical model based on reaction–diffusion equations for describing the repair of the medial collateral ligament when it has suffered a grade 2 sprain. We have used the finite element method to solve the equations of this. The results have simulated the tissue swelling at the time of injury, predicted PDGF influence, the concentration of fibroblasts migrating towards the place of injury and reproduced the random orientation of immature collagen fibres. These results agree with experimental data reported by other authors. The model describes wound healing during the 9 days following such injury.

Keywords:

• ligament repair
• mathematical model
• reaction–diffusion equation
• fibroblast migration
• growth factor
• collagen formation

Acknowledgements

This work forms part of the Mathematical Model of Mechanical–Biological Ligament Repair DIB code 202010013460 and Mechanical and Biomedical Engineering Simulation (Phase 2) DIB code 8008170, research projects financed with resources from the Research Department of Universidad Nacional de Colombia, Bogotá DC and the programme Virginia Gutiérrez de Pineda – Youth Researchers and Innovators 2009, financed by COLCIENCIAS via an agreement with the Universidad Nacional de Colombia in Bogotá.