A mathematical model of revascularization following anterior cruciate ligament reconstruction

Abstract

The anterior cruciate ligament (ACL) is a critical stabilizer of the knee that is frequently injured in sports. Due to its limited natural healing capacity, ACL tears generally require reconstruction using a graft (ACLR). This procedure initiates the process of ligamentization, where the graft transforms to possess properties closer to that of the native ligament. Despite the relatively high prevalence of this injury and the importance of the healing process, detailed knowledge of the dynamic changes during healing remains limited. This thesis presents the first mathematical model describing some of the changes that occur throughout ligamentization, focusing on the aspects of revascularization. The vascular density is of particular interest as it has been found to spike around two months postoperatively, coinciding with the timing of the weakest intra-articular graft strength. To bridge this knowledge gap, this model, constructed through an extensive literature review and validated based on real-world data, employs a system of ordinary differential equations (ODEs). It explores the interactions between inflammation, hypoxia, vascular endothelial growth factor (VEGF), and angiogenesis, each identified as key factors influencing vascular density. The model accurately captures the physiological processes and changes occurring throughout ligamentization and revascularization while highlighting critical healing stages where future research would be valuable. Looking forward, this model has the potential to be developed into a diagnostic tool that could be used to create personalized treatment and recovery plans by incorporating patient-specific data, potentially revolutionizing ACLR outcomes.Kinesiology & Health SciencesBachelors of Science (BS