A Mathematical Model Of Revascularization Following Anterior Cruciate Ligament Reconstruction

Due to the limited natural healing capacity of the anterior cruciate ligament (ACL), tears typically require surgical reconstruction using a graft, generally sourced from a tendon. This procedure initiates the process of ligamentization, during which the tendon graft gradually transforms to mimic the properties of the native ligament. Despite the high prevalence of ACL injuries and reconstructions, detailed knowledge of the dynamic physiological changes during ligamentization remains limited. PURPOSE: To develop and validate the first mathematical model simulating the dynamic changes during ligamentization following anterior cruciate ligament reconstruction (ACLR), focusing on revascularization due to its critical correlation with low intra-articular graft strength. METHODS: This model, created through a meta-analysis and validated with empirical data, uses a system of ordinary differential equations (ODEs) to simulate interactions among inflammation, hypoxia, vascular endothelial growth factor (VEGF), angiogenesis, and vascular density. The simulation was conducted in MATLAB, with checkpoints for model accuracy based on temporal alignment with literature findings on ACL healing dynamics. RESULTS: The model demonstrates a post-operative inflammatory spike reaching 103.08 pg/mL at 0.3 weeks, which, along with sustained hypoxia (lasting until 2.98 weeks), drives VEGF concentration to a peak of 2138.52 pg/mL at 2.4 weeks. Angiogenesis, indicated by the Chalkley score, peaks at 5.30 points at 6.5 weeks then declines as vascular maturation progresses. Vascular density reaches a maximum of 168.19 vessels/mm2 at 7.7 weeks before stabilizing at 119.27 vessels/mm2, aligning with native ACL levels. These data underscore key phases in ACL graft revascularization and healing. CONCLUSIONS: This model provides a novel framework for understanding the timing of critical biological changes during ligamentization after ACLR, thus informing future research on targeted intervention stages. Looking forward, it has the potential to be developed into a diagnostic tool for clinicians to create personalized treatment and recovery plans through the integration of patient-specific data, potentially reducing re-injury risk and improving ACLR recovery outcomes.