Analysis of Anterior Cruciate Ligament of the Human Knee Using a Mathematical Model

Anterior cruciate ligament (ACL) of the knee is often injured particularly in sports and other strenuous activities. Approaches for replacement of the ligament surround controversies due to complexities and varied outcome. In the present study, mechanical behavior of the ligament is analyzed during knee motion considering changing geometric arrangements of the ligament fibers and their material properties during both unloaded and loaded states. An analytical model with sagittal plane representation of the knee was employed. The two cruciate ligaments were modeled as bundles of fibers that were nonlinearly elastic. Flexion motion in the unloaded state was guided by selected fibers. Effects of external loads were then superimposed to simulate activity. In a simulated Drawer test with 130 N external force applied during 0–120° flexion, the ACL stretched increasingly in early to mid-flexion. From mid to high flexion range, the stretching effect decreased continuously. Further, anterior bundle of fibers in the ligament resisted the external load at each flexion angle. The posterior bundle of fibers contributed to resistance in low and high flexion only. The model calculations compared reasonably with in vitro experimental measurements on human knees that are available in the literature. In conclusion, the analysis indicates that surgical replacement of the ACL requires careful attention to ligament insertion positions on bones. Also, rehabilitation of ACL-injured or replaced knee requires carefully designed exercises to be safe and effective. Future work will also focus on parametric analysis.