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Purpose The purpose of this study was to determine the contribution of each of the ACL and medial ligament structures in resisting anteromedial rotatory instability (AMRI) loads applied in vitro. Methods Twelve knees were tested using a robotic system. It imposed loads simulating clinical laxity tests at 0° to 90° flexion: ±90 N anterior–posterior force, ±8 Nm varus–valgus moment, and ±5 Nm internal–external rotation, and the tibial displacements were measured in the intact knee. The ACL and individual medial structures—retinaculum, superficial and deep medial collateral ligament (sMCL and dMCL), and posteromedial capsule with oblique ligament (POL + PMC)—were sectioned sequentially. The tibial displacements were reapplied after each cut and the reduced loads required allowed the contribution of each structure to be calculated. Results For anterior translation, the ACL was the primary restraint, resisting 63–77% of the drawer force across 0° to 90°, the sMCL contributing 4–7%. For posterior translation, the POL + PMC contributed 10% of the restraint in extension; other structures were not significant. For valgus load, the sMCL was the primary restraint (40–54%) across 0° to 90°, the dMCL 12%, and POL + PMC 16% in extension. For external rotation, the dMCL resisted 23–13% across 0° to 90°, the sMCL 13–22%, and the ACL 6–9%. Conclusion The dMCL is the largest medial restraint to tibial external rotation in extension. Therefore, following a combined ACL + MCL injury, AMRI may persist if there is inadequate healing of both the sMCL and dMCL, and MCL deficiency increases the risk of ACL graft failure.

The Tau Method produces polynomial approximations of solutions of differential equations. The purpose of this paper is (i) to extend the recursive formulation of this method to general linear operator equations defined in a separable Hilbert space, and (ii) to develop an iterative refinement procedure which improves on the accuracy of Tau approximations. Applications to Fredholm integral equations demonstrate the effectiveness of this technique.