Measurement of 6 by 6 Stiffness Matrix of the Knee Joint: Basis for Biomechanical Principles of Knee Surgery

The knee is the largest joint in the human body and gets injured frequently because of its complex structural characteristics and the external load it carries. Stiffness is thought to be an important factor in musculoskeletal performance, either too much or too little stiffness may lead to injury. For the knee joint with 6 degrees of freedom, a 6 by 6 stiffness matrix, including both primary and secondary stiffness, can be built to improve the understanding of the load-carrying characteristics and structural properties of the knee. However, the quantifying of the stiffness matrix at different joint positions remains unclear. In some attempts to develop the stiffness matrix, linear elastic theory has always been assumed while the knee joint is a nonlinear system or the stiffness was measured separately on each degrees of freedom. Therefore, the overall objective of this work was to develop a protocol to derive the 6 by 6 stiffness matrix of the porcine knee joint by using a robotic testing system and investigate the knee stiffness coefficients as a function of joint positions. Six intact porcine cadaveric knees were used. 45 joint positions at 30°, 60°, and 90° of flexion were chosen as the target position. At each joint position, force perturbation was performed by inputting additional loads on all directions and measuring the corresponding displacements of 6 DOFs to derive the compliance matrix. Then the stiffness matrix could be calculated by inverting the whole compliance matrix. This method overcame the two major limitations previously: 1. Measure the stiffness matrix by assuming the knee joint was a linear system; 2. Measure the nonlinear stiffness throughout the range of motion instead of building a matrix. Thus, the current work successfully quantified the stiffness matrix at any desired joint positions. The primary stiffness from the stiffness matrices have been validated by literature and the quantification of secondary stiffness also has implications to knee function. The understanding of stiffness matrix and 6 by 6 joint biomechanics further provides an excellent foundation to pursue the improvement of the diagnostic procedure and surgical reconstruction of the knee joint