Calculating Individual and Total Muscular Translational Stiffness: A Knee Example

Research suggests that the knee joint may be dependent on an individual muscle's translational stiffness (KT) of the surrounding musculature to prevent or compensate for ligament tearing. Our primary goal was to develop an equation that calculates KT. We successfully derived such an equation that requires as input: a muscle's coordinates, force, and stiffness acting along its line of action. This equation can also be used to estimate the total joint muscular KT, in three orthogonal axes (AP: anterior-posterior; SI: superior-inferior; ML: medial-lateral), by summating individual muscle KT contributions for each axis. We then compared the estimates of our equation, using a commonly used knee model as input, to experimental data. Our total muscular KT predictions (44.0 N/mm), along the anterior/posterior axis (AP), matched the experimental data (52.2 N/mm) and was well within the expected variability (22.6 N/mm). We then estimated the total and individual muscular KT in two postures (0 deg and 90 deg of knee flexion), with muscles mathematically set to full activation. For both postures, total muscular KT was greatest along the SI-axis. The extensors provided the greatest KT for each posture and axis. Finally, we performed a sensitivity analysis to explore the influence of each input on the equation. It was found that pennation angle had the largest effect on SI KT, while muscle line of action coordinates largely influenced AP and ML muscular KT. This equation can be easily embedded within biomechanical models to calculate the individual and total muscular KT for any joint.