Quantifying the Multidimensional Impedance of the Shoulder During Volitional Contractions

The neuromuscular control of the shoulder requires regulation of 3D joint mechanics, but it is unknown how these mechanics vary during tasks that load the shoulder in different directions. The purpose of this study was to quantify how the 3D mechanics of the shoulder change with voluntary torque production. Eleven participants produced voluntary isometric torques in one of six directions along three measurement axes. Impedance was estimated by applying small, pseudorandom angular perturbations about the shoulder as participants maintained steady state torques. The nonparametric impedance frequency response functions estimated from the data were parameterized by a collection of second-order linear systems to model the 3D inertia, viscosity, and stiffness of the shoulder. Each component of the 3D stiffness matrix scaled linearly with volitional torque production. Viscosity also increased monotonically with torque but nonlinearly. The directions of maximal stiffness and viscosity were consistently aligned towards the direction of torque production. Further, the shoulder was least stiff and least viscous in the direction of internal/external rotation, suggesting it may be more prone to injury along this axis. These experimental findings and the corresponding mathematical model summarizing our results provide novel insights into how the neuromuscular system regulates 3D shoulder mechanics in response to volitional muscle activations.