Validation of an Algorithm for the Estimation of Human Passive Wrist Stiffness Based on a Subject-Specific Kinematic Model

Abnormal joint rigidity is a common symptom of many neurological disorders like Parkinson's disease and stroke. Joint rigidity is clinically described as increased resistance during passive joint movement and is quantitatively related to the static passive component of joint impedance, i.e., passive stiffness. Here, we introduce a novel approach to estimate the passive stiffness of the human wrist across two coupled Degrees of Freedom (DoFs): Flexo-Extension (FE) and Radio-Ulnar Deviation (RUD). This method employs a subject-specific kinematic model of the human wrist, treated as a universal joint with two skew-oblique axes (FE and RUD), not constrained to intersect or to be perpendicular. We tested this methodology on ten healthy volunteers using infrared cameras and a hand-held device equipped with a 6-axis load cell for manual wrist perturbations. We used motion and force/torque data to determine angles and torques at the wrist DoFs, and applied multiple linear regression to calculate the 2-by-2 stiffness matrix. Our findings align with existing literature in terms of stiffness behavior, showing stiffness anisotropy with the highest value predominantly along the RUD direction. However, compared to simplified wrist models with orthogonal and intersecting joint axes, and prior studies that approximate human axes to robot ones by assuming perfect alignment between them, our method reveals significant differences in the magnitude and orientation of the stiffness ellipse. By relaxing the constraints of axis orthogonality and intersection, as well as the assumption of alignment between human and measurement system axes, our subject-specific approach offers, for the first time, a more anatomically plausible estimation of wrist stiffness.