Patients with osteoarthritic knees have shorter orientation and tangent indicatrices during gait

BACKGROUND: This study introduces two novel outcomes that could be used to identify people with knee osteoarthritis from healthy controls. These outcomes examine the lengths of paths on a sphere derived from knee angle and knee position during gait. METHODS: Participants with moderate knee osteoarthritis (n=47) and no knee pathology (n=51) walked overground. The time-varying orientation matrices and position vectors of the knee (leg relative to the thigh) were measured, then arclength (constant speed) parameterized. The orientation matrix column aligned with the long axis of the leg, and the tangent, normal and binormal vectors (Frenet Frame) along the position vectors were calculated. These unit length vectors all scribe paths (indicatrices) on a unit sphere. The path lengths of these indicatrices, for all or part of a gait cycle, were the novel outcomes. A stepwise discriminant analysis defined a linear function that included those outcomes that best allocated a participant to the osteoarthritis or control group. FINDINGS: Group differences were best detected with the indicatrix lengths associated with the orientation of the leg's long axis over a gait cycle (P<0.001) and the tangent vector over the stance phase (P=0.014). Both outcomes were smaller in the knee osteoarthritis compared to control group. Walking speed was poorly correlated with all indicatrix lengths (rho<|0.484|) and a discriminate analysis correctly classified 83.7% of the participants. INTERPRETATION: Smaller indicatrix measures distinguished those with knee osteoarthritis from healthy controls. These outcomes introduce a promising new kinematic approach when examining gait data.