Application of Polynomial Regression Model for Joint Stiffness

Quasi-stiffness (joint stiffness) is often used to characterize leg properties during athletic and other activities and has been reported by a single slope of angle-moment curve. However, the joint angle-moment relationship of some relationship are not effectively represented by a simple linear regression model. Thus, the purpose of this analysis was to investigate the benefits of utilizing a 2^nd order polynomial regression (quadratic) model as compared to the linear model when calculating lower extremity joint stiffness incorporating subdivided eccentric phases. Thirty healthy and active college students performed 15 drop jumps from a 30-cm platform. The eccentric phase was identified as the time from initial foot contact (IC) to the lowest vertical position of the center of mass and subdivided into the loading and attenuation phases, separated by the peak vertical ground reaction force. Lower extremity joint stiffnesses (hip, knee, and ankle) for the loading and attenuation phases were calculated using a linear and quadratic model. Multiple 2 by 2 repeated measures ANOVAs were performed. In the post-hoc analyses, the quadratic model had greater goodness-of-fit (r ² and RMSE) than the linear model (p < .05) for all joints. The quadratic model revealed differences between the loading and attenuation phases for both hip (p = .001) and knee stiffness (p < .001). These results suggest that the quadratic model is more representative of the angle-moment relationship while subdividing the eccentric phase of a drop jump into the loading and attenuation phases.