Parametric equations to study and predict lower-limb joint kinematics and kinetics during human walking and slow running on slopes

Comprehensive data sets for lower-limb kinematics and kinetics during slope walking and running are important for understanding human locomotion neuromechanics and energetics and may aid the design of wearable robots (e.g., exoskeletons and prostheses). Yet, this information is difficult to obtain and requires expensive experiments with human participants in a gait laboratory. This study thus presents an empirical mathematical model that predicts lower-limb joint kinematics and kinetics during human walking and running as a function of surface gradient and stride cycle percentage. In total, 9 males and 7 females (age: 24.56 ± 3.16 years) walked at a speed of 1.25 m/s at five surface gradients (-15%, -10%, 0%, +10%, +15%) and ran at a speed of 2.25 m/s at five different surface gradients (-10%, -5%, 0%, +5%, +10%). Joint kinematics and kinetics were calculated at each surface gradient. We then used a Fourier series to generate prediction equations for each speed’s slope (3 joints x 5 surface gradients x [angle, moment, mechanical power]), where the input was the percentage in the stride cycle. Next, we modeled the change in value of each Fourier series’ coefficients as a function of the surface gradient using polynomial regression. This enabled us to model lower-limb joint angle, moment, and power as functions of the slope and as stride cycle percentages. The average adjusted R² for kinematic and kinetic equations was 0.92 ± 0.18. Lastly, we demonstrated how these equations could be used to generate secondary gait parameters (e.g., joint work) as a function of surface gradients. These equations could be used, for instance, in the design of exoskeletons for walking and running on slopes to produce trajectories for exoskeleton controllers or for educational purposes in gait studies.