A mathematical analysis to address the 6 degree-of-freedom segmental power imbalance

Segmental power is used in human movement analyses to indicate the source and net rate of energy transfer between the rigid bodies of biomechanical models. Segmental power calculations are performed using segment endpoint dynamics (kinetic method). A theoretically equivalent method is to measure the rate of change in a segment's mechanical energy state (kinematic method). However, these two methods have not produced experimentally equivalent results for segments proximal to the foot, with the difference in methods deemed the "power imbalance." In a 6 degree-of-freedom model, segments move independently, resulting in relative segment endpoint displacement and non-equivalent segment endpoint velocities at a joint. In the kinetic method, a segment's distal end translational velocity may be defined either at the anatomical end of the segment or at the location of the joint center (defined here as the proximal end of the adjacent distal segment). Our mathematical derivations revealed the power imbalance between the kinetic method using the anatomical definition and the kinematic method can be explained by power due to relative segment endpoint displacement. In this study, we tested this analytical prediction through experimental gait data from nine healthy subjects walking at a typical speed. The average absolute segmental power imbalance was reduced from 0.023 to 0.046 W/kg using the anatomical definition to ≤0.001 W/kg using the joint center definition in the kinetic method (95.56-98.39% reduction). Power due to relative segment endpoint displacement in segmental power analyses is substantial and should be considered in analyzing energetic flow into and between segments.