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

Anahid Ebrahimi; John D Collins; Thomas M Kepple; Kota Z Takahashi; Jill S Higginson; Steven J Stanhope

doi:10.1016/j.jbiomech.2017.10.034

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

J Biomech. 2018 Jan 3:66:186-193. doi: 10.1016/j.jbiomech.2017.10.034. Epub 2017 Nov 6.

Authors

Anahid Ebrahimi¹, John D Collins², Thomas M Kepple³, Kota Z Takahashi⁴, Jill S Higginson⁵, Steven J Stanhope⁶

Affiliations

¹ Department of Mechanical Engineering, University of Delaware, Newark, DE, USA. Electronic address: anahide@udel.edu.
² Naval Medical Center San Diego, San Diego, CA, USA; Biomechanics and Movement Science Interdisciplinary Program, University of Delaware, Newark, DE, USA.
³ C-motion, Inc., Germantown, MD, USA.
⁴ Department of Biomechanics, University of Nebraska at Omaha, Omaha, NE, USA.
⁵ Department of Mechanical Engineering, University of Delaware, Newark, DE, USA; Biomechanics and Movement Science Interdisciplinary Program, University of Delaware, Newark, DE, USA; Department of Biomedical Engineering, University of Delaware, Newark, DE, USA.
⁶ Department of Mechanical Engineering, University of Delaware, Newark, DE, USA; Biomechanics and Movement Science Interdisciplinary Program, University of Delaware, Newark, DE, USA; Department of Biomedical Engineering, University of Delaware, Newark, DE, USA; Department of Kinesiology and Applied Physiology, University of Delaware, Newark, DE, USA.

PMID: 29191634
DOI: 10.1016/j.jbiomech.2017.10.034

Abstract

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.

Keywords: Gait analysis; Kinematic method; Kinetic method; Rate of energy change.

Publication types

Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Adult
Biomechanical Phenomena
Energy Transfer
Foot / physiology
Gait / physiology*
Humans
Kinetics
Models, Biological*
Young Adult

Grants and funding

P20 GM109090/GM/NIGMS NIH HHS/United States