# American Institute of Mathematical Sciences

2012, 9(1): 123-145. doi: 10.3934/mbe.2012.9.123

## A statistical approach to the use of control entropy identifies differences in constraints of gait in highly trained versus untrained runners

 1 Department of Mathematics & Computer Science, Clarkson University, Potsdam, NY 13676, United States, United States, United States 2 Applied Physiology Laboratory, Eastern Michigan University, Ypsilanti, MI 48197, United States, United States

Received  February 2011 Revised  July 2011 Published  December 2011

Control entropy (CE) is a complexity analysis suitable for dynamic, non-stationary conditions which allows the inference of the control effort of a dynamical system generating the signal [4]. These characteristics make CE a highly relevant time varying quantity relevant to the dynamic physiological responses associated with running. Using High Resolution Accelerometry (HRA) signals we evaluate here constraints of running gait, from two different groups of runners, highly trained collegiate and untrained runners. To this end, we further develop the control entropy (CE) statistic to allow for group analysis to examine the non-linear characteristics of movement patterns in highly trained runners with those of untrained runners, to gain insight regarding gaits that are optimal for running. Specifically, CE develops response time series of individuals descriptive of the control effort; a group analysis of these shapes developed here uses Karhunen Loeve Analysis (KL) modes of these time series which are compared between groups by application of a Hotelling $T^{2}$ test to these group response shapes. We find that differences in the shape of the CE response exist within groups, between axes for untrained runners (vertical vs anterior-posterior and mediolateral vs anterior-posterior) and trained runners (mediolateral vs anterior-posterior). Also shape differences exist between groups by axes (vertical vs mediolateral). Further, the CE, as a whole, was higher in each axis in trained vs untrained runners. These results indicate that the approach can provide unique insight regarding the differing constraints on running gait in highly trained and untrained runners when running under dynamic conditions. Further, the final point indicates trained runners are less constrained than untrained runners across all running speeds.
Citation: Rana D. Parshad, Stephen J. McGregor, Michael A. Busa, Joseph D. Skufca, Erik Bollt. A statistical approach to the use of control entropy identifies differences in constraints of gait in highly trained versus untrained runners. Mathematical Biosciences & Engineering, 2012, 9 (1) : 123-145. doi: 10.3934/mbe.2012.9.123
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