CAN WE DETERMINE FATIGUE IN GAIT BY ANALYZING THE DYNAMICS OF A MATHEMATICAL MODEL?

Abstract

Motion analysis implies that sufficiently complex models of the human neuromusculoskeletal system can be used for the simulation and analysis of sports motions and, at least in principle, for the biomechanical optimization of the performance in the various sport disciplines. A new methodological assessment using the Fast Fourier Transform was created to compare the frequency patterns of the gait in terms of Phase space model as a mathematical space that represents all states of a system. In this respect, the n marker coordinates connected to a human body and the respective velocities establish a 2n-dimensional phase space and hence fully describe the movement. For example, the scalar product of the distance between shoulder and ankle was investigated using a Fast Fourier Transform (Muller, Vieten & Kilani, 2012.) Using similar approach, can we provide enough information to identify a certain degree of fatigue in running based just on one parameter, say the distance between the left hip joint and the tip of the left foot as a function of time? Our subjects walked/run at their individual speed on a treadmill by holding at both sidebars to get comparable movement patterns. A motion analysis was investigated with three infrared cameras at a frequency of 100Hz by Lukotronic System (LUKOtronic Lutz-Kovacs-Electronics OEG, Innsbruck, Austria). Eleven reflected markers were placed at the backside of the subjects. The scalar product of the distance between shoulder and ankle was investigated using a Fast Fourier Transform. To amplify the higher harmonical frequencies, the distance data was differentiated with respect to time. To be independent of individual walking speed, the frequency data was normalized afterwards. The area under the first peak (fundamental frequency) and the nine following peaks (higher harmonical frequencies) were measured. Next step in the methodology is filtering; followed by calculating the first derivative and thereafter the plot of the phase space (Vieten, 2007). This paper demonstrates that beside the traditional descriptive" studies (standard equipment and a moderate amount of work expenditure) and the simulations approach (usually with lots of effort, lots of equipment) a third avenue the “dynamical system approach" (DSA) exists. DSA promises new and exciting views of new and old problems while the expenditure in equipment and time is also affordable for smaller research groups.