Dynamics of Human Spine in Jumps Using Lyapunov Exponents
Eliza A. Banu, Dan B. Marghitu, P. K. Raju · 2009
Characterizing and quantifying the local dynamics of the human spine during various athletic exercises is important for therapeutic and physiotherapy reasons or athletic related effects on the human spine. In this study we computed the largest finite-time Lyapunov exponents for the spine of a human subject during an athletic exercise for several volunteers. The kinematic data was collected using the 3D motion capture system (Motion Realty Inc.). Four healthy male subjects were asked to perform two sets of 30 jumps. In order to draw a conclusion about the chaotic nature of the dynamics of the lumbar spine Lyapunov exponent spectrum was calculated for each volunteer which included four Lyapunov exponents, one negative, one very close to zero and two positive. Subjects 1, 2 and 4 registered a significant increase in the largest Lyapunov exponent from the first set jumps to the next. Subject 3 registered no change in the values of Lyapunov exponents. Nonlinear analysis of the human spine demonstrates the chaotic nature of the system. The computation of the largest Lyapunov exponents enables a more precise characterization of the dynamics of the human spine.