Biodynamic Analysis of Human Torso Stability using Finite Time Lyapunov Exponents
Low back pain is a common medical problem around the world afflicting 80% of the population some time in their life. Low back injury can result from a loss of torso stability causing excessive strain in soft tissue. This investigation seeks to apply existing methods to new applications and to develop new methods to assess torso stability. First, the time series averaged finite time Lyapunov exponent is calculated from data obtained during seated stability experiments. The Lyapunov exponent is found to increase with increasing task difficulty. Second, a new metric for evaluating torso stability is introduced, the threshold of stability. This parameter is defined as the maximum task difficulty in which dynamic stability can be maintained for the test duration. The threshold of stability effectively differentiates torso stability at two levels of visual feedback. Third, the state space distribution of the finite time Lyapunov exponent (FTLE) field is evaluated for deterministic and stochastic systems. Two new methods are developed to generate the FTLE field from time series data. Using these methods, Lagrangian coherent structures (LCS) are found for an inverted pendulum, the Acrobot, and planar wobble chair models. The LCS are ridges in the FTLE field that separate two inherently different types of motion when applied to rigid-body dynamic systems. As a result, LCS can be used to identify the boundaries of the basin of stability. Finally, these new methods are used to find the basin of stability from time series data collected from torso stability experiments. The LCS and basins of stability provide a richer understanding into the system dynamics when compared to existing methods.
By gaining a better understanding of torso stability, it is hoped this knowledge can be used to prevent low back injury and pain in the future. These new methods may also be useful in evaluating other biodynamic systems such as standing postural sway, knee stability, or hip stability as well as time series applications outside the area of biomechanics.