Bridge Between Predictability and Complexity in Human Gait
Presenter Type
UNO Graduate Student (Doctoral)
Major/Field of Study
Biomechanics
Other
Biomechanics
Advisor Information
Aaron D. Likens
Location
CEC RM #201/205/209
Presentation Type
Poster
Start Date
22-3-2024 9:00 AM
End Date
22-3-2024 10:15 AM
Abstract
Several different metrics can quantify the rich information of a system reflected in a time series. Entropy (Ent) quantifies how unpredictable a time series is. The Hurst exponent (H) quantifies the temporal correlation between datapoints of a time series. Ent and H have been applied to characterize complex systems, including the human body and its behavior. The Optimal Movement Variability Hypothesis (OMVH) claims an inverted U relationship between predictability and complexity (i.e., Ent and H) of human movement. However, the relationship between Ent and H has not been explained sufficiently. This study aims to investigate the relationship between Ent and H via analysis on simulated and empirical data. We hypothesized that Ent and H will have an inverted U relationship in both simulated stationary time series and empirical data. In addition, we hypothesized that Ent and H will have an inverse relationship in simulated nonstationary time series. For the simulated data, we simulated 2000 time series with different H. Half of the time series were stationary, and the other half were nonstationary. Each time series consisted of a 100,000 datapoints. Ent was computed for each time series. For the empirical data, we used gait kinematics collected from a 1426 walking trials. Each participant completed 18, 4-minute walking trials at a self-selected pace on an indoor track. Based on the gait kinematics, stride length, stride interval, hip, knee, and ankle range of motion, were computed per stride. Ent and the H were estimated for every gait feature computed. Multilevel models were built to examine the linear and potentially quadratic relationship between Ent and H for each gait feature. Simulated data revealed inverted J relationship between Ent and H for stationary time series. H greater than 0.5 showed greater decrease in Ent as H deviated from 0.5. In addition, the simulated data showed inverse relationship between Ent and H for nonstationary time series. Multilevel models for every gait feature revealed a significantly negative quadratic trend, meaning there were inverted U-like relationships between the Ent and H of gait features. Our results provide both mathematical and empirical evidence to support the OMVH. Despite the quadratic relationship observed from our models, our simulated data suggests that there can be a relationship between Ent and H that is more complex than a simple quadratic relationship. Further investigation using numerical methods are required to define the underlying equation between Ent and H.
Bridge Between Predictability and Complexity in Human Gait
CEC RM #201/205/209
Several different metrics can quantify the rich information of a system reflected in a time series. Entropy (Ent) quantifies how unpredictable a time series is. The Hurst exponent (H) quantifies the temporal correlation between datapoints of a time series. Ent and H have been applied to characterize complex systems, including the human body and its behavior. The Optimal Movement Variability Hypothesis (OMVH) claims an inverted U relationship between predictability and complexity (i.e., Ent and H) of human movement. However, the relationship between Ent and H has not been explained sufficiently. This study aims to investigate the relationship between Ent and H via analysis on simulated and empirical data. We hypothesized that Ent and H will have an inverted U relationship in both simulated stationary time series and empirical data. In addition, we hypothesized that Ent and H will have an inverse relationship in simulated nonstationary time series. For the simulated data, we simulated 2000 time series with different H. Half of the time series were stationary, and the other half were nonstationary. Each time series consisted of a 100,000 datapoints. Ent was computed for each time series. For the empirical data, we used gait kinematics collected from a 1426 walking trials. Each participant completed 18, 4-minute walking trials at a self-selected pace on an indoor track. Based on the gait kinematics, stride length, stride interval, hip, knee, and ankle range of motion, were computed per stride. Ent and the H were estimated for every gait feature computed. Multilevel models were built to examine the linear and potentially quadratic relationship between Ent and H for each gait feature. Simulated data revealed inverted J relationship between Ent and H for stationary time series. H greater than 0.5 showed greater decrease in Ent as H deviated from 0.5. In addition, the simulated data showed inverse relationship between Ent and H for nonstationary time series. Multilevel models for every gait feature revealed a significantly negative quadratic trend, meaning there were inverted U-like relationships between the Ent and H of gait features. Our results provide both mathematical and empirical evidence to support the OMVH. Despite the quadratic relationship observed from our models, our simulated data suggests that there can be a relationship between Ent and H that is more complex than a simple quadratic relationship. Further investigation using numerical methods are required to define the underlying equation between Ent and H.