Sample Entropy of Speed Power Spectrum as a Measure of Laparoscopic Surgical Instrument Trajectory Smoothness

In this study the complexity of the speed power spectrum is assessed as a metric for measuring trajectory smoothness. There are a variety of published methods for analyzing trajectory smoothness but many lack validity. This preliminary study took an information theoretic approach to assess trajectory smoothness by applying the sample entropy measure to the speed power spectrum of simulated and experimental trajectories. The complexity measurements of the speed power spectrum were compared to a traditional jerk-based measure of trajectory smoothness, namely $\log $-dimensionless jerk. The approach was first tested on basic simulated shape tracings with varying locations of sporadic movement, simulated as Gaussian noise. This method was duplicated in an experimental setting with the same shapes and locations of sporadic movement by capturing the trace trajectories using an electromagnetic motion tracking system. Finally, this approach was applied to kinematic data of laparoscopic surgical instrument tips, captured over 105 iterations of a basic surgical task. Analysis from all three testing scenarios showed that there is a statistically significant linear correlation between $\log $-dimensionless jerk and the sample entropy of speed power spectra.