The Use of Sample Entropy and Fuzzy Sample Entropy to Analyze Somatosensory Deficit in the COP of Quiet Standing

Abstract

The long-term objective of this research is to improve the current methods of postural sway analysis by optimizing the performance of entropy, a nonlinear parameter estimating predictability, and verifying its sensitivity for the clinical setting. Entropy has shown success in identifying sensory deficits using the center of pressure (COP) time series measured during quiet standing and could potentially improve upon current clinical methods used to assess fall risk. Recent studies have modified entropy algorithms to create ‘fuzzy’ versions of conventional entropy methods. Fuzzy entropy methods were initially developed for use with EMG signals, but they have shown promise in analyzing COP during quiet standing. Current studies utilizing entropy produce varying results depending on the type of experimental signal analyzed and input parameters used. There is little consistency across these studies in the signal processing methods of COP and input parameters are often assumed the same across experimental signals containing vastly different dynamic structures. A comparison of conventional and fuzzy entropy across a range of input parameters is necessary to determine the best methods for estimating entropy of quiet standing. This study will compare the most common method of entropy computation, Sample Entropy (SampEn), and its fuzzy counterpart, Fuzzy Sample Entropy (FSampEn), across a range of the radius input parameter, r, and at different down-sampled frequencies. The experimental signals used are COP time series of healthy, young subjects standing on different thicknesses of foam. Specific Aim 1 determined the best parameter selection practices and data modification methods for analyzing COP. According to previous studies, r should be at least three times the magnitude of the noise in the signal since the input parameter exists to overcome the challenge of the presence of noise. Due to the difficulty of estimating noise magnitude, studies utilizing entropy typically estimate R as the radius input parameter where r = R * standard deviation for each individual time series. This study estimated R through the analysis of the noise content of COP using the instrumental noise measured in zero trials and calculated its effect on COP through uncertainty propagation of the noise standard deviations. The measured noise was used as a basis for R, creating a range of R values to test that are multiples of the noise magnitude. Entropy is dependent on the frequency of the time series, so the data was analyzed at varying down sampled frequencies. A comparison was made between COP of the anterior-posterior (AP) and medial-lateral (ML) axes as well. A parameter selection study of each entropy method demonstrated how each one reacts to changing input parameters and data modification methods. Using the preferred selection methods found it Specific Aim 1, an R, down-sampling frequency and COP axis are chosen for each type of entropy to be used for experimental analysis. Specific Aim 2 compared FSampEn with SampEn values, assessing the utility of fuzzy entropy methods in postural sway analysis. Although fuzzy entropy methods consistently improved performance for EMG signals, the hypothesis that they would do the same for postural sway was proven wrong. SampEn provided the most consistent results with clear separation between levels of foam. This study opens up more questions that could be answered in future work. First, a spectral analysis is needed to get a better understanding of why SampEn performs best at frequencies well above those expected in postural sway COP. FSampEn can also be explored further by testing different fuzzy membership functions or comparing it to SampEn using COP velocity rather than position. Lastly, future studies can also look at the use of foam to simulate somatosensory deficit and how it relates to actual somatosensory deficits. All future studies should consider the use of a binary (2^n) sampling frequency to improve the range of valid down sampling frequencies.