Parameters Selection for Bivariate Multiscale Entropy Analysis of Postural Fluctuations in Fallers and Non-Fallers Older Adults

Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals.

On the use of approximate entropy and sample entropy with centre of pressure time-series

Background

Approximate entropy (ApEn) and sample entropy (SampEn) have been previously used to quantify the regularity in centre of pressure (COP) time-series in different experimental groups and/or conditions. ApEn and SampEn are very sensitive to their input parameters: m (subseries length), r (tolerance) and N (data length). Yet, the effects of changing those parameters have been scarcely investigated in the analysis of COP time-series. This study aimed to investigate the effects of changing parameters m, r and N on ApEn and SampEn values in COP time-series, as well as the ability of these entropy measures to discriminate between groups.

Methods

A public dataset of COP time-series was used. ApEn and SampEn were calculated for m = {2, 3, 4, 5}, r = {0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5} and N = {600, 1200} (30 and 60 s, respectively). Subjects were stratified in young adults (age < 60, n = 85), and older adults (age ≥ 60) with (n = 18) and without (n = 56) falls in the last year. The effects of changing parameters m, r and N on ApEn and SampEn were investigated with a three-way ANOVA. The ability of ApEn and SampEn to discriminate between groups was investigated with a mixed ANOVA (within-subject factors: m, r and N; between-subject factor: group). Specific combinations of m, r and N producing significant differences between groups were identified using the Tukey’s honest significant difference procedure.

Results

A significant three-way interaction between m, r and N confirmed the sensitivity of ApEn and SampEn to the input parameters. SampEn showed a higher consistency and ability to discriminate between groups than ApEn. Significant differences between groups were mostly observed in longer (N = 1200) COP time-series in the anterior-posterior direction. Those differences were observed for specific combinations of m and r, highlighting the importance of an adequate selection of input parameters.

Conclusions

Future studies should favour SampEn over ApEn and longer time-series (≥ 60 s) over shorter ones (e.g. 30 s). The use of parameter combinations such as SampEn (m = {4, 5}, r = {0.25, 0.3, 0.35}) is recommended.

Electronic supplementary material

The online version of this article (10.1186/s12984-018-0465-9) contains supplementary material, which is available to authorized users.

Relationship between a three-month physical conditioning "posture-balance-motricity and health education" (PBM-HE) program on postural and balance capacities of sedentary older adults: influence of initial motor profile

Background

The aims of this study were (i) to define the relationship between a physical reconditioning cycle using balance exercises and muscular-articular stress and the balance capabilities of sedentary older adults and (ii) to assess whether older adults with weaker equilibrium abilities have a significantly limited progression. Our sample consisted of 338 people (263 women, 75 men) with an age, weight and height of 74.4 years (+/− 8.6), 67 kg (+/− 13.6) and 161.4 cm (+/− 8) and with a body mass index of 25.6 (+/− 4.3). The functional evaluations consisted of individual motor profile tests, monopodal eyes open and eyes closed for 30 s, a Timed Up and Go test (TUG) and stabilometric measurements on hard ground with eyes open for a duration of 25.6 s. The physical repackaging protocol was based on the 12-week Posture-Balance-Motricity and Health Education (PBM-ES) method with two 90-min weekly group sessions.

Results

The evolution of the “posture” and “balance” variables was significantly associated with the equilibration capacities (p < 0.001). For unipedal stance with open eyes on the dominant and non-dominant sides, respectively, the progressions were significant for the profiles of middle (OR: 4.78 and 2.42) and low levels (OR: 4.34 and 1.66). Eyes-closed progressions were non-significant for the low-level balance profiles. For the COP Surface and Length variables, compared to those with high levels of balance, respectively, the progressions were significant for the middle- (OR: 1.41 and 2.98) and low-level (OR: 2.91 and 3.28) profiles.

Conclusions

After a 3-month bi-weekly PBM-HE program, we observed that sedentary older adults with the lowest initial level of balance progressed significantly more than high-level individuals, but only for basic motor abilities. It turns out that even among the most deconditioned people and older adults, very significant progress can be made. This increase requires an individualized training content focused on initial mobilizable capacities.

Multiscale Shannon's Entropy Modeling of Orientation and Distance in Steel Fiber Micro-Tomography Data

This paper is concerned with the modeling and analysis of the orientation and distance between steel fibers in X-ray micro-tomography data. The advantage of combining both orientation and separation in a model is that it helps provide a detailed understanding of how the steel fibers are arranged, which is easy to compare. The developed models are designed to summarize the randomness of the orientation distribution of the steel fibers both locally and across an entire volume based on multiscale entropy. Theoretical modeling, simulation, and application to real imaging data are shown here. The theoretical modeling of multiscale entropy for orientation includes a proof showing the final form of the multiscale taken over a linear range of scales. A series of image processing operations are also included to overcome interslice connectivity issues to help derive the statistical descriptions of the orientation distributions of the steel fibers. The results demonstrate that multiscale entropy provides unique insights into both simulated and real imaging data of steel fiber reinforced concrete.