Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson’s Disease
Abstract
:1. Introduction
2. Materials and Methods
2.1. Subjects
2.2. Procedures
2.3. Entropy Algorithms
2.3.1. Multiscale Entropy (MSE)
- 1.
- There will be correspondence if the distance between two vectors (xmi, xmj) is smaller than a predefined tolerance r. The distance between the two vectors was calculated using the norm of infinity:
- 2.
- If was less than or equal to the predefined tolerance r, we defined (xmi, xmj) a pair of m-dimensional matched vectors. Total number of pairs of m-dimensional matched vectors, given nm.
- 3.
- We repeated steps 1–3 for m = m + 1, where nm+1 represents the total number of (m + 1) dimensional matched vector pairs as shown in Figure 3.
- 4.
- The SampEn was defined as the logarithm of the ratio of to as in Equation (3):
2.3.2. Refined Composite Multiscale Entropy (RCMSE)
- (1)
- To obtain coarse-grained time series on different time scales, we utilized the coarse-graining process indicated in Equation (4).
- (2)
- For all coarse-grained series, the number of matched vector pairs, and , was determined at a scale factor of .
- (3)
- For , let denote the mean of . Equation (7) provides the RCMSE value at a scale factor of .
2.3.3. Complexity Index (CI)
2.4. Clinical Assessment
2.5. Statistical Analysis
3. Results
4. Discussion
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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swPD | HS | p | ||
---|---|---|---|---|
Age [mean(SD)] | 71.15 (5.12) | 69.14 (4.80) | 0.06 | |
Gender [n (%)] | F | 15 (29.41) | 27 (54) | 0.01 |
M | 36 (70.58) | 23 (46) | ||
Disease duration [mean(SD)] | 8.04 (4.70) | |||
HY [n (%)] | 1 | 10 (19.60) | ||
2 | 17 (33.33) | |||
3 | 24 (47.05) | |||
UPDRS III [mean(SD)] | 41.41 (18.22) | |||
UPDRS III < 32 [n (%)] | 16 (31.27) | |||
UPDRS III ≥ 32 [n (%)] | 22 (43.13) | |||
UPDRS III ≥ 58 [n (%)] | 13 (25.49) | |||
History of falls (n° of falls in the previous 6 months) [mean (SD)] | 1.35 (3.28) | |||
Gait speed (m/s) [mean (SD)] | 1.08 (0.25) | 1.09 (0.25) | 0.91 | |
Stance phase (% gait cycle) [mean (SD)] | 60.82 (2.27) | 61.41 (3.42) | 0.31 | |
Swing phase (% gait cycle) [mean (SD)] | 39.18 (2.27) | 38.59 (3.42) | 0.31 | |
Single support (% gait cycle) [mean (SD)] | 39.24 (2.92) | 37.93 (5.29) | 0.13 | |
Double support (% gait cycle) | 10.88 (2.33) | 11.90 (4.92) | 0.19 | |
Cadence (steps/min) [mean (SD)] | 103.37 (20.44) | 101.35 (14.06) | 0.60 | |
Stride length (m) [mean (SD)] | 0.94 (0.21) | 1.22 (0.22) | <0.00 | |
Pelvic tilt (°) [mean (SD)] | 3.33 (1.55) | 3.01 (1.13) | 0.25 | |
Pelvic obliquity (°) [mean (SD)] | 3.87 (2.16) | 5.38 (2.70) | 0.01 | |
Pelvic rotation (°) [mean (SD)] | 5.49 (3.29) | 6.68 (3.90) | 0.02 | |
HR AP [mean (SD)] | 1.66 (0.26) | 2.32 (0.64) | <0.00 | |
HR ML [mean (SD)] | 1.62 (0.25) | 2.23 (0.59) | <0.00 | |
HR V [mean (SD)] | 1.68 (0.28) | 2.41 (0.76) | <0.00 | |
stride length CV % [mean (SD)] | 39.26 (19.44) | 26.69 (13.76) | 0.00 |
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Castiglia, S.F.; Trabassi, D.; Conte, C.; Ranavolo, A.; Coppola, G.; Sebastianelli, G.; Abagnale, C.; Barone, F.; Bighiani, F.; De Icco, R.; et al. Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson’s Disease. Sensors 2023, 23, 4983. https://doi.org/10.3390/s23104983
Castiglia SF, Trabassi D, Conte C, Ranavolo A, Coppola G, Sebastianelli G, Abagnale C, Barone F, Bighiani F, De Icco R, et al. Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson’s Disease. Sensors. 2023; 23(10):4983. https://doi.org/10.3390/s23104983
Chicago/Turabian StyleCastiglia, Stefano Filippo, Dante Trabassi, Carmela Conte, Alberto Ranavolo, Gianluca Coppola, Gabriele Sebastianelli, Chiara Abagnale, Francesca Barone, Federico Bighiani, Roberto De Icco, and et al. 2023. "Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson’s Disease" Sensors 23, no. 10: 4983. https://doi.org/10.3390/s23104983
APA StyleCastiglia, S. F., Trabassi, D., Conte, C., Ranavolo, A., Coppola, G., Sebastianelli, G., Abagnale, C., Barone, F., Bighiani, F., De Icco, R., Tassorelli, C., & Serrao, M. (2023). Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson’s Disease. Sensors, 23(10), 4983. https://doi.org/10.3390/s23104983