{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T13:31:01Z","timestamp":1780320661200,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T00:00:00Z","timestamp":1745971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MS Research Australia (2019\u201322)"},{"name":"UoM-ECR Fellowship 2023"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Background: Using the local divergence exponent (LDE), it has been concluded that walking stability is impaired in people with multiple sclerosis (pwMS). However, the use of several calculation approaches hinders comparisons across studies. We aimed to determine whether using different parameters for state space reconstruction to calculate LDE affects the classification of pwMS. Methods: A total of 55 pwMS and 23 controls walked up and down a 20 m corridor for 5 min. The LDE was calculated using three different combinations of n-dimensions (dE) and time delays (\u03c4): (a) trial-specific, (b) median across subjects, and (c) fixed dE = 5 and \u03c4 = 10. The LDE was calculated using vertical (VT), mediolateral (ML), and anteroposterior (AP) accelerations, the norm (N), and 3D data from sensors placed on the sternum and lumbar. Classification accuracy across results obtained with different parameter combinations was compared using a Quadratic Discriminant Analysis (QDA). Results: The best classification accuracy, 84%, was achieved when using the LDE obtained with norm acceleration data from the sternum sensor with a fixed dE = 5 and \u03c4 = 10 and considering speed as a covariate. Lumbar LDEs were less accurate than sternum LDEs. Conclusions: LDEs calculated with a fixed dE = 5 and \u03c4 = 10 for the norm acceleration from a sternum-placed sensor can best classify pwMS. Using fixed parameters for the state space reconstruction, and consequently LDE calculation, can simplify the implementation of the LDE as a mobility biomarker in MS and provides evidence for future consensus for its calculation.<\/jats:p>","DOI":"10.3390\/s25092819","type":"journal-article","created":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T05:05:57Z","timestamp":1745989557000},"page":"2819","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multiple Sclerosis Classification Using the Local Divergence Exponent: Parameters Selection for State-Space Reconstruction"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3490-4521","authenticated-orcid":false,"given":"L. Eduardo","family":"Cofr\u00e9 Lizama","sequence":"first","affiliation":[{"name":"Department of Allied Health, School of Health Sciences, Swinburne University of Technology, Hawthorn, Melbourne, VIC 3122, Australia"},{"name":"Department of Medicine, Royal Melbourne Hospital, The University of Melbourne, Melbourne, VIC 3052, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liuhua","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3050, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tomas","family":"Kalincik","sequence":"additional","affiliation":[{"name":"Neuroimmunology Centre, Department of Neurology, Royal Melbourne Hospital, Melbourne, VIC 3052, Australia"},{"name":"Clinical Outcomes Research Unit, The University of Melbourne, Melbourne, VIC 3052, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mary P.","family":"Galea","sequence":"additional","affiliation":[{"name":"Department of Medicine, Royal Melbourne Hospital, The University of Melbourne, Melbourne, VIC 3052, Australia"},{"name":"Australian Rehabilitation Research Centre, Royal Melbourne Hospital, Melbourne, VIC 3052, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8353-4061","authenticated-orcid":false,"given":"Maya G.","family":"Panisset","sequence":"additional","affiliation":[{"name":"Department of Medicine, Royal Melbourne Hospital, The University of Melbourne, Melbourne, VIC 3052, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gervasoni, E., Anastasi, D., Di Giovanni, R., Solaro, C., Rovaris, M., Brichetto, G., Confalonieri, P., Tacchino, A., Carpinella, I., and Cattaneo, D. (2023). Uncovering Subtle Gait Deterioration in People with Early-Stage Multiple Sclerosis Using Inertial Sensors: A 2-Year Multicenter Longitudinal Study. Sensors, 23.","DOI":"10.3390\/s23229249"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.gaitpost.2020.02.006","article-title":"Gait stability at early stages of multiple sclerosis using different data sources","volume":"77","author":"Bruijn","year":"2020","journal-title":"Gait Posture"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.gaitpost.2023.02.009","article-title":"Optimal sensor location and direction to accurately classify people with early-stage MS using gait stability","volume":"102","author":"Panisset","year":"2023","journal-title":"Gait Posture"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"M\u00fcller, R., Schreff, L., Koch, L.-E., Oschmann, P., and Hamacher, D. (2021). Measuring Gait Stability in People with Multiple Sclerosis Using Different Sensor Locations and Time Scales. Sensors, 21.","DOI":"10.3390\/s21124001"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2030","DOI":"10.1016\/j.apmr.2017.11.010","article-title":"Dynamic Balance Is Related to Physiological Impairments in Persons With Multiple Sclerosis","volume":"99","author":"Peebles","year":"2018","journal-title":"Arch. Phys. Med. Rehabil."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1177\/13524585221094464","article-title":"Gait stability reflects motor tracts damage at early stages of multiple sclerosis","volume":"28","author":"Strik","year":"2022","journal-title":"Mult. Scler. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.gaitpost.2017.12.016","article-title":"The largest Lyapunov exponent of gait in young and elderly individuals: A systematic review","volume":"60","author":"Mehdizadeh","year":"2018","journal-title":"Gait Posture"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20120999","DOI":"10.1098\/rsif.2012.0999","article-title":"Assessing the stability of human locomotion: A review of current measures","volume":"10","author":"Bruijn","year":"2013","journal-title":"J. R. Soc. Interface"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"20200311","DOI":"10.1098\/rsif.2020.0311","article-title":"Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking","volume":"17","author":"Hussain","year":"2020","journal-title":"J. R. Soc. Interface"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"240333","DOI":"10.1098\/rsos.240333","article-title":"Effects of the kinematic variable, time delay and data length on test\u2013retest reliability of the maximal Lyapunov exponent of human walking","volume":"11","author":"Park","year":"2024","journal-title":"R. Soc. Open Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1007\/s10439-019-02216-1","article-title":"Selection Procedures for the Largest Lyapunov Exponent in Gait Biomechanics","volume":"47","author":"Raffalt","year":"2019","journal-title":"Ann. Biomed. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.clinbiomech.2019.05.013","article-title":"Impaired local dynamic stability during treadmill walking predicts future falls in patients with multiple sclerosis: A prospective cohort study","volume":"67","author":"Tajali","year":"2019","journal-title":"Clin. Biomech."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Janshen, L., Santuz, A., Ekizos, A., and Arampatzis, A. (2020). Fuzziness of muscle synergies in patients with multiple sclerosis indicates increased robustness of motor control during walking. Sci. Rep., 10.","DOI":"10.1038\/s41598-020-63788-w"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0167-2789(93)90009-P","article-title":"A practical method for calculating largest Lyapunov exponents from small data sets","volume":"65","author":"Rosenstein","year":"1993","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.jbiomech.2013.10.037","article-title":"A benchmark test of accuracy and precision in estimating dynamical systems characteristics from a time series","volume":"47","author":"Rispens","year":"2014","journal-title":"J. Biomech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1016\/j.jbiomech.2009.03.015","article-title":"Comparison of different state space definitions for local dynamic stability analyses","volume":"42","author":"Gates","year":"2009","journal-title":"J. Biomech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3403","DOI":"10.1103\/PhysRevA.45.3403","article-title":"Determining embedding dimension for phase-space reconstruction using a geometrical construction","volume":"45","author":"Kennel","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.jbiomech.2012.10.032","article-title":"Assessing gait stability: The influence of state space reconstruction on inter- and intra-day reliability of local dynamic stability during over-ground walking","volume":"46","author":"Rispens","year":"2013","journal-title":"J. Biomech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1109\/TNSRE.2020.2991636","article-title":"Local Dynamic Stability of Gait in People With Early Multiple Sclerosis and No-to-Mild Neurological Impairment","volume":"28","author":"Caronni","year":"2020","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2259","DOI":"10.1111\/ene.14866","article-title":"Instrumentally assessed gait quality is more relevant than gait endurance and velocity to explain patient-reported walking ability in early-stage multiple sclerosis","volume":"28","author":"Carpinella","year":"2021","journal-title":"Eur. J. Neurol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1103\/RevModPhys.65.1331","article-title":"The analysis of observed chaotic data in physical systems","volume":"65","author":"Abarbanel","year":"1993","journal-title":"Rev. Mod. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"James, G., Witten, D., Hastie, T., and Tibshirani, R. (2021). Classification. An Introduction to Statistical Learning: With Applications in R, Springer US.","DOI":"10.1007\/978-1-0716-1418-1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"032101","DOI":"10.1063\/5.0137223","article-title":"Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology","volume":"33","author":"Tan","year":"2023","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Carpinella, I., Bertoni, R., Anastasi, D., Cardini, R., Lencioni, T., Ferrarin, M., Cattaneo, D., and Gervasoni, E. (2024). Walk Longer! Using Wearable Inertial Sensors to Uncover Which Gait Aspects Should Be Treated to Increase Walking Endurance in People with Multiple Sclerosis. Sensors, 24.","DOI":"10.3390\/s24227284"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.gaitpost.2019.10.032","article-title":"Local dynamic stability during long-fatiguing walks in people with multiple sclerosis","volume":"76","author":"Arpan","year":"2020","journal-title":"Gait Posture"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hilfiker, R., Vaney, C., Gattlen, B., Meichtry, A., Deriaz, O., Lugon-Moulin, V., Anchisi-Bellwald, A.-M., Palaci, C., Foinant, D., and Terrier, P. (2013). Local dynamic stability as a responsive index for the evaluation of rehabilitation effect on fall risk in patients with multiple sclerosis: A longitudinal study. BMC Res. Notes, 6.","DOI":"10.1186\/1756-0500-6-260"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.jbiomech.2017.08.023","article-title":"Dynamic balance in persons with multiple sclerosis who have a falls history is altered compared to non-fallers and to healthy controls","volume":"63","author":"Peebles","year":"2017","journal-title":"J. Biomech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1186\/s12984-016-0118-9","article-title":"Fall-related gait characteristics on the treadmill and in daily life","volume":"13","author":"Rispens","year":"2016","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1115\/1.1336798","article-title":"Local Dynamic Stability Versus Kinematic Variability of Continuous Overground and Treadmill Walking","volume":"123","author":"Dingwell","year":"2000","journal-title":"J. Biomech. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Craig, J.J., Bruetsch, A.P., Lynch, S.G., and Huisinga, J.M. (2020). Trunk and foot acceleration variability during walking relates to fall history and clinical disability in persons with multiple sclerosis. Clin. Biomech., 80.","DOI":"10.1016\/j.clinbiomech.2020.105100"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.jneumeth.2008.12.015","article-title":"Statistical precision and sensitivity of measures of dynamic gait stability","volume":"178","author":"Bruijn","year":"2009","journal-title":"J. Neurosci. Methods"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Cofr\u00e9 Lizama, L.E., He, X., Kalincik, T., Galea, M.P., and Panisset, M.G. (2024). Sample Entropy Improves Assessment of Postural Control in Early-Stage Multiple Sclerosis. Sensors, 24.","DOI":"10.3390\/s24030872"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.gaitpost.2024.03.013","article-title":"Postural behaviour in people with multiple sclerosis: A complexity paradox","volume":"111","author":"Panisset","year":"2024","journal-title":"Gait Posture"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1016\/j.jbiomech.2016.03.019","article-title":"A comparison study of local dynamic stability measures of daily life walking in older adult community-dwelling fallers and non-fallers","volume":"49","author":"Ihlen","year":"2016","journal-title":"J. Biomech."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/9\/2819\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:24:49Z","timestamp":1760030689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/9\/2819"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,30]]},"references-count":34,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["s25092819"],"URL":"https:\/\/doi.org\/10.3390\/s25092819","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,30]]}}}