{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T09:52:17Z","timestamp":1791280337736,"version":"4.1.0"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","license":[{"start":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T00:00:00Z","timestamp":1791244800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T00:00:00Z","timestamp":1791244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12472037"],"award-info":[{"award-number":["12472037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12132009"],"award-info":[{"award-number":["12132009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Med Biol Eng Comput"],"DOI":"10.1007\/s11517-026-03688-9","type":"journal-article","created":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T09:02:13Z","timestamp":1791277333000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reduced-order analysis for gait kinematics of paraplegic patients based on spatiotemporal mode decomposition"],"prefix":"10.1007","author":[{"given":"Xin","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunzhe","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boyang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9438-1796","authenticated-orcid":false,"given":"Jianqiao","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,6]]},"reference":[{"key":"3688_CR1","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1109\/TNSRE.2003.819939","volume":"11","author":"JH van der Spek","year":"2003","unstructured":"van der Spek JH, Veltink PH, Hermens HJ, Koopman BF, Boom HB (2003) A model-based approach to stabilizing crutch supported paraplegic standing by artificial hip joint stiffness. IEEE Trans Neural Syst Rehabil Eng 11:443\u2013451. https:\/\/doi.org\/10.1109\/TNSRE.2003.819939","journal-title":"IEEE Trans Neural Syst Rehabil Eng"},{"key":"3688_CR2","doi-asserted-by":"publisher","DOI":"10.1186\/s12984-023-01206-8","volume":"20","author":"C Lassmann","year":"2023","unstructured":"Lassmann C, Ilg W, Rattay TW, Sch\u00f6ls L, Giese M, Haeufle DF (2023) Dysfunctional neuro-muscular mechanisms explain gradual gait changes in prodromal spastic paraplegia. J Neuroeng Rehabil 20:90. https:\/\/doi.org\/10.1186\/s12984-023-01206-8","journal-title":"J Neuroeng Rehabil"},{"key":"3688_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.dscb.2023.100097","volume":"11","author":"R Tedeschi","year":"2023","unstructured":"Tedeschi R (2023) Kinematic and plantar pressure analysis in Strumpell-Lorrain disease: a case report. Brain Disord 11:100097. https:\/\/doi.org\/10.1016\/j.dscb.2023.100097","journal-title":"Brain Disord"},{"key":"3688_CR4","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.ejpn.2010.07.009","volume":"15","author":"L Piccinini","year":"2011","unstructured":"Piccinini L, Cimolin V, D\u2019Angelo MG, Turconi AC, Crivellini M, Galli M (2011) 3D gait analysis in patients with hereditary spastic paraparesis and spastic diplegia: a kinematic, kinetic and EMG comparison. Eur J Paediatr Neurol 15:138\u2013145. https:\/\/doi.org\/10.1016\/j.ejpn.2010.07.009","journal-title":"Eur J Paediatr Neurol"},{"key":"3688_CR5","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.gaitpost.2011.09.018","volume":"35","author":"J Marsden","year":"2012","unstructured":"Marsden J, Ramdharry G, Stevenson V, Thompson A (2012) Muscle paresis and passive stiffness: key determinants in limiting function in hereditary and sporadic spastic paraparesis. Gait Posture 35:266\u2013271. https:\/\/doi.org\/10.1016\/j.gaitpost.2011.09.018","journal-title":"Gait Posture"},{"key":"3688_CR6","doi-asserted-by":"publisher","first-page":"1414","DOI":"10.1109\/TNSRE.2018.2821197","volume":"26","author":"WS Ang","year":"2018","unstructured":"Ang WS, Geyer H, Chen IM, Ang WT (2018) Objective assessment of spasticity with a method based on a human upper limb model. IEEE Trans Neural Syst Rehabil Eng 26:1414\u20131423. https:\/\/doi.org\/10.1109\/TNSRE.2018.2821197","journal-title":"IEEE Trans Neural Syst Rehabil Eng"},{"key":"3688_CR7","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s11044-022-09852-x","volume":"58","author":"M Febrer-Nafr\u00eda","year":"2023","unstructured":"Febrer-Nafr\u00eda M, Nasr A, Ezati M, Brown P, Font-Llagunes JM, McPhee J (2023) Predictive multibody dynamic simulation of human neuromusculoskeletal systems: a review. Multibody Syst Dyn 58:299\u2013339. https:\/\/doi.org\/10.1007\/s11044-022-09852-x","journal-title":"Multibody Syst Dyn"},{"key":"3688_CR8","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/S0268-0033(99)00044-3","volume":"15","author":"F Bahrami","year":"2000","unstructured":"Bahrami F, Riener R, Jabedar-Maralani P, Schmidt G (2000) Biomechanical analysis of sit-to-stand transfer in healthy and paraplegic subjects. Clin Biomech (Bristol, Avon) 15:123\u2013133. https:\/\/doi.org\/10.1016\/S0268-0033(99)00044-3","journal-title":"Clin Biomech (Bristol, Avon)"},{"key":"3688_CR9","doi-asserted-by":"publisher","unstructured":"Jovic J, Fraisse P, Coste CA, Bonnet V, Fattal C (2011) Improving valid and deficient body segment coordination to improve FES-assisted sit-to-stand in paraplegic subjects. Proc IEEE Int Conf Rehabil Robot:1\u20135. https:\/\/doi.org\/10.1109\/ICORR.2011.5975369.","DOI":"10.1109\/ICORR.2011.5975369"},{"key":"3688_CR10","doi-asserted-by":"publisher","DOI":"10.1097\/MD.0000000000038024","volume":"103","author":"X Liu","year":"2024","unstructured":"Liu X, Liang J, Liu Y (2024) Effects of walking speeds on lower extremity kinematic synergy in toe vertical position control: an experimental study. Medicine (Baltimore) 103:e38024. https:\/\/doi.org\/10.1097\/MD.0000000000038024","journal-title":"Medicine (Baltimore)"},{"key":"3688_CR11","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1080\/00222895.1987.10735403","volume":"19","author":"WA Sparrow","year":"1987","unstructured":"Sparrow WA, Donovan E, Van Emmerik R, Barry EB (1987) Using relative motion plots to measure changes in intra-limb and inter-limb coordination. J Mot Behav 19:115\u2013129. https:\/\/doi.org\/10.1080\/00222895.1987.10735403","journal-title":"J Mot Behav"},{"key":"3688_CR12","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.gaitpost.2007.12.005","volume":"28","author":"SE Farmer","year":"2008","unstructured":"Farmer SE, Pearce G, Stewart C (2008) Developing a technique to measure intra-limb coordination in gait: applicable to children with cerebral palsy. Gait Posture 28:217\u2013221. https:\/\/doi.org\/10.1016\/j.gaitpost.2007.12.005","journal-title":"Gait Posture"},{"key":"3688_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/s11517-025-03349-3","author":"X Zhang","year":"2025","unstructured":"Zhang X, Ren W, Jan YK et al (2025) Effects of infrapatellar straps on lower limb muscle synergies during running. Med Biol Eng Comput. https:\/\/doi.org\/10.1007\/s11517-025-03349-3","journal-title":"Med Biol Eng Comput"},{"key":"3688_CR14","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1016\/j.cmpb.2011.03.013","volume":"107","author":"H U\u011fuz","year":"2012","unstructured":"U\u011fuz H (2012) A hybrid system based on information gain and principal component analysis for the classification of transcranial Doppler signals. Comput Methods Programs Biomed 107:598\u2013609. https:\/\/doi.org\/10.1016\/j.cmpb.2011.03.013","journal-title":"Comput Methods Programs Biomed"},{"key":"3688_CR15","doi-asserted-by":"publisher","DOI":"10.3389\/fbioe.2022.843204","volume":"10","author":"L Xiang","year":"2022","unstructured":"Xiang L, Gu Y, Mei Q, Wang A, Shim V, Fernandez J (2022) Automatic classification of barefoot and shod populations based on the foot metrics and plantar pressure patterns. Front Bioeng Biotechnol 10:843204. https:\/\/doi.org\/10.3389\/fbioe.2022.843204","journal-title":"Front Bioeng Biotechnol"},{"key":"3688_CR16","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1016\/j.clinbiomech.2004.01.005","volume":"19","author":"A Daffertshofer","year":"2004","unstructured":"Daffertshofer A, Lamoth CJC, Meijer OG, Beek PJ (2004) PCA in studying coordination and variability: a tutorial. Clin Biomech 19:415\u2013428. https:\/\/doi.org\/10.1016\/j.clinbiomech.2004.01.005","journal-title":"Clin Biomech"},{"key":"3688_CR17","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.210161","volume":"8","author":"B Huang","year":"2021","unstructured":"Huang B, Xiong C, Chen W, Liang J, Sun BY, Gong X (2021) Common kinematic synergies of various human locomotor behaviours. R Soc Open Sci 8:210161. https:\/\/doi.org\/10.1098\/rsos.210161","journal-title":"R Soc Open Sci"},{"key":"3688_CR18","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0244582","volume":"16","author":"D \u00d3''Reilly","year":"2021","unstructured":"\u00d3\u2019Reilly D, Federolf P (2021) Identifying differences in gait adaptability across various speeds using movement synergy analysis. PLoS ONE 16:e0244582. https:\/\/doi.org\/10.1371\/journal.pone.0244582","journal-title":"PLoS ONE"},{"key":"3688_CR19","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.jelekin.2019.02.006","volume":"45","author":"G Martino","year":"2019","unstructured":"Martino G, Ivanenko Y, Serrao M, Ranavolo A, Draicchio F, Casali C, Lacquaniti F (2019) Locomotor coordination in patients with hereditary spastic paraplegia. J Electromyogr Kinesiol 45:61\u201369. https:\/\/doi.org\/10.1016\/j.jelekin.2019.02.006","journal-title":"J Electromyogr Kinesiol"},{"key":"3688_CR20","doi-asserted-by":"publisher","first-page":"5869238","DOI":"10.1155\/2016\/5869238","volume":"2016","author":"J Luo","year":"2016","unstructured":"Luo J, Tang J, Xiao X (2016) Abnormal gait behavior detection for elderly based on enhanced Wigner-Ville analysis and cloud incremental SVM learning. J Sens 2016:5869238. https:\/\/doi.org\/10.1155\/2016\/5869238","journal-title":"J Sens"},{"key":"3688_CR21","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s10439-025-03898-6","volume":"54","author":"SHM Rabie","year":"2026","unstructured":"Rabie SHM, Ghofrani S, Barghamadi H, Eslami M (2026) EFD in comparison with EWT for synthetic and EEG signal decomposition and classification of Alzheimer\u2019s disease and mild cognitive impairment. Ann Biomed Eng 54:531\u2013548. https:\/\/doi.org\/10.1007\/s10439-025-03898-6","journal-title":"Ann Biomed Eng"},{"key":"3688_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2026.110132","volume":"161","author":"S Baaziz","year":"2026","unstructured":"Baaziz S, Boukharfane R (2026) A combined spectral-geometric framework for inert and reacting shock-driven compressible mixing layers using DMD and optimal transport. Commun Nonlinear Sci Numer Simul 161:110132. https:\/\/doi.org\/10.1016\/j.cnsns.2026.110132","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3688_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2025.109221","volume":"276","author":"B Pialot","year":"2026","unstructured":"Pialot B, Guidi F, Muleki-Seya P, Boni E, Ramalli A, Varray F (2026) Dynamic mode decomposition as a framework for denoising ultrafast power doppler images. Comput Methods Programs Biomed 276:109221. https:\/\/doi.org\/10.1016\/j.cmpb.2025.109221","journal-title":"Comput Methods Programs Biomed"},{"key":"3688_CR24","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.cviu.2016.02.005","volume":"146","author":"NB Erichson","year":"2016","unstructured":"Erichson NB, Donovan C (2016) Randomized low-rank dynamic mode decomposition for motion detection. Comput Vis Image Underst 146:40\u201350. https:\/\/doi.org\/10.1016\/j.cviu.2016.02.005","journal-title":"Comput Vis Image Underst"},{"key":"3688_CR25","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1098\/rspa.1998.0193","volume":"454","author":"NE Huang","year":"1998","unstructured":"Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond A 454:903\u2013995. https:\/\/doi.org\/10.1098\/rspa.1998.0193","journal-title":"Proc R Soc Lond A"},{"key":"3688_CR26","doi-asserted-by":"publisher","first-page":"2359","DOI":"10.1007\/s11517-022-02615-y","volume":"60","author":"R Ho","year":"2022","unstructured":"Ho R, Hung K (2022) EEG analysis and classification based on cardinal spline empirical mode decomposition and synchrony features. Med Biol Eng Comput 60:2359\u20132372. https:\/\/doi.org\/10.1007\/s11517-022-02615-y","journal-title":"Med Biol Eng Comput"},{"key":"3688_CR27","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s11517-022-02736-4","volume":"61","author":"C Cruz-Montecinos","year":"2023","unstructured":"Cruz-Montecinos C, Garc\u00eda-Mass\u00f3 X, Maas H et al (2023) Detection of intermuscular coordination based on the causality of empirical mode decomposition. Med Biol Eng Comput 61:497\u2013509. https:\/\/doi.org\/10.1007\/s11517-022-02736-4","journal-title":"Med Biol Eng Comput"},{"key":"3688_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2022.105099","volume":"114","author":"B Vidya","year":"2022","unstructured":"Vidya B, Sasikumar P (2022) Parkinson\u2019s disease diagnosis and stage prediction based on gait signal analysis using EMD and CNN-LSTM network. Eng Appl Artif Intell 114:105099. https:\/\/doi.org\/10.1016\/j.engappai.2022.105099","journal-title":"Eng Appl Artif Intell"},{"key":"3688_CR29","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/TBME.2016.2536438","volume":"64","author":"P Ren","year":"2017","unstructured":"Ren P, Tang S, Fang F, Luo L, Xu L, Bringas-Vega ML, Valdes-Sosa PA (2017) Gait rhythm fluctuation analysis for neurodegenerative diseases by empirical mode decomposition. IEEE Trans Biomed Eng 64:52\u201360. https:\/\/doi.org\/10.1109\/TBME.2016.2536438","journal-title":"IEEE Trans Biomed Eng"},{"key":"3688_CR30","doi-asserted-by":"publisher","unstructured":"Yu TH, Wu CC (2019) An accelerometer based gait analysis system to detect gait abnormalities in cerebralspinal meningitis patients. Proc Int Conf Mach Learn Cybern:1\u20135. https:\/\/doi.org\/10.1109\/ICMLC48188.2019.8949256.","DOI":"10.1109\/ICMLC48188.2019.8949256"},{"key":"3688_CR31","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1038\/s41393-019-0350-9","volume":"57","author":"ASIA and ISCoS International Standards Committee","year":"2019","unstructured":"ASIA and ISCoS International Standards Committee (2019) The 2019 revision of the International Standards for Neurological Classification of Spinal Cord Injury (ISNCSCI)\u2014what\u2019s new? Spinal Cord 57:815\u2013817. https:\/\/doi.org\/10.1038\/s41393-019-0350-9","journal-title":"Spinal Cord"},{"key":"3688_CR32","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1038\/sj.sc.3100993","volume":"38","author":"JF Ditunno","year":"2000","unstructured":"Ditunno JF, Ditunno PL, Graziani V et al (2000) Walking index for spinal cord injury (WISCI): an international multicenter validity and reliability study. Spinal Cord 38:234\u2013243. https:\/\/doi.org\/10.1038\/sj.sc.3100993","journal-title":"Spinal Cord"},{"key":"3688_CR33","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1093\/ptj\/67.2.206","volume":"67","author":"RW Bohannon","year":"1987","unstructured":"Bohannon RW, Smith MB (1987) Interrater reliability of a modified Ashworth scale of muscle spasticity. Phys Ther 67:206\u2013207. https:\/\/doi.org\/10.1093\/ptj\/67.2.206","journal-title":"Phys Ther"},{"key":"3688_CR34","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1164\/ajrccm.166.1.at1102","volume":"166","author":"ATS Committee on Proficiency Standards for Clinical Pulmonary Function Laboratories","year":"2002","unstructured":"ATS Committee on Proficiency Standards for Clinical Pulmonary Function Laboratories (2002) ATS statement: guidelines for the six-minute walk test. Am J Respir Crit Care Med 166:111\u2013117. https:\/\/doi.org\/10.1164\/ajrccm.166.1.at1102","journal-title":"Am J Respir Crit Care Med"},{"key":"3688_CR35","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-024-55238-8","volume":"14","author":"S Fern\u00e1ndez-Canosa","year":"2024","unstructured":"Fern\u00e1ndez-Canosa S, Brocalero-Camacho A, Mart\u00ednez-Medina A, D\u00edez-Rodr\u00edguez E, Arias P, Oliviero A, Soto-Le\u00f3n V (2024) Fatigue insights from walking tests in spinal cord injury and multiple sclerosis individuals. Sci Rep 14:4761. https:\/\/doi.org\/10.1038\/s41598-024-55238-8","journal-title":"Sci Rep"},{"key":"3688_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/s10409-022-22140-x","volume":"38","author":"XY Wang","year":"2022","unstructured":"Wang XY, Guo JQ, Tian Q (2022) A forward-inverse dynamics modeling framework for human musculoskeletal multibody system. Acta Mech Sin 38:522140. https:\/\/doi.org\/10.1007\/s10409-022-22140-x","journal-title":"Acta Mech Sin"},{"key":"3688_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2023.111893","volume":"162","author":"YB Wang","year":"2024","unstructured":"Wang YB, Guo JQ, Tang H, Li XX, Guo SY, Tian Q (2024) Quantification of soft tissue artifacts using CT registration and subject-specific multibody modeling. J Biomech 162:111893. https:\/\/doi.org\/10.1016\/j.jbiomech.2023.111893","journal-title":"J Biomech"},{"key":"3688_CR38","doi-asserted-by":"publisher","first-page":"2750","DOI":"10.1016\/j.jbiomech.2008.06.001","volume":"41","author":"L Ren","year":"2008","unstructured":"Ren L, Jones RK, Howard D (2008) Whole body inverse dynamics over a complete gait cycle based only on measured kinematics. J Biomech 41:2750\u20132759. https:\/\/doi.org\/10.1016\/j.jbiomech.2008.06.001","journal-title":"J Biomech"},{"key":"3688_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2022.111143","volume":"139","author":"JQ Guo","year":"2022","unstructured":"Guo JQ, Chen JP, Wang J, Ren GX, Tian Q, Guo CB (2022) EMG-assisted forward dynamics simulation of subject-specific mandible musculoskeletal system. J Biomech 139:111143. https:\/\/doi.org\/10.1016\/j.jbiomech.2022.111143","journal-title":"J Biomech"},{"key":"3688_CR40","doi-asserted-by":"publisher","DOI":"10.1002\/9780470549148","volume-title":"Biomechanics and motor control of human movement","author":"DA Winter","year":"2009","unstructured":"Winter DA (2009) Biomechanics and motor control of human movement, 4th edn. Wiley, Hoboken. https:\/\/doi.org\/10.1002\/9780470549148","edition":"4th edn"},{"key":"3688_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2021.106116","volume":"206","author":"M \u015eeker","year":"2021","unstructured":"\u015eeker M, \u00d6zbek Y, Yener G, \u00d6zerdem MS (2021) Complexity of EEG dynamics for early diagnosis of Alzheimer\u2019s disease using permutation entropy neuromarker. Comput Methods Programs Biomed 206:106116. https:\/\/doi.org\/10.1016\/j.cmpb.2021.106116","journal-title":"Comput Methods Programs Biomed"},{"key":"3688_CR42","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/j.jbiomech.2010.09.015","volume":"44","author":"NE Helwig","year":"2011","unstructured":"Helwig NE, Hong S, Hsiao-Wecksler ET, Polk JD (2011) Methods to temporally align gait cycle data. J Biomech 44:561\u2013566. https:\/\/doi.org\/10.1016\/j.jbiomech.2010.09.015","journal-title":"J Biomech"},{"key":"3688_CR43","doi-asserted-by":"publisher","DOI":"10.3390\/s20226534","volume":"20","author":"R Dong","year":"2020","unstructured":"Dong R, Cai D, Ikuno S (2020) Motion capture data analysis in the instantaneous frequency-domain using Hilbert-Huang transform. Sensors (Basel) 20:6534. https:\/\/doi.org\/10.3390\/s20226534","journal-title":"Sensors (Basel)"},{"key":"3688_CR44","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1017\/S0022112010001217","volume":"656","author":"PJ Schmid","year":"2010","unstructured":"Schmid PJ (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656:5\u201328. https:\/\/doi.org\/10.1017\/S0022112010001217","journal-title":"J Fluid Mech"},{"key":"3688_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jneumeth.2015.10.010","volume":"258","author":"BW Brunton","year":"2016","unstructured":"Brunton BW, Johnson LA, Ojemann JG, Kutz JN (2016) Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition. J Neurosci Methods 258:1\u201315. https:\/\/doi.org\/10.1016\/j.jneumeth.2015.10.010","journal-title":"J Neurosci Methods"},{"key":"3688_CR46","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1152\/advan.00068.2010","volume":"34","author":"D Curran-Everett","year":"2010","unstructured":"Curran-Everett D (2010) Explorations in statistics: correlation. Adv Physiol Educ 34:186\u2013191. https:\/\/doi.org\/10.1152\/advan.00068.2010","journal-title":"Adv Physiol Educ"},{"key":"3688_CR47","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1140\/epjst\/e2013-01862-7","volume":"222","author":"M Riedl","year":"2013","unstructured":"Riedl M, M\u00fcller A, Wessel N (2013) Practical considerations of permutation entropy: a tutorial review. Eur Phys J Spec Top 222:249\u2013262. https:\/\/doi.org\/10.1140\/epjst\/e2013-01862-7","journal-title":"Eur Phys J Spec Top"},{"key":"3688_CR48","doi-asserted-by":"publisher","DOI":"10.3390\/e21040385","volume":"21","author":"D Cuesta-Frau","year":"2019","unstructured":"Cuesta-Frau D, Murillo-Escobar JP, Orrego DA, Delgado-Trejos E (2019) Embedded dimension and time series length. Practical influence on permutation entropy and its applications. Entropy 21:385. https:\/\/doi.org\/10.3390\/e21040385","journal-title":"Entropy"},{"key":"3688_CR49","doi-asserted-by":"publisher","first-page":"1603","DOI":"10.1007\/s11517-022-02766-y","volume":"61","author":"L Chou","year":"2023","unstructured":"Chou L, Gong S, Yang H et al (2023) A fast sample entropy for pulse rate variability analysis. Med Biol Eng Comput 61:1603\u20131617. https:\/\/doi.org\/10.1007\/s11517-022-02766-y","journal-title":"Med Biol Eng Comput"},{"key":"3688_CR50","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1007\/s10439-020-02616-8","volume":"49","author":"JM Yentes","year":"2021","unstructured":"Yentes JM, Raffalt PC (2021) Entropy analysis in gait research: methodological considerations and recommendations. Ann Biomed Eng 49:979\u2013990. https:\/\/doi.org\/10.1007\/s10439-020-02616-8","journal-title":"Ann Biomed Eng"},{"key":"3688_CR51","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s11517-025-03449-0","volume":"64","author":"EM Cirugeda","year":"2026","unstructured":"Cirugeda EM, Plancha E, Hidalgo VM et al (2026) Sinus rhythm maintenance in persistent atrial fibrillation: 12-lead ECG multiscale entropy characterization. Med Biol Eng Comput 64:335\u2013349. https:\/\/doi.org\/10.1007\/s11517-025-03449-0","journal-title":"Med Biol Eng Comput"},{"key":"3688_CR52","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.174102","volume":"88","author":"C Bandt","year":"2002","unstructured":"Bandt C, Pompe B (2002) Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 88:174102. https:\/\/doi.org\/10.1103\/PhysRevLett.88.174102","journal-title":"Phys Rev Lett"},{"key":"3688_CR53","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1109\/JBHI.2014.2326660","volume":"19","author":"GR Naik","year":"2015","unstructured":"Naik GR, Nguyen HT (2015) Nonnegative matrix factorization for the identification of EMG finger movements: evaluation using matrix analysis. IEEE J Biomed Health Inform 19:478\u2013485. https:\/\/doi.org\/10.1109\/JBHI.2014.2326660","journal-title":"IEEE J Biomed Health Inform"},{"key":"3688_CR54","doi-asserted-by":"publisher","first-page":"2646","DOI":"10.1109\/TBME.2020.2967154","volume":"67","author":"SK Dwivedi","year":"2020","unstructured":"Dwivedi SK, Ngeo J, Shibata T (2020) Extraction of nonlinear synergies for proportional and simultaneous estimation of finger kinematics. IEEE Trans Biomed Eng 67:2646\u20132658. https:\/\/doi.org\/10.1109\/TBME.2020.2967154","journal-title":"IEEE Trans Biomed Eng"},{"key":"3688_CR55","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.248069","volume":"227","author":"X Zhang","year":"2024","unstructured":"Zhang X, Sun R (2024) Joint synergy and muscle activity in the motion of the ankle-foot complex. J Exp Biol 227:jeb248069. https:\/\/doi.org\/10.1242\/jeb.248069","journal-title":"J Exp Biol"},{"key":"3688_CR56","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2020.588943","volume":"14","author":"D Ao","year":"2020","unstructured":"Ao D, Shourijeh MS, Patten C, Fregly BJ (2020) Evaluation of synergy extrapolation for predicting unmeasured muscle excitations from measured muscle synergies. Front Comput Neurosci 14:588943. https:\/\/doi.org\/10.3389\/fncom.2020.588943","journal-title":"Front Comput Neurosci"},{"key":"3688_CR57","doi-asserted-by":"publisher","first-page":"2024","DOI":"10.1016\/j.clinph.2014.02.001","volume":"125","author":"HB Hayes","year":"2014","unstructured":"Hayes HB, Chvatal SA, French MA, Ting LH, Trumbower RD (2014) Neuromuscular constraints on muscle coordination during overground walking in persons with chronic incomplete spinal cord injury. Clin Neurophysiol 125:2024\u20132035. https:\/\/doi.org\/10.1016\/j.clinph.2014.02.001","journal-title":"Clin Neurophysiol"},{"key":"3688_CR58","doi-asserted-by":"publisher","first-page":"2519","DOI":"10.1089\/neu.2017.5538","volume":"35","author":"WJ Sohn","year":"2018","unstructured":"Sohn WJ, Tan AQ, Hayes HB, Pochiraju S, Deffeyes J, Trumbower RD (2018) Variability of leg kinematics during overground walking in persons with chronic incomplete spinal cord injury. J Neurotrauma 35:2519\u20132529. https:\/\/doi.org\/10.1089\/neu.2017.5538","journal-title":"J Neurotrauma"},{"key":"3688_CR59","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/j.clineuro.2012.01.013","volume":"114","author":"WB McKay","year":"2012","unstructured":"McKay WB (2012) Neurophysiological characterization of the new anatomy and motor control that results from neurological injury or disease. Clin Neurol Neurosurg 114:447\u2013454. https:\/\/doi.org\/10.1016\/j.clineuro.2012.01.013","journal-title":"Clin Neurol Neurosurg"},{"key":"3688_CR60","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1162\/089976698300017467","volume":"10","author":"B Sch\u00f6lkopf","year":"1998","unstructured":"Sch\u00f6lkopf B, Smola A, M\u00fcller KR (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10:1299\u20131319. https:\/\/doi.org\/10.1162\/089976698300017467","journal-title":"Neural Comput"},{"key":"3688_CR61","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/j.humov.2007.01.015","volume":"26","author":"J Wu","year":"2007","unstructured":"Wu J, Wang J, Liu L (2007) Feature extraction via KPCA for classification of gait patterns. Hum Mov Sci 26:393\u2013411. https:\/\/doi.org\/10.1016\/j.humov.2007.01.015","journal-title":"Hum Mov Sci"},{"key":"3688_CR62","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2023.110205","volume":"194","author":"M Zare","year":"2023","unstructured":"Zare M, Nouri NM (2023) End-effects mitigation in empirical mode decomposition using a new correlation-based expansion model. Mech Syst Signal Process 194:110205. https:\/\/doi.org\/10.1016\/j.ymssp.2023.110205","journal-title":"Mech Syst Signal Process"},{"key":"3688_CR63","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2020.105281","volume":"89","author":"SH Li","year":"2020","unstructured":"Li SH, Liu XM, Lin AJ (2020) Fractional frequency hybrid model based on EEMD for financial time series forecasting. Commun Nonlinear Sci Numer Simul 89:105281. https:\/\/doi.org\/10.1016\/j.cnsns.2020.105281","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3688_CR64","doi-asserted-by":"publisher","first-page":"1059","DOI":"10.1109\/JBHI.2017.2734074","volume":"22","author":"M Nazari","year":"2018","unstructured":"Nazari M, Sakhaei SM (2018) Variational mode extraction: a new efficient method to derive respiratory signals from ECG. IEEE J Biomed Health Inform 22:1059\u20131067. https:\/\/doi.org\/10.1109\/JBHI.2017.2734074","journal-title":"IEEE J Biomed Health Inform"},{"key":"3688_CR65","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2026.110090","volume":"161","author":"QF Wang","year":"2026","unstructured":"Wang QF, Wu LX, Jiang L, Cheng X (2026) Consensus time-frequency representation via Multi-EMD operators for stable identification of seismic reflectors. Commun Nonlinear Sci Numer Simul 161:110090. https:\/\/doi.org\/10.1016\/j.cnsns.2026.110090","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3688_CR66","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1007\/s10237-019-01260-z","volume":"19","author":"JQ Guo","year":"2020","unstructured":"Guo JQ, Sun Y, Hao YX, Cui LG, Ren GX (2020) A mass-flowing muscle model with shape restrictive soft tissues: correlation with sonoelastography. Biomech Model Mechanobiol 19:911\u2013926. https:\/\/doi.org\/10.1007\/s10237-019-01260-z","journal-title":"Biomech Model Mechanobiol"},{"key":"3688_CR67","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.gaitpost.2019.10.024","volume":"75","author":"EP Washabaugh","year":"2020","unstructured":"Washabaugh EP, Augenstein TE, Krishnan C (2020) Functional resistance training during walking: mode of application differentially affects gait biomechanics and muscle activation patterns. Gait Posture 75:129\u2013136. https:\/\/doi.org\/10.1016\/j.gaitpost.2019.10.024","journal-title":"Gait Posture"}],"container-title":["Medical & Biological Engineering & Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-026-03688-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11517-026-03688-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-026-03688-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T09:02:14Z","timestamp":1791277334000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11517-026-03688-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,6]]},"references-count":67,"alternative-id":["3688"],"URL":"https:\/\/doi.org\/10.1007\/s11517-026-03688-9","relation":{},"ISSN":["0140-0118","1741-0444"],"issn-type":[{"value":"0140-0118","type":"print"},{"value":"1741-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,6]]},"assertion":[{"value":"8 July 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflicts of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors confirm that no generative AI or AI-assisted technologies were used in the writing, language editing, coding, data analysis, literature review, or figure preparation of this manuscript. No non-public or identifiable data of participants were entered into any external AI system.","order":2,"name":"Ethics","label":"Generative AI statement","group":{"name":"EthicsHeading","label":"Declarations"}}]}}