{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T07:52:12Z","timestamp":1790063532514,"version":"4.0.1"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T00:00:00Z","timestamp":1587600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["74841254153"],"award-info":[{"award-number":["74841254153"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The calculation of symmetry in amputee gait is a valuable tool to assess the functional aspects of lower limb prostheses and how it impacts the overall gait mechanics. This paper analyzes the vertical trajectory of the body center of mass (CoM) of a group formed by transfemoral amputees and non-amputees to quantitatively compare the symmetry level of this parameter for both cases. A decomposition of the vertical CoM into discrete Fourier series (DFS) components is performed for each subject\u2019s CoM trajectory to identify the main components of each pattern. A DFS-based index is then calculated to quantify the CoM symmetry level. The obtained results show that the CoM displays different patterns along a gait cycle for each amputee, which differ from the sine-wave shape obtained in the non-amputee case. The CoM magnitude spectrum also reveals more coefficients for the amputee waveforms. The different CoM trajectories found in the studied subjects can be thought as the manifestation of developed compensatory mechanisms, which lead to gait asymmetries. The presence of odd components in the magnitude spectrum is related to the asymmetric behavior of the CoM trajectory, given the fact that this signal is an even function for a non-amputee gait. The DFS-based index reflects this fact due to the high value obtained for the non-amputee reference, in comparison to the low values for each amputee.<\/jats:p>","DOI":"10.3390\/s20082392","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T10:46:22Z","timestamp":1587638782000},"page":"2392","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Symmetry Analysis of Amputee Gait Based on Body Center of Mass Trajectory and Discrete Fourier Transform"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4071-6244","authenticated-orcid":false,"given":"Claudia","family":"Ochoa-Diaz","sequence":"first","affiliation":[{"name":"Gama Engineering College, University of Brasilia, Brasilia 70910-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8229-0512","authenticated-orcid":false,"given":"Ant\u00f4nio","family":"Padilha L. B\u00f3","sequence":"additional","affiliation":[{"name":"LARA\/Department of Electrical Engineering, University of Brasilia, Brasilia 70910-900, Brazil"},{"name":"School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane 4072, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.apmr.2004.04.034","article-title":"The prevalence of knee pain and symptomatic knee osteoarthritis among veteran traumatic amputees and nonamputees","volume":"86","author":"Norvell","year":"2005","journal-title":"Arch. Phys. Med. Rehabil."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1016\/j.clinbiomech.2014.04.008","article-title":"The relationship between knee joint loading rate during walking and degenerative changes on magnetic resonance imaging","volume":"29","author":"Morgenroth","year":"2014","journal-title":"Clin. Biomech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1682\/JRRD.2006.11.0147","article-title":"Review of secondary physical conditions associated with lower-limb amputation and long-term prosthesis use","volume":"45","author":"Gailey","year":"2008","journal-title":"J. Rehabil. Res. Dev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.mehy.2013.11.012","article-title":"Asymmetrical movements of the lumbopelvic region: Is this a potential mechanism for low back pain in people with lower limb amputation?","volume":"82","author":"Devan","year":"2014","journal-title":"Med. Hypotheses"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.gaitpost.2011.02.003","article-title":"Biomechanics and physiological parameters during gait in lower-limb amputees: A systematic review","volume":"33","author":"Sagawa","year":"2011","journal-title":"Gait Posture"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1016\/j.humov.2011.09.004","article-title":"Functional gait asymmetry of unilateral transfemoral amputees","volume":"31","author":"Schaarschmidt","year":"2012","journal-title":"Hum. Mov. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/S0966-6362(02)00066-8","article-title":"Adjustments in gait symmetry with walking speed in trans-femoral and trans-tibial amputees","volume":"17","author":"Nolan","year":"2003","journal-title":"Gait Posture"},{"key":"ref_8","first-page":"1","article-title":"A preliminary investigation of pelvic obliquity patterns during gait in persons with transtibial and transfemoral amputation","volume":"37","author":"Michaud","year":"2000","journal-title":"J. Rehabil. Res. Dev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1080\/03093640500217182","article-title":"Trans-femoral amputee gait: Socket-pelvis constraints and compensation strategies","volume":"29","author":"Rabuffetti","year":"2005","journal-title":"Prosthet. Orthot. Int."},{"key":"ref_10","first-page":"1209","article-title":"Mechanical Work Adaptations of Above-Knee Amputee Ambulation","volume":"77","author":"Seroussi","year":"1996","journal-title":"Prosthet. Orthot. Int."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/03093640008726534","article-title":"The functional demands on the intact limb during walking for active trans-femoral and trans-tibial amputees","volume":"24","author":"Nolan","year":"2000","journal-title":"Prosthet. Orthot. Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.pmrj.2014.01.019","article-title":"Plantar Pressures and Ground Reaction Forces During Walking of Individuals With Unilateral Transfemoral Amputation","volume":"6","author":"Castro","year":"2014","journal-title":"J. Inj. Funct. Rehabil."},{"key":"ref_13","first-page":"172","article-title":"Use of force platform variables to quantify the effects of chiropractic manipulation on gait symmetry","volume":"10","author":"Robinson","year":"1987","journal-title":"J. Manipulative Physiol. Ther."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1123\/ijsb.8.1.11","article-title":"A multivariable analysis of lower-extremity kinematic asymmetry in running","volume":"8","author":"Vagenas","year":"1992","journal-title":"Int. J. Sport Biomech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/S0966-6362(00)00070-9","article-title":"Symmetry and limb dominance in able-bodied gait: A review","volume":"12","author":"Sadeghi","year":"2000","journal-title":"Gait Posture"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2127","DOI":"10.1109\/TBME.2011.2149521","article-title":"A new measure of movement symmetry in early Parkinson\u2019s disease patients using symbolic processing of inertial sensor data","volume":"58","author":"Salarian","year":"2011","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0013-4694(95)00209-X","article-title":"Components of EMG symmetry and variability in parkinsonian and healthy elderly gait","volume":"4","author":"Miller","year":"1996","journal-title":"Electroencephalogr. Clin. Neurophysiol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1016\/S1350-4533(01)00010-8","article-title":"Principal component analysis of the power developed in the flexion\/extension muscles of the hip in able-bodied gait","volume":"22","author":"Sadeghi","year":"2000","journal-title":"Med. Eng. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1109\/10.364516","article-title":"Characterization of human gait by means of body center of mass oscillations derived from ground reaction forces","volume":"42","author":"Crowe","year":"1995","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.gaitpost.2004.04.005","article-title":"Relationship between energy cost, gait speed, vertical displacement of centre of body mass and efficiency of pendulum-like mechanism in unilateral amputee gait","volume":"21","author":"Detrembleur","year":"2005","journal-title":"Gait Posture"},{"key":"ref_21","first-page":"776","article-title":"Mechanisms of Gait Asymmetry Due to Push-off Deficiency in Unilateral Amputees","volume":"4320","author":"Adamczyk","year":"2014","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1098\/rspb.2001.1761","article-title":"Mechanical and metabolic determinants of the preferred step width in human walking","volume":"268","author":"Donelan","year":"2001","journal-title":"Proc. Biol. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3717","DOI":"10.1242\/jeb.205.23.3717","article-title":"Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking","volume":"205","author":"Donelan","year":"2002","journal-title":"J. Exp. Biol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.jbiomech.2003.11.001","article-title":"Muscle mechanical work requirements during normal walking: The energetic cost of raising the body\u2019s center-of-mass is significant","volume":"37","author":"Neptune","year":"2004","journal-title":"J. Biomech."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Bo, A.P.L., Poignet, P., Widjaja, F., and Ang, W.T. (2008, January 20\u201325). Online pathological tremor characterization using extended Kalman filtering. Proceedings of the 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, BC, Canada.","DOI":"10.1109\/IEMBS.2008.4649516"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1109\/TNSRE.2016.2591783","article-title":"Automatic Human Movement Assessment With Switching Linear Dynamic System: Motion Segmentation and Motor Performance","volume":"25","author":"Hayashibe","year":"2017","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_27","unstructured":"Neumann, D.A. (2002). Kinesiology of the Musculoskeletal System, Mosby."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1002\/jor.1100080310","article-title":"Measurement of lower extremity kinematics durig level walking","volume":"8","author":"Kadaba","year":"1990","journal-title":"J. Orthop. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1016\/j.jbiomech.2011.03.014","article-title":"The mathematical description of the body centre of mass 3D path in human and animal locomotion","volume":"44","author":"Minetti","year":"2011","journal-title":"J. Biomech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1109\/TBME.2006.870222","article-title":"Center of mass approximation and prediction as a function of body acceleration","volume":"53","author":"Betker","year":"2006","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/1743-0003-2-19","article-title":"Gait variability: Methods, modeling and meaning","volume":"2","author":"Hausdorff","year":"2005","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6891","DOI":"10.3390\/s140406891","article-title":"IMU-Based Joint Angle Measurement for Gait Analysis","volume":"14","author":"Seel","year":"2014","journal-title":"Sensors"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"7085","DOI":"10.1109\/JSEN.2018.2852363","article-title":"Polymer Optical Fiber Sensors in Wearable Devices: Toward Novel Instrumentation Approaches for Gait Assistance Devices","volume":"18","author":"Frizera","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Pandit, S., Godiyal, A.K., Vimal, A.K., Singh, U., Joshi, D., and Kalyanasundaram, D. (2018). An Affordable Insole-Sensor-Based Trans-Femoral Prosthesis for Normal Gait. Sensors, 18.","DOI":"10.3390\/s18030706"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.maturitas.2018.12.008","article-title":"Gait speed assessed by a 4-m walk test is not representative of daily-life gait speed in community-dwelling adults","volume":"121","author":"Jonkman","year":"2019","journal-title":"Maturitas"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3496","DOI":"10.1038\/s41598-019-39695-0","article-title":"Relationship between Daily and In-laboratory Gait Speed among Healthy Community-dwelling Older Adults","volume":"9","author":"Takayanagi","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1186\/s12984-016-0154-5","article-title":"Free-living gait characteristics in ageing and Parkinson\u2019s disease: Impact of environment and ambulatory bout length","volume":"13","author":"Godfrey","year":"2016","journal-title":"J. Neuroeng. Rehabil."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2392\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:23:33Z","timestamp":1760361813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,23]]},"references-count":37,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20082392"],"URL":"https:\/\/doi.org\/10.3390\/s20082392","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,23]]}}}