The mathematical description of the body centre of mass 3D path in human and animal locomotion
Abstract Although the 3D trajectory of the body centre of mass during ambulation constitutes the ‘locomotor signature’ at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematic...
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| Veröffentlicht in: | Journal of biomechanics 2011-05, Vol.44 (8), p.1471-1477 |
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| creator | Minetti, Alberto E Cisotti, Caterina Mian, Omar S |
| description | Abstract Although the 3D trajectory of the body centre of mass during ambulation constitutes the ‘locomotor signature’ at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768–1830, analysis of periodic events) and of Jules Antoine Lissajous (1822–1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and running humans, and the re-processing of previously published data on trotting and galloping horses, as moving on a treadmill, allowed to obtain closed loops for the body centre of mass showing general and individual locomotor characteristics. The mechanical dynamics due to the different energy exchange, the asymmetry along each 3D axis, and the sagittal and lateral energy recovery, among other parameters, were evaluated for each gait according to the present methodology. The proposed mathematical description of the 3D trajectory of the body centre of mass could be used to better understand the physiology and biomechanics of normal locomotion, from monopods to octopods, and to evaluate individual deviations with respect to average values as resulting from gait pathologies and the restoration of a normal pattern after pharmacological, physiotherapeutic and surgical treatments. |
| doi_str_mv | 10.1016/j.jbiomech.2011.03.014 |
| format | Article |
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By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768–1830, analysis of periodic events) and of Jules Antoine Lissajous (1822–1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and running humans, and the re-processing of previously published data on trotting and galloping horses, as moving on a treadmill, allowed to obtain closed loops for the body centre of mass showing general and individual locomotor characteristics. The mechanical dynamics due to the different energy exchange, the asymmetry along each 3D axis, and the sagittal and lateral energy recovery, among other parameters, were evaluated for each gait according to the present methodology. The proposed mathematical description of the 3D trajectory of the body centre of mass could be used to better understand the physiology and biomechanics of normal locomotion, from monopods to octopods, and to evaluate individual deviations with respect to average values as resulting from gait pathologies and the restoration of a normal pattern after pharmacological, physiotherapeutic and surgical treatments.</description><identifier>ISSN: 0021-9290</identifier><identifier>EISSN: 1873-2380</identifier><identifier>DOI: 10.1016/j.jbiomech.2011.03.014</identifier><identifier>PMID: 21463861</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Adult ; Animals ; Biological and medical sciences ; Biomechanical Phenomena ; Biomechanics ; Biomechanics. Biorheology ; Centre of mass ; Computer Simulation ; Fourier Analysis ; Fundamental and applied biological sciences. Psychology ; Gait ; Gait - physiology ; Human ; Humans ; Imaging, Three-Dimensional - methods ; Lissajous contour ; Locomotion ; Locomotion signature ; Male ; Mathematical analysis ; Models, Statistical ; Models, Theoretical ; Movement ; Parametric equations ; Physical Medicine and Rehabilitation ; Three dimensional ; Tissues, organs and organisms biophysics ; Trajectories ; Vertebrates: body movement. Posture. Locomotion. Flight. Swimming. Physical exercise. Rest. Sports</subject><ispartof>Journal of biomechanics, 2011-05, Vol.44 (8), p.1471-1477</ispartof><rights>Elsevier Ltd</rights><rights>2011 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><rights>Copyright © 2011 Elsevier Ltd. All rights reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c512t-39987ebb6a99e7dbdb143e47d27a3aefbba6b4ddb067eafc07a83a19e9787d883</citedby><cites>FETCH-LOGICAL-c512t-39987ebb6a99e7dbdb143e47d27a3aefbba6b4ddb067eafc07a83a19e9787d883</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/1035116901?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995,64385,64387,64389,72469</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24181143$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/21463861$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Minetti, Alberto E</creatorcontrib><creatorcontrib>Cisotti, Caterina</creatorcontrib><creatorcontrib>Mian, Omar S</creatorcontrib><title>The mathematical description of the body centre of mass 3D path in human and animal locomotion</title><title>Journal of biomechanics</title><addtitle>J Biomech</addtitle><description>Abstract Although the 3D trajectory of the body centre of mass during ambulation constitutes the ‘locomotor signature’ at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768–1830, analysis of periodic events) and of Jules Antoine Lissajous (1822–1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and running humans, and the re-processing of previously published data on trotting and galloping horses, as moving on a treadmill, allowed to obtain closed loops for the body centre of mass showing general and individual locomotor characteristics. The mechanical dynamics due to the different energy exchange, the asymmetry along each 3D axis, and the sagittal and lateral energy recovery, among other parameters, were evaluated for each gait according to the present methodology. The proposed mathematical description of the 3D trajectory of the body centre of mass could be used to better understand the physiology and biomechanics of normal locomotion, from monopods to octopods, and to evaluate individual deviations with respect to average values as resulting from gait pathologies and the restoration of a normal pattern after pharmacological, physiotherapeutic and surgical treatments.</description><subject>Adult</subject><subject>Animals</subject><subject>Biological and medical sciences</subject><subject>Biomechanical Phenomena</subject><subject>Biomechanics</subject><subject>Biomechanics. Biorheology</subject><subject>Centre of mass</subject><subject>Computer Simulation</subject><subject>Fourier Analysis</subject><subject>Fundamental and applied biological sciences. Psychology</subject><subject>Gait</subject><subject>Gait - physiology</subject><subject>Human</subject><subject>Humans</subject><subject>Imaging, Three-Dimensional - methods</subject><subject>Lissajous contour</subject><subject>Locomotion</subject><subject>Locomotion signature</subject><subject>Male</subject><subject>Mathematical analysis</subject><subject>Models, Statistical</subject><subject>Models, Theoretical</subject><subject>Movement</subject><subject>Parametric equations</subject><subject>Physical Medicine and Rehabilitation</subject><subject>Three dimensional</subject><subject>Tissues, organs and organisms biophysics</subject><subject>Trajectories</subject><subject>Vertebrates: body movement. Posture. Locomotion. Flight. Swimming. Physical exercise. Rest. Sports</subject><issn>0021-9290</issn><issn>1873-2380</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqFkk1v1DAQhiMEotvCX6gsIcQpwRNnbeeCqAoFpEocKFcsf0y0Dkm82AnS_nsc7ZZKvfRge2Q_88oz7xTFJdAKKPD3fdUbH0a0u6qmABVlFYXmWbEBKVhZM0mfFxtKayjbuqVnxXlKPaVUNKJ9WZzV0HAmOWyKX3c7JKOed5g3b_VAHCYb_X72YSKhI_mFmOAOxOI0R1yvRp0SYZ_IPqcRP5HdMuqJ6Mnl5ccsMQQbxrAqvCpedHpI-Pp0XhQ_bz7fXX8tb79_-XZ9dVvaLdRzydpWCjSG67ZF4Ywz0DBshKuFZho7YzQ3jXOGcoG6s1RoyTS02AopnJTsonh31N3H8GfBNKvRJ4vDoCcMS1JSUr7NnRFPk7wRGW5oJt88IvuwxCmXoYCyLQBvKWSKHykbQ0oRO7WPuQnxkCG1WqV6dW-VWq1SlKlsVU68PMkvZkT3P-3emwy8PQE6ZWO6qCfr0wPXgISsk7mPRw5zg_96jCpZj5NF5yPaWbngn_7Lh0cSdvDTOg6_8YDpoW6VakXVj3Ww1rkCyBFnnP0DtbvJWQ</recordid><startdate>20110517</startdate><enddate>20110517</enddate><creator>Minetti, Alberto E</creator><creator>Cisotti, Caterina</creator><creator>Mian, Omar S</creator><general>Elsevier Ltd</general><general>Elsevier</general><general>Elsevier Limited</general><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7QP</scope><scope>7TB</scope><scope>7TS</scope><scope>7X7</scope><scope>7XB</scope><scope>88E</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>8G5</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>K9.</scope><scope>LK8</scope><scope>M0S</scope><scope>M1P</scope><scope>M2O</scope><scope>M7P</scope><scope>MBDVC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>Q9U</scope><scope>7X8</scope></search><sort><creationdate>20110517</creationdate><title>The mathematical description of the body centre of mass 3D path in human and animal locomotion</title><author>Minetti, Alberto E ; Cisotti, Caterina ; Mian, Omar S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c512t-39987ebb6a99e7dbdb143e47d27a3aefbba6b4ddb067eafc07a83a19e9787d883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Adult</topic><topic>Animals</topic><topic>Biological and medical sciences</topic><topic>Biomechanical Phenomena</topic><topic>Biomechanics</topic><topic>Biomechanics. Biorheology</topic><topic>Centre of mass</topic><topic>Computer Simulation</topic><topic>Fourier Analysis</topic><topic>Fundamental and applied biological sciences. Psychology</topic><topic>Gait</topic><topic>Gait - physiology</topic><topic>Human</topic><topic>Humans</topic><topic>Imaging, Three-Dimensional - methods</topic><topic>Lissajous contour</topic><topic>Locomotion</topic><topic>Locomotion signature</topic><topic>Male</topic><topic>Mathematical analysis</topic><topic>Models, Statistical</topic><topic>Models, Theoretical</topic><topic>Movement</topic><topic>Parametric equations</topic><topic>Physical Medicine and Rehabilitation</topic><topic>Three dimensional</topic><topic>Tissues, organs and organisms biophysics</topic><topic>Trajectories</topic><topic>Vertebrates: body movement. Posture. Locomotion. Flight. Swimming. Physical exercise. Rest. Sports</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Minetti, Alberto E</creatorcontrib><creatorcontrib>Cisotti, Caterina</creatorcontrib><creatorcontrib>Mian, Omar S</creatorcontrib><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Physical Education Index</collection><collection>ProQuest_Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Medical Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ProQuest Biological Science Collection</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>ProQuest research library</collection><collection>Biological Science Database</collection><collection>Research Library (Corporate)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>ProQuest Central Basic</collection><collection>MEDLINE - Academic</collection><jtitle>Journal of biomechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Minetti, Alberto E</au><au>Cisotti, Caterina</au><au>Mian, Omar S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The mathematical description of the body centre of mass 3D path in human and animal locomotion</atitle><jtitle>Journal of biomechanics</jtitle><addtitle>J Biomech</addtitle><date>2011-05-17</date><risdate>2011</risdate><volume>44</volume><issue>8</issue><spage>1471</spage><epage>1477</epage><pages>1471-1477</pages><issn>0021-9290</issn><eissn>1873-2380</eissn><abstract>Abstract Although the 3D trajectory of the body centre of mass during ambulation constitutes the ‘locomotor signature’ at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768–1830, analysis of periodic events) and of Jules Antoine Lissajous (1822–1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and running humans, and the re-processing of previously published data on trotting and galloping horses, as moving on a treadmill, allowed to obtain closed loops for the body centre of mass showing general and individual locomotor characteristics. The mechanical dynamics due to the different energy exchange, the asymmetry along each 3D axis, and the sagittal and lateral energy recovery, among other parameters, were evaluated for each gait according to the present methodology. The proposed mathematical description of the 3D trajectory of the body centre of mass could be used to better understand the physiology and biomechanics of normal locomotion, from monopods to octopods, and to evaluate individual deviations with respect to average values as resulting from gait pathologies and the restoration of a normal pattern after pharmacological, physiotherapeutic and surgical treatments.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><pmid>21463861</pmid><doi>10.1016/j.jbiomech.2011.03.014</doi><tpages>7</tpages></addata></record> |
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| subjects | Adult Animals Biological and medical sciences Biomechanical Phenomena Biomechanics Biomechanics. Biorheology Centre of mass Computer Simulation Fourier Analysis Fundamental and applied biological sciences. Psychology Gait Gait - physiology Human Humans Imaging, Three-Dimensional - methods Lissajous contour Locomotion Locomotion signature Male Mathematical analysis Models, Statistical Models, Theoretical Movement Parametric equations Physical Medicine and Rehabilitation Three dimensional Tissues, organs and organisms biophysics Trajectories Vertebrates: body movement. Posture. Locomotion. Flight. Swimming. Physical exercise. Rest. Sports |
| title | The mathematical description of the body centre of mass 3D path in human and animal locomotion |
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