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 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.
Copyright © 2011 Elsevier Ltd. All rights reserved.
Publication Date: 2011-04-03 PubMed ID: 21463861DOI: 10.1016/j.jbiomech.2011.03.014Google Scholar: Lookup The Equine Research Bank provides access to a large database of publicly available scientific literature. Inclusion in the Research Bank does not imply endorsement of study methods or findings by Mad Barn.
- Journal Article
- Research Support
- Non-U.S. Gov't
Summary
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This research introduces a mathematical system for analyzing the three-dimensional motion path of the center of mass in walking or running humans and animals. The proposed method helps to understand normal locomotion dynamics, can detect individual variations, and can evaluate the effectiveness of various interventions to correct gait abnormalities.
Background and Objectives
- While the three-dimensional (3D) trajectory, or path, of the body’s center of mass during walking or running constitutes the so-called “locomotor signature” for humans and other bipedal or quadrupedal species, there has previously been no established quantitative method to describe this phenomenon.
- This inability to effectively quantify and study these paths in a systematic manner has limited the understanding and analysis of normal and abnormal locomotion in both humans and animals.
- The goal of this study was to create a method that can capture both the spatial and dynamical aspects of the 3D trajectory of the body center of mass. With such a method, one could potentially gain deeper insights into the biomechanics of walking or running and be able to assess deviations from the norm due to various pathological conditions or their treatment.
Methods and Key Findings
- The researchers developed a method that integrates the mathematical discoveries of Jean Baptiste Joseph Fourier, who analyzed periodic events, and Jules Antoine Lissajous, who came up with a parametric equation for closed loops.
- This new model was then tested by analyzing the motion of walking and running humans, as well as the motion of trotting and galloping horses on a treadmill. From these analyses, closed loops for the body center of mass were generated that displayed both general and individual locomotor characteristics.
- The researchers evaluated several parameters for each gait, which included mechanical dynamics due to various energy exchanges, asymmetry along each 3D axis, and sagittal and lateral energy recovery, among others.
Conclusions and Implications
- The proposed mathematical description of the 3D trajectory of the body center of mass could be very useful for understanding the biomechanics and physiology of normal locomotion in humans and animals, ranging from monopods (one-legged organisms) to octopods (eight-legged organisms).
- Moreover, the model could also help in detecting and quantifying deviations from average motion paths due to gait pathologies. This would be particularly valuable in evaluating the effectiveness of interventions such as pharmacological, physiotherapeutic, or surgical treatments in restoring a normal locomotion pattern.
Cite This Article
APA
Minetti AE, Cisotti C, Mian OS.
(2011).
The mathematical description of the body centre of mass 3D path in human and animal locomotion.
J Biomech, 44(8), 1471-1477.
https://doi.org/10.1016/j.jbiomech.2011.03.014 Publication
Researcher Affiliations
- Department of Human Physiology, University of Milano, Via Mangiagalli 32, 20133 Milan, Italy. alberto.minetti@unimi.it
MeSH Terms
- Adult
- Animals
- Biomechanical Phenomena
- Computer Simulation
- Fourier Analysis
- Gait / physiology
- Humans
- Imaging, Three-Dimensional / methods
- Locomotion
- Male
- Models, Statistical
- Models, Theoretical
- Movement
Citations
This article has been cited 18 times.- Chang JT, Ragatz A, Ganesh A, Quiros Padilla AP, Devins MR, Mihova CV, Milton JG. Center of Mass (CoM) Motions and Foot Placement During Treadmill Walking Using One Time-of-Flight Camera. Sensors (Basel) 2025 Sep 19;25(18).
- Bergamini E, Cereatti A, Pavei G. Walking symmetry is speed and index dependent. Sci Rep 2024 Aug 22;14(1):19548.
- Takiyama K, Yokoyama H. Speed-dependent modulations of asymmetric center of body mass trajectory in the gait of above-knee amputee subjects. Front Sports Act Living 2023;5:1304141.
- Feletti F, Bracco C, Maria Molisso T, Bova L, Aliverti A. Analysis of Fluency of Movement in Parkour Using a Video and Inertial Measurement Unit Technology. J Hum Kinet 2023 Oct;89:5-18.
- Luciano F, Ruggiero L, Minetti A, Pavei G. Comparison of three-dimensional body centre of mass trajectories during locomotion through zero- and one-dimensional statistics. Sci Rep 2022 Oct 22;12(1):17777.
- Mobbs RJ, Natarajan P, Fonseka RD, Betteridge C, Ho D, Mobbs R, Sy L, Maharaj M. Walking orientation randomness metric (WORM) score: pilot study of a novel gait parameter to assess walking stability and discriminate fallers from non-fallers using wearable sensors. BMC Musculoskelet Disord 2022 Mar 29;23(1):304.
- Basel J, Simonetti E, Bergamini E, Pillet H. On the impact of the erroneous identification of inertial sensors' locations on segments and whole-body centers of mass accelerations: a sensitivity study in one transfemoral amputee. Med Biol Eng Comput 2021 Oct;59(10):2115-2126.
- Pequera G, Ramírez Paulino I, Biancardi CM. Common motor patterns of asymmetrical and symmetrical bipedal gaits. PeerJ 2021;9:e11970.
- Simonetti E, Bergamini E, Vannozzi G, Bascou J, Pillet H. Estimation of 3D Body Center of Mass Acceleration and Instantaneous Velocity from a Wearable Inertial Sensor Network in Transfemoral Amputee Gait: A Case Study. Sensors (Basel) 2021 Apr 30;21(9).
- Ochoa-Diaz C, Padilha L Bó A. Symmetry Analysis of Amputee Gait Based on Body Center of Mass Trajectory and Discrete Fourier Transform. Sensors (Basel) 2020 Apr 23;20(8).
- Tesio L, Rota V. The Motion of Body Center of Mass During Walking: A Review Oriented to Clinical Applications. Front Neurol 2019;10:999.
- Askew GN, McFarlane LA, Minetti AE, Buckley JG. Energy cost of ambulation in trans-tibial amputees using a dynamic-response foot with hydraulic versus rigid 'ankle': insights from body centre of mass dynamics. J Neuroeng Rehabil 2019 Mar 14;16(1):39.
- Pavei G, Seminati E, Cazzola D, Minetti AE. On the Estimation Accuracy of the 3D Body Center of Mass Trajectory during Human Locomotion: Inverse vs. Forward Dynamics. Front Physiol 2017;8:129.
- Sabatini AM, Mannini A. Ambulatory Assessment of Instantaneous Velocity during Walking Using Inertial Sensor Measurements. Sensors (Basel) 2016 Dec 21;16(12).
- Sabatini AM, Ligorio G, Mannini A. Fourier-based integration of quasi-periodic gait accelerations for drift-free displacement estimation using inertial sensors. Biomed Eng Online 2015 Nov 23;14:106.
- Tanabe S, Saitoh E, Ohtsuka K, Teranishi T, Tomita Y, Muraoka Y. Simple method to reduce the effect of patient positioning variation on three-dimensional motion analysis during treadmill gait. Clin Pract 2013 Aug 2;3(2):e30.
- Seminati E, Nardello F, Zamparo P, Ardigò LP, Faccioli N, Minetti AE. Anatomically asymmetrical runners move more asymmetrically at the same metabolic cost. PLoS One 2013;8(9):e74134.
- Ellis RG, Howard KC, Kram R. The metabolic and mechanical costs of step time asymmetry in walking. Proc Biol Sci 2013 Apr 7;280(1756):20122784.
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