The mathematical description of the body centre of mass 3D path in human and animal locomotion.

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.