An analytical formulation of the law of intersegmental coordination during human locomotion

Abstract

The law of intersegmental coordination is a kinematic law that describes the coordination patterns among the elevation angles of the lower limb segments during locomotion (Borghese et al. in J Physiol 494:863-879, 1996). This coordination pattern reduces the number of degrees of freedom of the lower limb to two, i.e. the elevation angles covary along a plane in angular space. The properties of the plane that constrains the time course of the elevation angles have been extensively studied, and its orientation was found to be correlated with gait velocity and energy expenditure (Bianchi et al. in J Neurophysiol 79:2155-2170, 1998). Here, we present a mathematical model that represents the rotations of the elevation angles in terms of simple oscillators with appropriate phase shifts between them. The model explains what requirements the time courses of the elevation angles must fulfill in order for the angular covariation relationship to be planar. Moreover, an analytical formulation is proposed for both the orientation of the plane and for the eccentricity of the nearly elliptical shape that is generated within this plane, in terms of the amplitudes and relative phases of the first harmonics of the segments elevation angles. The model presented here sheds some new light on the possible interactions among the Central Pattern Generators possibly underlying the control of biped locomotion. The model precisely specifies how any two segments in the limb interact, and how a change in gait velocity affects the orientation of the intersegmental coordination plane mainly through a change in phase shifts between the segments. Implications of this study with respect to neural control of locomotion and other motor activities are discussed.