Coordination patterns of oscillatory movements, such as in various forms of locomotion and various gaits, are currently well understood as arising from a constant relative phase. For example, the relative phase between movements of the hindlegs in a quadruped mammal, is half a cycle during walking and running, and slightly more than zero cycles during gallop. In the field of Coordination Dynamics, such patterns can be modeled by systems of coupled oscillators. During free (spontaneous) behavior, however, most movements are not strictly oscillatory, but rather quasi-periodic or discrete. Generalization of the relative phase for understanding coordination patterns of free movement is thus not straightforward.

In order to investigate this problem we analyzed free locomotor ("open field") behavior of ferrets, measured by video tracking 10 points of the body axis and feet at a rate of 2 5 Hz [1]. We suggest a framework in which the basic building block is oscillatory movement . Any other movement, such as a discrete movement, can be regarded as part of an oscillato ry movement, and its phase can thus be measured. We introduce a numeric algorithm for the measurement of phase in such movements. Coordination patterns between concurrent movements of several body segments can thus be captured by their relative phase, even when they are not oscillatory. For example, a slight phase delay in the movement of each successive segm ent will result in a traveling wave pattern, such as the traveling wave that was extensive ly studied in the undulation swimming of the lamprey. We used this framework to show that in the free locomotion of ferrets, lateral movements of the body axis during both forward locomotion and turning can be regarded as a traveling wave [1]. Turning is considered as a n asymmetric wave in which the movement of each segment is part of an "off center" oscilla tory movement. Reinterpretation of data from the literature indicates that turning in the lamprey also consists of the same asymmetric wave.

Modeling and recognition of the building blocks of spontaneous behavior is a difficult problem because such building blocks are in fact complex coordination patterns between man y degrees of freedom. The application of relative phase and traveling waves may promote ou r understanding of this problem, and integrate diverse disciplines such as Coordination Dy namics, neural mechanisms of locomotion and open field measurement of spontaneous and drug- induced behavior.

References

1. Kafkafi, N.; Golani, I. (1998). A traveling wave of lateral movement coordinates both turning and forward walking in the ferret. Biological Cybernetics, 78, 441-453.

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