Biological oscillations for learning walking coordination: dynamic recurrent neural network functionally models physiological central pattern generator

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Abstract
The existence of dedicated neuronal modules such as those organized in the cerebral cortex, thalamus, basal ganglia, cerebellum, or spinal cord raises the question of how these functional modules are coordinated for appropriate motor behavior. Study of human locomotion offers an interesting field for addressing this central question. The coordination of the elevation of the 3 leg segments under a planar covariation rule (Borghese et al., 1996) was recently modeled (Barliya et al., 2009) by phase-adjusted simple oscillators shedding new light on the understanding of the central pattern generator (CPG) processing relevant oscillation signals. We describe the use of a dynamic recurrent neural network (DRNN) mimicking the natural oscillatory behavior of human locomotion for reproducing the planar covariation rule in both legs at different walking speeds. Neural network learning was based on sinusoid signals integrating frequency and amplitude features of the first three harmonics of the sagittal elevation angles of the thigh, shank, and foot of each lower limb. We verified the biological plausibility of the neural networks. Best results were obtained with oscillations extracted from the first three harmonics in comparison to oscillations outside the harmonic frequency peaks. Physiological replication steadily increased with the number of neuronal units from 1 to 80, where similarity index reached 0.99. Analysis of synaptic weighting showed that the proportion of inhibitory connections consistently increased with the number of neuronal units in the DRNN. This emerging property in the artificial neural networks resonates with recent advances in neurophysiology of inhibitory neurons that are involved in central nervous system oscillatory activities. The main message of this study is that this type of DRNN may offer a useful model of physiological central pattern generator for gaining insights in basic research and developing clinical applications.