Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

Abstract

The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model, proposed conceptually by T.G. Brown in 1911, is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. A system of ordinary differential equations with a physiologically-inspired coupling locus of interactions captures the timing relationship for bilateral coordination of limbs in locomotion and is typically solved numerically. Consequently, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The computational load of the analytical solution was decreased by an order of magnitude when compared to the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling asymmetric locomotion and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results support the idea that many different combinations of network states, even within the same anatomical CPG structure, may generate the same behavioral outcomes.\n\nAuthor SummaryUsing a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds, which represent high-level modality within the motor system. Furthermore, we tested the ability of this simple structure to embed steering control using the velocity signal in the models inputs or within the internal connectivity of its elements. Both mechanisms can produce the same behavioral outcome, pointing to the methodological challenges of modeling central pattern generators and demonstrating the possibility of spinal circuit adaptations to asymmetric short- or long-term conditions in health and disease.