Neuromechanical Model of Rat Hindlimb Walking with Two-Layer CPGs

Abstract

This work demonstrates a neuromechanical model of rat hindlimb locomotion undergoing nominal walking with perturbations. In the animal, two types of responses to perturbations are observed: resetting and non-resetting deletions. This suggests that the animal locomotor system contains a memory-like organization. To model this phenomenon, we built a synthetic nervous system that uses separate rhythm generator and pattern formation layers to activate antagonistic muscle pairs about each joint in the sagittal plane. Our model replicates the resetting and non-resetting deletions observed in the animal. In addition, in the intact (i.e., fully afferented) rat walking simulation, we observe slower recovery after perturbation, which is different from the deafferented animal experiment. These results demonstrate that our model is a biologically feasible description of some of the neural circuits in the mammalian spinal cord that control locomotion, and the difference between our simulation and fictive motion shows the importance of sensory feedback on motor output. This model also demonstrates how the pattern formation network can activate muscle synergies in a coordinated way to produce stable walking, which motivates the use of more complex synergies activating more muscles in the legs for three-dimensional limb motion.

Keywords: muscle synergies; pattern formation; rat; rhythm generator; synthetic nervous system.

Figure A1

Limb joint motion during a non-resetting experiment. The stimulus is applied to the left hip pattern formation extensor neuron from 2 to 2.5 s with a current of −10 nA.

Figure 1

(A) Single limb joint control network. (B) Neuron activities of half-center neurons and motoneurons without feedback. Excitatory stimulus with a current of 2 nA applied to an extensor half-center neuron from 2 to 2.1 s (blue area). EXT: Extensor; FLX: Flexor; HC: Half-center neuron; IN: Interneuron; MN: Motoneuron; RE: Renshaw cell.

Figure 2

(A) Hypothetical synthetic nervous system for a single limb. (B) Limb joint control network that forms active pattern of motoneurons. Coordinating pathways are inhibitory (filled circles) or excitatory (filled triangles). Pathways inspired by biological research are indicated by colored synapses of magenta, blue, and brown [26]. Hypothesized pathways are in black. MLR: Midbrain locomotor region.

Figure 3

Biomechanical model of a rat hindlimb. Motion is constrained in the sagittal plane with hinge joints. The two bars on the ground support the body.

Figure 4

Synthetic nervous system. (A) Single limb control hierarchy. (B) Rhythm generator configuration. (C) Pattern formation network. (D) Sensory-motor network. AD: Adaptor; EXT: Extensor; FLX: Flexor; IN: Interneuron; PF: Pattern formation; RE: Renshaw cell; RG: Rhythm generation.

Figure 5

Rhythm generator performance under different conditions. Excitatory stimulus applied from 1.5 to 2.5 s (orange area) with a current of 2 nA. Inhibitory stimulus applied from 3.5 to 4.5 s (blue area) with a current of −2 nA. Both stimuli applied to extensor and flexor rhythm generator neurons simulate descending signals from the midbrain locomotor region. The simulation startup transient, corresponding to the first 0.5 s is not shown. EXT: Extensor; FLX: Flexor; MN: Motoneuron; PF: Pattern formation; RG: Rhythm generation.

Figure 6

“Memory” function of a two-layer CPG. The first stimulus applied to extensor pattern formation neuron from 1 to 1.1 s (blue area) with a current of 2 nA and duration of 0.1 s is shorter than one swing–stance period. The second stimulus is applied from 2.5 to 3.5 s (orange area) with a current of 2 nA and duration of 1 s is longer than one swing–stance period. The simulation startup transients are not shown for the first 0.5 s. MN: Motoneuron; PF: Pattern formation; RG: Rhythm generation.

Figure 7

(Left) Workspace and Siemens Neurostar X-ray fluoroscope. (Right) Recording of a rat walking on the treadmill.

Figure 8

Limb joint motion during a non-resetting experiment. The stimulus is applied to the left hip pattern formation extensor neuron from 2 to 2.1 s with a current of −10 nA.

Figure 9

Neuron activities during non-resetting experiment. Inhibitory stimuli applied to the left hip pattern formation extensor neuron from 2 s to 2.1 s with a current of −10 nA. MN: Motoneuron; PF: Pattern formation; RG: Rhythm generation.

Figure 10

Limb joint motion for a resetting experiment. The stimulus is applied to the left hip rhythm generator extensor neuron from 2 to 2.1 s with a current of −10 nA.

Figure 11

Images from X-ray video recordings of rat walking on a treadmill. Red marks are applied on the mid spine and all joints of a rat left hindlimb in order to track joint motion.

Figure 12

Rat left hindlimb schematic and joint motion. The ankle and the knee motion rhythms are similar, but the timing and the magnitude are different.

Figure 13

Comparison of animal joint motion profiles with simulation results. Animal data (solid lines); simulation results from this present work with the knee–ankle synergy (dashed lines); simulation results from our previous model [8] (dotted lines) with separate hip, knee and ankle pattern formation circuits.