Biomechanical and Sensory Feedback Regularize the Behavior of Different Locomotor Central Pattern Generators.

This work presents an in-depth numerical investigation into a hypothesized two-layer central pattern generator (CPG) that controls mammalian walking and how different parameter choices might affect the stepping of a simulated neuromechanical model. Particular attention is paid to the functional role of features that have not received a great deal of attention in previous work: the weak cross-excitatory connectivity within the rhythm generator and the synapse strength between the two layers. Sensitivity evaluations of deafferented CPG models and the combined neuromechanical model are performed. Locomotion frequency is increased in two different ways for both models to investigate whether the model's stability can be predicted by trends in the CPG's phase response curves (PRCs). Our results show that the weak cross-excitatory connection can make the CPG more sensitive to perturbations and that increasing the synaptic strength between the two layers results in a trade-off between forced phase locking and the amount of phase delay that can exist between the two layers. Additionally, although the models exhibit these differences in behavior when disconnected from the biomechanical model, these differences seem to disappear with the full neuromechanical model and result in similar behavior despite a variety of parameter combinations. This indicates that the neural variables do not have to be fixed precisely for stable walking; the biomechanical entrainment and sensory feedback may cancel out the strengths of excitatory connectivity in the neural circuit and play a critical role in shaping locomotor behavior. Our results support the importance of including biomechanical models in the development of computational neuroscience models that control mammalian locomotion.

Analyzing Modeled Torque Profiles to Understand Scale-Dependent Active Muscle Responses in the Hip Joint.

Animal locomotion is influenced by a combination of constituent joint torques (e.g., due to limb inertia and passive viscoelasticity), which determine the necessary muscular response to move the limb. Across animal size-scales, the relative contributions of these constituent joint torques affect the muscular response in different ways. We used a multi-muscle biomechanical model to analyze how passive torque components change due to an animal's size-scale during locomotion. By changing the size-scale of the model, we characterized emergent muscular responses at the hip as a result of the changing constituent torque profile. Specifically, we found that activation phases between extensor and flexor torques to be opposite between small and large sizes for the same kinematic motion. These results suggest general principles of how animal size affects neural control strategies. Our modeled torque profiles show a strong agreement with documented hindlimb torque during locomotion and can provide insights into the neural organization and muscle activation behavior of animals whose motion has not been extensively documented.

Extending the Functional Subnetwork Approach to a Generalized Linear Integrate-and-Fire Neuron Model.

Engineering neural networks to perform specific tasks often represents a monumental challenge in determining network architecture and parameter values. In this work, we extend our previously-developed method for tuning networks of non-spiking neurons, the "Functional subnetwork approach" (FSA), to the tuning of networks composed of spiking neurons. This extension enables the direct assembly and tuning of networks of spiking neurons and synapses based on the network's intended function, without the use of global optimization or machine learning. To extend the FSA, we show that the dynamics of a generalized linear integrate and fire (GLIF) neuron model have fundamental similarities to those of a non-spiking leaky integrator neuron model. We derive analytical expressions that show functional parallels between: (1) A spiking neuron's steady-state spiking frequency and a non-spiking neuron's steady-state voltage in response to an applied current; (2) a spiking neuron's transient spiking frequency and a non-spiking neuron's transient voltage in response to an applied current; and (3) a spiking synapse's average conductance during steady spiking and a non-spiking synapse's conductance. The models become more similar as additional spiking neurons are added to each population "node" in the network. We apply the FSA to model a neuromuscular reflex pathway two different ways: Via non-spiking components and then via spiking components. These results provide a concrete example of how a single non-spiking neuron may model the average spiking frequency of a population of spiking neurons. The resulting model also demonstrates that by using the FSA, models can be constructed that incorporate both spiking and non-spiking units. This work facilitates the construction of large networks of spiking neurons and synapses that perform specific functions, for example, those implemented with neuromorphic computing hardware, by providing an analytical method for directly tuning their parameters without time-consuming optimization or learning.

Neuromechanical Model of Rat Hindlimb Walking with Two-Layer CPGs.

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.

A Functional Subnetwork Approach to Designing Synthetic Nervous Systems That Control Legged Robot Locomotion.

A dynamical model of an animal's nervous system, or synthetic nervous system (SNS), is a potentially transformational control method. Due to increasingly detailed data on the connectivity and dynamics of both mammalian and insect nervous systems, controlling a legged robot with an SNS is largely a problem of parameter tuning. Our approach to this problem is to design functional subnetworks that perform specific operations, and then assemble them into larger models of the nervous system. In this paper, we present networks that perform addition, subtraction, multiplication, division, differentiation, and integration of incoming signals. Parameters are set within each subnetwork to produce the desired output by utilizing the operating range of neural activity, R, the gain of the operation, k, and bounds based on biological values. The assembly of large networks from functional subnetworks underpins our recent results with MantisBot.

Reactive stepping with functional neuromuscular stimulation in response to forward-directed perturbations.

BACKGROUND: Implanted motor system neuroprostheses can be effective at increasing personal mobility of persons paralyzed by spinal cord injuries. However, currently available neural stimulation systems for standing employ patterns of constant activation and are unreactive to changing postural demands. METHODS: In this work, we developed a closed-loop controller for detecting forward-directed body disturbances and initiating a stabilizing step in a person with spinal cord injury. Forward-directed pulls at the waist were detected with three body-mounted triaxial accelerometers. A finite state machine was designed and tested to trigger a postural response and apply stimulation to appropriate muscles so as to produce a protective step when the simplified jerk signal exceeded predetermined thresholds. RESULTS: The controller effectively initiated steps for all perturbations with magnitude between 10 and 17.5 s body weight, and initiated a postural response with occasional steps at 5% body weight. For perturbations at 15 and 17.5% body weight, the dynamic responses of the subject exhibited very similar component time periods when compared with able-bodied subjects undergoing similar postural perturbations. Additionally, the reactive step occurred faster for stronger perturbations than for weaker ones (p < .005, unequal varience t-test.) CONCLUSIONS: This research marks progress towards a controller which can improve the safety and independence of persons with spinal cord injury using implanted neuroprostheses for standing.

Design process and tools for dynamic neuromechanical models and robot controllers.

We present a serial design process with associated tools to select parameter values for a posture and locomotion controller for simulation of a robot. The controller is constructed from dynamic neuron and synapse models and simulated with the open-source neuromechanical simulator AnimatLab 2. Each joint has a central pattern generator (CPG), whose neurons possess persistent sodium channels. The CPG rhythmically inhibits motor neurons that control the servomotor's velocity. Sensory information coordinates the joints in the leg into a cohesive stepping motion. The parameter value design process is intended to run on a desktop computer, and has three steps. First, our tool FEEDBACKDESIGN uses classical control methods to find neural and synaptic parameter values that stably and robustly control servomotor output. This method is fast, testing over 100 parameter value variations per minute. Next, our tool CPGDESIGN generates bifurcation diagrams and phase response curves for the CPG model. This reveals neural and synaptic parameter values that produce robust oscillation cycles, whose phase can be rapidly entrained to sensory feedback. It also designs the synaptic conductance of inter-joint pathways. Finally, to understand sensitivity to parameters and how descending commands affect a leg's stepping motion, our tool SIMSCAN runs batches of neuromechanical simulations with specified parameter values, which is useful for searching the parameter space of a complicated simulation. These design tools are demonstrated on a simulation of a robot, but may be applied to neuromechanical animal models or physical robots as well.