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As neural networks have become increasingly prolific solutions to modern problems in science and engineering, there has been a congruent rise in the popularity of the numerical machine learning techniques used to design them. While numerical methods are highly generalizable, they also tend to produce unintuitive networks with inscrutable behavior. One solution to the problem of network interpretability is to use analytical design techniques, but these methods are relatively underdeveloped compared to their numerical alternatives. To increase the utilization of analytical techniques and eventually facilitate the symbiotic integration of both design strategies, it is necessary to improve the efficacy of analytical methods on fundamental function approximation tasks that can be used to perform more complex operations. Toward this end, this manuscript extends the design constraints of the addition and subtraction subnetworks of the functional subnetwork approach (FSA) to arbitrarily many inputs, and then derives new constraints for an alternative neural encoding/decoding scheme. This encoding/decoding scheme involves storing information in the activation ratio of a subnetwork’s neurons, rather than directly in their membrane voltages. We show that our new “relative” encoding/decoding scheme has both qualitative and quantitative advantages compared to the existing “absolute” encoding/decoding scheme, including helping to mitigate saturation and improving approximation accuracy. Our relative encoding scheme will be extended to other functional subnetworks in future work to assess its advantages on more complex operations. 

This paper presents a biologically inspired control system developed for maintaining balance in a simulated human atop an oscillating platform. This work advances our previous research by adapting a human balance controller to an inverted pendulum and controlled by linear-Hill muscle models. To expedite neuron/synapse parameter value selection, we employ a novel two-stage process that pairs a previously developed analytic method with particle swarm optimization. Using the parameter values found analytically as inputs for particle swarm optimization (PSO), we take advantage of the benefits of each method while avoiding their pitfalls. Our results show that PSO optimization allowed improved balance control from modest (<10%) changes to the synaptic parameters. The improved performance was accompanied by muscle coactivations, however, and further refinement is needed to better align overall behavior of the neural controller with biological systems. 

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. 

Abstract The domestic dog is interesting to investigate because of the wide range of body size, body mass, and physique in the many breeds. In the last several years, the number of clinical and biomechanical studies on dog locomotion has increased. However, the relationship between body structure and joint load during locomotion, as well as between joint load and degenerative diseases of the locomotor system (e.g. dysplasia), are not sufficiently understood. Collecting this data through in vivo measurements/records of joint forces and loads on deep/small muscles is complex, invasive, and sometimes unethical. The use of detailed musculoskeletal models may help fill the knowledge gap. We describe here the methods we used to create a detailed musculoskeletal model with 84 degrees of freedom and 134 muscles. Our model has three key-features: three-dimensionality, scalability, and modularity. We tested the validity of the model by identifying forelimb muscle synergies of a walking Beagle. We used inverse dynamics and static optimization to estimate muscle activations based on experimental data. We identified three muscle synergy groups by using hierarchical clustering. The activation patterns predicted from the model exhibit good agreement with experimental data for most of the forelimb muscles. We expect that our model will speed up the analysis of how body size, physique, agility, and disease influence neuronal control and joint loading in dog locomotion. 

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.