Biological Central Pattern Generators Research Articles

A new biological central pattern generator model and its relationship with the motor units.

The central pattern generator (CPG) is a key neural-circuit component of the locomotion control system. Recently, numerous molecular and genetic approaches have been proposed for investigating the CPG mechanisms. The rhythm in the CPG locomotor circuits comes from the activity in the ipsilateral excitatory neurons whose output is controlled by inter-neuron inhibitory connections. Conventional models for simulating the CPG mechanism are complex Hodgkin-Huxley-type models. Inspired by biological investigations and the continuous-time Matsuoka model, we propose new integral-order and fractional-order CPG models, which consider time delays and synaptic interfaces. The phase diagrams exhibit limit cycles and periodic solutions, in agreement with the CPG biological characteristics. As well, the fractional-order model shows state transitions with order variations. In addition, we investigate the relationship between the CPG and the motor units through the construction of integral-order and fractional-order coupling models. Simulations of these coupling models show that the states generated by the three motor units are in accordance with the experimentally-obtained states in previous studies. The proposed models reveal that the CPG can regulate limb locomotion patterns through connection weights and synaptic interfaces. Moreover, in comparison to the integral-order models, the fractional-order ones appear to be more effective, and hence more suitable for describing the dynamics of the CPG biological system.

Electronics-free pneumatic circuits for controlling soft-legged robots.

Pneumatically actuated soft robots have recently shown promise for their ability to adapt to their environment. Previously, these robots have been controlled with electromechanical components, such as valves and pumps, that are typically bulky and expensive. Here, we present an approach for controlling the gaits of soft-legged robots using simple pneumatic circuits without any electronic components. This approach produces locomotive gaits using ring oscillators composed of soft valves that generate oscillating signals analogous to biological central pattern generator neural circuits, which are acted upon by pneumatic logic components in response to sensor inputs. Our robot requires only a constant source of pressurized air to power both control and actuation systems. We demonstrate this approach by designing pneumatic control circuits to generate walking gaits for a soft-legged quadruped with three degrees of freedom per leg and to switch between gaits to control the direction of locomotion. In experiments, we controlled a basic walking gait using only three pneumatic memory elements (valves). With two oscillator circuits (seven valves), we were able to improve locomotion speed by 270%. Furthermore, with a pneumatic memory element we designed to mimic a double-pole double-throw switch, we demonstrated a control circuit that allowed the robot to select between gaits for omnidirectional locomotion and to respond to sensor input. This work represents a step toward fully autonomous, electronics-free walking robots for applications including low-cost robotics for entertainment and systems for operation in environments where electronics may not be suitable.

Computational exposition of multistable rhythms in 4-cell neural circuits

The co-existence of multistable rhythms generated by oscillatory neural circuits made up of 4 and more cells, their onset, stability conditions, and the transitions between such rhythms are not well understood. This is partly due to the lack of appropriate visual and computational tools. In this study, we employ modern computational approaches including unsupervised machine learning (clustering) algorithms and fast parallel simulations powered by graphics processing units (GPUs) to further extend our previously developed techniques based on the theory of dynamical systems and bifurcations. This allows us to analyze the fundamental principles and mechanisms that ensure the robustness and multifunctionality of such neural circuits. In addition, we examine how network topology affects the dynamics, and the rhythmic patterns transition/bifurcate as network configurations are altered and the intrinsic properties of the cells and the synapses are varied. This study elaborates on a set of inhibitory coupled 4-cell circuits that can exhibit a variety of mono- and multistable rhythms including pacemakers, paired half-centers, traveling-waves, synchronized states, as well as various chimeras. Our detailed analysis is helpful to generate verifiable hypotheses for neurophysiological experiments with biological central pattern generators.

Engineering reaction-diffusion networks with properties of neural tissue.

We present an experimental system of networks of coupled non-linear chemical reactors, which we theoretically model within a reaction-diffusion framework. The networks consist of patterned arrays of diffusively coupled nanoliter-scale reactors containing the Belousov-Zhabotinsky (BZ) reaction. Microfluidic fabrication techniques are developed that provide the ability to vary the network topology and the reactor coupling strength and offer the freedom to choose whether an arbitrary reactor is inhibitory or excitatory coupled to its neighbor. This versatile experimental and theoretical framework can be used to create a wide variety of chemical networks. Here we design, construct and characterize chemical networks that achieve the complexity of central pattern generators (CPGs), which are found in the autonomic nervous system of a variety of organisms.

Prescription of rhythmic patterns for legged locomotion

As the engine behind many life phenomena, motor information generated by the central nervous system plays a critical role in the activities of all animals. In this work, a novel, macroscopic and model-independent approach is presented for creating different patterns of coupled neural oscillations observed in biological central pattern generators (CPG) during the control of legged locomotion. Based on a simple distributed state machine, which consists of two nodes sharing pre-defined number of resources, the concept of oscillatory building blocks (OBBs) is summarised for the production of elaborated rhythmic patterns. Various types of OBBs can be designed to construct a motion joint of one degree of freedom with adjustable oscillatory frequencies and duty cycles. An OBB network can thus be potentially built to generate a full range of locomotion patterns of a legged animal with controlled transitions between different rhythmic patterns. It is shown that gait pattern transition can be achieved by simply changing a single parameter of an OBB module. Essentially, this simple mechanism allows for the consolidation of a methodology for the construction of artificial CPG architectures behaving as an asymmetric Hopfield neural network. Moreover, the proposed CPG model introduced here is amenable to analogue and/or digital circuit integration.

Silicon central pattern generators for cardiac diseases.

Cardiac rhythm management devices provide therapies for both arrhythmias and resynchronisation but not heart failure, which affects millions of patients worldwide. This paper reviews recent advances in biophysics and mathematical engineering that provide a novel technological platform for addressing heart disease and enabling beat-to-beat adaptation of cardiac pacing in response to physiological feedback. The technology consists of silicon hardware central pattern generators (hCPGs) that may be trained to emulate accurately the dynamical response of biological central pattern generators (bCPGs). We discuss the limitations of present CPGs and appraise the advantages of analog over digital circuits for application in bioelectronic medicine. To test the system, we have focused on the cardio-respiratory oscillators in the medulla oblongata that modulate heart rate in phase with respiration to induce respiratory sinus arrhythmia (RSA). We describe here a novel, scalable hCPG comprising physiologically realistic (Hodgkin-Huxley type) neurones and synapses. Our hCPG comprises two neurones that antagonise each other to provide rhythmic motor drive to the vagus nerve to slow the heart. We show how recent advances in modelling allow the motor output to adapt to physiological feedback such as respiration. In rats, we report on the restoration of RSA using an hCPG that receives diaphragmatic electromyography input and use it to stimulate the vagus nerve at specific time points of the respiratory cycle to slow the heart rate. We have validated the adaptation of stimulation to alterations in respiratory rate. We demonstrate that the hCPG is tuneable in terms of the depth and timing of the RSA relative to respiratory phase. These pioneering studies will now permit an analysis of the physiological role of RSA as well as its any potential therapeutic use in cardiac disease.

Frequency modulation of large oscillatory neural networks

Dynamical systems which generate periodic signals are of interest as models of biological central pattern generators and in a number of robotic applications. A basic functionality that is required in both biological modelling and robotics is frequency modulation. This leads to the question of whether there are generic mechanisms to control the frequency of neural oscillators. Here we describe why this objective is of a different nature, and more difficult to achieve, than modulating other oscillation characteristics (like amplitude, offset, signal shape). We propose a generic way to solve this task which makes use of a simple linear controller. It rests on the insight that there is a bidirectional dependency between the frequency of an oscillation and geometric properties of the neural oscillator's phase portrait. By controlling the geometry of the neural state orbits, it is possible to control the frequency on the condition that the state space can be shaped such that it can be pushed easily to any frequency.

Phase-lag return mappings for a 3 cell multifunctional central pattern generator

We describe and expand on a novel computational approach to reduce detailed models of central pattern generation to equationless return mapping for the phase lags between the constituting bursting interneurons [1]. Such mappings are then studied geometrically as the model parameters, including coupling properties of inhibitory and excitatory synapses, or external inputs are varied. Bifurcations of the fixed points and invariant circles of the mappings corresponding to various types of rhythmic activity are examined. These changes uncover possible biophysical mechanisms for control and modulation of motor-pattern generation. Our analysis does not require knowledge of the equations that model the system, and so provides a powerful new approach to studying detailed models, applicable to a variety of biological phenomena beyond motor control. Motifs of three coupled cells are a common network configuration including models of biological central pattern generators. We demonstrate our technique on a motif of three reciprocally coupled, inhibitory and excitatory, cells that is able to produce multiple patterns of bursting rhythms. In particular, we examine the qualitative geometric structure of two-dimensional maps for phase lag between the cells. This reveals the organizing centers of emergent polyrhythmic patterns and their bifurcations, as the asymmetry of the synaptic coupling is varied. The presence of multistability and the types of attractors in the network are shown to be determined by the duty cycle of bursting, as well as coupling interactions. Figure 1 (A). We defined phase-lags for a 3 cell CPG model on a 2D torus. (B) A “flattened” phase-lag mapping showing convergence to 5 distinct attractors. Each stable fixed point represents a rhythmic output of the CPG

Feed forward and feedback control for over-ground locomotion in anaesthetized cats

The biological central pattern generator (CPG) integrates open and closed loop control to produce over-ground walking. The goal of this study was to develop a physiologically based algorithm capable of mimicking the biological system to control multiple joints in the lower extremities for producing over-ground walking. The algorithm used state-based models of the step cycle each of which produced different stimulation patterns. Two configurations were implemented to restore over-ground walking in five adult anaesthetized cats using intramuscular stimulation (IMS) of the main hip, knee and ankle flexor and extensor muscles in the hind limbs. An open loop controller relied only on intrinsic timing while a hybrid-CPG controller added sensory feedback from force plates (representing limb loading), and accelerometers and gyroscopes (representing limb position). Stimulation applied to hind limb muscles caused extension or flexion in the hips, knees and ankles. A total of 113 walking trials were obtained across all experiments. Of these, 74 were successful in which the cats traversed 75% of the 3.5 m over-ground walkway. In these trials, the average peak step length decreased from 24.9 ± 8.4 to 21.8 ± 7.5 (normalized units) and the median number of steps per trial increased from 7 (Q1 = 6, Q3 = 9) to 9 (8, 11) with the hybrid-CPG controller. Moreover, within these trials, the hybrid-CPG controller produced more successful steps (step length ≤ 20 cm; ground reaction force ≥ 12.5% body weight) than the open loop controller: 372 of 544 steps (68%) versus 65 of 134 steps (49%), respectively. This supports our previous preliminary findings, and affirms that physiologically based hybrid-CPG approaches produce more successful stepping than open loop controllers. The algorithm provides the foundation for a neural prosthetic controller and a framework to implement more detailed control of locomotion in the future.

Biologically inspired motion synthesis method of two-legged robot with compliant feet

SUMMARYThis work presents biologically inspired method of gait generation. It uses the reference to the periodic signals generated by biological central pattern generator. The coupled oscillators with correction functions are used to produce leg joint trajectories. The human gait is the reference pattern. The features of generated gait are compared to the human walk. The spring-loaded foot design is presented together with experimental results.

A Silicon Central Pattern Generator Controls Locomotion in Vivo

We present a neuromorphic silicon chip that emulates the activity of the biological spinal central pattern generator (CPG) and creates locomotor patterns to support walking. The chip implements ten integrate-and-fire silicon neurons and 190 programmable digital-to-analog converters that act as synapses. This architecture allows for each neuron to make synaptic connections to any of the other neurons as well as to any of eight external input signals and one tonic bias input. The chip's functionality is confirmed by a series of experiments in which it controls the motor output of a paralyzed animal in real-time and enables it to walk along a three-meter platform. The walking is controlled under closed-loop conditions with the aide of sensory feedback that is recorded from the animal's legs and fed into the silicon CPG. Although we and others have previously described biomimetic silicon locomotor control systems for robots, this is the first demonstration of a neuromorphic device that can replace some functions of the central nervous system in vivo.

Control of multistability in ring circuits of oscillators

The essential dynamics of some biological central pattern generators (CPGs) can be captured by a model consisting of N neurons connected in a ring. These circuits, like many oscillatory nonlinear circuits of sufficient complexity, are capable of multistability, that is, of generating different firing patterns distinguished by the phasic relationships between the firing in each circuit element (neuron). Moreover, a shift in firing pattern can be induced by a transient perturbation. A systematic approach, based on phase-response curve (PRC) theory, was used to determine the optimum timing for perturbations that induce a shift in the firing pattern. The first step was to visualize the solution space of the ring circuit, including the attractive basins for each stable firing pattern; this was possible using the relative phase of N-1 oscillators, with respect to an arbitrarily selected reference oscillator, as coordinate axes. The trajectories in this phase space were determined using an iterative mapping based only on the PRCs of the uncoupled component oscillators; this algorithm was called a circuit emulator. For an accurate mapping of the attractive basin of each pattern exhibited by the ring circuit, the emulator had to take into account the effect of a perturbation or input on the timing of two bursts following the onset of the perturbation, rather than just one. The visualization of the attractive basins for rings of two, three, and four oscillators enabled the accurate prediction of the amounts of phase resetting applied to up to N-1 oscillators within a cycle that would induce a transition from any pattern to any another pattern. Finally, the timing and synaptic characterization of an input called the switch signal was adjusted to produce the desired amount of phase resetting.

Intrinsic modulation of pulse-coupled integrate-and-fire neurons

Intrinsic neuromodulation is observed in sensory and neuromuscular circuits and in biological central pattern generators. We model a simple neuronal circuit with a system of two pulse-coupled integrate-and-fire neurons and explore the parameter regimes for periodic firing behavior. The inclusion of biologically realistic features shows that the speed and onset of neuronal response plays a crucial role in determining the firing phase for periodic rhythms. We explore the neurophysiological function of distributed delays arising from both the synaptic transmission process and dendritic structure as well as discrete delays associated with axonal communication delays. Bifurcation and stability diagrams are constructed with a mixture of simple analysis, numerical continuation and the Kuramoto phase-reduction technique. Moreover, we show that, for asynchronous behavior, the strength of electrical synapses can control the firing rate of the system.