A multiconductance silicon neuron with biologically matched dynamics

Bursting Dynamics Based on the Persistent Na+ and Na+/K+ Pump Currents: A Dynamic Clamp Approach

Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).

Optimal solid state neurons

Bioelectronic medicine is driving the need for neuromorphic microcircuits that integrate raw nervous stimuli and respond identically to biological neurons. However, designing such circuits remains a challenge. Here we estimate the parameters of highly nonlinear conductance models and derive the ab initio equations of intracellular currents and membrane voltages embodied in analog solid-state electronics. By configuring individual ion channels of solid-state neurons with parameters estimated from large-scale assimilation of electrophysiological recordings, we successfully transfer the complete dynamics of hippocampal and respiratory neurons in silico. The solid-state neurons are found to respond nearly identically to biological neurons under stimulation by a wide range of current injection protocols. The optimization of nonlinear models demonstrates a powerful method for programming analog electronic circuits. This approach offers a route for repairing diseased biocircuits and emulating their function with biomedical implants that can adapt to biofeedback.

Hodgkin-Huxley Neuron and FPAA Dynamics

We present the experimental silicon results on the dynamics of a Hodgkin-Huxley neuron implemented on a reconfigurable platform. The circuit has been inspired by the similarity between biology and silicon, by modeling ion channels and their time constants. Another significant motivation behind this paper is to make the system available to circuit designers as well as users in the neuroscience community. The open-source tool infrastructure and a remote system ease the accessibility of our system to a number of users. We demonstrate the reproducibility of the results by replicating the dynamics across different boards along with responses from different inputs and with different parameters. The reconfigurability enables one to make use of a single primary design to obtain a variety of results. The measurements are taken from the system compiled on a field programmable analog array fabricated on a 350-nm process.

Optoelectronic system for brain neuronal network stimulation

We propose an optoelectronic system for stimulation of living neurons. The system consists of an electronic circuit based on the FitzHugh–Nagumo model, an optical fiber, and a photoelectrical converter. We used this system for electrical stimulation of hippocampal living neurons in acute hippocampal brain slices (350-μm thick) obtained from a 20–28 days old C57BL/6 mouse or a Wistar rat. The main advantage of our system over other similar stimulators is that it contains an optical fiber for signal transmission instead of metallic wires. The fiber is placed between the electronic circuit and stimulated neurons and provides galvanic isolation from external electrical and magnetic fields. The use of the optical fiber allows avoiding electromagnetic noise and current flows which could affect metallic wires. Furthermore, it gives us the possibility to simulate “synaptic plasticity” by adaptive signal transfer through optical fiber. The proposed optoelectronic system (hybrid neural circuit) provides a very high efficiency in stimulating hippocampus neurons and can be used for restoring brain activity in particular regions or replacing brain parts (neuroprosthetics) damaged due to a trauma or neurodegenerative diseases.

Neuromorphic neural interfaces: from neurophysiological inspiration to biohybrid coupling with nervous systems

OBJECTIVE

Computation in nervous systems operates with different computational primitives, and on different hardware, than traditional digital computation and is thus subjected to different constraints from its digital counterpart regarding the use of physical resources such as time, space and energy. In an effort to better understand neural computation on a physical medium with similar spatiotemporal and energetic constraints, the field of neuromorphic engineering aims to design and implement electronic systems that emulate in very large-scale integration (VLSI) hardware the organization and functions of neural systems at multiple levels of biological organization, from individual neurons up to large circuits and networks. Mixed analog/digital neuromorphic VLSI systems are compact, consume little power and operate in real time independently of the size and complexity of the model.

APPROACH

This article highlights the current efforts to interface neuromorphic systems with neural systems at multiple levels of biological organization, from the synaptic to the system level, and discusses the prospects for future biohybrid systems with neuromorphic circuits of greater complexity.

MAIN RESULTS

Single silicon neurons have been interfaced successfully with invertebrate and vertebrate neural networks. This approach allowed the investigation of neural properties that are inaccessible with traditional techniques while providing a realistic biological context not achievable with traditional numerical modeling methods. At the network level, populations of neurons are envisioned to communicate bidirectionally with neuromorphic processors of hundreds or thousands of silicon neurons. Recent work on brain-machine interfaces suggests that this is feasible with current neuromorphic technology.

SIGNIFICANCE

Biohybrid interfaces between biological neurons and VLSI neuromorphic systems of varying complexity have started to emerge in the literature. Primarily intended as a computational tool for investigating fundamental questions related to neural dynamics, the sophistication of current neuromorphic systems now allows direct interfaces with large neuronal networks and circuits, resulting in potentially interesting clinical applications for neuroengineering systems, neuroprosthetics and neurorehabilitation.

Microfluidic Neurons, a New Way in Neuromorphic Engineering?

This article describes a new way to explore neuromorphic engineering, the biomimetic artificial neuron using microfluidic techniques. This new device could replace silicon neurons and solve the issues of biocompatibility and power consumption. The biological neuron transmits electrical signals based on ion flow through their plasma membrane. Action potentials are propagated along axons and represent the fundamental electrical signals by which information are transmitted from one place to another in the nervous system. Based on this physiological behavior, we propose a microfluidic structure composed of chambers representing the intra and extracellular environments, connected by channels actuated by Quake valves. These channels are equipped with selective ion permeable membranes to mimic the exchange of chemical species found in the biological neuron. A thick polydimethylsiloxane (PDMS) membrane is used to create the Quake valve membrane. Integrated electrodes are used to measure the potential difference between the intracellular and extracellular environments: the membrane potential.

Artificial Electrical Morris-Lecar Neuron

In this paper, an experimental electronic neuron based on a complete Morris-Lecar model is presented, which is able to become an experimental unit tool to study collective association of coupled neurons. The circuit design is given according to the ionic currents of this model. The experimental results are compared with the theoretical prediction, leading to a good agreement between them, which therefore validate the circuit. The use of some parts of the circuit is also possible for other neurons models, namely for those based on ionic currents.

A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators.

Real-time biomimetic Central Pattern Generators in an FPGA for hybrid experiments

This investigation of the leech heartbeat neural network system led to the development of a low resources, real-time, biomimetic digital hardware for use in hybrid experiments. The leech heartbeat neural network is one of the simplest central pattern generators (CPG). In biology, CPG provide the rhythmic bursts of spikes that form the basis for all muscle contraction orders (heartbeat) and locomotion (walking, running, etc.). The leech neural network system was previously investigated and this CPG formalized in the Hodgkin–Huxley neural model (HH), the most complex devised to date. However, the resources required for a neural model are proportional to its complexity. In response to this issue, this article describes a biomimetic implementation of a network of 240 CPGs in an FPGA (Field Programmable Gate Array), using a simple model (Izhikevich) and proposes a new synapse model: activity-dependent depression synapse. The network implementation architecture operates on a single computation core. This digital system works in real-time, requires few resources, and has the same bursting activity behavior as the complex model. The implementation of this CPG was initially validated by comparing it with a simulation of the complex model. Its activity was then matched with pharmacological data from the rat spinal cord activity. This digital system opens the way for future hybrid experiments and represents an important step toward hybridization of biological tissue and artificial neural networks. This CPG network is also likely to be useful for mimicking the locomotion activity of various animals and developing hybrid experiments for neuroprosthesis development.

Electrical Morris-Lecar neuron

In this study, an experimental electronic neuron based on Morris-Lecar model is presented, able to become an experimental unit tool to study collective association of robust coupled neurons. The circuit design is given according to the ionic currents of this model. The experimental results are compared to the theoretical prediction, leading to validate this circuit.

Dynamical system design for silicon neurons using phase reduction approach

In the present paper, we apply a computer-aided phase reduction approach to dynamical system design for silicon neurons (SiNs). Firstly, we briefly review the dynamical system design for SiNs. Secondly, we summarize the phase response properties of circuit models of previous SiNs to clarify design criteria in our approach. From a viewpoint of the phase reduction theory, as a case study, we show how to tune circuit parameters of the resonate-and-fire neuron (RFN) circuit as a hybrid type SiN. Finally, we demonstrate delay-induced synchronization in a silicon spiking neural network that consists of the RFN circuits.

Active processing of spatio-temporal input patterns in silicon dendrites

Capturing the functionality of active dendritic processing into abstract mathematical models will help us to understand the role of complex biophysical neurons in neuronal computation and to build future useful neuromorphic analog Very Large Scale Integrated (aVLSI) neuronal devices. Previous work based on an aVLSI multi-compartmental neuron model demonstrates that the compartmental response in the presence of either of two widely studied classes of active mechanisms, is a nonlinear sigmoidal function of the degree of either input temporal synchrony OR input clustering level. Using the same silicon model, this work expounds the interaction between both active mechanisms in a compartment receiving input patterns of varying temporal AND spatial clustering structure and demonstrates that this compartmental response can be captured by a combined sigmoid and radial-basis function over both input dimensions. This paper further shows that the response to input spatio-temporal patterns in a one-dimensional multi-compartmental dendrite, can be described by a radial-basis like function of the degree of temporal synchrony between the inter-compartmental inputs.

A bionics chemical synapse

Implementation of the current mode CMOS circuit for chemical synapses (AMPA and NMDA receptors) with dynamic change of glutamate as the neurotransmitter input is presented in this paper. Additionally, circuit realisation for receptor GABA(A) and GABA(B) with an electrical signal which symbolises γ-Aminobutyric Acid (GABA) perturbation is introduced. The chemical sensor for glutamate sensing is the modified ISFET with enzyme (glutamate oxidase) immobilisation. The measured results from these biomimetics chemical synapse circuits closely match with the simulation result from the mathematical model. The total power consumption of the whole chip (four chemical synapse circuits and all auxiliary circuits) is 168.3 μW. The total chip area is 3 mm(2) in 0.35-μm AMS CMOS technology.

A neuromorphic VLSI design for spike timing and rate based synaptic plasticity

Triplet-based Spike Timing Dependent Plasticity (TSTDP) is a powerful synaptic plasticity rule that acts beyond conventional pair-based STDP (PSTDP). Here, the TSTDP is capable of reproducing the outcomes from a variety of biological experiments, while the PSTDP rule fails to reproduce them. Additionally, it has been shown that the behaviour inherent to the spike rate-based Bienenstock-Cooper-Munro (BCM) synaptic plasticity rule can also emerge from the TSTDP rule. This paper proposes an analogue implementation of the TSTDP rule. The proposed VLSI circuit has been designed using the AMS 0.35 μm CMOS process and has been simulated using design kits for Synopsys and Cadence tools. Simulation results demonstrate how well the proposed circuit can alter synaptic weights according to the timing difference amongst a set of different patterns of spikes. Furthermore, the circuit is shown to give rise to a BCM-like learning rule, which is a rate-based rule. To mimic an implementation environment, a 1000 run Monte Carlo (MC) analysis was conducted on the proposed circuit. The presented MC simulation analysis and the simulation result from fine-tuned circuits show that it is possible to mitigate the effect of process variations in the proof of concept circuit; however, a practical variation aware design technique is required to promise a high circuit performance in a large scale neural network. We believe that the proposed design can play a significant role in future VLSI implementations of both spike timing and rate based neuromorphic learning systems.

Improving noise resistance of intrinsic rhythms in a square-wave burster model

The square-wave burster (Wang and Rinzel, 2003) is a class of autonomous bursting cells that share a bifurcation structure. It is known that this class of cells is involved in the generation of various life-supporting rhythms. In our research to realize an electronic circuit that mimics the rhythm generating mechanism in the square-wave burster, our circuit experimentally exhibited severe fluctuations in its rhythmic activity. We have found a noise-sensitive region in the phase portrait of the ideal model and have proposed modifications of the model that can reduce this fluctuation. A possible modification to ionic-conductance neuron models (Kohno and Aihara, 2011) was inspired by them. This modification, however, cannot be applied to a group of square-wave bursters, including the Butera-Rinzel-Smith model (Butera et al., 1999; Del Negro et al., 2001), which is a model of the pre-Bötzinger complex bursting neuron that plays a crucial role in the generation of respiration rhythms, because this modification premises that the slow dynamics originates from an activation gate variable of a hyperpolarizing ionic current. However, in some square-wave bursters, they are controlled by an inactivation gate variable of a depolarizing ionic current. In this study, we proposed a similar modification with a completely different mechanism that can be applied to this group of square-wave bursters. In the presence of noises, the modified Butera-Rinzel-Smith model can generate rhythmic activity that is more stable and similar to biological observations than the original model. The mechanisms underlying this modification are explained with noisy bifurcation diagrams.

An FPGA-Based Silicon Neuronal Network with Selectable Excitability Silicon Neurons

This paper presents a digital silicon neuronal network which simulates the nerve system in creatures and has the ability to execute intelligent tasks, such as associative memory. Two essential elements, the mathematical-structure-based digital spiking silicon neuron (DSSN) and the transmitter release based silicon synapse, allow us to tune the excitability of silicon neurons and are computationally efficient for hardware implementation. We adopt mixed pipeline and parallel structure and shift operations to design a sufficient large and complex network without excessive hardware resource cost. The network with 256 full-connected neurons is built on a Digilent Atlys board equipped with a Xilinx Spartan-6 LX45 FPGA. Besides, a memory control block and USB control block are designed to accomplish the task of data communication between the network and the host PC. This paper also describes the mechanism of associative memory performed in the silicon neuronal network. The network is capable of retrieving stored patterns if the inputs contain enough information of them. The retrieving probability increases with the similarity between the input and the stored pattern increasing. Synchronization of neurons is observed when the successful stored pattern retrieval occurs.

Tunable neuromimetic integrated system for emulating cortical neuron models

Nowadays, many software solutions are currently available for simulating neuron models. Less conventional than software-based systems, hardware-based solutions generally combine digital and analog forms of computation. In previous work, we designed several neuromimetic chips, including the Galway chip that we used for this paper. These silicon neurons are based on the Hodgkin–Huxley formalism and they are optimized for reproducing a large variety of neuron behaviors thanks to tunable parameters. Due to process variation and device mismatch in analog chips, we use a full-custom fitting method in voltage-clamp mode to tune our neuromimetic integrated circuits. By comparing them with experimental electrophysiological data of these cells, we show that the circuits can reproduce the main firing features of cortical cell types. In this paper, we present the experimental measurements of our system which mimic the four most prominent biological cells: fast spiking, regular spiking, intrinsically bursting, and low-threshold spiking neurons into analog neuromimetic integrated circuit dedicated to cortical neuron simulations. This hardware and software platform will allow to improve the hybrid technique, also called “dynamic-clamp,” that consists of connecting artificial and biological neurons to study the function of neuronal circuits.

Biophysical Neural Spiking, Bursting, and Excitability Dynamics in Reconfigurable Analog VLSI

We study a range of neural dynamics under variations in biophysical parameters underlying extended Morris-Lecar and Hodgkin-Huxley models in three gating variables. The extended models are implemented in NeuroDyn, a four neuron, twelve synapse continuous-time analog VLSI programmable neural emulation platform with generalized channel kinetics and biophysical membrane dynamics. The dynamics exhibit a wide range of time scales extending beyond 100 ms neglected in typical silicon models of tonic spiking neurons. Circuit simulations and measurements show transition from tonic spiking to tonic bursting dynamics through variation of a single conductance parameter governing calcium recovery. We similarly demonstrate transition from graded to all-or-none neural excitability in the onset of spiking dynamics through the variation of channel kinetic parameters governing the speed of potassium activation. Other combinations of variations in conductance and channel kinetic parameters give rise to phasic spiking and spike frequency adaptation dynamics. The NeuroDyn chip consumes 1.29 mW and occupies 3 mm × 3 mm in 0.5 μm CMOS, supporting emerging developments in neuromorphic silicon-neuron interfaces.

A Systematic Method for Configuring VLSI Networks of Spiking Neurons

An increasing number of research groups are developing custom hybrid analog/digital very large scale integration (VLSI) chips and systems that implement hundreds to thousands of spiking neurons with biophysically realistic dynamics, with the intention of emulating brainlike real-world behavior in hardware and robotic systems rather than simply simulating their performance on general-purpose digital computers. Although the electronic engineering aspects of these emulation systems is proceeding well, progress toward the actual emulation of brainlike tasks is restricted by the lack of suitable high-level configuration methods of the kind that have already been developed over many decades for simulations on general-purpose computers. The key difficulty is that the dynamics of the CMOS electronic analogs are determined by transistor biases that do not map simply to the parameter types and values used in typical abstract mathematical models of neurons and their networks. Here we provide a general method for resolving this difficulty. We describe a parameter mapping technique that permits an automatic configuration of VLSI neural networks so that their electronic emulation conforms to a higher-level neuronal simulation. We show that the neurons configured by our method exhibit spike timing statistics and temporal dynamics that are the same as those observed in the software simulated neurons and, in particular, that the key parameters of recurrent VLSI neural networks (e.g., implementing soft winner-take-all) can be precisely tuned. The proposed method permits a seamless integration between software simulations with hardware emulations and intertranslatability between the parameters of abstract neuronal models and their emulation counterparts. Most important, our method offers a route toward a high-level task configuration language for neuromorphic VLSI systems.

A library of analog operators based on the hodgkin-huxley formalism for the design of tunable, real-time, silicon neurons

In this paper, we present a library of analog operators used for the analog real-time computation of the Hodgkin-Huxley formalism. These operators make it possible to design a silicon (Si) neuron that is dynamically tunable, and that reproduces different kinds of neurons. We used an original method in neuromorphic engineering to characterize this Si neuron. In electrophysiology, this method is well known as the "voltage-clamp" technique. We also compare the features of an application-specific integrated circuit built with this library with results obtained from software simulations. We then present the complex behavior of neural membrane voltages and the potential applications of this Si neuron.

Silicon-Neuron Design: A Dynamical Systems Approach

We present an approach to design spiking silicon neurons based on dynamical systems theory. Dynamical systems theory aids in choosing the appropriate level of abstraction, prescribing a neuron model with the desired dynamics while maintaining simplicity. Further, we provide a procedure to transform the prescribed equations into subthreshold current-mode circuits. We present a circuit design example, a positive-feedback integrate-and-fire neuron, fabricated in 0.25 μm CMOS. We analyze and characterize the circuit, and demonstrate that it can be configured to exhibit desired behaviors, including spike-frequency adaptation and two forms of bursting.

Dynamics and bifurcations in a silicon neuron

In this paper, the nonlinear dynamical phenomenon associated with a silicon neuron are described. The neuron has one transient sodium (activating and inactivating) channel and one activating potassium channel. These channels do not model specific equations; instead they directly mimic the desired voltage clamp responses. This allows us to create silicon structures that are very compact (six transistors and three capacitors) with activation and inactivation parameters being tuned by floating-gate (FG) transistors. Analysis of the bifurcation conditions allow us to identify regimes in the parameter space that are desirable for biasing the circuit. We show a subcritical Hopf-bifurcation which is characteristic of class 2 excitability in Hodgkin-Huxley (H-H) neurons. We also show a Hopf bifurcation at higher values of stimulating current, a phenomenon also observed in real neurons and termed excitation block. The phenomenon of post-inhibitory rebound and frequency preference are displayed and intuitive explanations based on the circuit are provided. The compactness and low-power nature of the circuit shall allow us to integrate a large number of these neurons on a chip to study complicated network behavior.

Real-time simulation of biologically realistic stochastic neurons in VLSI

Neuronal variability has been thought to play an important role in the brain. As the variability mainly comes from the uncertainty in biophysical mechanisms, stochastic neuron models have been proposed for studying how neurons compute with noise. However, most papers are limited to simulating stochastic neurons in a digital computer. The speed and the efficiency are thus limited especially when a large neuronal network is of concern. This brief explores the feasibility of simulating the stochastic behavior of biological neurons in a very large scale integrated (VLSI) system, which implements a programmable and configurable Hodgkin-Huxley model. By simply injecting noise to the VLSI neuron, various stochastic behaviors observed in biological neurons are reproduced realistically in VLSI. The noise-induced variability is further shown to enhance the signal modulation of a neuron. These results point toward the development of analog VLSI systems for exploring the stochastic behaviors of biological neuronal networks in large scale.

Analog VLSI Biophysical Neurons and Synapses With Programmable Membrane Channel Kinetics

We present and characterize an analog VLSI network of 4 spiking neurons and 12 conductance-based synapses, implementing a silicon model of biophysical membrane dynamics and detailed channel kinetics in 384 digitally programmable parameters. Each neuron in the analog VLSI chip (NeuroDyn) implements generalized Hodgkin-Huxley neural dynamics in 3 channel variables, each with 16 parameters defining channel conductance, reversal potential, and voltage-dependence profile of the channel kinetics. Likewise, 12 synaptic channel variables implement a rate-based first-order kinetic model of neurotransmitter and receptor dynamics, accounting for NMDA and non-NMDA type chemical synapses. The biophysical origin of all 384 parameters in 24 channel variables supports direct interpretation of the results of adapting/tuning the parameters in terms of neurobiology. We present experimental results from the chip characterizing single neuron dynamics, single synapse dynamics, and multi-neuron network dynamics showing phase-locking behavior as a function of synaptic coupling strength. Uniform temporal scaling of the dynamics of membrane and gating variables is demonstrated by tuning a single current parameter, yielding variable speed output exceeding real time. The 0.5 CMOS chip measures 3 mm 3 mm, and consumes 1.29 mW.

An analog circuit implementation of a quadratic integrate and fire neuron

Silicon neurons are of importance both to implement hybrid electronic-biological system as well as to develop fundamental understanding of the neurobiological systems they emulate. We have implemented a hardware version of the quadratic integrate and fire neural model. The quadratic integrate and fire neuron differs from the more common integrate and fire neuron in that the model, and thus the hardware, intrinsically generate spikes. Readily available discrete surface mount components are used to make the hardware available to a wider audience and facilitate experimentation.

Biophysical synaptic dynamics in an analog VLSI network of Hodgkin-Huxley neurons

We study synaptic dynamics in a biophysical network of four coupled spiking neurons implemented in an analog VLSI silicon microchip. The four neurons implement a generalized Hodgkin-Huxley model with individually configurable rate-based kinetics of opening and closing of Na+ and K+ ion channels. The twelve synapses implement a rate-based first-order kinetic model of neurotransmitter and receptor dynamics, accounting for NMDA and non-NMDA type chemical synapses. The implemented models on the chip are fully configurable by 384 parameters accounting for conductances, reversal potentials, and pre/post-synaptic voltage-dependence of the channel kinetics. We describe the models and present experimental results from the chip characterizing single neuron dynamics, single synapse dynamics, and multi-neuron network dynamics showing phase-locking behavior as a function of synaptic coupling strength. The 3mm x 3mm microchip consumes 1.29 mW power making it promising for applications including neuromorphic modeling and neural prostheses.

Nonlinear electronic circuit with neuron like bursting and spiking dynamics

It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin-Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast-slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.

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.

Transistor analogs of emergent iono-neuronal dynamics

Neuromorphic analog metal-oxide-silicon (MOS) transistor circuits promise compact, low-power, and high-speed emulations of iono-neuronal dynamics orders-of-magnitude faster than digital simulation. However, their inherently limited input voltage dynamic range vs power consumption and silicon die area tradeoffs makes them highly sensitive to transistor mismatch due to fabrication inaccuracy, device noise, and other nonidealities. This limitation precludes robust analog very-large-scale-integration (aVLSI) circuits implementation of emergent iono-neuronal dynamics computations beyond simple spiking with limited ion channel dynamics. Here we present versatile neuromorphic analog building-block circuits that afford near-maximum voltage dynamic range operating within the low-power MOS transistor weak-inversion regime which is ideal for aVLSI implementation or implantable biomimetic device applications. The fabricated microchip allowed robust realization of dynamic iono-neuronal computations such as coincidence detection of presynaptic spikes or pre- and postsynaptic activities. As a critical performance benchmark, the high-speed and highly interactive iono-neuronal simulation capability on-chip enabled our prompt discovery of a minimal model of chaotic pacemaker bursting, an emergent iono-neuronal behavior of fundamental biological significance which has hitherto defied experimental testing or computational exploration via conventional digital or analog simulations. These compact and power-efficient transistor analogs of emergent iono-neuronal dynamics open new avenues for next-generation neuromorphic, neuroprosthetic, and brain-machine interface applications.

Spinal cord injury: present and future therapeutic devices and prostheses

A range of passive and active devices are under development or are already in clinical use to partially restore function after spinal cord injury (SCI). Prosthetic devices to promote host tissue regeneration and plasticity and reconnection are under development, comprising bioengineered bridging materials free of cells. Alternatively, artificial electrical stimulation and robotic bridges may be used, which is our focus here. A range of neuroprostheses interfacing either with CNS or peripheral nervous system both above and below the lesion are under investigation and are at different stages of development or translation to the clinic. In addition, there are orthotic and robotic devices which are being developed and tested in the laboratory and clinic that can provide mechanical assistance, training or substitution after SCI. The range of different approaches used draw on many different aspects of our current but limited understanding of neural regeneration and plasticity, and spinal cord function and interactions with the cortex. The best therapeutic practice will ultimately likely depend on combinations of these approaches and technologies and on balancing the combined effects of these on the biological mechanisms and their interactions after injury. An increased understanding of plasticity of brain and spinal cord, and of the behavior of innate modular mechanisms in intact and injured systems, will likely assist in future developments. We review the range of device designs under development and in use, the basic understanding of spinal cord organization and plasticity, the problems and design issues in device interactions with the nervous system, and the possible benefits of active motor devices.

Neurotech for neuroscience: unifying concepts, organizing principles, and emerging tools

The ability to tackle analysis of the brain at multiple levels simultaneously is emerging from rapid methodological developments. The classical research strategies of "measure," "model," and "make" are being applied to the exploration of nervous system function. These include novel conceptual and theoretical approaches, creative use of mathematical modeling, and attempts to build brain-like devices and systems, as well as other developments including instrumentation and statistical modeling (not covered here). Increasingly, these efforts require teams of scientists from a variety of traditional scientific disciplines to work together. The potential of such efforts for understanding directed motor movement, emergence of cognitive function from neuronal activity, and development of neuromimetic computers are described by a team that includes individuals experienced in behavior and neuroscience, mathematics, and engineering. Funding agencies, including the National Science Foundation, explore the potential of these changing frontiers of research for developing research policies and long-term planning.

Versatile biologically inspired electronic neuron

We present a biologically inspired electronic neuron based on a conductance model. The channels are constructed using linearly voltage controlled field effect transistors. A two channel and a three channel circuit is developed. The dynamical behavior of this system is studied, showing for the two channel circuit either class-I or class-II excitability and for the three channel circuit bursting and spike frequency adaptation. Voltage-clamp-type measurements, similar to the ones frequently used in neuroscience, are employed in order to determine the conductance characteristics of the electronic channels. We develop an empirical model based on these measurements that reproduces the different dynamical behaviors of the electronic neuron. We found that post-inhibitory rebound is present in the two channel circuit. Reliability and precision of spike timing is induced in the three channel circuit by injecting noise in the control variable of the slow channel that provides a negative feedback. The circuit is appropriate for the design of large scale electronic neural devices that can be used in mixed electronic-biological systems.

Thermodynamically equivalent silicon models of voltage-dependent ion channels

We model ion channels in silicon by exploiting similarities between the thermodynamic principles that govern ion channels and those that govern transistors. Using just eight transistors, we replicate--for the first time in silicon--the sigmoidal voltage dependence of activation (or inactivation) and the bell-shaped voltage-dependence of its time constant. We derive equations describing the dynamics of our silicon analog and explore its flexibility by varying various parameters. In addition, we validate the design by implementing a channel with a single activation variable. The design's compactness allows tens of thousands of copies to be built on a single chip, facilitating the study of biologically realistic models of neural computation at the network level in silicon.

Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses

A mixed-signal very large scale integration (VLSI) chip for large scale emulation of spiking neural networks is presented. The chip contains 2400 silicon neurons with fully programmable and reconfigurable synaptic connectivity. Each neuron implements a discrete-time model of a single-compartment cell. The model allows for analog membrane dynamics and an arbitrary number of synaptic connections, each with tunable conductance and reversal potential. The array of silicon neurons functions as an address-event (AE) transceiver, with incoming and outgoing spikes communicated over an asynchronous event-driven digital bus. Address encoding and conflict resolution of spiking events are implemented via a randomized arbitration scheme that ensures balanced servicing of event requests across the array. Routing of events is implemented externally using dynamically programmable random-access memory that stores a postsynaptic address, the conductance, and the reversal potential of each synaptic connection. Here, we describe the silicon neuron circuits, present experimental data characterizing the 3 mm x 3 mm chip fabricated in 0.5-microm complementary metal-oxide-semiconductor (CMOS) technology, and demonstrate its utility by configuring the hardware to emulate a model of attractor dynamics and waves of neural activity during sleep in rat hippocampus.

A comparative analysis of multi-conductance neuronal models in silico

We demonstrate that a previously presented flexible silicon-neuron architecture can implement three disparate conductance-based neuron models with both fast and slow dynamics. By exploiting the real-time nature of this physical implementation, we mapped the model dynamics across a large region of parameter space. We also found that two of these dynamically different models represent points in a contiguous bursting space that spans between the two models. By systematically varying the model parameters, we also found that multiple, diverse trajectories in parameter space connected the two canonical bursting points. In addition, we found that the combination of parameter values keeps the neuron in the bursting region. These findings demonstrate the usefulness of the silicon-neuron architecture as a neural-modeling tool and illustrate its versatility as a platform for a multi-behavioral neuron that resembles its living analog.

Sensory Feedback in a Half-Center Oscillator Model

We hypothesize that one role of sensorimotor feedback for rhythmic movements in biological organisms is to synchronize the frequency of movements to the mechanical resonance of the body. Our hypothesis is based on recent studies that have shown the advantage of moving at mechanical resonance and how such synchronization may be possible in biology. We test our hypothesis by developing a physical system that consists of a silicon-neuron central pattern generator (CPG), which controls the motion of a beam, and position sensors that provide feedback information to the CPG. The silicon neurons that we use are integrated circuits that generate neural signals based on the Hodgkin-Huxley dynamics. We use this physical system to develop a model of the interaction between the sensory feedback and the complex dynamics of the neurons to create the closed-loop system behavior. This model is then used to describe the conditions under which our hypothesis is valid and the general effects of sensorimotor feedback on the rhythmic movements of this system.

Two-dimensional variation of bursting properties in a silicon-neuron half-center oscillator

We are developing hardware models of central pattern generators (CPGs) to enhance neural prostheses, create biologically based controllers for autonomous machines, and to better understand how biology creates stable and robust movements. Previously, we designed and implemented an analog integrated circuit model of a neuron with Hodgkin-Huxley like dynamics, the silicon neuron. In this work, we use silicon neurons to implement a half-center oscillator and show that the underlying dynamics of this CPG produce bursting behaviors that are well matched to the biological counterpart on which our model is based. In addition, we demonstrate the robustness of the bursting behavior by systematically varying two parameters in each silicon neuron and mapping the corresponding effects on the bursting.

Analog-digital simulations of full conductance-based networks of spiking neurons with spike timing dependent plasticity

We introduce and test a system for simulating networks of conductance-based neuron models using analog circuits. At the single-cell level, we use custom-designed analog circuits (ASICs) that simulate two types of spiking neurons based on Hodgkin-Huxley like dynamics: "regular spiking" excitatory neurons with spike-frequency adaptation, and "fast spiking" inhibitory neurons. Synaptic interactions are mediated by conductance-based synaptic currents described by kinetic models. Connectivity and plasticity rules are implemented digitally through a real time interface between a computer and a PCI board containing the ASICs. We show a prototype system of a few neurons interconnected with synapses undergoing spike-timing dependent plasticity (STDP), and compare this system with numerical simulations. We use this system to evaluate the effect of parameter dispersion on the behavior of small circuits of neurons. It is shown that, although the exact spike timings are not precisely emulated by the ASIC neurons, the behavior of small networks with STDP matches that of numerical simulations. Thus, this mixed analog-digital architecture provides a valuable tool for real-time simulations of networks of neurons with STDP. They should be useful for any real-time application, such as hybrid systems interfacing network models with biological neurons.

A MOSFET-based model of a Class 2 nerve membrane

We have constructed a nerve membrane using MOSFET circuitry, which can be a basic element of an FET-based neural system. Its mechanism of action potentials generation is designed to reproduce that of the Hodgkin-Huxley equations. The responses to singlet, doublet, repetitive pulse, and sustained stimuli are analyzed to show that it exhibits similar properties to the Hodgkin-Huxley equations; namely, 1) excitable dynamics with generation of action potentials, 2) the existence of a chaotic response to periodic stimuli, and 3) Class 2 excitability. It is known that Class 2 excitability is generated by an inverted Hopf bifurcation. We have applied Hopf bifurcation theory to our nerve membrane's system equations and have shown a routine for ascertaining whether a certain parameter set generates an inverted Hopf bifurcation.

Using a hybrid neural system to reveal regulation of neuronal network activity by an intrinsic current

The generation of rhythmic patterns by neuronal networks is a complex phenomenon, relying on the interaction of numerous intrinsic and synaptic currents, as well as modulatory agents. To investigate the functional contribution of an individual ionic current to rhythmic pattern generation in a network, we constructed a hybrid system composed of a silicon model neuron and a heart interneuron from the heartbeat timing network of the medicinal leech. When the model neuron and a heart interneuron are connected by inhibitory synapses, they produce rhythmic activity similar to that observed in the heartbeat network. We focused our studies on investigating the functional role of the hyperpolarization-activated inward current (I(h)) on the rhythmic bursts produced by the network. By introducing changes in both the model and the heart interneuron, we showed that I(h) determines both the period of rhythmic bursts and the balance of activity between the two sides of the network, because the amount and the activation/deactivation time constant of I(h) determines the length of time that a neuron spends in the inhibited phase of its burst cycle. Moreover, we demonstrated that the model neuron is an effective replacement for a heart interneuron and that changes made in the model can accurately mimic similar changes made in the living system. Finally, we used a previously developed mathematical model (Hill et al. 2001) of two mutually inhibitory interneurons to corroborate these findings. Our results demonstrated that this hybrid system technique is advantageous for investigating neuronal properties that are inaccessible with traditional techniques.