The Neurobiological Basis of Cognition: Identification by Multi-Input, Multioutput Nonlinear Dynamic Modeling: A method is proposed for measuring and modeling human long-term memory formation by mathematical analysis and computer simulation of nerve-cell dynamics

Brain augmentation and neuroscience technologies: current applications, challenges, ethics and future prospects

Ever since the dawn of antiquity, people have strived to improve their cognitive abilities. From the advent of the wheel to the development of artificial intelligence, technology has had a profound leverage on civilization. Cognitive enhancement or augmentation of brain functions has become a trending topic both in academic and public debates in improving physical and mental abilities. The last years have seen a plethora of suggestions for boosting cognitive functions and biochemical, physical, and behavioral strategies are being explored in the field of cognitive enhancement. Despite expansion of behavioral and biochemical approaches, various physical strategies are known to boost mental abilities in diseased and healthy individuals. Clinical applications of neuroscience technologies offer alternatives to pharmaceutical approaches and devices for diseases that have been fatal, so far. Importantly, the distinctive aspect of these technologies, which shapes their existing and anticipated participation in brain augmentations, is used to compare and contrast them. As a preview of the next two decades of progress in brain augmentation, this article presents a plausible estimation of the many neuroscience technologies, their virtues, demerits, and applications. The review also focuses on the ethical implications and challenges linked to modern neuroscientific technology. There are times when it looks as if ethics discussions are more concerned with the hypothetical than with the factual. We conclude by providing recommendations for potential future studies and development areas, taking into account future advancements in neuroscience innovation for brain enhancement, analyzing historical patterns, considering neuroethics and looking at other related forecasts.

A Multi-Channel Asynchronous Neurostimulator With Artifact Suppression for Neural Code-Based Stimulations

A novel neurostimulator for generating neural code-based, precise, asynchronous electrical stimulation pulses is designed, fabricated, and characterized. Through multiplexing, this system can deliver constant current biphasic pulses, with arbitrary temporal patterns, and pulse parameters to 32 electrodes using one pulse generator. The design also features a stimulus artifact suppression (SAS) technique that can be integrated with commercial amplifiers. Using an array of CMOS switches, electrodes are disconnected from recording amplifiers during stimulation, while the input of the recording system is shorted to ground through another CMOS switch to suppress ringing in the recording system. The timing of the switches used to block and suppress the stimulus artifact are crucial and are determined by the electrochemical properties of the electrode. This system allows stimulation and recording from the same electrodes to monitor local field potentials with short latencies from the region of stimulation for achieving feedback control of neural stimulation. In this way, timing between each pulse is controlled by inputs from an external source and stimulus magnitude is controlled by feed-back from neural response from the stimulated tissue. The system was implemented with low-power and compact packaged microchips to constitute an effective, cost-efficient, and miniaturized neurostimulator. The device has been first evaluated in phantom preparations and then tested in hippocampi of behaving rats. Benchtop results demonstrate the capability of the stimulator to generate arbitrary spatio-temporal pattern of stimulation pulses dictated by random number generators (RNGs) to control magnitude and timing between each individual biphasic pulse. In vivo results show that evoked potentials elicited by the neurostimulator can be recorded ∼2 ms after the termination of stimulus pulses from the same electrodes where stimulation pulses are delivered, whereas commercial amplifiers without such an artifact suppression typically result in tens to hundreds of milliseconds recovery period. This neurostimulator design is desirable in a variety of neural interface applications, particularly hippocampal memory prosthesis aiming to restore cognitive functions by reinstating neural code transmissions in the brain.

Memory Prosthesis: Is It Time for a Deep Neuromimetic Computing Approach?

Memory loss, one of the most dreaded afflictions of the human condition, presents considerable burden on the world's health care system and it is recognized as a major challenge in the elderly. There are only a few neuromodulation treatments for memory dysfunctions. Open loop deep brain stimulation is such a treatment for memory improvement, but with limited success and conflicting results. In recent years closed-loop neuroprosthesis systems able to simultaneously record signals during behavioral tasks and generate with the use of internal neural factors the precise timing of stimulation patterns are presented as attractive alternatives and show promise in memory enhancement and restoration. A few such strides have already been made in both animals and humans, but with limited insights into their mechanisms of action. Here, I discuss why a deep neuromimetic computing approach linking multiple levels of description, mimicking the dynamics of brain circuits, interfaced with recording and stimulating electrodes could enhance the performance of current memory prosthesis systems, shed light into the neurobiology of learning and memory and accelerate the progress of memory prosthesis research. I propose what the necessary components (nodes, structure, connectivity, learning rules, and physiological responses) of such a deep neuromimetic model should be and what type of data are required to train/test its performance, so it can be used as a true substitute of damaged brain areas capable of restoring/enhancing their missing memory formation capabilities. Considerations to neural circuit targeting, tissue interfacing, electrode placement/implantation, and multi-network interactions in complex cognition are also provided.

Multi-Input, Multi-Output Neuronal Mode Network Approach to Modeling the Encoding Dynamics and Functional Connectivity of Neural Systems

This letter proposes a novel method, multi-input, multi-output neuronal mode network (MIMO-NMN), for modeling encoding dynamics and functional connectivity in neural ensembles such as the hippocampus. Compared with conventional approaches such as the Volterra-Wiener model, linear-nonlinear-cascade (LNC) model, and generalized linear model (GLM), the NMN has several advantages in terms of estimation accuracy, model interpretation, and functional connectivity analysis. We point out the limitations of current neural spike modeling methods, especially the estimation biases caused by the imbalanced class problem when the number of zeros is significantly larger than ones in the spike data. We use synthetic data to test the performance of NMN with a comparison of the traditional methods, and the results indicate the NMN approach could reduce the imbalanced class problem and achieve better predictions. Subsequently, we apply the MIMO-NMN method to analyze data from the human hippocampus. The results indicate that the MIMO-NMN method is a promising approach to modeling neural dynamics and analyzing functional connectivity of multi-neuronal data.

Neurotechnologies for Human Cognitive Augmentation: Current State of the Art and Future Prospects

Recent advances in neuroscience have paved the way to innovative applications that cognitively augment and enhance humans in a variety of contexts. This paper aims at providing a snapshot of the current state of the art and a motivated forecast of the most likely developments in the next two decades. Firstly, we survey the main neuroscience technologies for both observing and influencing brain activity, which are necessary ingredients for human cognitive augmentation. We also compare and contrast such technologies, as their individual characteristics (e.g., spatio-temporal resolution, invasiveness, portability, energy requirements, and cost) influence their current and future role in human cognitive augmentation. Secondly, we chart the state of the art on neurotechnologies for human cognitive augmentation, keeping an eye both on the applications that already exist and those that are emerging or are likely to emerge in the next two decades. Particularly, we consider applications in the areas of communication, cognitive enhancement, memory, attention monitoring/enhancement, situation awareness and complex problem solving, and we look at what fraction of the population might benefit from such technologies and at the demands they impose in terms of user training. Thirdly, we briefly review the ethical issues associated with current neuroscience technologies. These are important because they may differentially influence both present and future research on (and adoption of) neurotechnologies for human cognitive augmentation: an inferior technology with no significant ethical issues may thrive while a superior technology causing widespread ethical concerns may end up being outlawed. Finally, based on the lessons learned in our analysis, using past trends and considering other related forecasts, we attempt to forecast the most likely future developments of neuroscience technology for human cognitive augmentation and provide informed recommendations for promising future research and exploitation avenues.

Modeling Nonlinear Synaptic Dynamics: A Laguerre-Volterra Network Framework for Improved Computational Efficiency in Large Scale Simulations

Synapses are key components in signal transmission in the brain, often exhibiting complex non-linear dynamics. Yet, they are often crudely modelled as linear exponential equations in large-scale neuron network simulations. Mechanistic models that use detailed channel receptor kinetics more closely replicate the nonlinear dynamics observed at synapses, but use of such models are generally restricted to small scale simulations due to their computational complexity. Previously, we have developed an ``input-output'' (IO) synapse model using the Volterra functional series to estimate nonlinear synaptic dynamics. Here, we present an improvement on the IO synapse model using the extbf{Laguerre-Volterra network (LVN) framework. We demonstrate that utilization of the LVN framework helps reduce memory requirements and improves the simulation speed in comparison to the previous iteration of the IO synapse model. We present results that demonstrate the accuracy, memory efficiency, and speed of the LVN model that can be extended to simulations with large numbers of synapses. Our efforts enable complex nonlinear synaptic dynamics to be modelled in large-scale network models, allowing us to explore how synaptic activity may influence network behavior and affects memory, learning, and neurodegenerative diseases.

Omitted Variable Bias in GLMs of Neural Spiking Activity

Generalized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables, as well as the dynamics of single neurons. However, in any given experiment, many variables that have an impact on neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how postspike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single-neuron firing. Omitted variable bias can appear in any model with confounders-where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Acute in vivo testing of a conformal polymer microelectrode array for multi-region hippocampal recordings

OBJECTIVE

The success of a cortical prosthetic device relies upon its ability to attain resolvable spikes from many neurons in particular neural networks over long periods of time. Traditionally, lifetimes of neural recordings are greatly limited by the body's immune response against the foreign implant which causes neuronal death and glial scarring. This immune reaction is posited to be exacerbated by micromotion between the implant, which is often rigid, and the surrounding, soft brain tissue, and attenuates the quality of recordings over time.

APPROACH

In an attempt to minimize the foreign body response to a penetrating neural array that records from multiple brain regions, Parylene C, a flexible, biocompatible polymer was used as the substrate material for a functional, proof-of-concept neural array with a reduced elastic modulus. This probe array was designed and fabricated to have 64 electrodes positioned to match the anatomy of the rat hippocampus and allow for simultaneous recordings between two cell-body layers of interest. A dissolvable brace was used for deep-brain penetration of the flexible array.

MAIN RESULTS

Arrays were electrochemically characterized at the benchtop, and a novel insertion technique that restricts acute insertion injury enabled accurate target placement of four, bare, flexible arrays to greater than 4 mm deep into the rat brain. Arrays were tested acutely and in vivo recordings taken intra-operatively reveal spikes in both targeted regions of the hippocampus with spike amplitudes and noise levels similar to those recorded with microwires. Histological staining of a sham array implanted for one month reveals limited astrocytic scarring and neuronal death around the implant.

SIGNIFICANCE

This work represents one of the first examples of a penetrating polymer probe array that records from individual neurons in structures that lie deep within the brain.

A memory efficient implementation scheme of Gauss error function in a Laguerre-Volterra network for neuroprosthetic devices

Cognitive neural prosthesis is a manmade device which can be used to restore or compensate for lost human cognitive modalities. The generalized Laguerre-Volterra (GLV) network serves as a robust mathematical underpinning for the development of such prosthetic instrument. In this paper, a hardware implementation scheme of Gauss error function for the GLV network targeting reconfigurable platforms is reported. Numerical approximations are formulated which transform the computation of nonelementary function into combinational operations of elementary functions, and memory-intensive look-up table (LUT) based approaches can therefore be circumvented. The computational precision can be made adjustable with the utilization of an error compensation scheme, which is proposed based on the experimental observation of the mathematical characteristics of the error trajectory. The precision can be further customizable by exploiting the run-time characteristics of the reconfigurable system. Compared to the polynomial expansion based implementation scheme, the utilization of slice LUTs, occupied slices, and DSP48E1s on a Xilinx XC6VLX240T field-programmable gate array has decreased by 94.2%, 94.1%, and 90.0%, respectively. While compared to the look-up table based scheme, 1.0×10¹⁷ bits of storage can be spared under the maximum allowable error of 1.0×10^-3. The proposed implementation scheme can be employed in the study of large-scale neural ensemble activity and in the design and development of neural prosthetic device.

The volterra functional series is a viable alternative to kinetic models for synaptic modeling--calibration and benchmarking

Synaptic transmission is governed by a series of complex and highly nonlinear mechanisms and pathways in which the dynamics have a profound influence on the overall signal sent to the postsynaptic cell. In simulation, these mechanisms are often represented through kinetic models governed by state variables and rate law equations. Calculations of such ordinary differential equations (ODEs) in kinetic models can be computationally intensive, and although algorithms have been optimally developed to handle ODEs efficiently, simulation of numerous, large and complex kinetic models requires a prohibitively large amount of computational power. Here we present an alternative representation of ionotropic glutamatergic receptors AMPAr and NMDAr kinetic models consisting of input-output surrogates of the receptor models which can capture the nonlinear dynamics seen in the kinetic models. We benchmark this Input-Output (IO) synapse model and compare it with kinetic receptor models to evaluate the simulation time required when using either synapse model, as well as the number of time steps each model needs for simulation. While remaining faithful to the original dynamics of the model, our results indicate that the IO synapse model requires less simulation time than the kinetic models under conditions which elicit normal physiological responses, thereby improving computational efficiency while preserving the complex non-linear dynamics of the receptors. These IO surrogates therefore constitute an appealing alternative to kinetic models in large scale networks simulations.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Identifying and tracking simulated synaptic inputs from neuronal firing: insights from in vitro experiments

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.

Identification of functional synaptic plasticity from spiking activities using nonlinear dynamical modeling

This paper presents a systems identification approach for studying the long-term synaptic plasticity using natural spiking activities. This approach consists of three modeling steps. First, a multi-input, single-output (MISO), nonlinear dynamical spiking neuron model is formulated to estimate and represent the synaptic strength in means of functional connectivity between input and output neurons. Second, this MISO model is extended to a nonstationary form to track the time-varying properties of the synaptic strength. Finally, a Volterra modeling method is used to extract the synaptic learning rule, e.g., spike-timing-dependent plasticity, for the explanation of the input-output nonstationarity as the consequence of the past input-output spiking patterns. This framework is developed to study the underlying mechanisms of learning and memory formation in behaving animals, and may serve as the computational basis for building the next-generation adaptive cortical prostheses.

Extraction and restoration of hippocampal spatial memories with non-linear dynamical modeling

To build a cognitive prosthesis that can replace the memory function of the hippocampus, it is essential to model the input-output function of the damaged hippocampal region, so the prosthetic device can stimulate the downstream hippocampal region, e.g., CA1, with the output signal, e.g., CA1 spike trains, predicted from the ongoing input signal, e.g., CA3 spike trains, and the identified input-output function, e.g., CA3-CA1 model. In order for the downstream region to form appropriate long-term memories based on the restored output signal, furthermore, the output signal should contain sufficient information about the memories that the animal has formed. In this study, we verify this premise by applying regression and classification modelings of the spatio-temporal patterns of spike trains to the hippocampal CA3 and CA1 data recorded from rats performing a memory-dependent delayed non-match-to-sample (DNMS) task. The regression model is essentially the multiple-input, multiple-output (MIMO) non-linear dynamical model of spike train transformation. It predicts the output spike trains based on the input spike trains and thus restores the output signal. In addition, the classification model interprets the signal by relating the spatio-temporal patterns to the memory events. We have found that: (1) both hippocampal CA3 and CA1 spike trains contain sufficient information for predicting the locations of the sample responses (i.e., left and right memories) during the DNMS task; and more importantly (2) the CA1 spike trains predicted from the CA3 spike trains by the MIMO model also are sufficient for predicting the locations on a single-trial basis. These results show quantitatively that, with a moderate number of unitary recordings from the hippocampus, the MIMO non-linear dynamical model is able to extract and restore spatial memory information for the formation of long-term memories and thus can serve as the computational basis of the hippocampal memory prosthesis.

A customizable stochastic state point process filter (SSPPF) for neural spiking activity

Stochastic State Point Process Filter (SSPPF) is effective for adaptive signal processing. In particular, it has been successfully applied to neural signal coding/decoding in recent years. Recent work has proven its efficiency in non-parametric coefficients tracking in modeling of mammal nervous system. However, existing SSPPF has only been realized in commercial software platforms which limit their computational capability. In this paper, the first hardware architecture of SSPPF has been designed and successfully implemented on field-programmable gate array (FPGA), proving a more efficient means for coefficient tracking in a well-established generalized Laguerre-Volterra model for mammalian hippocampal spiking activity research. By exploring the intrinsic parallelism of the FPGA, the proposed architecture is able to process matrices or vectors with random size, and is efficiently scalable. Experimental result shows its superior performance comparing to the software implementation, while maintaining the numerical precision. This architecture can also be potentially utilized in the future hippocampal cognitive neural prosthesis design.

On parsing the neural code in the prefrontal cortex of primates using principal dynamic modes

Nonlinear modeling of multi-input multi-output (MIMO) neuronal systems using Principal Dynamic Modes (PDMs) provides a novel method for analyzing the functional connectivity between neuronal groups. This paper presents the PDM-based modeling methodology and initial results from actual multi-unit recordings in the prefrontal cortex of non-human primates. We used the PDMs to analyze the dynamic transformations of spike train activity from Layer 2 (input) to Layer 5 (output) of the prefrontal cortex in primates performing a Delayed-Match-to-Sample task. The PDM-based models reduce the complexity of representing large-scale neural MIMO systems that involve large numbers of neurons, and also offer the prospect of improved biological/physiological interpretation of the obtained models. PDM analysis of neuronal connectivity in this system revealed "input-output channels of communication" corresponding to specific bands of neural rhythms that quantify the relative importance of these frequency-specific PDMs across a variety of different tasks. We found that behavioral performance during the Delayed-Match-to-Sample task (correct vs. incorrect outcome) was associated with differential activation of frequency-specific PDMs in the prefrontal cortex.

Identification of sparse neural functional connectivity using penalized likelihood estimation and basis functions

One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.

An analysis of the expression locus of long-term potentiation in hippocampal CA1 neurons

Long-term potentiation (LTP) has long been understood as an increase in the potency of a synaptic connection between two neurons. In this study, we combine a previously developed two-stage cascade model with electrophysiological recordings of rat hippocampal CA1 pyramidal cells both before and after LTP to analyze linear and nonlinear contributions of pre and post-synaptic partners to the strengthening of their synaptic connectivity. The result suggests that the major nonlinear expression locus of LTP exists in the post-synaptic side. Additionally, the report reveals that LTP should be understood not only in the traditional view as a change in the magnitude of communication between two cells, but also as a change in their temporal coding properties of information exchange.

A programmable analog subthreshold biomimetic model for bi-directional communication with the brain

In this paper, we present a hardware implementation of a second order Laguerre Expansion of Volterra Kernel (LEV) model with four basis functions. The model is versatile enough to be applied at different abstraction levels (synapse, neuron, or network of neurons) and is implemented with analog building blocks in a modular manner. These analog blocks, realized using low power subthreshold CMOS transistors, can serve as a basis for large-scale hardware systems that emulate multi-input multi-output (MIMO) spike transformations in populations of neurons. The normalized mean square error between the signals produced by the circuit LEV implementation and the ideal LEV model is 8.15%. The total power consumption of the analog circuitry is less than 33nW.

Channel identification machines

We present a formal methodology for identifying a channel in a system consisting of a communication channel in cascade with an asynchronous sampler. The channel is modeled as a multidimensional filter, while models of asynchronous samplers are taken from neuroscience and communications and include integrate-and-fire neurons, asynchronous sigma/delta modulators and general oscillators in cascade with zero-crossing detectors. We devise channel identification algorithms that recover a projection of the filter(s) onto a space of input signals loss-free for both scalar and vector-valued test signals. The test signals are modeled as elements of a reproducing kernel Hilbert space (RKHS) with a Dirichlet kernel. Under appropriate limiting conditions on the bandwidth and the order of the test signal space, the filter projection converges to the impulse response of the filter. We show that our results hold for a wide class of RKHSs, including the space of finite-energy bandlimited signals. We also extend our channel identification results to noisy circuits.

Design of optimal stimulation patterns for neuronal ensembles based on Volterra-type hierarchical modeling

This paper presents a general methodology for the optimal design of stimulation patterns applied to neuronal ensembles in order to elicit a desired effect. The methodology follows a variant of the hierarchical Volterra modeling approach that utilizes input-output data to construct predictive models that describe the effects of interactions among multiple input events in an ascending order of interaction complexity. The illustrative example presented in this paper concerns the multi-unit activity of CA1 neurons in the hippocampus of a rodent performing a learned delayed-nonmatch-to-sample (DNMS) task. The multi-unit activity of the hippocampal CA1 neurons is recorded via chronically implanted multi-electrode arrays during this task. The obtained model quantifies the likelihood of having correct performance of the specific task for a given multi-unit (spatiotemporal) activity pattern of a CA1 neuronal ensemble during the 'sample presentation' phase of the DNMS task. The model can be used to determine computationally (off-line) the 'optimal' multi-unit stimulation pattern that maximizes the likelihood of inducing the correct performance of the DNMS task. Our working hypothesis is that application of this optimal stimulation pattern will enhance performance of the DNMS task due to enhancement of memory formation and storage during the 'sample presentation' phase of the task.

Role of the hippocampus in memory formation: restorative encoding memory integration neural device as a cognitive neural prosthesis

Remind, which stands for "restorative encoding memory integration neural device," is a Defense Advanced Research Projects Agency (DARPA)-sponsored program to construct the first-ever cognitive prosthesis to replace lost memory function and enhance the existing memory capacity in animals and, ultimately, in humans. Reaching this goal involves understanding something fundamental about the brain that has not been understood previously: how the brain internally codes memories. In developing a hippocampal prosthesis for the rat, we have been able to demonstrate a multiple-input, multiple- output (MIMO) nonlinear model that predicts in real time the spatiotemporal codes for specific memories required for correct performance on a standard learning/memory task, i.e., delayed-nonmatch-to-sample (DNMS) memory. The MIMO model has been tested successfully in a number of contexts; most notably, in animals with a pharmacologically disabled hippocampus, we were able to reinstate long-term memories necessary for correct DNMS behavior by substituting a MIMO model-predicted code, delivered by electrical stimulation to the hippocampus through an array of electrodes, resulting in spatiotemporal hippocampal activity that is normally generated endogenously. We also have shown that delivering the same model-predicted code to electrode-implanted control animals with a normally functioning hippocampus substantially enhances animals memory capacity above control levels. These results in rodents have formed the basis for extending the MIMO model to nonhuman primates; this is now underway as the last step of the REMIND program before developing a MIMO-based cognitive prosthesis for humans.

A nonlinear autoregressive Volterra model of the Hodgkin-Huxley equations

We propose a new variant of Volterra-type model with a nonlinear auto-regressive (NAR) component that is a suitable framework for describing the process of AP generation by the neuron membrane potential, and we apply it to input-output data generated by the Hodgkin-Huxley (H-H) equations. Volterra models use a functional series expansion to describe the input-output relation for most nonlinear dynamic systems, and are applicable to a wide range of physiologic systems. It is difficult, however, to apply the Volterra methodology to the H-H model because is characterized by distinct subthreshold and suprathreshold dynamics. When threshold is crossed, an autonomous action potential (AP) is generated, the output becomes temporarily decoupled from the input, and the standard Volterra model fails. Therefore, in our framework, whenever membrane potential exceeds some threshold, it is taken as a second input to a dual-input Volterra model. This model correctly predicts membrane voltage deflection both within the subthreshold region and during APs. Moreover, the model naturally generates a post-AP afterpotential and refractory period. It is known that the H-H model converges to a limit cycle in response to a constant current injection. This behavior is correctly predicted by the proposed model, while the standard Volterra model is incapable of generating such limit cycle behavior. The inclusion of cross-kernels, which describe the nonlinear interactions between the exogenous and autoregressive inputs, is found to be absolutely necessary. The proposed model is general, non-parametric, and data-derived.

On-chip systolic networks for real-time tracking of pairwise correlations between neurons in a large-scale network

The correlation map of neurons emerges as an important mathematical framework for a spectrum of applications including neural circuit modeling, neurologic disease bio-marking and neuroimaging. However, constructing a correlation map is computationally expensive, especially when the number of neurons is large. This paper proposes a hardware design using hierarchical systolic arrays to calculate pairwise correlations between neurons. Through mapping a computationally efficient algorithm for cross-correlation onto a massively parallel structure, the hardware is able to construct the correlation maps in a much shorter time. The proposed architecture was evaluated using a field programmable gate array. The results show that the computational delay of the hardware for constructing correlation maps increases linearly with the number of neurons, whereas the growth of delay is quadratic for a software-based serial approach. Also, the efficiency of our method for detecting abnormal behaviors of neural circuits is demonstrated by analyzing correlation maps of retinal neurons.

Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes

A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the "inputs" and "outputs", respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The "scaling-up" issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.

Modeling neuron-glia interactions: from parametric model to neuromorphic hardware

Recent experimental evidence suggests that glial cells are more than just supporting cells to neurons - they play an active role in signal transmission in the brain. We herein propose to investigate the importance of these mechanisms and model neuron-glia interactions at synapses using three approaches: A parametric model that takes into account the underlying mechanisms of the physiological system, a non-parametric model that extracts its input-output properties, and an ultra-low power, fast processing, neuromorphic hardware model. We use the EONS (Elementary Objects of the Nervous System) platform, a highly elaborate synaptic modeling platform to investigate the influence of astrocytic glutamate transporters on postsynaptic responses in the detailed micro-environment of a tri-partite synapse. The simulation results obtained using EONS are then used to build a non-parametric model that captures the essential features of glutamate dynamics. The structure of the non-parametric model we use is specifically designed for efficient hardware implementation using ultra-low power subthreshold CMOS building blocks. The utilization of the approach described allows us to build large-scale models of neuron/glial interaction and consequently provide useful insights on glial modulation during normal and pathological neural function.

A hippocampal cognitive prosthesis: multi-input, multi-output nonlinear modeling and VLSI implementation

This paper describes the development of a cognitive prosthesis designed to restore the ability to form new long-term memories typically lost after damage to the hippocampus. The animal model used is delayed nonmatch-to-sample (DNMS) behavior in the rat, and the "core" of the prosthesis is a biomimetic multi-input/multi-output (MIMO) nonlinear model that provides the capability for predicting spatio-temporal spike train output of hippocampus (CA1) based on spatio-temporal spike train inputs recorded presynaptically to CA1 (e.g., CA3). We demonstrate the capability of the MIMO model for highly accurate predictions of CA1 coded memories that can be made on a single-trial basis and in real-time. When hippocampal CA1 function is blocked and long-term memory formation is lost, successful DNMS behavior also is abolished. However, when MIMO model predictions are used to reinstate CA1 memory-related activity by driving spatio-temporal electrical stimulation of hippocampal output to mimic the patterns of activity observed in control conditions, successful DNMS behavior is restored. We also outline the design in very-large-scale integration for a hardware implementation of a 16-input, 16-output MIMO model, along with spike sorting, amplification, and other functions necessary for a total system, when coupled together with electrode arrays to record extracellularly from populations of hippocampal neurons, that can serve as a cognitive prosthesis in behaving animals.

Analog low-power hardware implementation of a Laguerre-Volterra model of intracellular subthreshold neuronal activity

The right level of abstraction for a model mimicking a neural function is often difficult to determine. There are trade-offs between capturing biological complexities on one hand and the scalability and efficiency of the model on the other. In this work, we describe a nonlinear Laguerre-Volterra model of the synaptic temporal integration of input spikes to postsynaptic potentials. This model is then efficiently implemented using analog subthreshold circuits and can serve as a foundation for future large-scale hardware systems that can emulate multi-input multi-output (MIMO) spike transformations in populations of neurons. The normalized mean square error in estimating real data using the circuit implementation of this model is less than 15%. The model components are modular and its parameters are adjustable for modeling temporal integration by neurons in other brain regions. The total power consumption of this nonlinear Laguerre-Volterra system is less than 5nW.

Nonlinear dynamic modeling of neuron action potential threshold during synaptically driven broadband intracellular activity

Activity-dependent variation of neuronal thresholds for action potential (AP) generation is one of the key determinants of spike-train temporal-pattern transformations from presynaptic to postsynaptic spike trains. In this study, we model the nonlinear dynamics of the threshold variation during synaptically driven broadband intracellular activity. First, membrane potentials of single CA1 pyramidal cells were recorded under physiologically plausible broadband stimulation conditions. Second, a method was developed to measure AP thresholds from the continuous recordings of membrane potentials. It involves measuring the turning points of APs by analyzing the third-order derivatives of the membrane potentials. Four stimulation paradigms with different temporal patterns were applied to validate this method by comparing the measured AP turning points and the actual AP thresholds estimated with varying stimulation intensities. Results show that the AP turning points provide consistent measurement of the AP thresholds, except for a constant offset. It indicates that 1) the variation of AP turning points represents the nonlinearities of threshold dynamics; and 2) an optimization of the constant offset is required to achieve accurate spike prediction. Third, a nonlinear dynamical third-order Volterra model was built to describe the relations between the threshold dynamics and the AP activities. Results show that the model can predict threshold accurately based on the preceding APs. Finally, the dynamic threshold model was integrated into a previously developed single neuron model and resulted in a 33% improvement in spike prediction.

A cortical neural prosthesis for restoring and enhancing memory

A primary objective in developing a neural prosthesis is to replace neural circuitry in the brain that no longer functions appropriately. Such a goal requires artificial reconstruction of neuron-to-neuron connections in a way that can be recognized by the remaining normal circuitry, and that promotes appropriate interaction. In this study, the application of a specially designed neural prosthesis using a multi-input/multi-output (MIMO) nonlinear model is demonstrated by using trains of electrical stimulation pulses to substitute for MIMO model derived ensemble firing patterns. Ensembles of CA3 and CA1 hippocampal neurons, recorded from rats performing a delayed-nonmatch-to-sample (DNMS) memory task, exhibited successful encoding of trial-specific sample lever information in the form of different spatiotemporal firing patterns. MIMO patterns, identified online and in real-time, were employed within a closed-loop behavioral paradigm. Results showed that the model was able to predict successful performance on the same trial. Also, MIMO model-derived patterns, delivered as electrical stimulation to the same electrodes, improved performance under normal testing conditions and, more importantly, were capable of recovering performance when delivered to animals with ensemble hippocampal activity compromised by pharmacologic blockade of synaptic transmission. These integrated experimental-modeling studies show for the first time that, with sufficient information about the neural coding of memories, a neural prosthesis capable of real-time diagnosis and manipulation of the encoding process can restore and even enhance cognitive, mnemonic processes.

Changes of hippocampal CA3-CA1 population nonlinear dynamics across different training sessions in rats performing a memory-dependent task

Delayed-nonmatch-to-sample (DNMS) task is memory-dependent. Hippocampal CA3 and CA1 cells were shown to be encoding the required spatial and temporal information to complete this task. In order to identify possible changes in neural population nonlinear dynamics during learning of the DNMS task, we have first modeled the input-output transformation of spike trains across brain subregions from learning animals using a multiple-input, multiple-output (MIMO) nonlinear dynamic model. The feedforward and feedback kernels describing the relations between hippocampal CA3 and CA1 subregions have shown significant changes at different training sessions.

Rethinking the cognitive revolution from a neural perspective: how overuse/misuse of the term 'cognition' and the neglect of affective controls in behavioral neuroscience could be delaying progress in understanding the BrainMind

Words such as cognition, motivation and emotion powerfully guide theory development and the overall aims and goals of behavioral neuroscience research. Once such concepts are accepted generally as natural aspects of the brain, their influence can be pervasive and long lasting. Importantly, the choice of conceptual terms used to describe and study mental/neural functions can also constrain research by forcing the results into seemingly useful 'conceptual' categories that have no discrete reality in the brain. Since the popularly named 'cognitive revolution' in psychological science came to fruition in the early 1970s, the term cognitive or cognition has been perhaps the most widely used conceptual term in behavioral neuroscience. These terms, similar to other conceptual terms, have potential value if utilized appropriately. We argue that recently the term cognition has been both overused and misused. This has led to problems in developing a usable shared definition for the term and to promotion of possible misdirections in research within behavioral neuroscience. In addition, we argue that cognitive-guided research influenced primarily by top-down (cortical toward subcortical) perspectives without concurrent non-cognitive modes of bottom-up developmental thinking, could hinder progress in the search for new treatments and medications for psychiatric illnesses and neurobehavioral disorders. Overall, linkages of animal research insights to human psychology may be better served by bottom-up (subcortical to cortical) affective and motivational 'state-control' perspectives, simply because the lower networks of the brain are foundational for the construction of higher 'information-processing' aspects of mind. Moving forward, rapidly expanding new techniques and creative methods in neuroscience along with more accurate brain concepts, may help guide the development of new therapeutics and hopefully more accurate ways to describe and explain brain-behavior relationships.

Nonlinear dynamic modeling of synaptically driven single hippocampal neuron intracellular activity

A high-order nonlinear dynamic model of the input-output properties of single hippocampal CA1 pyramidal neurons was developed based on synaptically driven intracellular activity. The purpose of this study is to construct a model that: 1) can capture the nonlinear dynamics of both subthreshold activities [postsynaptic potentials (PSPs)] and suprathreshold activities (action potentials) in a single formalism; 2) is sufficiently general to be applied to any spike-input and spike-output neurons (point process input and point process output neural systems); and 3) is computationally efficient. The model consisted of three major components: 1) feedforward kernels (up to third order) that transform presynaptic action potentials into PSPs; 2) a constant threshold, above which action potentials are generated; and 3) a feedback kernel (first order) that describes spike-triggered after-potentials. The model was applied to CA1 pyramidal cells, as they were electrically stimulated with broadband Poisson random impulse trains through the Schaffer collaterals. The random impulse trains used here have physiological properties similar to spiking patterns observed in CA3 hippocampal neurons. PSPs and action potentials were recorded from the soma of CA1 pyramidal neurons using whole-cell patch-clamp recording. We evaluated the model performance separately with respect to PSP waveforms and the occurrence of spikes. The average normalized mean square error of PSP prediction is 14.4%. The average spike prediction error rate is 18.8%. In summary, although prediction errors still could be reduced, the model successfully captures the majority of high-order nonlinear dynamics of the single-neuron intracellular activity. The model captures the general biophysical processes with a small set of open parameters that are directly constrained by the intracellular recording, and thus, can be easily applied to any spike-input and spike-output neuron.

Dynamic nonlinear modeling of interactions between neuronal ensembles using principal dynamic modes

We present a novel methodology for modeling the interactions between neuronal ensembles that utilizes the concept of Principal Dynamic Modes (PDM) and their associated nonlinear functions (ANF). This new approach seeks to reduce the complexity of the multi-input/multi-output (MIMO) model of the interactions between neuronal ensembles--an issue of critical practical importance in scaling up the MIMO models to incorporate hundreds (or even thousands) of input-output neurons. Global PDMs were extracted from the data using estimated first-order and second-order kernels and singular value decomposition (SVD). These global PDMs represent an efficient "coordinate system" for the representation of the MIMO model. The ANFs of the PDMs are estimated from the histograms of the combinations of PDM output values that lead to output spikes. For initial testing and validation of this approach, we applied it to a set of data collected at the pre-frontal cortex of a non-human primate during a behavioral task (Delayed Match-to-Sample). Recorded spike trains from Layer-2 neurons were viewed as the "inputs" and from Layer-5 neurons as the outputs. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The results indicate that this methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance.

Tracking the changes of hippocampal population nonlinear dynamics in rats learning a memory-dependent task

Neurobiological processes associated with learning are known to be highly nonlinear, dynamical, and time-varying. Characterizing the time-varying functional input-output properties of neural systems is a critical step to understand the neurobiological basis of learning. In this paper, we present a study on tracking of the changes of neural dynamics in rat hippocampus during learning of a memory-dependent delayed nonmatch-to-sample (DNMS) task. The rats were first trained to perform the DNMS task without a delay between the sample and response events. After reaching a performance level, they were subjected to the DNMS task with variable delays with a 5s mean duration. Spike trains were recorded from hippocampal CA3 (input) and CA1 (output) regions during all training sessions and constitute the input-output data for modeling. We applied the time-varying Generalized Laguerre-Volterra Model to study the changes of the CA3-CA1 nonlinear dynamics using these data. Result showed significant changes in the Volterra kernels after the introduction of delays. This result suggests that the CA3-CA1 nonlinear dynamics established in the initial training sessions underwent a functional reorganization as animals were learning to perform the task that now requires delays.

A two-stage cascade nonlinear dynamical model of single neurons for the separation and quantification of pre- and post-synaptic mechanisms of synaptic transmission

Neurons receive pre-synaptic spike trains and transform them into post-synaptic spike trains. This spike train to spike train temporal transformation underlies all cognitive functions performed by neurons, e.g., learning and memory. The transformation is a highly nonlinear dynamical process that involves both pre- and post-synaptic mechanisms. The ability to separate and quantify the nonlinear dynamics of pre- and post-synaptic mechanism is needed to gain insights into this transformation. In this study, we developed a Volterra kernel based two-stage cascade model of synaptic transmission using synaptically-driven intracellular activities, to which broadband stimulation conditions were imposed. The first stage of the model represents the pre-synaptic mechanisms and describes the nonlinear dynamical transformation from pre-synaptic spike trains to transmitter vesicle release strengths. The vesicle release strengths were obtained from the intracellularly recorded excitatory post-synaptic currents (EPSCs). The second stage of the model represents the post-synaptic mechanisms and describes the nonlinear dynamical transformation from release strengths to excitatory post-synaptic potentials (EPSPs). One application of this cascade model is to analyze the pre- and post-synaptic mechanism change induced by long-term potentiation (LTP). This future application is expected to shed new light on the expression locus of LTP.