Laguerre-Volterra model and architecture for MIMO system identification and output prediction

A generalized mathematical model is proposed for behaviors prediction of biological causal systems with multiple inputs and multiple outputs (MIMO). The system properties are represented by a set of model parameters, which can be derived with random input stimuli probing it. The system calculates predicted outputs based on the estimated parameters and its novel inputs. An efficient hardware architecture is established for this mathematical model and its circuitry has been implemented using the field-programmable gate arrays (FPGAs). This architecture is scalable and its functionality has been validated by using experimental data gathered from real-world measurement.

Donor/recipient enhancement of memory in rat hippocampus

The critical role of the mammalian hippocampus in the formation, translation and retrieval of memory has been documented over many decades. There are many theories of how the hippocampus operates to encode events and a precise mechanism was recently identified in rats performing a short-term memory task which demonstrated that successful information encoding was promoted via specific patterns of activity generated within ensembles of hippocampal neurons. In the study presented here, these “representations” were extracted via a customized non-linear multi-input multi-output (MIMO) mathematical model which allowed prediction of successful performance on specific trials within the testing session. A unique feature of this characterization was demonstrated when successful information encoding patterns were derived online from well-trained “donor” animals during difficult long-delay trials and delivered via online electrical stimulation to synchronously tested naïve “recipient” animals never before exposed to the delay feature of the task. By transferring such model-derived trained (donor) animal hippocampal firing patterns via stimulation to coupled naïve recipient animals, their task performance was facilitated in a direct “donor-recipient” manner. This provides the basis for utilizing extracted appropriate neural information from one brain to induce, recover, or enhance memory related processing in the brain of another subject.

Facilitation of memory encoding in primate hippocampus by a neuroprosthesis that promotes task-specific neural firing

OBJECTIVE

Memory accuracy is a major problem in human disease and is the primary factor that defines Alzheimer's, ageing and dementia resulting from impaired hippocampal function in the medial temporal lobe. Development of a hippocampal memory neuroprosthesis that facilitates normal memory encoding in nonhuman primates (NHPs) could provide the basis for improving memory in human disease states.

APPROACH

NHPs trained to perform a short-term delayed match-to-sample (DMS) memory task were examined with multi-neuron recordings from synaptically connected hippocampal cell fields, CA1 and CA3. Recordings were analyzed utilizing a previously developed nonlinear multi-input multi-output (MIMO) neuroprosthetic model, capable of extracting CA3-to-CA1 spatiotemporal firing patterns during DMS performance.

MAIN RESULTS

The MIMO model verified that specific CA3-to-CA1 firing patterns were critical for the successful encoding of sample phase information on more difficult DMS trials. This was validated by the delivery of successful MIMO-derived encoding patterns via electrical stimulation to the same CA1 recording locations during the sample phase which facilitated task performance in the subsequent, delayed match phase, on difficult trials that required more precise encoding of sample information.

SIGNIFICANCE

These findings provide the first successful application of a neuroprosthesis designed to enhance and/or repair memory encoding in primate brain.

The contribution of relative activation levels between populations of cells to network activity in a large-scale biologically realistic model of the hippocampus

In previously published work, we showed the progress we've made towards creating a large-scale, biologically realistic model of the rat hippocampus, starting with the projection from entorhinal cortex (EC) to the dentate gyrus (DG). We created the model to help us study how the common components of neurobiological systems in mammals - large numbers of neurons with intricate, branching morphologies; active, non-linear membrane properties; nonuniform distributions throughout membrane surface of these non-linear conductances; non-uniform and topographic connectivity between pre- and post-synaptic neurons; and activity-dependent changes in synaptic function - combine and contribute to give a particular brain region its "neural processing" properties. In this work, we report on the results of a series of simulations we ran to test the role of feed-forward and feedback inhibition in the dentate gyrus. We find that a) the system shows rhythmic bands of activity only in the presence of feedback inhibition, b) that the frequency of rhythmicity increases with increasing amounts of feed-forward inhibition, c) that it decreases with increasing amounts of feedback inhibition, and d) that strong excitatory inputs appear to enhance and prolong the amount of rhythmicity in the system.

Conformal ceramic electrodes that record glutamate release and corresponding neural activity in primate prefrontal cortex

Conformal ceramic electrodes utilized in prior recordings of nonhuman primate prefrontal cortical layer 2/3 and layer 5 neurons were used in this study to record tonic glutamate concentration and transient release in layer 2/3 PFC. Tonic glutamate concentration increased in the Match (decision) phase of a visual delayed-match-to-sample (DMS) task, while increased transient glutamate release occurred in the Sample (encoding) phase of the task. Further, spatial vs. object-oriented DMS trials evoked differential changes in glutamate concentration. Thus the same conformal recording electrodes were capable of electrophysiological and electrochemical recording, and revealed similar evidence of neural processing in layers 2/3 and layer 5 during cognitive processing in a behavioral task.

Influence of ionotropic receptors localization on glutamatergic synaptic response to paired-pulse stimulation protocol

Paired-pulse protocol is a stimulation pattern that is often used to characterize short-term changes in synaptic potency. Responses to such protocol often yield varying results, going from a depressing response to a facilitated one following the second pulse. Similarly, experimental results have shown that synaptic structures are dynamic and receptors move along the postsynaptic membrane. The present study provides insights on the impact of glutamatergic receptors localization with respect to the neurotransmitters release site on the postsynaptic currents measured; it also proposes an explanation on the diversity of responses observed experimentally. The platform we used is the EONS/RHENOMS modeling platform widely described in the literature, which encompasses a multitude of highly detailed subsynaptic elements to most faithfully replicate synaptic function.

Influence of ionotropic receptor location on their dynamics at glutamatergic synapses

In this paper we study the effects of the location of ionotropic receptors, especially AMPA and NMDA receptors, on their function at excitatory glutamatergic synapses. As few computational models only allow to evaluate the influence of receptor location on state transition and receptor dynamics, we present an elaborate computational model of a glutamatergic synapse that takes into account detailed parametric models of ionotropic receptors along with glutamate diffusion within the synaptic cleft. Our simulation results underscore the importance of the wide spread distribution of AMPA receptors which is required to avoid massive desensitization of these receptors following a single glutamate release event while NMDA receptor location is potentially optimal relative to the glutamate release site thus, emphasizing the contribution of location dependent effects of the two major ionotropic receptors to synaptic efficacy.

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.

Real-time prediction of neuronal population spiking activity using FPGA

A field-programmable gate array (FPGA)-based hardware architecture is proposed and utilized for prediction of neuronal population firing activity. The hardware system adopts the multi-input multi-output (MIMO) generalized Laguerre-Volterra model (GLVM) structure to describe the nonlinear dynamic neural process of mammalian brain and can switch between the two important functions: estimation of GLVM coefficients and prediction of neuronal population spiking activity (model outputs). The model coefficients are first estimated using the in-sample training data; then the output is predicted using the out-of-sample testing data and the field estimated coefficients. Test results show that compared with previous software implementation of the generalized Laguerre-Volterra algorithm running on an Intel Core i7-2620M CPU, the FPGA-based hardware system can achieve up to 2.66×10(3) speedup in doing model parameters estimation and 698.84 speedup in doing model output prediction. The proposed hardware platform will facilitate research on the highly nonlinear neural process of the mammal brain, and the cognitive neural prosthesis design.

A dual mode FPGA design for the hippocampal prosthesis

One important step towards the cognitive neural prosthesis design is to achieve real-time prediction of neuronal firing pattern. An FPGA-based hardware computational platform is designed to guarantee this hard real-time signal processing requirement. The proposed platform can work in dual modes: generalized Laguerre-Volterra model parameters estimation and output prediction, and can switch between these two important system functions. Compared with the traditional software-based platform implemented in C, the hardware platform achieves better efficiency in doing the biocomputations by up to thousandfold speedup in this process.

Nonlinear dynamical model based control of in vitro hippocampal output

This paper describes a modeling-control paradigm to control the hippocampal output (CA1 response) for the development of hippocampal prostheses. In order to bypass a damaged hippocampal region (e.g., CA3), downstream hippocampal signal (e.g., CA1 responses) needs to be reinstated based on the upstream hippocampal signal (e.g., dentate gyrus responses) via appropriate stimulations to the downstream (CA1) region. In this approach, we optimize the stimulation signal to CA1 by using a predictive DG-CA1 nonlinear model (i.e., DG-CA1 trajectory model) and an inversion of the CA1 input-output model (i.e., inverse CA1 plant model). The desired CA1 responses are first predicted by the DG-CA1 trajectory model and then used to derive the optimal stimulation intensity through the inverse CA1 plant model. Laguerre-Volterra kernel models for random-interval, graded-input, contemporaneous-graded-output system are formulated and applied to build the DG-CA1 trajectory model and the CA1 plant model. The inverse CA1 plant model to transform desired output to input stimulation is derived from the CA1 plant model. We validate this paradigm with rat hippocampal slice preparations. Results show that the CA1 responses evoked by the optimal stimulations accurately replicate the CA1 responses recorded in the hippocampal slice with intact trisynaptic pathway.

Nonlinear model for Dynamic Synapse Neural Network

This paper presents a simplified nonlinear model for Dynamic Synapse Neural Network (DSNN) which is based on nonlinear dynamics of neurons in the hippocampus, using a recurrent neural network. The proposed model will be utilized in place of DSNN for various applications which require simpler implementation and faster training, maintaining the same performance as a nonlinear system model, classifier, or pattern recognizer. This model was tested in two different structure and training methods, by learning the input-output relationship of a few DSNNs with sets of experimentally-determined coefficients. The results showed that this model can capture DSNN's complicated nonlinear dynamics in a temporal domain with less computational cost and faster training.

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.

Synaptic dynamics: Linear model and adaptation algorithm

Linear model for synapse temporal dynamics and learning algorithm for synaptic adaptation in spiking neural networks are presented. The proposed linear model substantially simplifies analysis and training of spiking neural networks, meanwhile accurately models facilitation and depression dynamics in synapse. The learning rule is biologically plausible and is capable of simultaneously adjusting both of LTP and STP parameters of individual synapses in a network. To prove efficiency of the system, a small size spiking neural network is trained for generating different spike and bursting patterns of cortical neurons. The simulation results revealed that the linear model of synaptic dynamics along with the proposed STDP based learning algorithm can provide a practical tool for simulating and training very large scale spiking neural circuitry comprising of significant number of synapses and neurons.

Modeling of the nervous system: from modulation of glutamatergic and gabaergic molecular dynamics to neuron spiking activity

One of the fundamental characteristics of the brain is its hierarchical and temporal organization: scales in both space and time must be considered to fully grasp the system's underlying mechanisms and their impact on brain function. Complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. These integrations across hierarchies of the nervous system are sufficiently complex to have impeded the development of routine multi-level modeling methodologies. The present study describes an example of our multiscale efforts to rise from the biomolecular level to the neuron level. We more specifically describe how we integrate biomolecular mechanisms taking place at glutamatergic and gabaergic synapses and integrate them to study the impact of these modifications on spiking activity of a CA1 pyramidal cell in the hippocampus.

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.

The role of topography in the transformation of spatiotemporal patterns by a large-scale, biologically realistic model of the rat dentate gyrus

A large-scale, biologically realistic, computational model of the rat hippocampus is being constructed to study the input-output transformation that the hippocampus performs. In the initial implementation, the layer II entorhinal cortex neurons, which provide the major input to the hippocampus, and the granule cells of the dentate gyrus, which receive the majority of the input, are modeled. In a previous work, the topography, or the wiring diagram, connecting these two populations had been derived and implemented. This paper explores the consequences of two features of the topography, the distribution of the axons and the size of the neurons' axon terminal fields. The topography converts streams of independently generated random Poisson trains into structured spatiotemporal patterns through spatiotemporal convergence achievable by overlapping axon terminal fields. Increasing the axon terminal field lengths allowed input to converge over larger regions of space resulting in granule activation across a greater area but did not increase the total activity as a function of time as the number of targets per input remained constant. Additional simulations demonstrated that the total distribution of spikes in space depends not on the distribution of the presynaptic axons but the distribution of the postsynaptic population. Analyzing spike counts emphasizes the importance of the postsynaptic distribution, but it ignores the fact that each individual input may be carrying unique information. Therefore, a metric should be created that relates and tracks individual inputs as they are propagated and integrated through hippocampus.

Closing the loop in primate prefrontal cortex: inter-laminar processing

Prefrontal cortical (PFC) activity in the primate brain emerging from minicolumnar microcircuits plays a critical role in cognitive processes dealing with executive control of behavior. However, the specific operations of columnar laminar processing in prefrontal cortex (PFC) are not completely understood. Here we show via implementation of unique microanatomical recording and stimulating arrays, that minicolumns in PFC are involved in the executive control of behavior in rhesus macaque nonhuman primates (NHPs) performing a delayed-match-to-sample (DMS) task. PFC neurons demonstrate functional interactions between pairs of putative pyramidal cells within specified cortical layers via anatomically oriented minicolumns. Results reveal target-specific, spatially tuned firing between inter-laminar (layer 2/3 and layer 5) pairs of neurons participating in the gating of information during the decision making phase of the task with differential correlations between activity in layer 2/3 and layer 5 in the integration of spatial vs. object-specific information for correct task performance. Such inter-laminar processing was exploited by the interfacing of an online model which delivered stimulation to layer 5 locations in a pattern associated with successful performance thereby closing the columnar loop externally in a manner that mimicked normal processing in the same task. These unique technologies demonstrate that PFC neurons encode and process information via minicolumns which provides a closed loop form of "executive function," hence disruption of such inter-laminar processing could form the bases for cognitive dysfunction in primate brain.

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.

A computational model to investigate astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking

Over the past decades, our view of astrocytes has switched from passive support cells to active processing elements in the brain. The current view is that astrocytes shape neuronal communication and also play an important role in many neurodegenerative diseases. Despite the growing awareness of the importance of astrocytes, the exact mechanisms underlying neuron-astrocyte communication and the physiological consequences of astrocytic-neuronal interactions remain largely unclear. In this work, we define a modeling framework that will permit to address unanswered questions regarding the role of astrocytes. Our computational model of a detailed glutamatergic synapse facilitates the analysis of neural system responses to various stimuli and conditions that are otherwise difficult to obtain experimentally, in particular the readouts at the sub-cellular level. In this paper, we extend a detailed glutamatergic synaptic model, to include astrocytic glutamate transporters. We demonstrate how these glial transporters, responsible for the majority of glutamate uptake, modulate synaptic transmission mediated by ionotropic AMPA and NMDA receptors at glutamatergic synapses. Furthermore, we investigate how these local signaling effects at the synaptic level are translated into varying spatio-temporal patterns of neuron firing. Paired pulse stimulation results reveal that the effect of astrocytic glutamate uptake is more apparent when the input inter-spike interval is sufficiently long to allow the receptors to recover from desensitization. These results suggest an important functional role of astrocytes in spike timing dependent processes and demand further investigation of the molecular basis of certain neurological diseases specifically related to alterations in astrocytic glutamate uptake, such as epilepsy.

Columnar processing in primate pFC: evidence for executive control microcircuits

A common denominator for many cognitive disorders of human brain is the disruption of neural activity within pFC, whose structural basis is primarily interlaminar (columnar) microcircuits or "minicolumns." The importance of this brain region for executive decision-making has been well documented; however, because of technological constraints, the minicolumnar basis is not well understood. Here, via implementation of a unique conformal multielectrode recording array, the role of interlaminar pFC minicolumns in the executive control of task-related target selection is demonstrated in nonhuman primates performing a visuomotor DMS task. The results reveal target-specific, interlaminar correlated firing during the decision phase of the trial between multielectrode recording array-isolated minicolumnar pairs of neurons located in parallel in layers 2/3 and layer 5 of pFC. The functional significance of individual pFC minicolumns (separated by 40 μm) was shown by reduced correlated firing between cell pairs within single minicolumns on error trials with inappropriate target selection. To further demonstrate dependence on performance, a task-disrupting drug (cocaine) was administered in the middle of the session, which also reduced interlaminar firing in minicolumns that fired appropriately in the early (nondrug) portion of the session. The results provide a direct demonstration of task-specific, real-time columnar processing in pFC indicating the role of this type of microcircuit in executive control of decision-making in primate brain.

Facilitation and restoration of cognitive function in primate prefrontal cortex by a neuroprosthesis that utilizes minicolumn-specific neural firing

OBJECTIVE

Maintenance of cognitive control is a major concern for many human disease conditions; therefore, a major goal of human neuroprosthetics is to facilitate and/or recover the cognitive function when such circumstances impair appropriate decision making.

APPROACH

Minicolumnar activity from the prefrontal cortex (PFC) was recorded from nonhuman primates trained to perform a delayed match to sample (DMS), via custom-designed conformal multielectrode arrays that provided inter-laminar recordings from neurons in the PFC layer 2/3 and layer 5. Such recordings were analyzed via a previously demonstrated nonlinear multi-input-multi-output (MIMO) neuroprosthesis in rodents, which extracted and characterized multicolumnar firing patterns during DMS performance.

MAIN RESULTS

The MIMO model verified that the conformal recorded individual PFC minicolumns responded to entrained target selections in patterns critical for successful DMS performance. This allowed the substitution of task-related layer 5 neuron firing patterns with electrical stimulation in the same recording regions during columnar transmission from layer 2/3 at the time of target selection. Such stimulation improved normal task performance, but more importantly, recovered performance when applied as a neuroprosthesis following the pharmacological disruption of decision making in the same task.

SIGNIFICANCE

These findings provide the first successful application of neuroprosthesis in the primate brain designed specifically to restore or repair the disrupted cognitive function.

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.

Closing the loop for memory prosthesis: detecting the role of hippocampal neural ensembles using nonlinear models

A major factor involved in providing closed loop feedback for control of neural function is to understand how neural ensembles encode online information critical to the final behavioral endpoint. This issue was directly assessed in rats performing a short-term delay memory task in which successful encoding of task information is dependent upon specific spatio-temporal firing patterns recorded from ensembles of CA3 and CA1 hippocampal neurons. Such patterns, extracted by a specially designed nonlinear multi-input multi-output (MIMO) nonlinear mathematical model, were used to predict successful performance online via a closed loop paradigm which regulated trial difficulty (time of retention) as a function of the "strength" of stimulus encoding. The significance of the MIMO model as a neural prosthesis has been demonstrated by substituting trains of electrical stimulation pulses to mimic these same ensemble firing patterns. This feature was used repeatedly to vary "normal" encoding as a means of understanding how neural ensembles can be "tuned" to mimic the inherent process of selecting codes of different strength and functional specificity. The capacity to enhance and tune hippocampal encoding via MIMO model detection and insertion of critical ensemble firing patterns shown here provides the basis for possible extension to other disrupted brain circuitry.

A nonlinear model for hippocampal cognitive prosthesis: memory facilitation by hippocampal ensemble stimulation

Collaborative investigations have characterized how multineuron hippocampal ensembles encode memory necessary for subsequent successful performance by rodents in a delayed nonmatch to sample (DNMS) task and utilized that information to provide the basis for a memory prosthesis to enhance performance. By employing a unique nonlinear dynamic multi-input/multi-output (MIMO) model, developed and adapted to hippocampal neural ensemble firing patterns derived from simultaneous recorded CA1 and CA3 activity, it was possible to extract information encoded in the sample phase necessary for successful performance in the nonmatch phase of the task. The extension of this MIMO model to online delivery of electrical stimulation delivered to the same recording loci that mimicked successful CA1 firing patterns, provided the means to increase levels of performance on a trial-by-trial basis. Inclusion of several control procedures provides evidence for the specificity of effective MIMO model generated patterns of electrical stimulation. Increased utility of the MIMO model as a prosthesis device was exhibited by the demonstration of cumulative increases in DNMS task performance with repeated MIMO stimulation over many sessions on both stimulation and nonstimulation trials, suggesting overall system modification with continued exposure. Results reported here are compatible with and extend prior demonstrations and further support the candidacy of the MIMO model as an effective cortical prosthesis.