Search

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.

This letter examines the results of input-output (nonparametric) modeling based on the analysis of data generated by a mechanism-based (parametric) model of CA3-CA1 neuronal connections in the hippocampus. The motivation is to obtain biological insight into the interpretation of such input-output (Volterra-equivalent) models estimated from synthetic data. The insights obtained may be subsequently used to interpretat input-output models extracted from actual experimental data. Specifically, we found that a simplified parametric model may serve as a useful tool to study the signal transformations in the hippocampal CA3-CA1 regions. Input-output modeling of model-based synthetic data show that GABAergic interneurons are responsible for regulating neuronal excitation, controlling the precision of spike timing, and maintaining network oscillations, in a manner consistent with previous studies. The input-output model obtained from real data exhibits intriguing similarities with its synthetic-data counterpart, demonstrating the importance of a dynamic resonance in the system/model response around 2 Hz to 3 Hz. Using the input-output model from real data as a guide, we may be able to amend the parametric model by incorporating more mechanisms in order to yield better-matching input-output model. The approach we present can also be applied to the study of other neural systems and pathways.

In this paper, we have introduced a general modeling approach for dynamic nonlinear systems that utilizes a variant of the simulated annealing algorithm for training the Laguerre-Volterra network (LVN) to overcome the local minima and convergence problems and employs a pruning technique to achieve sparse LVN representations with l 1 regularization. We tested this new approach with computer simulated systems and extended it to autoregressive sparse LVN (ASLVN) model structures that are suitable for input-output modeling of nonlinear systems that exhibit transitions in dynamic states, such as the Hodgkin-Huxley (H-H) equations of neuronal firing. Application of the proposed ASLVN to the H-H equations yields a more parsimonious input-output model with improved predictive capability that is amenable to more insightful physiological/biological interpretation.

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., (Copyright © 2014 Elsevier B.V. All rights reserved.)

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin-Huxley (H-H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.

Although an anatomical connection from CA1 to CA3 via the Entorhinal Cortex (EC) and through backprojecting interneurons has long been known it exist, it has never been examined quantitatively on the single neuron level, in the in-vivo nonpatholgical, nonperturbed brain. Here, single spike activity was recorded using a multi-electrode array from the CA3 and CA1 areas of the rodent hippocampus (N = 7) during a behavioral task. The predictive power from CA3→CA1 and CA1→CA3 was examined by constructing Multivariate Autoregressive (MVAR) models from recorded neurons in both directions. All nonsignificant inputs and models were identified and removed by means of Monte Carlo simulation methods. It was found that 121/166 (73 %) CA3→CA1 models and 96/145 (66 %) CA1→CA3 models had significant predictive power, thus confirming a predictive 'Granger' causal relationship from CA1 to CA3. This relationship is thought to be caused by a combination of truly causal connections such as the CA1→EC→CA3 pathway and common inputs such as those from the Septum. All MVAR models were then examined in the frequency domain and it was found that CA3 kernels had significantly more power in the theta and beta range than those of CA1, confirming CA3's role as an endogenous hippocampal pacemaker.

Background: Neural information processing involves a series of nonlinear dynamical input/output transformations between the spike trains of neurons/neuronal ensembles. Understanding and quantifying these transformations is critical both for understanding neural physiology such as short-term potentiation and for developing cognitive neural prosthetics., New Method: A novel method for estimating Volterra kernels for systems with point-process inputs and outputs is developed based on elementary probability theory. These Probability Based Volterra (PBV) kernels essentially describe the probability of an output spike given q input spikes at various lags t1, t2, …, tq., Results: The PBV kernels are used to estimate both synthetic systems where ground truth is available and data from the CA3 and CA1 regions rodent hippocampus. The PBV kernels give excellent predictive results in both cases. Furthermore, they are shown to be quite robust to noise and to have good convergence and overfitting properties. Through a slight modification, the PBV kernels are shown to also deal well with correlated point-process inputs., Comparison With Existing Methods: The PBV kernels were compared with kernels estimated through least squares estimation (LSE) and through the Laguerre expansion technique (LET). The LSE kernels were shown to fair very poorly with real data due to the large amount of input noise. Although the LET kernels gave the best predictive results in all cases, they require prior parameter estimation. It was shown how the PBV and LET methods can be combined synergistically to maximize performance., Conclusions: The PBV kernels provide a novel and intuitive method of characterizing point-process input-output nonlinear systems., (Copyright © 2014 Elsevier B.V. All rights reserved.)

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.

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.

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.

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.

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.

Intracortical recordings comprise both fast events, action potentials (APs), and slower events, known as local field potentials (LFPs). Although it is believed that LFPs mostly reflect local synaptic activity, it is unclear which of their signal components are most closely related to synaptic potentials and would therefore be causally related to the occurrence of individual APs. This issue is complicated by the significant contribution from AP waveforms, especially at higher LFP frequencies. In recordings of single-cell activity and LFPs from the human temporal cortex, we computed quantitative, nonlinear, causal dynamic models for the prediction of AP timing from LFPs, at millisecond resolution, before and after removing AP contributions to the LFP. In many cases, the timing of a significant number of single APs could be predicted from spike-free LFPs at different frequencies. Not surprisingly, model performance was superior when spikes were not removed. Cells whose activity was predicted by the spike-free LFP models generally fell into one of two groups: in the first group, neuronal spike activity was associated with specific phases of low LFP frequencies, lower spike activity at high LFP frequencies, and a stronger linear component in the spike-LFP model; in the second group, neuronal spike activity was associated with larger amplitude of high LFP frequencies, less frequent phase locking, and a stronger nonlinear model component. Spike timing in the first group was better predicted by the sign and level of the LFP preceding the spike, whereas spike timing in the second group was better predicted by LFP power during a certain time window before the spike.

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.

The prefrontal cortex (PFC) has been postulated to play critical roles in cognitive control and the formation of long-term memories. To gain insights into the neurobiological mechanism of such high-order cognitive functions, it is important to understand the input-output transformational properties of the PFC micro-circuitry. In this study, we identify the functional connectivity between the Layer 2/3 (input) neurons and the Layer 5 (output) neurons using a previously developed generalized Volterra model (GVM). Input-output spike trains are recorded from the PFCs of nonhuman primates performing a memory-dependent delayed match-to-sample task with a customized conformal ceramic multi-electrode array. The GVM describes how the input spike trains are transformed into the output spike trains by the PFC micro-circuitry and represents the transformation in the form of Volterra kernels. Results show that Layer 2/3 neurons have strong and transient facilitatory effects on the firings of Layer 5 neurons. The magnitude and temporal range of the input-output nonlinear dynamics are strikingly different from those of the hippocampal CA3-CA1. This form of functional connectivity may have important implications to understanding the computational principle of the PFC.

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.

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input-output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3-CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.

The increasing availability of multiunit recordings gives new urgency to the need for effective analysis of "multidimensional" time-series data that are derived from the recorded activity of neuronal ensembles in the form of multiple sequences of action potentials--treated mathematically as point-processes and computationally as spike-trains. Whether in conditions of spontaneous activity or under conditions of external stimulation, the objective is the identification and quantification of possible causal links among the neurons generating the observed binary signals. A multiple-input/multiple-output (MIMO) modeling methodology is presented that can be used to quantify the neuronal dynamics of causal interrelationships in neuronal ensembles using spike-train data recorded from individual neurons. These causal interrelationships are modeled as transformations of spike-trains recorded from a set of neurons designated as the "inputs" into spike-trains recorded from another set of neurons designated as the "outputs." The MIMO model is composed of a set of multiinput/single-output (MISO) modules, one for each output. Each module is the cascade of a MISO Volterra model and a threshold operator generating the output spikes. The Laguerre expansion approach is used to estimate the Volterra kernels of each MISO module from the respective input-output data using the least-squares method. The predictive performance of the model is evaluated with the use of the receiver operating characteristic (ROC) curve, from which the optimum threshold is also selected. The Mann-Whitney statistic is used to select the significant inputs for each output by examining the statistical significance of improvements in the predictive accuracy of the model when the respective inputs is included. Illustrative examples are presented for a simulated system and for an actual application using multiunit data recordings from the hippocampus of a behaving rat.

Multiple-input multiple-output nonlinear dynamic model of spike train to spike train transformations was previously formulated for hippocampal-cortical prostheses. This paper further described the statistical methods of selecting significant inputs (self-terms) and interactions between inputs (cross-terms) of this Volterra kernel-based model. In our approach, model structure was determined by progressively adding self-terms and cross-terms using a forward stepwise model selection technique. Model coefficients were then pruned based on Wald test. Results showed that the reduced kernel models, which contained much fewer coefficients than the full Volterra kernel model, gave good fits to the novel data. These models could be used to analyze the functional interactions between neurons during behavior.

We are developing a biomimetic electronic neural prosthesis to replace regions of the hippocampal brain area that have been damaged by disease or insult. We have used the hippocampal slice preparation as the first step in developing such a prosthesis. The major intrinsic circuitry of the hippocampus consists of an excitatory cascade involving the dentate gyrus (DG), CA3, and CA1 subregions; this trisynaptic circuit can be maintained in a transverse slice preparation. Our demonstration of a neural prosthesis for the hippocampal slice involves: (i) surgically removing CA3 function from the trisynaptic circuit by transecting CA3 axons, (ii) replacing biological CA3 function with a hardware VLSI (very large scale integration) model of the nonlinear dynamics of CA3, and (iii) through a specially designed multi-site electrode array, transmitting DG output to the hardware device, and routing the hardware device output to the synaptic inputs of the CA1 subregion, thus by-passing the damaged CA3. Field EPSPs were recorded from the CA1 dendritic zone in intact slices and "hybrid" DG-VLSI-CA1 slices. Results show excellent agreement between data from intact slices and transected slices with the hardware-substituted CA3: propagation of temporal patterns of activity from DG-->VLSI-->CA1 reproduces that observed experimentally in the biological DG-->CA3-->CA1 circuit.

This paper presents a novel modeling approach for neural systems with point-process inputs and outputs (binary time-series of 0's and 1's) that utilizes Boolean operators of modulo-2 multiplication and addition, corresponding to the logical AND and OR operations respectively. The form of the employed mathematical model is akin to a "Boolean-Volterra" model that contains the product terms of all relevant input lags in a hierarchical order, where terms of order higher than first represent nonlinear interactions among the various lagged values of each input point-process or among lagged values of various inputs (if multiple inputs exist) as they reflect on the output. The coefficients of this Boolean model are also binary variables that indicate the presence or absence of the respective term in each specific model/system. Simulations are used to explore the properties of such models and the feasibility of accurate estimation of such models from short data-records in the presence of noise (i.e. spurious spikes). The results demonstrate the feasibility of obtaining reliable estimates of such models, even in the presence of considerable noise in the input and/or output, thus making the proposed approach an attractive candidate for modeling neural systems in a practical context.

Much of the research on cannabinoids (CBs) has focused on their effects at the molecular and synaptic level. However, the effects of CBs on the dynamics of neural circuits remains poorly understood. This study aims to disentangle the effects of CBs on the functional dynamics of the hippocampal Schaffer collateral synapse by using data-driven nonparametric modeling. Multi-unit activity was recorded from rats doing an working memory task in control sessions and under the influence of exogenously administered tetrahydrocannabinol (THC), the primary CB found in marijuana. It was found that THC left firing rate unaltered and only slightly reduced theta oscillations. Multivariate autoregressive models, estimated from spontaneous spiking activity, were then used to describe the dynamical transformation from CA3 to CA1. They revealed that THC served to functionally isolate CA1 from CA3 by reducing feedforward excitation and theta information flow. The functional isolation was compensated by increased feedback excitation within CA1, thus leading to unaltered firing rates. Finally, both of these effects were shown to be correlated with memory impairments in the working memory task. By elucidating the circuit mechanisms of CBs, these results help close the gap in knowledge between the cellular and behavioral effects of CBs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

One of the fundamental principles of cortical brain regions, including the hippocampus, is that information is represented in the ensemble firing of populations of neurons, i.e., spatio-temporal patterns of electrophysiological activity. The hippocampus has long been known to be responsible for the formation of declarative, or fact-based, memories. Damage to the hippocampus disrupts the propagation of spatio-temporal patterns of activity through hippocampal internal circuitry, resulting in a severe anterograde amnesia. Developing a neural prosthesis for the damaged hippocampus requires restoring this multiple-input, multiple-output transformation of spatio-temporal patterns of activity. Because the, mechanisms underlying synaptic transmission and generation of electrical activity in neurons are inherently nonlinear, any such prosthesis must be based on a nonlinear multiple-input, multiple-output model. In this paper, we have formulated the transformational process of multi-site propagation of spike activity between two subregions of the hippocampus (CA3 and CA1) as the identification of a multiple-input, multiple-output (MIMO) system, and proposed that it can be decomposed into a series of multiple-input, single-output (MISO) systems. Each MISO system is modeled as a physiologically plausible structure that consists of 1) linear/nonlinear feedforward Volterra kernels modeling synaptic transmission and dendritic integration, 2) a linear feedback Volterra kernel modeling spike-triggered after-potentials, 3) a threshold for spike generation, 4) a summation process for somatic integration, and 5) a noise term representing intrinsic neuronal noise and the contributions of unobserved inputs. Input and output spike trains were recorded from hippocampal CA3 and CA1 regions of rats performing a spatial delayed-nonmatch-to-sample memory task that requires normal hippocampal function. Kernels were expanded with Laguerre basis functions and estimated using a maximum-likelihood method. Complexity of the feedforward kernel was progressively increased to capture higher-order system nonlinear dynamics. Results showed higher prediction accuracies as kernel complexity increased. Self-kernels describe the nonlinearities within each input. Cross-kernels capture the nonlinear interaction between inputs. Second- and third-order nonlinear models were found to successfully predict the CA1 output spike distribution based on CA3 input spike trains. First-order, linear models were shown to be insufficient. [ABSTRACT FROM AUTHOR]

The encoding of mechanical stimuli into action potentials in two types of spider mechanoreceptor neurons is modeled by use of the principal dynamic modes (PDM) methodology. The PDM model is equivalent to the general Wiener–Bose model and consists of a minimum set of linear dynamic filters (PDMs), followed by a multivariate static nonlinearity and a threshold function. The PDMs are obtained by performing eigen-decomposition of a matrix constructed using the first-order and second-order Volterra kernels of the system, which are estimated by means of the Laguerre expansion technique, utilizing measurements of pseudorandom mechanical stimulation (input signal) and the resulting action potentials (output signal). The static nonlinearity, which can be viewed as a measure of the probability of action potential firing as a function of the PDM output values, is computed as the locus of points of the latter that correspond to output action potentials. The performance of the model is assessed by computing receiver operating characteristic (ROC) curves, akin to the ones used in decision theory and quantified by computing the area under the ROC curve. Three PDMs are revealed by the analysis. The first PDM exhibits a high-pass characteristic, illustrating the importance of the velocity of slit displacement in the generation of action potentials at the mechanoreceptor output, while the second and third PDMs exhibit band-pass and low-pass characteristics, respectively. The corresponding three-input nonlinearity exhibits asymmetric behavior with respect to its arguments, suggesting directional dependence of the mechanoreceptor response on the mechanical stimulation and the PDM outputs, in agreement to our findings from a previous study (Ann Biomed Eng 27:391–402, 1999). Differences between the Type A and B neurons are observed in the zeroth-order Volterra kernels (related to the average firing), as well as in the magnitudes of the second and third PDMs that perform band-pass and low-pass processing of the input signal, respectively. [ABSTRACT FROM AUTHOR]