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.

Linear and Nonlinear Modeling of Cerebral Flow Autoregulation Using Principal Dynamic Modes

Cerebral Flow Autoregulation (CFA) is the dynamic process by which cerebral blood flow is maintained within physiologically acceptable bounds during fluctuations of cerebral perfusion pressure. The distinction is made with “static” flow autoregulation under steady-state conditions of perfusion pressure, described by the celebrated “autoregulatory curve” with a homeostatic plateau. This paper studies the dynamic CFA during changes in perfusion pressure, which attains critical clinical importance in patients with stroke, traumatic brain injury and neurodegenerative disease with a cerebrovascular component. Mathematical and computational models have been used to advance our quantitative understanding of dynamic CFA and to elucidate the underlying physiological mechanisms by analyzing the relation between beat-to-beat data of mean arterial blood pressure (viewed as input) and mean cerebral blood flow velocity(viewed as output) of a putative CFA system. Although previous studies have shown that the dynamic CFA process is nonlinear, most modeling studies to date have been linear. It has also been shown that blood CO2 tension affects the CFA process. This paper presents a nonlinear modeling methodology that includes the dynamic effects of CO2 tension (or its surrogate, end-tidal CO2) as a second input and quantifies CFA from short data-records of healthy human subjects by use of the modeling concept of Principal Dynamic Modes (PDMs). The PDMs improve the robustness of the obtained nonlinear models and facilitate their physiological interpretation. The results demonstrate the importance of including the CO2 input in the dynamic CFA study and the utility of nonlinear models under hypercapnic or hypocapnic conditions.

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.

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.

Functional connectivity between Layer 2/3 and Layer 5 neurons in prefrontal cortex of nonhuman primates during a delayed match-to-sample task

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.

Relationships between spike-free local field potentials and spike timing in human temporal cortex

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.

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.

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.

Diagnostic biomarkers for Alzheimer's disease using dynamic nonlinear models based on Principal Dynamic Modes

Sensitive and robust diagnostic biomarkers for Alzheimer's disease (AD) were sought using dynamic nonlinear models of the causal interrelationships among time-series (beat-to-beat) data of arterial blood pressure, end-tidal CO(2) and cerebral blood flow velocity collected in human subjects (4 AD patients and 4 control subjects). These models were based on Principal Dynamic Modes (PDM) and yielded a reliable biomarker for AD diagnosis in the form of the "Effective CO(2) Reactivity Index" (ECRI). The results from this initial set of subjects corroborated the efficacy of the ECRI biomarker for accurate AD diagnosis.

Estimation and statistical validation of event-invariant nonlinear dynamic models of hippocampal CA3-CA1 population activities

To develop hippocampal prosthetic devices that can restore the memory-dependent cognitive functions lost in diseases or injuries, it is essential to build a computational model that sufficiently captures the transformations of multiple memories performed by hippocampal sub-regions. A universal model with a single set of coefficients for all memories is desirable, since it can transform the memories without explicitly knowing what those memories represent and thus avoids switching between multiple models for multiple memories in implementation. In this study, we test the feasibility of such universal models of hippocampal CA3-CA1 by estimating the multi-input, multi-output (MEMO) nonlinear dynamic models using input (CA3) and output (CA1) spike trains recorded during multiple behavioral events representing multiple memories from rats performing a delayed nonmatch-to-sample task. We further statistically evaluated the model performances of the MEMO models on the different events. Results show that the models accurately replicate the output spike patterns during those events, and thus can be used as event-invariant nonlinear dynamic models that continuously predict the ongoing CA1 spatio-temporal patterns as the ongoing CA3 spatio-temporal patterns unfold.

A switching control strategy for the attenuation of blood glucose disturbances

In this computational study we consider a generalized minimal model structure for the intravenously infused insulin-blood glucose dynamics, which can represent a wide variety of diabetic patients, and augment this model structure with a glucose rate disturbance signal that captures the aggregate effects of various internal and external factors on blood glucose. Then we develop a model-based, switching controller, which attempts to balance between optimal performance, reduced computational complexity and avoidance of dangerous hypoglycaemic events. We evaluate the proposed algorithm relative to the widely studied proportional-derivative controller for the regulation of blood glucose with continuous insulin infusions. The results show that the proposed switching control strategy can regulate blood glucose much better than the proportional-derivative controller for all the different types of diabetic patients examined. This new algorithm is also shown to be remarkably robust in the event of concurrent, unknown variations in critical parameters of the adopted model.

Modeling of nonlinear nonstationary dynamic systems with a novel class of artificial neural networks

This paper introduces a novel neural-network architecture that can be used to model time-varying Volterra systems from input-output data. The Volterra systems constitute a very broad class of stable nonlinear dynamic systems that can be extended to cover nonstationary (time-varying) cases. This novel architecture is composed of parallel subnets of three-layer perceptrons with polynomial activation functions, with the output of each subnet modulated by an appropriate time function that gives the summative output its time-varying characteristics. The paper shows the equivalence between this network architecture and the class of time-varying Volterra systems, and demonstrates the range of applicability of this approach with computer-simulated examples and real data. Although certain types of nonstationarities may not be amenable to this approach, it is hoped that this methodology will provide the practical tools for modeling some broad classes of nonlinear, nonstationary systems from input-output data, thus advancing the state of the art in a problem area that is widely viewed as a daunting challenge.

Sparse generalized Laguerre-Volterra model of neural population dynamics

To understand the function of a brain region, e.g., hippocampus, it is necessary to model its input-output property. Such a model can serve as the computational basis of the development of cortical prostheses restoring the transformation of population neural activities performed by the brain region. We formulate a sparse generalized Laguerre-Volterra model (SGLVM) for the multiple-input, multiple-output (MIMO) transformation of spike trains. A SGLVM consists of a set of feedforward Laguerre-Volterra kernels, a feedback Laguerre-Volterra kernel, and a probit link function. The sparse model representation involving only significant self and cross terms is achieved through statistical model selection and cross-validation methods. The SGLVM is applied successfully to the hippocampal CA3-CA1 population dynamics.

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

The successful development of neural prostheses requires an understanding of the neurobiological bases of cognitive processes, i.e., how the collective activity of populations of neurons results in a higher level process not predictable based on knowledge of the individual neurons and/or synapses alone. We have been studying and applying novel methods for representing nonlinear transformations of multiple spike train inputs (multiple time series of pulse train inputs) produced by synaptic and field interactions among multiple subclasses of neurons arrayed in multiple layers of incompletely connected units. We have been applying our methods to study of the hippocampus, a cortical brain structure that has been demonstrated, in humans and in animals, to perform the cognitive function of encoding new long-term (declarative) memories. Without their hippocampi, animals and humans retain a short-term memory (memory lasting approximately 1 min), and long-term memory for information learned prior to loss of hippocampal function. Results of more than 20 years of studies have demonstrated that both individual hippocampal neurons, and populations of hippocampal cells, e.g., the neurons comprising one of the three principal subsystems of the hippocampus, induce strong, higher order, nonlinear transformations of hippocampal inputs into hippocampal outputs. For one synaptic input or for a population of synchronously active synaptic inputs, such a transformation is represented by a sequence of action potential inputs being changed into a different sequence of action potential outputs. In other words, an incoming temporal pattern is transformed into a different, outgoing temporal pattern. For multiple, asynchronous synaptic inputs, such a transformation is represented by a spatiotemporal pattern of action potential inputs being changed into a different spatiotemporal pattern of action potential outputs. Our primary thesis is that the encoding of short-term memories into new, long-term memories represents the collective set of nonlinearities induced by the three or four principal subsystems of the hippocampus, i.e., entorhinal cortex-to-dentate gyrus, dentate gyrus-to-CA3 pyramidal cell region, CA3-to-CA1 pyramidal cell region, and CA1-to-subicular cortex. This hypothesis will be supported by studies using in vivo hippocampal multineuron recordings from animals performing memory tasks that require hippocampal function. The implications for this hypothesis will be discussed in the context of "cognitive prostheses"-neural prostheses for cortical brain regions believed to support cognitive functions, and that often are subject to damage due to stroke, epilepsy, dementia, and closed head trauma.

Autonomic neural control of cerebral hemodynamics

Despite the rich innervation of the cerebral vasculature by both sympathetic and parasympathetic nerves, the role of autonomic control in cerebral circulation and, particularly, cerebral hemodynamics is not entirely clear. Previous animal studies have reported inconsistent results regarding the effects of electrical stimulation or denervation on cerebral blood flow (CBF), cerebral pressure-flow relationship, and cerebral vessel response to metabolic stimuli. Moreover, with the advance of transcranial Doppler ultrasound (TCD), which yields accurate measurements of CBF velocity (CBFV) with high time resolution, it has been found that in humans CBFV in the middle cerebral artery decreased substantially during lower body negative pressure (LBNP) and head-up tilt in the absence of systemic hypotension, which suggests the presence of cerebral vasoconstriction associated with augmented sympathetic nerve activity during orthostatic stress. These observations were based on assessing static measures of cerebral circulation, i.e., mean values of artevial blood pressure (ABP) and CBF with a low time resolution.

Boolean modeling of neural systems with point-process inputs and outputs. Part II: Application to the rat hippocampus

This paper presents a pilot application of the Boolean-Volterra modeling methodology presented in the companion paper (Part I) that is suitable for the analysis of systems with point-process inputs and outputs (e.g., recordings of the activity of neuronal ensembles). This application seeks to discover the causal links between two neuronal ensembles in the hippocampus of a behaving rat. The experimental data come from multi-unit recordings in the CA3 and CA1 regions of the hippocampus in the form of sequences of action potentials-treated mathematically as point-processes and computationally as spike-trains-that are collected in vivo during two behavioral tasks. The modeling objective is to identify and quantify the causal links among the neurons generating the recorded activity, using Boolean-Volterra models estimated directly from the data according to the methodological framework presented in the companion paper. The obtained models demonstrate the feasibility of the proposed approach using short data-records and provide some insights into the functional properties of the system (e.g., regarding the presence of rhythmic characteristics in the neuronal dynamics of these ensembles), making the proposed methodology an attractive tool for the analysis and modeling of multi-unit recordings from neuronal systems in a practical context.

Boolean modeling of neural systems with point-process inputs and outputs. Part I: theory and simulations

This paper presents a new modeling approach for neural systems with point-process (spike) inputs and outputs that utilizes Boolean operators (i.e. modulo 2 multiplication and addition that correspond to the logical AND and OR operations respectively, as well as the AND_NOT logical operation representing inhibitory effects). The form of the employed mathematical models 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-Volterra 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 their accurate estimation 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, with excitatory and inhibitory terms, in the presence of considerable noise (spurious spikes) in the outputs and/or the inputs in a computationally efficient manner. A pilot application of this approach to an actual neural system is presented in the companion paper (Part II).

Nonlinear modeling of the dynamic effects of infused insulin on glucose: comparison of compartmental with Volterra models

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted "minimal model" and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.

Nonlinear modeling of neural population dynamics for hippocampal prostheses

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.

Functional connectivity through nonlinear modeling: an application to the rat hippocampus

Implementation of neuroprosthetic devices requires a reliable and accurate quantitative representation of the input-output transformations performed by the involved neuronal populations. Nonparametric, data driven models with predictive capabilities are excellent candidates for these purposes. When modeling input-output relations in multi-input neuronal systems, it is important to select the subset of inputs that are functionally and causally related to the output. Inputs that do not convey information about the actual transformation not only increase the computational burden but also affect the generalization of the model. Moreover, a reliable functional connectivity measure can provide patterns of information flow that can be linked to physiological and anatomical properties of the system. We propose a method based on the Volterra modeling approach that selects distinct subsets of inputs for each output based on the prediction of the respective models and its statistical evaluation. The algorithm builds successive models with increasing number of inputs and examines whether the inclusion of additional inputs benefits the predictive accuracy of the overall model. It also explores possible second-order (inter-modulatory) interactions among the inputs. The method was applied to multi-unit recordings from the CA3 (input) and CA1 (output) regions of the hippocampus in behaving rats, in order to reveal spatiotemporal connectivity maps of the input-output transformation taking place in the CA3-CA1 synapse.

Computational study of an augmented minimal model for glycaemia control

In this paper we introduce a new model structure for the metabolic effects of intravenous insulin on blood glucose in man and derive its parameter values from the widely used model of Sorensen. The proposed model attempts to combine the advantages of the existing comprehensive and minimal models. Validation of the new model is done through deriving equivalent nonparametric nonlinear models in the form of Principal Dynamic Modes. We show that the new structure can represent the insulin-glucose dynamics of healthy subjects as well as Type 1 and Type 2 diabetics, with appropriate adjustment in its parameters.