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Analysis of beat-to-beat spontaneous cerebral hemodynamic data has yielded predictive dynamic models of cerebral hemodynamics and has shown previously that patients with Mild Cognitive Impairment (MCI) exhibit significantly reduced cerebral vasomotor reactivity to CO 2 relative to cognitively normal control subjects [1]. The present work examines the heart-rate reflex (HRR) dynamics of 46 MCI patients compared to 20 control subjects, using closed-loop modeling of HRR under resting conditions of spontaneous variations of arterial blood pressure (baroreflex) and end-tidal CO 2 (chemoreflex). These subject-specific predictive dynamic models are obtained via the methodology of Principal Dynamic Modes [2] and allow the computation of model-based markers of baroreflex and chemoreflex function. We found that the chemoreflex gain is significantly weakened in MCI patients relative to controls (p=0.0086), while the baroreflex is not significantly affected. These findings offer another tool for diagnosis and monitoring of MCI (via model-based markers), when used in conjunction with current methods.

To understand how memory information is encoded in the hippocampus, we build classification models to decode memory features from hippocampal CA3 and CA1 spatio-temporal patterns of spikes recorded from epilepsy patients performing a memory-dependent delayed match-to-sample task. The classification model consists of a set of B-spline basis functions for extracting memory features from the spike patterns, and a sparse logistic regression classifier for generating binary categorical output of memory features. Results show that classification models can extract significant amount of memory information with respects to types of memory tasks and categories of sample images used in the task, despite the high level of variability in prediction accuracy due to the small sample size. These results support the hypothesis that memories are encoded in the hippocampal activities and have important implication to the development of hippocampal memory prostheses.

In order to build hippocampal prostheses for restoring memory functions, we build multi-input, multi-output (MIMO) nonlinear dynamical models of the human hippocampus. Spike trains are recorded from the hippocampal CA3 and CA1 regions of epileptic patients performing a memory-dependent delayed match-to-sample task. Using CA3 and CA1 spike trains as inputs and outputs respectively, second-order sparse generalized Laguerre-Volterra models are estimated with group lasso and local coordinate descent methods to capture the nonlinear dynamics underlying the spike train transformations. These models can accurately predict the CA1 spike trains based on the ongoing CA3 spike trains and thus will serve as the computational basis of the hippocampal memory prosthesis.

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.

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.

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.

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.

This computational study demonstrates the efficacy of regulating blood glucose in Type 1 diabetics with a Model Predictive Control strategy, utilizing a nonparametric / Principal Dynamic Modes model. For this purpose, a stochastic glucose disturbance signal is introduced and a simple methodology for predicting its future values is developed. The results of our simulations confirm that the proposed algorithm achieves very good performance, is computationally efficient and avoids hypoglycaemic events.

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.

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.

Generalized Volterra kernel model (GVM) is developed in spirits of the generalized linear model (GLM) and used to predict EMG signals based on M1 cortical spike trains during a prehension task. The GVM for EMG consists of a cascade of a multiple-input-single-output Volterra kernel model (VM) and an exponential activation function. Without loss of generality, the exponential activation function constrains the unbounded VM output within the positive range, which fully covers the dynamic range of the rectified EMG signals. Results show that GVMs are more accurate than the VMs due to this asymptotic property.

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.

This paper presents the results of computational studies that compare simulated parametric and nonparametric models in terms of their ability to obtain reliable quantitative descriptions of the dynamic effects of variable infusions of insulin on blood glucose concentration in human subjects. In the nonparametric modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. The parametric models considered are the extensively studied "minimal model" and an augmented variant of the latter that incorporates the process of insulin secretion by the pancreas in response to elevated blood glucose. This model represents the actual closed-loop operating conditions of the system. The presented results demonstrate the feasibility of obtaining data-driven (i.e. inductive) nonparametric models in a realistic operating context, without resorting to the restrictive prior assumptions of model structure that are necessary for the numerous parametric (compartmental) models proposed previously. The rationale underpinning the nonparametric approach is that prior assumptions regarding the model structure may lead to results that are improperly constrained or biased by preconceived notions. Thus, it may be preferable to let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models that imposes no such constraints.

Normal aging is associated with changes in the cardiovascular system and more specifically in cerebral circulation. Sex-dependent changes in cerebrovascular CO2 reactivity, which may be related to hormonal levels, have been also reported. We therefore examined cerebral hemodynamics, i.e., dynamic pressure autoregulation and CO2 reactivity, by employing beat-to-beat values of mean arterial blood pressure and middle cerebral artery blood flow velocity, as well as breath-to-breath values of end-tidal CO2 tension during baseline and sustained, end-tidal forcing induced hypercapnia in pre- and post-menopausal women. For this purpose, we employed a recently proposed nonlinear, multiple-input model of cerebral hemodynamics. The results suggest that dynamic autoregulation and reactivity in response to spontaneous fluctuations are not affected in postmenopausal women and that CO2 reactivity to the larger, experimentally-induced hypercapnic stimuli are affected mildly. A significant decrease in CO2 reactivity to spontaneous fluctuations was also observed during hypercapnia in all three groups.