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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.

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.

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.

A new modeling approach of hippocampal nonlinear dynamics is presented. It is based on Principal Dynamics Modes (PDMs) derived from the Volterra kernels quantifying the hippocampal transformations. The approach is illustrated using data obtained from acute hippocampal slice preparations and from behaving rats performs a memory task. The resulting PDM models are comparable in performance to the Volterra models and require significantly less representational and implementational overhead.

Dentate granule cells receive inputs from the entorhinal cortex as the "perforant path". There are two components of the perforant path: the lateral component (LPP) and the medial component (MPP). LPP and MPP convey different sensory modality information. It remains elusive as to how signals from different inputs interact and integrate at the granule cell level. We attempted to address this issue by using nonlinear systems analytic methods. Granule cell EPSPs and action potentials were recorded intracellularly from in vitro hippocampal slices of the rat. MPP and LPP were activated simultaneously by two independent Poisson random trains. Poisson-Volterra kernel models were estimated using Laguerre expansion of Volterra kernel technique. In the kernel models, self-kernels represent the intrinsic input/output properties of each pathway, while cross-kernels quantify the interactions between the two inputs. Short-term plasticity (STP) was revealed by both 2nd order self and cross kernels. We reason that the underlying mechanisms of the STP are diffusely distributed along input-specific synapses, dendritic tree and soma. The plasticity held by the dendritic tree/soma and synapses can be divided and referred to as neuronal and synaptic plasticity respectively. We argue that the cross kernel properties are determined primarily by neuronal plasticity while the self kernel properties are controlled largely by synaptic plasticity. Our experimental data suggest that linear summation of the membrane potential of the postsynaptic neuron can only partially explain the neuronal plasticity. Both supra- and sublinear summations were observed. Thus, the neuronal plasticity is likely to be the product of passive and active processes of the postsynaptic neuron and plays a pivotal role in multiple inputs integration.

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.

We present a new method to characterize the nonlinearities resulting from the co-activity of two pathways that converge on a common postsynaptic element. We investigated the nonlinear dynamic interactions between the lateral perforant pathway (LPP) and the Medial Perforant Pathway (MPP) of the hippocampal dentate gyrus, and the effects of these cross-pathway interactions on granule cell output. A third order Volterra-Poisson modeling approach was implemented to capture the interactions between the two pathways. The kernels presented pathway specific signatures as they capture the nonlinear dynamics of each pathway individually in the form of self-kernels, and the nonlinear interactions between the two pathways in the form of cross-kernels. Data were collected in-vitro from acute slices of adult rats via a multi-electrode array recording system. The stimuli were dual-site random impulse trains with Poisson distributed inter-impulse intervals. The recorded responses from the granule cells were population spikes, simplified as discrete impulses with variable amplitudes. Our results indicated that the third order nonlinear interactions between the LPP and the MPP needs to be included in the model in order to achieve adequate predictive accuracy and indicate that this approach can be generalized to complex interactions between distinct inputs to the same set of neurons.

A multi-input modeling approach is introduced to quantify hippocampal neural dynamics. It is based on the Volterra modeling approach extended to multiple inputs. The computed Volterra kernels allow quantitative description of hippocampal transformations and define a predictive model that can produce responses to arbitrary input patterns. Electrophysiological data from several CA3 and CA1 cells in behaving rats were recorded simultaneously using an array of penetrating electrodes. This activity was used to compute kernels up to third order for single and multiple input cases. Representative sets of kernels illustrate the variability of the dynamics of the CA3-CA1 transformations. Our model's predictive accuracy was evaluated using ROC curves.

Nonlinear kernel models are developed and estimated for the spike train transformation from hippocampal CA3 region to CA1 region. The physiologically plausible model structure consists of nonlinear feedforward kernels that model synaptic transmission and dendritic integration, a linear feedback kernel that models spike-triggered after potential, a threshold, an adder, and a noise term that assesses the system uncertainties. Model parameters are estimated using maximum-likelihood method. Model goodness-of-fit is evaluated using correlation measures and time-rescaling theorem. First order, linear model is shown to be insufficient. Second and third order nonlinear models can successfully predict the output spike distribution.

Inversion layer ultrasonic transducers have been investigated recently as an interesting approach in wideband transducer design. In this paper we present an analytical model of multilayer ultrasonic transducers with an inversion layer. Our analysis of the wave propagation problem of an inversion layer transducer includes a functional decomposition of the electrical input impedance. It becomes clear from this decomposition that an inversion layer transducer can be modeled as three elements in series connection, i.e., a clamped capacitance, a classical motional impedance, and a coupled motional impedance. The first two elements make up the classical model of a single element transducer. The coupled motional impedance describes the coupled interaction between the regular and the inverted piezoelectric sublayers, and thus reflects the effect of an inversion layer. We present examples which show that inversion layer transducers are advantageous in achieving such useful features as dual-frequency operation mode as used in harmonic imaging or broadband performance desired in most ultrasonic applications.

Half-thickness inversion layer high-frequency ultrasonic transducers were fabricated using lithium niobate (LiNbO3) single crystal plate. The transducers developed for this study used a 36 degrees rotated Y-cut LiNbO3 thin plate with an active element thickness of 115 microm. The designed center frequency was in the range of 30 to 60 MHz. Half-thickness inversion layer was formed after the sample was annealed at a high temperature, and it is shown that the inversion layer thickness can be controlled by the temperature. Silver powder/epoxy composite and parylene were used as acoustic matching layers. A lossy silver epoxy was used as the backing material. Using an analytical method, the electrical impedance for different inversion layer ratios was determined. The measured resonant frequency was consistent with the modeled data. Even-order higher frequency broadband ultrasonic transducers with a center frequency at 60 MHz was obtained using half-thickness inversion layer of LiNbO3 single crystal.

The effect of spontaneous beat-to-beat mean arterial blood pressure fluctuations and breath-to-breath end-tidal CO2 fluctuations on beat-to-beat cerebral blood flow velocity variations is studied using the Laguerre-Volterra network methodology for multiple-input nonlinear systems. The observations made from experimental measurements from ten healthy human subjects reveal that, whereas pressure fluctuations explain most of the high-frequency blood flow velocity variations (above 0.04 Hz), end-tidal CO2 fluctuations as well as nonlinear interactions between pressure and CO2 have a considerable effect in the lower frequencies (below 0.04 Hz). They also indicate that cerebral autoregulation is strongly nonlinear and dynamic (frequency-dependent). Nonlinearities are mainly active in the low-frequency range (below 0.04 Hz) and are more prominent in the dynamics of the end-tidal CO2-blood flow velocity relationship. Significant nonstationarities are also revealed by the obtained models, with greater variability evident for the effects of CO2 on blood flow velocity dynamics.