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A modeling approach to characterize the nonlinear dynamic transformations of the dentate gyrus of the hippocampus is presented and experimentally validated. The dentate gyrus is the first region of the hippocampus which receives and integrates sensory information via the perforant path. The perforant path is composed of two distinct pathways: 1) the lateral path and 2) the medial perforant path. The proposed approach examines and captures the short-term dynamic characteristics of these two pathways using a nonparametric, third-order Poisson-Volterra model. The nonlinear characteristics of the two pathways are represented by Poisson-Volterra kernels, which are quantitative descriptors of the nonlinear dynamic transformations. The kernels were computed with experimental data from in vitro hippocampal slices. The electrophysiological activity was measured with custom-made multielectrode arrays, which allowed selective stimulation with random impulse trains and simultaneous recordings of extracellular field potential activity. The results demonstrate that this mathematically rigorous approach is suitable for the multipathway complexity of the hippocampus and yields interpretable models that have excellent predictive capabilities. The resulting models not only accurately predict previously reported electrophysiological descriptors, such as paired pulses, but more important, can be used to predict the electrophysiological activity of dentate granule cells to arbitrary stimulation patterns at the perforant path. Index Terms--Dentate gyrus, electrophysiology, hippocampus, Laguerre expansion, multielectrode arrays, nonlinear modeling, perforant path, synaptic transmission, Volterra kernel.

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. Index Terms--Feedback, hippocampus, Laguerre expansion, multiple-input, multiple-output system, spatio-temporal pattern, spike, time-rescaling theorem, Volterra kernel.

The effect of spontaneous beat-to-beat mean arterial blood pressure fluctuations and breath-to-breath end-tidal C[O.sub.2] 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 C[O.sub.2] fluctuations as well as nonlinear interactions between pressure and C[O.sub.2] 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 C[O.sub.2]-blood flow velocity relationship. Significant nonstationarities are also revealed by the obtained models, with greater variability evident for the effects of C[O.sub.2] on blood flow velocity dynamics. Index Terms--Cerebral autoregulation, cerebral hemodynamics, Laguerre-Volterra network, nonlinear modeling, nonstationary systems, Volterra kernels.

We compared the dynamic characteristics in renal autoregulation of blood flow of normotensive Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR), using both linear and nonlinear systems analysis. Linear analysis yielded only limited information about the differences in dynamics between SDR and SHR. The predictive ability, as determined by normalized mean-square errors (NMSE), of a third-order Volterra model is better than for a linear model. This decrease in NMSE with a third-order model from that of a linear model is especially evident at frequencies below 0.2 Hz. Furthermore, NMSE are significantly higher in SHR than SDR, suggesting a more complex nonlinear system in SHR. The contribution of the third-order kernel in describing the dynamics of renal autoregulation in arterial blood pressure and blood flow was found to be important. Moreover, we have identified the presence of nonlinear interactions between the oscillatory components of the myogenic mechanism and tubuloglomerular feedback (TGF) at the level of whole kidney blood flow in SDR. An interaction between these two mechanisms had previously been revealed for SDR only at the single nephron level. However, nonlinear interactions between the myogenic and TGF mechanisms are not detected for SHR. Index Terms - Hypertensive, Laguerre functions, myogenic, nonlineal system identification, renal autoregulation, TGF.

A methodology for modeling spike-output neural systems from input-output data is proposed, which makes use of 'neuronal modes' (NM) and 'multi-input threshold' (MT) operators. The modeling concept of NM's was introduced in a previously published paper in order to provide concise and general mathematical representations of the nonlinear dynamics involved in signal transformation and coding by a class of neural systems. This paper presents and demonstrates (with computer simulations) a method by which the NM's are determined using the 1st- and 2nd-order kernel estimates of the system, obtained from input-output data. The MT operator (i.e., a binary operator with multiple real-valued operands which are the outputs of the NM's) possesses an intrinsic refractory mechanism and generates the sequence of output spikes. The spike-generating characteristics of the MT operator are determined by the 'trigger regions' defined on the basis of data. This approach is offered as a reasonable compromise between modeling complexity and prediction accuracy, which may provide a common methodological framework for modeling a certain class of neural systems.

In order to assess the linearity of the mechanisms subserving renal blood flow autoregulation, broad-band arterial pressure fluctuations at three different power levels were induced experimentally and the resulting renal blood flow responses were recorded. Linear system analysis methods were applied in both the time and frequency domain. In the frequency domain, spectral estimates employing FFT, autoregressive moving average (ARMA) and moving average (MA) methods were used; only the MA model showed two vascular control mechanisms active at 0.02-0.05 Hz and 0.1-0.18 Hz consistent with previous experimental findings (Holstein-Rathlou et al., Amer. J. Physiol., vol. 258, 1990.). In the time domain, impulse response functions obtained from the MA model indicated likewise the presence of these two vascular control mechanisms, but the ARMA model failed to show any vascular control mechanism at 0.02-0.05 Hz. The residuals (i.e., model prediction errors) of the MA model were smaller than the ARMA model for all levels of arterial pressure forcings. The observed low coherence values and the significant model residuals in the 0.02-0.05 Hz frequency range suggest that the tubuloglomerular feedback (TGF) active in this frequency range is a nonlinear vascular control mechanism. In addition, experimental results suggest that the operation of the TGF mechanism is more evident at low/moderate pressure fluctuations and becomes overwhelmed when the arterial pressure forcing is too high.

The development of a new laser-induced fluorescence (LIF) spectroscopy technique for the measurement of the attenuation spectrum of tissue is described. The technique, termed laser-induced fluorescence attenuation spectroscopy (LIFAS), has been applied to study the effects of hypoxia on the in vivo optical properties of renal and myocardial tissue in the 350-600-nm band. Excimer laser (Xe-Cl) is used to excite a small volume of the tissue (rabbit model, N = 20) and induce autofluorescence. The emitted LIF is monitored fiberoptically at two locations that are unevenly displaced about the fluorescing volume. The optical attenuation of the tissue is calculated from the dual LIF measurements by assuming an exponential decay of the fluorescence with distance. The results indicate that hypoxia modulates the attenuation spectrum leading to characteristic changes in its shape. Primarily, the spectral profile becomes more concave between 455 nm and 505 nm and two spectral peaks at about 540 and 580 nm disappear leaving in their place a single peak at about 555 nm. The attenuation spectra of normoxic and hypoxic tissue are used to train partial least squares multivariate model for spectral classification. The model detected acute renal and myocardial hypoxia with an accuracy greater than 90% (range: 90%-96%) and 74% (range: 74%-90%), respectively. Index Terms--Heart, hyperoxia, hypoxia, ischemia, kidney, laser-induced fluorescence spectroscopy (LIFS) , myocardium, optical absorption, optical attenuation, renal, spectroscopy.

The scientific and clinical importance of cerebral hemodynamics has generated considerable interest in their quantitative understanding via computational modeling. In particular, two aspects of cerebral hemodynamics, cerebral flow autoregulation (CFA) and CO2 vasomotor reactivity (CVR), have attracted much attention because they are implicated in many important clinical conditions and pathologies (orthostatic intolerance, syncope, hypertension, stroke, vascular dementia, mild cognitive impairment, Alzheimer's disease, and other neurodegenerative diseases with cerebrovascular components). Both CFA and CVR are dynamic physiological processes by which cerebral blood flow is regulated in response to fluctuations in cerebral perfusion pressure and blood CO2 tension. Several modeling studies to date have analyzed beat-to-beat hemodynamic data in order to advance our quantitative understanding of CFA–CVR dynamics. A confounding factor in these studies is the fact that the dynamics of the CFA–CVR processes appear to vary with time (i.e., changes in cerebrovascular characteristics) due to neural, endocrine, and metabolic effects. This paper seeks to address this issue by tracking the changes in linear time-invariant models obtained from short successive segments of data from ten healthy human subjects. The results suggest that systemic variations exist but have stationary statistics and, therefore, the use of time-invariant modeling yields “time-averaged models” of physiological and clinical utility. [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 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. [ABSTRACT FROM AUTHOR]