Paul Koch

Effect of local synaptic strengthening on global activity-wave growth in the hippocampus.

Analysis of a continuum model of the hippocampus shows that strengthening of the synaptic connections within localized regions can convert the global activity-wave properties from decay to growth. These growing waves can play a part in the implantation of long-term memory in the higher brain regions. The wavelength of the fastest-growing mode decreases with increasing local synaptic strength and can be modified by the chemical state as reflected by synaptic sensitivity to stimuli. The temporal period of the response is a constant, equal to twice the delay time exhibited by some of the hippocampal inhibitory neurons (“d-cells”). The value for the period obtained from this relationship and measurement of the delay time agrees with the hippocampal gamma rhythm. For normal hippocampal function the proportion of d-cells is limited to one-third the total number of inhibitory neurons.

A continuum model of activity waves in layered neuronal networks: a neuropsychology of brainstem seizures.

We model and brainstem as two layers of respectively purely excitatory and purely inhibitory cells, with instantaneous synaptic interactions within a layer, but with a variable time delay between the layers. For appropriate values of the connection parameters, this configuration provides an attentional mechanism. As the inhibitory delay increases, input signals are, at first, increasingly amplified and confined spatially. At larger delays, the amplified activity propagates into other regions allowing for spatial summation. The temporal frequency of the amplified activity decreases with increasing delay, but its spatial frequency remains relatively constant. As the delay increases through a critical region, a new regime is reached in which highly amplified activity occurs simultaneously over large areas. This regime exhibits many properties of seizure activity.

Synaptic strengthening and continuum activity-wave growth in temporal sequencing during cognitive tasks.

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A layered neural continuum architecture in attention and seizure disorders

Neural continuum theory concerns regions containing large numbers of neurons. Connections within a region are not specified and those between regions are probabilistic. Constituent cells can be treated as purely “excitatory” or “inhibitory”. In a layered geometry, with a time delay between layers, delay is the variable controlling the linear behavior of the system, in particular, growth of small disturbances. Two layers of cells of opposite types structurally resemble and functionally model the attention centers of the brain (the reticular formation). Attention shifts among competing regions through changes in local inhibitory time waves and their spatial propagation. Increase in delay above a critical value, leads to large amplitude, spatially uniform activity; nonlinear extension of the two-layer model predicts potentials in qualitative agreement with those observed during seizures. The preferentially amplified spatial-frequency of normal waves remains relatively constant with delay. Since it is proportional to the locally varying mean lateral axonal extent, spatial-frequency is a signature by which the most compelling region can be recognized by higher brain centers.

A continuum model of activity waves in layered neuronal networks: computer models of brain-stem seizures

A model of dysfunctional brain-stem activity as nonlinear homogeneous disturbances in a structure consisting of excitatory and inhibitory layers is presented. Cortical EEG traces are identified with the time derivative of the active fraction of excitatory cells. Increase in the time delay between the layers causes the onset of periodic nonlinear oscillations. Change in the biochemical state can cause rapid oscillations similar to seizures.<<ETX>>

Typology of nonlinear activity waves in a layered neural continuum

Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the “holographic memory” (); wave mixing provides a plausible cause of the competition called “neural Darwinism” (); finally the consecutive generation of growing neural waves can explain the discontinuousness of “psychological time” ().

Cortical Activity waves are the physical carriers of memory and thought

Growing and propagating waves of neural activity are the natural resonant modes of synaptic energy. In a layered geometry typifying the mammalian cortex, a time delay (T) in inter-layer signals effectively controls the temporal and spatial frequencies of the waves. As a function of T, two very different types of wave can grow from ubiquitous noise. One is coherent, and its resonant spatial frequency increases with increasing T. However, further increase eventually leads to a discontinuous increase in both wavelength and temporal frequency. The result is a region of T values wherein two waves grow simultaneously and interfere in random fashion. This remarkable duality, whose origin is in the phase relations of the amplified waves, leads us to propose that coherent waves are instrumental in the retrieval of memory and random waves embody original thought.

COMPUTATIONAL AND NONCOMPUTATIONAL SYSTEMS IN BRAIN AND COGNITION: CAN ONE MASK THE OTHER?

A theory is developed based on the premise that nonneural processes occur in the brain exemplified as spatial working memory, and is the seat of consciousness. Additionally, wave storage of spatial information, a Bose condensate to support the waves, and the location of wave storage are provided as illustrative, “existence proofs” that a coherent theory can be built along these lines in agreement with the data. The theory can be built argues on functional grounds that a nonneural spatial memory may serve a vital biological function. This article demonstrate how this same non-neural memory can bridge the explanatory gap to consciousness, in agreement with the facts. The article proposes a possible mechanism and location for the nonneural component.

Numbers, models, and understanding of natural intelligence: computational neuroscience in the service of clinical neuropsychology.

What we call computational neuroscience involves construction of mathematical and numerical models for understanding cognitive phenomena. This issue is devoted to showing how it can also be used to help in the analysis of cognitive defects. Although the models may seem abstract to clinicians, they are based on the reality of brain anatomy. The theoretical papers presented here are connectionist : They posit a network of cells connected by synapses whose weights are modified during learning . Architecture of connectionist models has progressed and ramified considerably since they were first introduced, and we include some examples of the current state of the art. The final work presented here is concerned with the connection of the constructed models with clinical experience and experiment.

VISUALIZATION IN THE NEUROSCIENCES: SEEING ABSTRACTIONS IN REAL TIME

One explicit goal of visualization in the neurosciences is to present data to human observers in a way that is informative and meaningful, on the one hand, yet intuitive and effortless on the other. Multidimensional data visualization is concerned with the question “How can we display high-dimensional data elements in a low-dimensional environment, such as on a computer screen or the printed page?” This goal is often pursued by attaching “features” such as hue, intensity, spatial location, and size to each data element. Features are chosen to reveal properties of data elements as well as relationships among them. An ad hoc assignment of features to individual data dimensions may not result in a useful visualization tool. Indeed, too often the tool itself interferes with the viewers ability to extract the desired information due to a poor choice of feature assignment. The articles presented in this issue address the concerns of representing data to better elucidate complex concepts in the neurosciences.