Applications Of Temporal Coding In Signal Processing

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Processing strategies employed by natural neuronal systems could have potential benefit for signal processing and integration. The system with the most obvious applications is the visual system. Current techniques cannot match the speed and robustness of human vision. One obvious application is using a neurally based algorithm for segmentation of data from imaging techniques such as functional magnetic resonance imaging (fMRI), in situ hybridization, and confocal microscopy. This would involve converting an image into a matrix of current injections proportional to each pixel's gray-scale value and using that as input into a computational model of the visual system.

Earlier work with a model of the retina5657 showed that synchronous oscillations have characteristics that make computational vision models useful tools for image processing (Figure 2.7). The power of synchronous oscillations is proportional to the size of the stimulus, which makes them useful for noise filtering and for discriminating large-vs.-small objects as well as rapid segmentation. Depending upon the desired feature size, the sensitivity to noise can be set by the user. One of the key insights from this spiking-neuron model is that delayed inhibition is necessary for synchronous oscillations. So, by adjusting the gain and the time constant of the inhibition, one can control the power of the oscillations and thus the degree of filtering. The retinal model emphasizes adjacent pixels with roughly equivalent contrast by grouping them into synchronous blobs. Performance should improve for a model based on cortical V1 neurons.

FIGURE 2.7 An oscillatory feedback loop in a retinal model. 1) Stimulation of the ganglion cells by the bipolar cells produces action potentials that propagate down the optic nerve. 2) Simultaneously, action potentials back-propagate through the dendrites of the ganglion cells, across gap junctions, and activate amacrine cells. 3) The spiking amacrine cells send action potentials along their axons to 4) inhibit the adjacent ganglion cells. 5) This delays spiking in the ganglion cells until the release of amacrine cell inhibition and so produces an interval with no spikes (t). 6) The feedback loop is completed by back-propagating spikes from the ganglion on the left traveling back to the ganglion cell on the right. Arrowheads indicate direction of action potentials. bipolar cells (BP), amacrine cells (AC), retinal ganglion cells (GC), and optic nerve (ON). Adapted from Stephens et al. (2006). (From Stephens, G. J., Neuenschwander, S., George, J. S., Singer, W. & Kenyon, G. T. See globally, spike locally: oscillations in a retinal model encode large visual features. Biol Cybern 95, 327-348 (2006).)

A computational model of oriented edge detectors would allow more-complex segmentation than the retinal model. There is also the potential to combine all of the different types of cortical detectors into a single network that can segment based on color, texture, motion, and binocular disparity. Figure 2.8 shows a diagram of a model of V1 edge detectors developed for this purpose. They are equivalent to simple cells as described by Hubel and Wiesel.77,78 These simple cells are modeled after pyramidal neurons in layer 4C and receive their primary input from the LGN. To simplify the model, input to the network is implemented as current injections. Oriented receptive fields are formed by retinotopic projections to V1 along the orientation preference (i.e., a vertical edge detector would receive input from a vertical line of input cells). The stimulus later also provides input to three groups of inhibitory interneurons: oriented feedforward, nonoriented feedforward, and inhibitory feedback. The interneurons inhibit the pyramidal cells and also form a mutually inhibitory loop. The feedforward interneurons sharpen the orientation tuning of the pyramidal neurons, and the feedback interneurons provide the slow inhibition to pyramidal cells necessary for oscillations. The internal feedback loop increases the dynamic range of the inhibitory interneurons and thus helps to keep the orientation

Mini Pendants Over Occasional Table
FIGURE 2.8 Diagram of network model based on V1 cortex. Filled circles are inhibitory synapses and hollow circles are excitatory synapses. Receptive fields for the pyramidal neurons and oriented feedforward inhibitory neurons are formed according to the model of Hubel and Wiesel.77,78

tuning insensitive to changes in contrast. Finally, the pyramidal neurons mutually excite each other. This excitation is selective and is designed to enhance the interactions between neurons that would fall along a smooth curve.79 The connections between two neurons whose receptive fields (both orientational and positional in visual space) are tangent to the same circle have the maximal synaptic weight.79

To get smooth contours to oscillate synchronously, two elements are necessary: mutual excitation of neurons along the contour (cocircularity) and slow feedback inhibition. Slow feedback inhibition prevents a pyramidal cell from firing unless the other neurons are also firing. Cocircular connections help to ensure that most of the neurons along the contour fire at the peak of the cycle and extend the oscillations along the curve. Synchronous oscillations are used as a tag for all of the pixels in an image that belong to the same object. Each object in an image would have a different tag to assist in further processing.

The problems solved by the olfactory system are analogous to the problem of analyzing biomarker data to determine the efficacy of a drug. Each involves the analysis of output from multiple detectors. Because multiple processes modulate each biomarker, both physiological and pathological, a change in any one biomarker is difficult to interpret. This is similar to activation of a projection neuron in the locust antenna lobe. The spatial and temporal response of a population of neurons is necessary to identify an odor. A potentially powerful bioinformatics tool could be based on the olfactory system, in which both the presence and the magnitude of changes in biomarkers would be coded as changes in the number and timing of action potentials in a population of neurons. Because synchrony can also be used to dynamically bind the different features of a stimulus,80 synchronous oscillations extend the capabilities of traditional neural networks.8182

Hopfield et al. showed that a spiking neuron model is better than a conventional neural network model for solving the analog match problem, where several input channels are active to varying degrees, depending upon the stimulus.83 Both the number and the timing of the spikes can represent information. Realistic spiking neurons may therefore allow the construction of more-complex models of data by encoding information temporally, thus facilitating data processing.

Hopfield presents a model that is relevant for bioinformatics.84 This model uses both rate and temporal coding to solve problems where information about the identity and amount of activation of a detector is necessary for pattern recognition, such as in the olfactory system. A network of neurons into which a current is injected and which is modulated by a sinusoidal oscillation will produce a spike at each peak of the oscillation. The timing of the spike depends upon the strength of the stimulus: the stronger the input current, the earlier in the phase the neuron fires. The degree to which a detector is activated determines when the neuron fires in the cycle. Thus the characteristics of the stimulus (the ratios of the different components) are encoded as a temporal pattern of activity in the principal cells of the olfactory bulb. This temporal pattern can be decoded in the cortex by neurons sensitive to the timing of their inputs.

One problem with analyzing biomarkers is the need to compare changes in a scale-invariant manner. A disease process or pharmacologic response will produce a pattern of changes in a set of biomarkers (Figure 2.9). The ratio of these changes and the different scales at which they are measured are important factors in recognizing these patterns. This is a problem the olfactory system has solved. Odors are complex mixtures of airborne molecules where the minor components can be an important part of the odor.

Another possibility is to use an olfactory network-based model as a tool for molecular detection. The first step would involve separating a complex mixture into its component molecules using either gas or liquid chromatography. Each molecule could then be analyzed using a mass spectrometer (to get its molecular weight) and an infrared spectrometer (to determine the molecule's functional groups). The output from these devices could then be converted into a pattern of input currents for the olfactory network. Finally, these patterns could be decorrelated from similar molecules with overlapping PN patterns, and the representation could be diluted by the divergent PN projections to the Kenyon cells. A broad chemotropic map in the model antenna lobe could be based on a combination of molecular weight, hydrophobicity, and isoelectric point. Mapping within each subregion could be based on the molecule's functional groups.

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FIGURE 2.9 (A) Changes in levels of biomarkers after pathologic or pharmacologic perturbation. (B) Different processes could be modulating those biomarkers, making it difficult to interpret any changes.

A system of tools could be constructed from multiple neuronal networks to discover complex, multidimensional associations (Figure 2.10). For example, the effects of a series of drugs can be characterized by a series of in situ hybridization images. A visual-cortex-based tool could analyze these images, and an olfactory network could store the drugs. Then, correlations between the in situ images and the molecular profile of the drug could be systematically explored.

Higher Cognitive Functions

Synchronous oscillations have also been proposed to be the foundation of other complex phenomena, such as decision making, attention, and consciousness.38 Attentional mechanisms bias processing toward the brain regions necessary for a task. Global synchronous oscillations make up the "dynamic core" of conscious behavior, while local oscillations involved in lower-level functions such as sensory processing would be subconscious (Figure 2.11). Cognition requires the large-scale coordination of multiple neuronal networks. Deficits in synchronous activity have been linked to pathologies involving large-scale neuronal network coordination, including schizophrenia75 and autism.76

Our brains naturally tend to break complex objects into simpler components, just as we build up complicated concepts from simpler ideas. One conceivable

FIGURE 2.10 Schematic diagram illustrating a potential tool for constructing a neuronal network-based data model. Data are encoded through either visual or olfactory networks, depending on the characteristics of the data. Associations between elements of the data are formed by the hippocampus. The user could define important types of associations that could be enhanced by the prefrontal cortex network by increasing the power of oscillations in the target brain regions.

FIGURE 2.10 Schematic diagram illustrating a potential tool for constructing a neuronal network-based data model. Data are encoded through either visual or olfactory networks, depending on the characteristics of the data. Associations between elements of the data are formed by the hippocampus. The user could define important types of associations that could be enhanced by the prefrontal cortex network by increasing the power of oscillations in the target brain regions.

mechanism for how our brains accomplish this is to dynamically bind the neural circuits (themselves bound by synchronous oscillations) encompassing the simple components together via gamma-band synchronous oscillations. Indeed, even novel ideas could be generated by the transient confluence of previously unconnected neural assemblies. The components must already be present if the mind is to make the linkage.

As neuronal models that instantiate these principles become more complex, the more such models enter the realm of artificial intelligence (AI).97 Indeed, this may be a prerequisite for truly powerful bioinformatics tools. This approach to AI might have some substantial advantages over conventional AI techniques,98 which include expert systems, agent-based networks, neural networks, and semantic networks. These coarse-grained, high-level approaches require built-in representation of the problems they solve and have limited flexibility to handle unforeseen conjunctions of data. A bottom-up model of cognition allows the system to determine its own representation of the problem and provides the flexibility to link the very different types of data required by different cognitive tasks.

FIGURE 2.11 Synchronous oscillations link activity across brain regions to form cell assemblies.

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