Neural Field Theory of Nonlinear Wave-Wave and Wave-Neuron Processes

Abstract

Biophysical processes related to the modulation of cellular mechanisms occur due to either presynaptic or postsynaptic effects. These processes involve some physiological phenomena whose different dynamics can potentially be distinguished via traces they leave in the power spectra of brain activity and/or connectivity fluctuations. Systematic expansion of NFT equations in terms of nonlinear response functions is formulated in Chapter 2 to enable a wide variety of nonlinear wave-wave and wave-neuron processes. This theory helps to handle neural quantities such as firing rates, neural field, soma voltage, threshold, and coupling strength, along with their steady state values and perturbations. Many physiological processes such as facilitation, habituation, and refractoriness can be interpreted as the consequences of neural feedbacks that allow presynaptic and postsynaptic firing rates to modulate firing thresholds or synaptic strengths at a given location. NFT is used to analyze such feedback processes to determine their signatures, which are measurable through fluctuations in the power spectra of brain activity in Chapter 3. Depending on the feedback processes, these signatures include either enhancement or reduction of low-frequency activities, effects near the alpha resonance (enhancements and/or resonance splitting), and the appearance of new resonances. Physiological phenomena related to nonlinear feedback processes can potentially be identified and distinguished by means of these different spectral signatures. The spatiotemporal power spectra of connectivity fluctuations are also analyzed via NFT in Chapter 4, which also show distinctive features. Some spectral signatures result from the contributions from discrete spatial modes to the frequency power spectra depending on feedbacks. Some of these appear to be characteristic of just one feedback type and can potentially be used as diagnostics in experiments. Some ideas for future work are mentioned in Chapter 5.