Abstract
An expansion of the corticothalamic transfer function into eigenmodes and resonant poles is used to derive a simple formula for evoked response potentials (ERPs) in various states of arousal. The transfer function corresponds to the cortical response to an external stimulus, which encodes all the information and properties of the linear system. This approach links experimental observations of resonances and characteristic timescales in brain activity with physically based neural field theory (NFT). The present work greatly simplifies the formula of the analytical ERP, and separates its spatial part (eigenmodes) from the temporal part (poles). Within this framework, calculations involve contour integrations that yield an explicit expression for ERPs. The dominant global mode is considered explicitly in more detail to study how the ERP varies with time in this mode and to illustrate the method. For each arousal state in sleep and wake, the resonances of the system are determined and it is found that five poles are sufficient to study the main dynamics of the system in waking eyes-open and eyes-closed states. Similarly, it is shown that six poles suffice to reproduce ERPs in rapid-eye movement sleep, sleep state 1, and sleep state 2 states, whereas just four poles suffice to reproduce the dynamics in slow wave sleep. Thus, six poles are sufficient to preserve the main global ERP dynamics of the system for all states of arousal. These six poles correspond to the dominant resonances of the system at slow-wave, alpha, and beta frequencies. These results provide the basis for simplified analytic treatment of brain dynamics and link observations more closely to theory.
Highlights
Evoked response potentials (ERPs) reflect the electrical activity of the brain triggered by sensory stimuli or events (Niedermeyer and Lopes Da Silva, 1999)
Traditional phenomenological analysis reduces evoked response potentials (ERPs) to a small set of “components” defined by amplitudes and latencies each of which correspond to a peak or trough in the waveform (Luck, 2014); each component is presumed to be generated by a group of excitatory or inhibitory neurons that have a certain cognitive role (Luck and Kappenman, 2013), but there is no explicit link to physiology and it is common to omit most data points and focus on only amplitudes and latencies of a few components
We apply the results to the different arousal states by plotting the locations of poles for different cases of number of poles and finding the root mean square error to study the convergence of T(f ) and ERP(t) to their exact results
Summary
Evoked response potentials (ERPs) reflect the electrical activity of the brain triggered by sensory stimuli or events (Niedermeyer and Lopes Da Silva, 1999). ERPs have been widely used to provide windows on cognitive processes such as attention and perception (Luck and Kappenman, 2013). Traditional phenomenological analysis reduces ERPs to a small set of “components” defined by amplitudes and latencies (time delays after the stimulus) each of which correspond to a peak or trough in the waveform (Luck, 2014); each component is presumed to be generated by a group of excitatory or inhibitory neurons that have a certain cognitive role (Luck and Kappenman, 2013), but there is no explicit link to physiology and it is common to omit most data points and focus on only amplitudes and latencies of a few components. It has been widely recognized that ERPs can be treated as impulse responses whose building blocks are damped sinusoids that reflect the dynamics of the underlying physical system that generates them (Kelly and Reilly, 1983)
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