Modal-Polar Representation of Evoked Response Potentials in Multiple Arousal States - El-Zghir, Rawan K.; Gabay, Natasha C.; Robinson, Peter A. (Frontiers in Human Neuroscience, 2021)
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. This approach bridges tractably between experimental observations of resonances and characteristic timescales in brain activity and 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 stage 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 stage 1, and sleep stage 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.