A feedback systems approach to modeling neural firing-rate homeostasis

We consider a cortical neural population model in an effort to understand the basic mechanisms that regulate and maintain "normal" neural firing-rate despite changes in the cortical input level. Towards this goal, we have postulated the existence of internal feedback structures that functionally model firing-rate homeostasis via the balance of excitation and inhibition. In particular, normal internal feedback action maintains normal firing-rate by regulating the strength of excitatory input from pyramidal neurons in other cortical populations, and the strength of inhibitory input from interneurons. We observe that a pathology in the internal feedback that regulates the inhibitory input can lead to seizure-like high amplitude oscillations. These arise from two mechanisms, namely, excessive specific recurrent excitation between cortical populations, and excessive non-specific excitatory input. Further, we develop an external closed-loop control technique where the controller acts to achieve the operational objective of maintaining normal firing-rate. In addition to that, the external controller is also successful in avoiding the occurrence of "seizures". The results of this analysis are consistent with recent experimental observations in the epileptic brain, and have an interesting physical interpretation and implications for the treatment of disorders such as epilepsy.