Homeostatic dynamics, hysteresis and synchronization in a low-dimensional model of burst suppression

Abstract

Burst suppression, a pattern of the electroencephalogram characterized by quasi-periodic alternation of high-voltage activity (burst) and isoelectric silence (suppression), is typically associated with states of unconsciousness, such as in deep general anesthesia and certain etiologies of coma. Recent computational models for burst suppression have attributed the slow (up to tens of seconds) time-scale of burst termination and re-initiation to cycling in supportive physiological process, such as cerebral metabolism. That is, activity-dependent substrate ('energy') depletion during bursts, followed by substrate recovery during suppression. Such a model falls into the category of a fast-slow dynamical system, commonly used to describe neuronal bursting more generally. Here, following this basic paradigm, we develop a low dimensional mean field model for burst suppression that adds several new features and capabilities to previous models. Most notably, this new model includes explicit homeostatic interactions wherein the rates of substrate recovery are tied to neuronal activity in a supply demand loop, creating a physiologically consistent, reciprocal interaction between the neural and substrate processes. We develop formal analysis of the model dynamics, showing, in particular, the capability of the model to produce burst-like activity as a consequence of neuronal downregulation only, without any direct perturbation to the substrate dynamics. Further, we use a synchronization analysis to contrast different mechanisms for spatially local versus global bursting. The analysis performed generates characterizations that are consistent with experimental observations of spatiotemporal features such as burst onset, duration, and spatial organization and, moreover, generates predictions regarding the presence of bistability and hysteresis in the underlying system. Thus, the model provides new dynamical insight into the mechanisms of burst suppression and, moreover, a tractable platform for more detailed future characterizations.

Electroencephalographic features of discontinuous activity in anesthetized infants and children

“…Burst suppression of the anesthetized brain has been described by neuro-metabolic models [35,36]. Along with literature regarding the occurrence of burst suppression as suggestive of harm, as noted above, burst suppression has also been a desired endpoint in the use of pentobarbital and other agents used for neuroprotection in neuro-critical care for patients with brain injuries, refractory seizures and other conditions.…”

“…Along with literature regarding the occurrence of burst suppression as suggestive of harm, as noted above, burst suppression has also been a desired endpoint in the use of pentobarbital and other agents used for neuroprotection in neuro-critical care for patients with brain injuries, refractory seizures and other conditions. At the molecular level, models posit that the cycling between burst periods and quiescent periods reflects changing extracellular calcium or adenosine trisphosphate (ATP) levels, which in turn impact on membrane conductance and neurotransmitter release [35,36].…”

Isoflurane but Not Halothane Prevents and Reverses Helpless Behavior: A Role for EEG Burst Suppression?

“…In contrast to their reciprocal effects on a number of signal transduction mechanisms, ISO and HALO exert different effects on brain metabolism and cellular energetics. At clinically relevant doses, ISO and HALO have disparate effects on the cerebral metabolic rate of oxygen (CMRO 2 ) ( Algotsson et al, 1988 ; Kuroda et al, 1996 ), differences that may account for the pronounced dissimilarity in their effects on cortical EEG ( Ching et al, 2012 ; S. Liu and Ching, 2017 ). Burst suppression, identical to that associated with ISO anesthesia, occurs under a variety of conditions associated with depressed CMRO 2 including hypothermia ( Stecker et al, 2001 ; Madhok et al, 2012 ; Chen et al, 2013 ) and hypoxic coma ( Hofmeijer and van Putten, 2016 ).…”

Network dynamics in the healthy and epileptic developing brain

“…Dynamic features not directly visible in EEG analysis—such as the microstate dynamics described above—are not commonly considered in the analysis of clinical EEG recordings. There is an emerging literature on the computational analysis of EIEE phenotypes (Japaridze et al, 2013 ; Japaridze et al, 2016 ) and related abnormal EEG patterns (Ching, Purdon, Vijayan, Kopell, & Brown, 2012 ; Liu & Ching, 2017 ; Zubler et al, 2014 ). But our understanding of intrinsic network dynamics in these phenotypes is still limited.…”