Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

Abstract

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of approximately 3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.

Time-delayed feedback in neurosystems

“…One could also consider the application of the feedback scheme to both subsystems and the effects of different values of the control parameters for each subsystem, but these investigations are beyond the scope of this work. Previously, time-delayed feedback has also been used to influence noise-induced oscillations of a single excitable system Janson et al 2004;Prager et al 2007), of systems below a Hopf bifurcation (Pomplun et al 2005;Schöll et al 2005;Flunkert & Schöll 2007;Pototsky & Janson 2007) or below a global bifurcation (Hizanidis et al 2006;Hizanidis & Schöll 2008) and of spatially extended reactiondiffusion systems Stegemann et al 2006;Dahlem et al 2008). Extensions to multiple time-delay control schemes have also been considered (Hövel et al 2007, submitted;Pomplun et al 2007;).…”

“…Various global delayed feedback schemes have been proposed as effective and robust therapy of neurological diseases with pathological synchronization causing tremor (Rosenblum & Pikovsky 2004;Popovych et al 2005). They have been contrasted with local delayed feedback methods (Gassel et al 2007(Gassel et al , 2008Dahlem et al 2008).…”

ECoG-based short-range recurrent stimulation techniques to stabilize tissue at risk of progressive damage: Theory based on clinical observations

“…Below SD shown by functional magnetic resonance imaging (fMRI) in a migraine patient [2]. In theoretical studies [3,4,5], a mechanism was presented suggesting how a failure of internal feedback could be a putative mechanism of SD patterns in acute stroke. This failing internal feedback control is now suggested to be replaced by ECoG-based short-range recurrent functional stimulation that initiates the normal hyperperfusion haemodynamic response in a demand-controlled way and stabilizes the tissue at risk during the critical phase of SD passage.…”

Control of coherence resonance in semiconductor superlattices

“…Typical examples of such systems are lasers where the delay enters through the coupling to external cavities (optical feedback) [37,38,39] and neurons, where the signal propagation yields a delay time [40].…”