Control of Traveling Waves in the Mammalian Cortex

Abstract

We experimentally confirmed predictions that modulation of the neuronal threshold with electrical fields can speed up, slow down, and even block traveling waves in neocortical slices. The predictions are based on a Wilson-Cowan-type integro-differential equation model of propagating neocortical activity. Wave propagation could be modified quickly and reversibly within targeted regions of the network. To the best of our knowledge, this is the first example of direct modulation of the threshold to control wave propagation in a neural system.Traveling waves in excitable media are commonly observed in physical [1,2], chemical [3], and biological [4][5][6] systems. Mathematical models have been developed in conjunction with these experimental systems to provide a deeper understanding of the dynamics and infer how individual experimental parameters of the system, such as threshold, contribute to these dynamics [5,[7][8][9][10]. Rapid access to system parameters would offer the means to control pattern formation and dynamics in these systems.Successful modulation of dynamics has been accomplished in chemical, cardiac, and neural systems. In the Belousov-Zhabotinsky chemical reaction system, modulation of excitability through local changes in illumination of a light sensitive catalyst allowed control of wave propagation [11]. Electric fields modulated activity propagation in heart tissue [12]. The propagation speed of excitation waves in neocortex has been slowed by pharmacologically interfering with chemical synaptic transmission [13].It has been previously shown that electric fields can modulate neuronal thresholds by quickly and reversibly polarizing asymmetric neurons [14]. Electric fields as small as 140 μV/mm have been observed to modulate neural firing [15]. Polarization occurs on time scales of about 20 ms and can be maintained for many seconds or minutes [16]. Applied electric fields have been used to adaptively control seizure formation in vitro [17], modulate epileptiform activity in vivo, and dynamically probe activity changes associated with impending seizures [18].We show here that electric fields can quickly alter traveling wave dynamics in ways predicted by theory through direct modulation of neuronal threshold. To our knowledge, this is the first report of control of wave propagation through direct modulation of excitability threshold in any neural system. Wilson and Cowan [19] developed a set of integro-differential equations to form a continuum model of cortex which demonstrated traveling waves. This model was recently modified [20] to represent traveling pulse propagation in disinhibited neocortex [21]. The model predicts that

Switching between gamma and theta: Dynamic network control using subthreshold electric fields

“…Electric field application did not stop the wave propagation in theta and theta-gamma regimes. It did modify wave characteristics to some extent: hyperpolarizing field tends to decrease the speed of wave propagation and increase the latency of wave initiation (and vice versa for depolarizing field), similar to experimental wave control findings with localized electric fields in the neocortex [14]. The number of gamma spikes per theta cycle in our simulations could also be smoothly modulated by the electric field.…”

Large-scale neural dynamics: Simple and complex

“…This strong dependence of the wave speed on the threshold θ has now been indirectly established in rat cortical slices (bathed in the GABA A blocker picrotoxin) [62]. An applied positive (negative) electric field across the slice increased (decreased) the speed of wave propagation, consistent with (24) assuming that a positive (negative) electric field reduces (increases) the threshold θ.…”

Waves, bumps, and patterns in neural field theories

“…Waves in the form of travelling fronts and pulses have now been observed in a variety of slice preparations [20,21,22,42,43]. To establish properties of waves in a model neural system it is convenient to introduce the coordinate ξ = x − ct and seek functions U(ξ, t) = u(x − ct, t) that satisfy (9).…”