## Chaotic desynchronization as the therapeutic mechanism of deep brain stimulation

Wednesday, July 13, 2011

Charles J. Wilson, Bryce Beverlin II, Theoden Netoff Frontiers System Neurosci. 2011, 5:50.

High frequency deep-brain stimulation of the subthalamic nucleus (DBS) relieves many of the symptoms of Parkinson's disease in humans and animal models. Although the treatment has seen widespread use, its therapeutic mechanism remains paradoxical. The subthalamic nucleus is excitatory, so its stimulation at rates higher than its normal firing rate should worsen the disease by increasing subthalamic excitation of the globus pallidus. The therapeutic effectiveness of DBS is also frequency and intensity sensitive, and the stimulation must be periodic; aperiodic stimulation at the same mean rate is ineffective. These requirements are not adequately explained by existing models, whether based on firing rate changes or on reduced bursting. Here we report modeling studies suggesting that high frequency periodic excitation of the subthalamic nucleus may act by desynchronizing the firing of neurons in the globus pallidus, rather than by changing the firing rate or pattern of individual cells. Globus pallidus neurons are normally desynchronized, but their activity becomes correlated in Parkinson's disease. Periodic stimulation may induce chaotic desynchronization by interacting with the intrinsic oscillatory mechanism of globus pallidus neurons. Our modeling results suggest a mechanism of action of deep brain stimulation and a pathophysiology of Parkinsonism in which synchrony, rather than firing rate, is the critical pathological feature.

*Figure 1: Notation. *

*Two trajectories of a spontaneously active neuron firing with period Tc are shown, one unperturbed (black) and one perturbed by the stimulus presented at period Ts. The phase-dependent change in the period caused by the stimulus is Δt. Stimulation latencies relative to cell firing are indicated by ts, and response latencies relative to the stimulus are labeled tr.*

*Figure 2: Chaotic desynchronization in a model neuron.*

*(A) Two uncoupled conductance-based simulated neurons before and during stimulation with high frequency current pulses. (B) The neurons' phase relationship is disturbed during the stimulation. (C) The phase-resetting curve (PRC), a simplification of the neuron model consisting of a phase-dependent phase shift by a current pulse. (D) Iterative phase map. The phase of the stimulus for the next stimulation is calculated from its PRC and its phase on the previous cycle. (E) Phase map for chaotic desynchronization, leading to a non-repeating non-random sequence of phases. (F) Phase differences for two initially nearby trajectories in the chaotic map. (G) Map of stimulus strength and frequency dependence of firing patterns using the Lyapunov exponent. Negative Lyapunov exponents (white to blue) indicate phase convergence and synchrony. Positive Lyapunov exponents (red to orange) indicate chaotic phase divergence. Lyapunov exponents near zero, indicating neither active synchronization nor desynchronization, are shown black. Inhibitory current pulses also produce chaotic firing and divergence of trajectories, but over a different range of rates.*

*Figure 3: Stochastic phase map. *

*(A) The phase-resetting curve for a model neuron in globus pallidus with confidence intervals. (B) Stochastic maps for periodic stimulation at two frequencies, the cell's natural frequency (f0) and twice that. The stochastic map gives the probability distribution of stimulus phases on the next interspike interval given a distribution for the previous interval. (C) Lyapunov exponents for the stochastic map. (D) Entropy of a simulated network of 100 stochastic neurons correlated by shared random synaptic input. Periodic high frequency stimulation synchronizes (lowers entropy) or disrupts synchrony (raises entropy) as predicted by the Lyapunov exponent. (E) & (F) Rastergrams and entropy of a simulated network over six cycles during stimulation as indicated in D. (G) Randomizing stimulus interval (measured by coefficient of variation) decreases the entropy of the population.*

*Figure 4: Compound synaptic phase-resetting curve of globus pallidus neurons for subthalamic stimulation. *

*(A) The connections between the subthalamic nucleus and globus pallidus neurons in the internal (GPi) and external (GPe) segments. Red indicates excitation; blue is inhibition (B) Post-stimulus histogram of single stimuli with latencies of 1 ms for excitation and 1.5 ms for inhibition, and excitatory and inhibitory current time constants of 2.5 ms and 6.0 ms respectively. (C) Compound synaptic phase-resetting curves for three stimulus intensities. (D) Stimulus intensity and frequency map of Lyapunov exponents for the stochastic compound subthalamo-pallidal phase map, based on a baseline firing rate of 60 spikes/s. (E) Stationary probability distributions of firing time relative to DBS stimulation at 114 Hz, for the same 3 stimulus intensities shown in C. (F) Steady state average firing rate during 114 Hz. DBS across the range of stimulus intensities. *