Browsing by Author "Dovzhenok, Andrey"

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    Exploring Neuronal Bistability at the Depolarization Block
    (Public Library of Science, 2012) Dovzhenok, Andrey; Kuznetsov, Alexey S.; Mathematical Sciences, School of Science
    Many neurons display bistability--coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to be involved in short-term memory in particular by allowing a brief signal to elicit long-lasting changes in firing. In this paper, we focus on bistability that allows for a choice between tonic spiking and depolarization block in a wide range of the depolarization levels. We consider the spike-producing currents in two neurons, models of which differ by the parameter values. Our dopaminergic neuron model displays bistability in a wide range of applied currents at the depolarization block. The Hodgkin-Huxley model of the squid giant axon shows no bistability. We varied parameter values for the model to analyze transitions between the two parameter sets. We show that bistability primarily characterizes the inactivation of the Na(+) current. Our study suggests a connection between the amount of the Na(+) window current and the length of the bistability range. For the dopaminergic neuron we hypothesize that bistability can be linked to a prolonged action of antipsychotic drugs.
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    Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson’s Disease
    (Public Library of Science, 2013) Dovzhenok, Andrey; Park, Choongseok; Worth, Robert M.; Rubchinsky, Leonid L.; Mathematical Sciences, School of Science
    Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson's disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson's disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.
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    On the Origin of Tremor in Parkinson’s Disease
    (Public Library of Science, 2012) Dovzhenok, Andrey; Rubchinsky, Leonid L.; Mathematical Sciences, School of Science
    The exact origin of tremor in Parkinson's disease remains unknown. We explain why the existing data converge on the basal ganglia-thalamo-cortical loop as a tremor generator and consider a conductance-based model of subthalamo-pallidal circuits embedded into a simplified representation of the basal ganglia-thalamo-cortical circuit to investigate the dynamics of this loop. We show how variation of the strength of dopamine-modulated connections in the basal ganglia-thalamo-cortical loop (representing the decreasing dopamine level in Parkinson's disease) leads to the occurrence of tremor-like burst firing. These tremor-like oscillations are suppressed when the connections are modulated back to represent a higher dopamine level (as it would be the case in dopaminergic therapy), as well as when the basal ganglia-thalamo-cortical loop is broken (as would be the case for ablative anti-parkinsonian surgeries). Thus, the proposed model provides an explanation for the basal ganglia-thalamo-cortical loop mechanism of tremor generation. The strengthening of the loop leads to tremor oscillations, while the weakening or disconnection of the loop suppresses them. The loop origin of parkinsonian tremor also suggests that new tremor-suppression therapies may have anatomical targets in different cortical and subcortical areas as long as they are within the basal ganglia-thalamo-cortical loop.