In this paper we present a numerical study of a mathematical model that describes the continuous temporal evolution of membrane potentials in a GABAergic neuronal network. This model, with stochastic and evolutionary characteristics, is an application of the version introduced in1 where the authors present the continuous time version of a new class of stochastic models for biological neural networks.More specifically, the computational simulations of the model provide numerical results describing spiking neuron with electrophysiological characteristics of a brain region called substantia nigra pars reticulada, emphasizing changes in desynchronized firing activity and how changes in individual activity propagate through the network.
Dopamine, a neurotransmitter well known for regulating movement, reward, and learning, is emerging as one of the neuromodulators of wakefulness. Drugs that increase the level of dopamine in the brain (including, but not limited to, nicotine) also increase feelings of wakefulness. Diseases that are characterized by low dopamine levels, like Parkinson's disease, also are related to sleep disorders.In this work we investigate the influence that nicotine and alcohol exert on sleep, modeling the coupling of reward and thalamocortical circuits in a reward-attention circuit. Computer simulations of the circuit reflect the spiking behavior of neurons in the network under the presence or absence of nicotine or alcohol.Each neuron in the reward-attention model represents a population of cells in the circuit, and is described by a coupled system of nonlinear differential equations that replicates essential neurophysiological properties of the population. The computational simulations highlight aspects of clinical insomnia symptoms in Parkinson's disease, attention deficit hyperactivity disorder and autism spectrum disorder.Our results imply that nicotine can disrupt sleep, promoting wakefulness. In contrast, alcohol increases sleep latency (time to fall asleep). Also, the simulations suggest that alcohol has a sedative effect in people with insomnia.
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