Abstract
AbstractThe problem of the transformation of microscopic information to the macroscopic level is an intriguing challenge in computational neuroscience, but also of general mathematical importance. Here, a phenomenological mathematical model is introduced that simulates the internal information processing of brain compartments. Synaptic potentials are integrated over small number of realistically coupled neurons to obtain macroscopic quantities. The striatal complex, an important part of the basal ganglia circuit in the brain for regulating motor activity, has been investigated as an example for the validation of the model.
Highlights
The brain nuclei, as parts of complex brain networks, are comprised by different types of inter- and projection neurons within subnetworks of highly complex structure
Adult brain nuclei are considered after their final development, as part of information processing pathways
The normalized distribution function ρz : Ω → [0, 1] as the kernel of the averaging operator will complete the information required for the integration of synaptic potentials across the network of brain regions
Summary
The brain nuclei, as parts of complex brain networks, are comprised by different types of inter- and projection neurons within subnetworks of highly complex structure. There are traditional network approaches on the effects of properties such as the local connectivity of neurons on the striatal function (Wickens et al [21]) These studies concentrate merely on the network structure of a particular brain region e.g. striatum and even do not contain some important features such as the role of large spiny neurons in the striatal function. Because of the importance of the global and ultrastructural morphology for the information integration process in a nucleus and the dependency of their values on the spatial distribution of neurons, they shall be modelled as spatial variables parametrized by the neuron (neurotransmitter) type. Within the information on the adherence functions of n-cells (global morphology variables) and the distribution of neurons, the averaging of synaptic potentials across the network of nuclei is completed. The general formulation of the averaging operator suggest its suitability for other discrete multiscale problems, especially in the research area of material sciences
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