טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKanter Ayelet
SubjectThe Impact of Synaptic Depression on Up-Down States
in Neural Networks :Dynamical Systems' Persprctive
DepartmentDepartment of Biomedical Engineering
Supervisor Professor Ron Meir
Full Thesis textFull thesis text - English Version


Abstract

The presence of voltage transitions between two distinct membrane potentials in the spontaneously active cortex referred to as the up and down states, is thought to be of critical importance in cognitive functions such as attention and working memory. In this study we develop a simple mathematical model which exhibits some of the properties related to this phenomenon, and the dynamics of which suggest an explanation for the transition between the up and down states. We introduce the development and analysis of a two-dimensional, rate based network model of excitatory cells combined with short-term synaptic depression. The model is based on the assumption that depression acts as a negative feedback process to excitation, thus creating typical periodic behavior that are a fundamental characteristic of neural networks. The network model is based on a single-cell Quadratic Integrate and Fire (QIF) scheme from which we derive the relevant Fokker-Planck equation and average first passage time, to assess the population's mean steady state firing rate. The dynamics of the model is qualitatively analyzed using the phase plane analysis method. The QIF is a spike generating model that enables bistable activity, and leads to relatively simple expressions for its mean steady state firing rate. Moreover, a unique feature of this phenomenological model is that its parameters can be related to biophysical variables. This characteristic is used in the analysis of the model in order to compare its results with those found in physiological data.