Study Of Granger Causality In Neuronal Network

In the research of brain function it is fundamentally important to know the neuronal network structure.Among the mathematical methods of network structure reconstruction,Granger causality(GC)is the one that is popular and highlighted,thanks to its simplicity,easy-to-use,ready-to-use softwares presented,applicable to a very general class of data and has well established explanation under Gaussian assumption.However,the use of GC in the highly nonlinear neuronal system is an violation to the basic GC theory assumption which is linear regression based.Still,GC is a popular analyzing tool in the neuroscience.And it's seems that some experimental results indicating that the GC did recover the network structure correctly.To solve this contradictory situation,this thesis will discuss the correctness of network reconstruction by GC in simulated neuronal system.Through extensive parameter scan,the GC network reconstruction quality of Integrate-and-Fire and Hodgkin-Huxley neuron model network are shown to be high.In order to explain this result,by detailed study of neural dynamics and the GC theory,the relationship neural dynamics – spike trigged average – residual covariance – GC is established,and through this reasoning chain,the GC reconstruction quality can be explained.In the rest part,some practical application problems are discussed,mainly the GC reconstruction quality under the situation that when not all neurons are measured.As a byproduct,the author also developed a fast GC algorithm which makes the GC calculation fast enough to analyze a network consist of thousands of neurons.