The Research Of Estimating Synaptic Input Parameters In The Integrate-and Fire Model

In order to understand the working mechanism of the human brain, estimatingsynaptic parameters in neuronal models has very important significance. Theseparameters can be divided into two types. The first type of parameters containsparameters characterizing the neuronal electrochemical characteristics, such asmembrane time constant, ion channel conductance. These parameters are usually relatedto the intrinsic properties of the cell and have a direct biological interpretation, whichare stable and can be deduced by some indirect methods. The second types ofparameters are determined by the properties of the input signal to the cell. Theseparameters may vary rapidly and can be estimated only by assuming that the membranepotential obeys the equation of the given model. So the input signal is the most relevantparameters in the model. For the given neuronal model, without firing threshold,input parameter is estimated using least squares method. As a firing threshold isintroduced, the firing threshold is considered as a absorbing boundary, its membranepotential transition probability density is derived. Then, the MLE is introduced toestimate input parameters in the model. The numerical results show that the leastsquares estimation depends on the regime, it is only applicable to the sub-threshold andthreshold regime. The maximum likelihood estimation works well in all cases with theimportant advantage that it does not depend on the regime. Both in terms of scope orestimation precision, maximum likelihood estimation is superior to least squaresestimate.