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Estimating the Parameters of Fitzhugh-Nagumo Neurons from Neural Spiking Data

Diğer Başlık: Sinirsel Ateşleme Verisinden Fitzhugh-Nagumo Noron Modelinin Parametre Kestirimi

Oluşturulma Tarihi: 02-11-2020

Niteleme Bilgileri

Tür: Tez

Alt Tür: Doktora

Yayınlanma Durumu: Yayınlanmamış

Dosya Biçimi: PDF

Dil: İngilizce

Konu(lar): Elektrik mühendisliği. Elektronik. Nükleer mühendislik,

Yazar(lar): Abosharb, Laila Hassn A. (Yazar), Doruk, Reşat Özgür (Yazar),

Emeği Geçen(ler):


Yayın Tarihi: 13-02-2020


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Anahtar Kelimeler

Neuron modeling, Fitzhugh-Nagumo model, In-homogeneous Poisson processes, Neural spiking, Maximum likelihood estimation


Özet

In this thesis, we attempt to estimate the parameters of a single Fitzhugh-Nagumo neuron based on the neural spiking data. In this model, the input is an electric current serves as the stimulus while the output is considered to be the firing rate of neural spiking. The difference from the conventional system identification techniques is that no continuous variation of the response (the membrane potential or firing rate) is available. Instead, the data consists of the peak timings of action potentials called as spikes. One major property of these is that they are generated as a result of stochastic processes (ion channel stochasticity). Thanks to the arrival processes in statistics one can implement likelihood functions to estimate those parameters. In the simulation frame work one needs either to simulate the neural spiking or use a set of spike trains obtained from realistic data. For algorithmic testing of the methodologies developed in this research an inhomogeneous Poisson process is simulated using the firing rate response of a Fitzhugh-Nagumo model with known nominal parameters. The firing rate response is obtained from a predefined stimulus which is in Fourier series form with superimposed cosines. The simulations are repeated multiple times with different stimulus phases (phases of cosine functions in Fourier series) to obtain enough statistical content. The simulated stimulus-response data is then provided to the inhomogeneous Poisson likelihood functions (derived under Local Bernoulli approximation) to obtain an estimate of the neuron model parameters. The mean estimated values are presented as tables and their statistical analysis are presented graphically. The graphs present the variations of the standard deviations of the estimates against different values of stimulus component sizes, base frequency, amplitude and number of samples. In addition, in order to validate the performance of the methodologies developed in this thesis a realistic stimulus/response data is obtained from external sources (H1 neurons of blowflies) and the algorithms are applied. Here the vision system of the flies are stimulated by a 20 minute white noise stimulus and the neural spikes are collected. It is also convenient to test the algorithm with a different set of data other than Fouries series based ones. The computational environment is based on MATLAB and its constrained optimization routine fmincon is used in the likelihood estimation.



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