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The analysis for ionic channels is a very essential problem in
the biomedical studies. From the past studies, the
physiologists believe that the properties of the currents
flowing in the ionic channel satisfy a Markov chain; therefore,
the Markov model is used mostly often as the model for the
underlying ionic channel kinetics. As there are distortions and
noises accompanying with the sampled current signals, the
problem can be re-addressed as searching for an appropriate
approach of signal processing to build up the optimal Markov
model for the underlying channel current signals. Approaches of
maximum likelihood estimation of the model parameters have been
widely applied to ionic channel analysis problem; and the
hidden Markov model (HMM) is the most popular method. However,
there still exists some problems if the algorithms associated
with the traditional HMM are used without any practical
considerations and modifications. In this thesis, from
extensive simulation experiments, we have a more complete study
of the applicability and limits of the proposed approaches to
the ionic channel problems. In this thesis, we investigate (1)
the maximum likelihood estimation on the kinetics domain by a
local optimizer, Steepest Descent, and a quasi- global
optimizer, Simulated Annealing, respectively; (2) the
restoration of underlying ideal channel signal based on the
maximum likelihood estimation on the transition probability
matrix by HMM. In the experiments, we compute the errors of
estimation and/or restoration according to various RMS of noise
and kinetic rates. The results of experiments show that (1) the
performance of the quasi-global optimizer on estimating the
kinetics matrix is better than the local optimizer; (2) the
restoration based on the estimation on the transition
probability matrix is a good alternative, but further error
analysis for kinetics matrix is not implied from the error of
restoration.
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