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Periodic stimuli are known to induce chaotic oscillations in the squid giant axon for a certain range of frequencies, a behaviour modelled by the Hodgkin-Huxley equations. Inthe presence of chaotic oscillations, similarity between neural responses depends on their temporal nature as firing times and amplitudes together reflect the true dynamics of theneuron. This thesis presents a method to estimate similarity between neural responses exhibiting chaotic oscillations by using both amplitude fluctuations and firing times. It isobserved that identical stimuli have similar effect on the neural dynamics and therefore, as the temporal inputs to the neuron are identical, the occurrence of similar dynamicalpatterns result in a high estimate of similarity, which correlates with the observed temporal similarity. The information about a neural activity is encoded in a neural response and usually the underlying stimulus that triggers the activity is unknown. Thus, this thesis also presents anumerical solution to reconstruct stimuli from Hodgkin-Huxley neural responses while retrieving the neural dynamics. The stimulus is reconstructed by first retrieving themaximal conductances of the ion channels and then solving the Hodgkin-Huxley equations for the stimulus. The results show that the reconstructed stimulus is a good approximationof the original stimulus, while the retrieved the neural dynamics, which represent the voltage-dependent changes in the ion channels, help to understand the changes in neuralbiochemistry. As high non-linearity of neural dynamics renders analytical inversion of a neuron an arduous task, a numerical approach provides a local solution to the problem ofstimulus reconstruction and neural dynamics retrieval. |
