Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering

First Advisor

Dr. Damon A. Miller

Second Advisor

Dr. John W. Gesink

Third Advisor

Dr. Melinda E. Koelling

Fourth Advisor

Dr. Cindy L. Linn


Optimal control, Neuron models, Bifurcation dynamics, Control theory, Control systems, Neuroscience


Hodgkin-Huxley type conductance-based models can simulate the e ffect of time-varying injected stimulus currents on the neuron membrane voltage. The dynamics simulated by these model types enables investigation of the biophysical basis of neuronal activity which is fundamental to higher level function. Broadened understanding the basis of nervous system function could lead to development of eff ective treatment for related diseases, disorders, and the e ffects of trauma. In this dissertation, optimal control is used with conductance-based neuron models to develop a "Reduced Energy Input Stimulus Discovery Method." Within the method, an objective function balances two competing criteria: tracking a reference membrane voltage resulting from a stimulus current and reducing the squared input stimulus current `energy' of that stimulus current. The technique enables computation of optimal input current stimuli that provide differing emphasis on either reference membrane potential tracking or input stimulus current energy reduction. Differences between mathematically optimal and reference stimulus-response signal pairs serve as a source of investigation for furthering understanding of neural dynamics. The method is applied to investigations including four fundamental bifurcation types in a reduced-order, conductance-based neuron model as well as the classical Hodgkin-Huxley model. Experimental feasibility of the approach is demonstrated by applying optimal current stimuli to neurons of the leech Hirudo verbana using single cell intracellular stimulation and recording techniques with sharp micro- electrodes. Applicability may include finding reduced energy current stimuli for treatment of neurological diseases and prosthesis control.


5th Advisor: Dr. Frank L. Severance

Access Setting

Dissertation-Open Access