Bang-bang control development of permeability changes in a membrane model.
Subtitle: Permeability correction mechanisms inherent in the Hodgkin-Huxley model.
Publisher: OSU Libraries
Published: 1997
Place of publication: Corvallis, OR
Description: The application of systems and control theory to membrane physiology is presented here. Modeling efforts have focused on describing those physiologically realistic mechanisms which govern the regulation of membrane permeability in nerve. The motivation behind identifying such mechanisms lies in understanding the morphology of neural activity on a meaningful and analytically tractable level. The suggested merit of integrating control theory into the analysis lies in providing how a membrane effectively adapts to changes in permeability and through what governing mechanisms. The value in producing such an understanding lies in mirroring biological reality in a more formal manner than could be achieved solely through experimental means. A bang-bang control policy describing the permeability correction mechanisms is developed using Liapunov's Stability Criteria. Both changes in membrane potential and kinetic rates are required to implement the policy. The policy describes the inherent mechanisms of the membrane which act to drive its permeability from unstable firing to the resting potential state. It is shown that these permeability changes in state are governed by a switching function that depends on the membrane potential and a dominant controlling parameter. The control policy is discussed in the context of solutions of the Hodgkin-Huxley Equations of Ionic Hypothesis.
Table of contents: title: Chapter 1. Thesis Overview; title: 1.1. Introduction: Thesis Objective and Motivation; title: 1.1.1. Research Objective; title: 1.1.2. Motivation and Value; title: 1.2. The Role of Current Developments in Neurogenic Dynamic Modeling; title: 1.2.1. History in Brief; title: 1.2.2. Related Literature; title: 1.3. Overview of Proposed Analysis, Expectations, and Order of Presentation; title: Chapter 2. The Equations of Ionic Hypothesis; title: 2.1. The Hodgkin-Huxley Model; title: 2.2. Membrane Electrical Equivalent and Engineering Circuit Approximation; title: Chapter 3. State Formulation of the Hodgkin-Huxley Equations and the Presentation of Numerical Results; title: 3.1. State Structuring of the Hodgkin-Huxley Equations; title: 3.2. Membrane Currents and Time-Varying Conductances; title: Chapter 4. The Dynamical Description: The Hodgkin-Huxley Membrane as a Bang-Bang Controller; title: 4.1. Overview; title: 4.2. Methods; title: 4.3. Stability and Control in the Hodgkin-Huxley Membrane; title: 4.3.1. Liapunov Function Generation Case 1: No Control Input (u = 0); title: 4.3.2. Systems Plots and Physical Interpretation of Results; title: 4.3.3. Case 2: Synthesis of a Control Policy (u =/ 0); title: 4.4. Suggested Method for Introducing the Additive Control; title: 4.5. Conclusion; title: 4.6 Suggestions for Future Directions; title: Bibliography; title: Appendix. Computer Code used in Simulating the Hodgkin-Huxley Equations of Ionic Hypothesis