Optimal Control of Disease Processes

Robert F. Stengel
Princeton University

sponsored by The Alfred P. Sloan Foundation

The first phase of the project demonstrated a progression of methods for treating disease, beginning with a simple abstract model of the humoral immune system. With this model, we first show how to calculate the optimal treatment protocol when all information about immune system dynamics, the nature of the pathogenic attack, and the efficacy of drugs is known without error. Computations suggest the therapy that defeats the pathogen while preserving the virtual patient's health and minimizing the side effects of treatment.

Next, we establish a framework for feeding back the measured response of the immune system -- including evolving concentrations of pathogens, plasma cells, and antibodies, as well as a measure of organic health -- to adjust the therapy for uncertain knowledge of the pathogen's effect. For this simple model, the pathogen may represent free viruses or extracellular bacteria, while representative control elements may be antibiotics, antigens from killed (i.e., non-toxic) pathogens, pre-formed antibodies, or anti-inflammatory drugs. We develop a control structure that is analogous to what one might find in an aircraft or robot, except here the control is applied to assist natural immune response.

The third step modifies the feedback controller to account for variability in the measurements and for a reduced measurement set. Measurements contain error, and it may not be able to observe every element of the system's dynamic state.

The second phase of research involves the enhancement of adaptive immune response, the body's major defense mechanism against intracellular bacteria and viruses, such as the human immunodeficiency virus (HIV), and cancer. Here, the dynamic model is entirely different, but the control-theoretic approach is the same. Effecting a complete cure is an elusive goal because viruses mutate, by-passing the therapeutic effect of drugs that control a pathogen in its initial form. We hope to shed new light on this goal and to improve protocols for administering known therapies, e.g., the triple-drug combination called Highly Active Antiretroviral Therapy (HAART) for HIV. When dealing with such complex issues as HIV mutation, the control structure itself must be adaptive, changing to accommodate the varying nature of the threat. By combining the results of laboratory and clinical experiments with the application of optimal control theory, we will suggest new ways of treating disease and aid the process of discovering new therapies.


Last updated January 2, 2007.
Copyright (c) 2007 by Robert F. Stengel. All rights reserved.