Motivation: Therapeutic enhancement of innate immune response to microbial attack is addressed as the optimal control of a dynamic system. Interactions between an invading pathogen and the innate immune system are characterized by four non-linear, ordinary differential equations that describe rates of change of pathogen, plasma cell, and antibody concentrations, and of an indicator of organic health. Without therapy, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen; the response pattern depends on the initial concentration of pathogens in the simulated attack. In the model, immune response can be augmented by therapeutic agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. A previous paper demonstrated open-loop optimal control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal (Stengel et al., 2002). Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and control usage, providing implicit control over harmful side effects. Results: We demonstrate the ability of neighboring-optimal feedback control to account for a range of unknown initial conditions and persistent input of pathogens by adjusting the therapy to account for perturbations from the nominal-optimal response history. We examine therapies that combine open-loop control of one agent with closed-loop control of another. We show that optimal control theory points the way toward new protocols for treatment and cure of human diseases.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Molecular Biology
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics