The mathematical models (usually ordinary differential equation (ODE) models) created to describe the dynamics of the inflammatory response are complex, highly nonlinear systems. As a result, existing methodologies that are typically useful for estimating parameters and finding appropriate control measures have limited effectiveness when applied to such nonlinear systems. We propose to develop and apply adaptive control and parameter estimation techniques for this problem and explore more complex and realistic settings than previously examined. This will subsequently involve developing new and modifying current mathematical theories to ensure the methods are stable and robust. The methods that arise from this work will also be applicable for a variety of processes that can only be adequately described by complex, nonlinear ODE models.
The inflammatory response is a crucial process for restoring health following a wide range of biological stresses. However, uncontrolled systemic inflammation is also the primary cause of organ failure and death in victims of severe trauma, infections, and many other conditions leading to admission to an intensive care unit. Controlling inflammation, while a key focus of clinicians, is a challenging endeavor. The complexity of the inflammatory response makes it extremely difficult to predict the effects of therapeutic interventions. Much needed effort has been put toward the creation of mathematical models to better understand the mechanisms that orchestrate a systemic inflammatory response. However, little work has been done to develop strategies to control the process and restore a dysfunctional inflammatory response to a healthy equilibrium by delivering appropriate interventions in the correct amounts and at the right times. The main goal of our proposal then is to modify existing and develop new techniques to address this need.