Acute Inammatory Response to Endotoxin Challenge: Model Development, Parameter Estimation, and Treatment Control

Bacterial lipopolysaccharides (LPS; endotoxins) are the major outer surface membrane components present in almost all Gram-negative bacteria and act as extremely strong stimulators of innate or natural immunity in diverse eukaryotic species ranging from insects to humans. They also induce acute in ammatory response comparable to bacterial infection. Like most biological processes, modeling the in ammatory response involves using highly nonlinear dynamic systems of differential equations with a relatively large number of parameters. Several researchers have within the last seven years developed mathematical models of acute in ammatory response to infection; some of these models are low-order and are biologically irrelevant due to oversimplification of the real process. The high-order models on the contrary, are highly complex, computationally expensive and constitute challenges in calibrating the model to experimental data.;In the first phase of our work, we propose and validate a number of competing models of acute in ammatory response to compare with a recently developed model in the literature. Our desire to come up with models that can accurately predict the observed dynamics of the pro and anti-inflammatory cytokines led us to conduct sensitivity analysis, subset selection and parameter estimation in order to obtain accurate parameter values from existing data. Next, we employ a model selection technique to aid with selecting the "best" model among all the potential candidates. In addition, we prove the existence and uniqueness of a solution to our "top choice" model as well as study the model's steady state and stability behavior.;At the next phase, we study the model under an open-loop optimal control based treatment strategy, this is the first step to achieving our goal of proposing treatment therapies to regulate inflammation. Since open-loop control problems do not have the ability to incorporate unexpected disturbances in the system as time progresses, we implement a feedback scheme known as Nonlinear Model Predictive Control (NMPC). In general, a better approach to implement NMPC is to combine it with Kalman filter. Hence, we demonstrate how this is done with an example where noise was added to our in silico simulated results to create an experimental data with noise. Unscented Kalman Filter (UKF) was then used to filter the noisy data and estimate the unobserved states at every recalculation step in the NMPC scheme.