INTRODUCTION: The acute inflammatory response system is responsible for the initial action of the body against acute biological stress, such as bacterial infection (endotoxin) or tissue trauma. Such response action involves a cascade of events mediated by an array of cells and molecules to eliminate invading pathogens and repair damaged tissues [1]. For a normally functioning response system, the inflammation eventually subsides and the body returns to basal level. However, an excessive inflammatory response can lead to further tissue damage, organ dysfunction, or possibly death [2]. To control the inflammatory response system, organisms have developed regulatory mechanisms such as pro- and anti-inflammatory mediators. In general, the pro-inflammatory elements (e.g., interleukin-6 (IL-6), tumor necrosis factor (TNF)) up-regulate the inflammatory actions; whereas, the anti-inflammatory elements (e.g., interleukin-10 (IL-10)) down-regulate the inflammation response [3]. In this study, an ordinary differential equation (ODE) model of the acute inflammation response was developed to capture the dynamics of inflammatory cells and the dynamics and interactions of various pro- and anti-inflammatory mediators.

METHODS: The mathematical model consists of 8 ODEs and 42 parameters. The dependent variables include the concentration of endotoxin challenge (P), concentration of activated phagocytic cells (N), tissue damage marker (D), pro-inflammatory mediator concentrations (IL-6 and TNF), IL-10 concentration (which is an anti-inflammatory cytokine), and other anti-inflammatory moderator concentrations (Ca). The differential equations include biologically-motivated saturation terms (e.g., Hill functions), thus making the model nonlinear. Values for some of the parameters were obtained from A. Reynolds et al [4]. In order to calibrate the model, data was obtained from experiments performed on Sprague-Dawley rats by Dr. Y. Vodovotz and colleagues at the University of Pittsburgh (Department of Surgery). Model parameters were estimated using experimental data of endotoxin challenges at 3 and 12 mg/kg via the nonlinear least square technique [5]. Finally model validation was performed by comparing the model predictions at an endotoxin challenge level of 6 mg/kg with experimental data at the same level.

RESULTS: The introduction of an endotoxin challenge (P) activates the phagocytic cells (N), which in turn, up-regulates all the mediators (TNF, IL-10, IL-6, and Ca). Furthermore, the mediators have a positive or a negative feedback based on their functionality (pro- or anti-inflammatory) on the process. The sepsis model successfully captured the dynamics of pro-inflammatory (IL-6 and TNF) and anti-inflammatory (IL-10 and Ca) mediators during endotoxin challenge to rat at dose levels of 3, 6, and 12 mg/kg. Model predictions of the activated phagocytic cells (N) in response to endotoxin challenges at the same dose levels were also consistent with the experimental data.

CONCLUSION: The model successfully emulated the acute inflammatory response to endotoxin challenges at different dose levels. This 8-state model may provide further insight of the various interactions between phagocytic cells and pro/anti-inflammatory mediators. With further validation, the model may provide more information regarding the critical levels of various elements of the inflammatory response system which could lead to sepsis. Finally, this model is a test-bed on which control strategies can be tested. One formulation is model-based control of inflammatory mediators in patients under biological stress by adjusting blood flow through an external recirculation adsorption column.

REFERENCES:

[1] J. Day, J. Rubin, Y. Vodovotz, C.C. Chow, A. Reynolds, and G. Clermont. A reduced mathematical model of the acute inflammatory response. II. Capturing scenarios of repeated endotoxin administration. J. Theor. Biol., 242: 237 - 256, 2006

[2] R.J. Goris, T.P. te Boekhorst, J.K. Nuytinck, J.S. Gimbrere. Multiple-organ failure. Generalized autodestructive inflammation? Arch. Surg., 120: 1109 - 1115, 1985

[3] C. Nathan. Points of control in inflammation. Nature, 420: 846 - 852, 2002

[4] A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz, and G.B. Ermentrout . A reduced mathematical model of the acute inflammatory response. I. Derivation of model and analysis of anti-inflammation. J. Theor. Biol., 242: 220 - 236, 2006

[5] E. Carson, C. Cobelli. Modelling methodology for physiology and medicine. San Diego, CA; Academic Press, 2001