Researchers have put significant effort in exploring the corticosteroid effect in modulating the dynamics of an inflammatory response 1-6. Although, there is a physiologic rationale for the use of corticosteroids in a systemic inflammatory response syndrome, long-term studies are needed to address optimal drug dosing, duration of treatment and timing of intervention that suffices to reverse the shock of an unresolved inflammatory response that accompanies critical illness 7. The development of mathematical models that capture the complexity of biological systems through the dynamic integration of their elementary components facilitates the rationalization and evaluation of the effectiveness of various treatment interruptions. Designing therapeutic strategies that target the intrinsic dynamics of systemic inflammation is not a trivial task given the fact that a drug can either be administered as an intravenous injection or as an infusion. Each route of drug administration encompasses a set of various parameters such as duration of treatment (for infusion), frequency of injections (for injection), drug dose and it may account for a different biological response. In this study assuming that corticosteroids serve as the putative controllers of an endotoxin-induced inflammatory response a number of questions need to be addressed: “Can we indentify a regime of steroid-based interventions that modulate efficiently the dynamics of an exuberant inflammatory response? Can we distinguish therapeutic strategies that have a critical effect on the response of the system? Do different routes of drug administration account for the manifestation of salient dynamic features of the perturbed state of the system?” It is important to realize that such questions formulate a combinatorial problem that precipitates the development of constraint integer optimization algorithms and motivates the research goals of this study. In the present study we will explore the possibility of formulating a mixed-integer optimization algorithm that opens the research avenues to establish an in silico corticosteroid control policy against an in vivo human response to endotoxin.

The experimental data analyzed in this study were generated as part of the Inflammation and Host Response to Injury Large Scale Collaborative Project funded by the USPHS, U54 GM621119. Human subjects were injected intravenously with endotoxin (CC-RE, lot 2) at a dose of 2-ng/kg body weight (endotoxin treated subjects) and 0.9% sodium chloride (placebo treated subjects). Blood samples were collected and the transcript abundance of leukocytes was measured before endotoxin administration (0hr) and 2, 4, 6, 9 and 24 hrs after endotoxin injection. Parts of these data have been published in 8-10; however the analyses in this article represents an approach that has not been previously published.

Based on our prior work, we developed a NF-kappaB dependent indirect response model of an endotoxin-induced inflammation that integrates mechanistically the opposing effect of two signaling pathways; one associated with the activation of NF-kB that drives downstream the transcriptional activation of inflammatory mediators and one related to the genomic signaling of exogenous corticosteroids; as the putative controllers of inflammation. The development of such a mechanistic model allows us to gain insight about how the system responds to a multitude of external signals through the dynamic interaction of signaling modules. We prompt to formulate a mixed-integer optimization algorithm that takes different routes of drug administration into account via the potential of binary variables. The primary objective is to capture the best corticosteroid intervention strategy under the perturbation of a high concentration of LPS that accounts for the most rapid inflammatory recovery. Therefore, we are interested in identifying an ensemble of steroid interventions that modulate the activity of NF-kappaB so that to rapidly approximate its reference trajectory (baseline) despite the implications of a high LPS stimulus.

Consequently, the formulation of a mixed-integer optimization framework enables us to evaluate the efficacy of particular corticosteroid interventions against the progression of systemic inflammation. Such a framework lays the foundation of an open loop control algorithm that defines research windows shedding invaluable insight on the complex dynamics of the system. Moreover, identifying a regime of optimal intervention strategies may be theoretically tractable but experimentally not practically feasible to validate. However, our approach serves as a critical enabler to improve our understanding about alternative optimal ways of modulating the inflammatory response.

1. Annane, D.; Sebille, V.; Charpentier, C.; Bollaert, P. E.; Francois, B.; Korach, J. M.; Capellier, G.; Cohen, Y.; Azoulay, E.; Troche, G.; Chaumet-Riffaut, P.; Bellissant, E., Effect of treatment with low doses of hydrocortisone and fludrocortisone on mortality in patients with septic shock. Jama 2002, 288, (7), 862-71.

2. Barber, A. E.; Coyle, S. M.; Marano, M. A.; Fischer, E.; Calvano, S. E.; Fong, Y.; Moldawer, L. L.; Lowry, S. F., Glucocorticoid therapy alters hormonal and cytokine responses to endotoxin in man. J Immunol 1993, 150, (5), 1999-2006.

3. Barber, A. E.; Coyle, S. M.; Fischer, E.; Smith, C.; van der Poll, T.; Shires, G. T.; Lowry, S. F., Influence of hypercortisolemia on soluble tumor necrosis factor receptor II and interleukin-1 receptor antagonist responses to endotoxin in human beings. Surgery 1995, 118, (2), 406-10; discussion 410-1.

4. Richardson, R. P.; Rhyne, C. D.; Fong, Y.; Hesse, D. G.; Tracey, K. J.; Marano, M. A.; Lowry, S. F.; Antonacci, A. C.; Calvano, S. E., Peripheral blood leukocyte kinetics following in vivo lipopolysaccharide (LPS) administration to normal human subjects. Influence of elicited hormones and cytokines. Ann Surg 1989, 210, (2), 239-45.

5. Hawes, A. S.; Rock, C. S.; Keogh, C. V.; Lowry, S. F.; Calvano, S. E., In vivo effects of the antiglucocorticoid RU 486 on glucocorticoid and cytokine responses to Escherichia coli endotoxin. Infect Immun 1992, 60, (7), 2641-7.

6. Calvano, S. E.; Albert, J. D.; Legaspi, A.; Organ, B. C.; Tracey, K. J.; Lowry, S. F.; Shires, G. T.; Antonacci, A. C., Comparison of numerical and phenotypic leukocyte changes during constant hydrocortisone infusion in normal humans with those in thermally injured patients. Surg Gynecol Obstet 1987, 164, (6), 509-20.

7. Jahan, A., Septic shock in the postoperative patient: three important management decisions. Cleve Clin J Med 2006, 73 Suppl 1, S67-71.

8. Calvano, S. E.; Xiao, W.; Richards, D. R.; Felciano, R. M.; Baker, H. V.; Cho, R. J.; Chen, R. O.; Brownstein, B. H.; Cobb, J. P.; Tschoeke, S. K.; Miller-Graziano, C.; Moldawer, L. L.; Mindrinos, M. N.; Davis, R. W.; Tompkins, R. G.; Lowry, S. F., A network-based analysis of systemic inflammation in humans. Nature 2005, 437, (7061), 1032-7.

9. Foteinou, P.; Calvano, S.; Lowry, S.; Androulakis, I., An indirect response model of endotoxin-induced systemic inflammation. Journal of Critical Care 2007, 22, (4), 337-338.

10. Storey, J. D.; Xiao, W.; Leek, J. T.; Tompkins, R. G.; Davis, R. W., Significance analysis of time course microarray experiments. Proc Natl Acad Sci U S A 2005, 102, (36), 12837-42.

11. Ramakrishnan, R.; DuBois, D. C.; Almon, R. R.; Pyszczynski, N. A.; Jusko, W. J., Fifth-generation model for corticosteroid pharmacodynamics: application to steady-state receptor down-regulation and enzyme induction patterns during seven-day continuous infusion of methylprednisolone in rats. J Pharmacokinet Pharmacodyn 2002, 29, (1), 1-24.