Mathematical Biosciences and Engineering (MBE)

Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation
Pages: 739 - 763, Volume 7, Issue 4, October 2010

doi:10.3934/mbe.2010.7.739      Abstract        References        Full text (612.0K)                  Related Articles

Judy Day - Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Ave, 377 Jennings Hall, Columbus, OH 43210, United States (email)
Jonathan Rubin - Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, United States (email)
Gilles Clermont - Department of Critical Care Medicine, University of Pittsburgh Medical Center, 3550 Terrace St, Pittsburgh, PA 15261, United States (email)

1 D. Annane, V. Sebille, C. Charpentier, P. E. Bollaert, B. Francois, J. M. Korach, G. Capellier, Y. Cohen, E. Azoulay, G. Troche, P. Chaumet-Riffaut and E. Bellissant, Effect of treatment with low doses of hydrocortisone and fludrocortisone on mortality in patients with septic shock, JAMA, 288 (2002), 862-871.
2 R. C. Bone, The search for a magic bullet to fight sepsis, JAMA, 269 (1993), 2266-2267.
3 R. C. Bone, Why sepsis trials fail, JAMA, 276 (1996), 565-566.
4 R. C. Bone, Immunologic dissonance: A continuing evolution in our understanding of the systemic inflammatory response syndrome (SIRS) and the multiple organ dysfunction syndrome (MODS), Ann. Intern. Med., 125 (1996), 680-687.
5 C. C. Chow, G. Clermont, R. Kumar, C. Lagoa, Z. Tawadrous, D. Gallo, B. Betten, J. Bartels, G. Constantine, M. P. Fink, T. R. Billiar and Y. Vodovotz, The acute inflammatory response in diverse shock states, Shock, 24 (2005), 74-84.
6 A. S. Cross, S. M. Opal, K. Bhattacharjee, S. T. Donta, P. N. Peduzzi, E. Furer, J. U. Que and S. J. Cryz, Immunotherapy of sepsis: Flawed concept or faulty implementation?, Vaccine, 17 (Suppl. 3) (1999), S13-S21.
7 A. S. Cross and S. M. Opal, A new paradigm for the treatment of sepsis: Is it time to consider combination therapy, Ann. Intern. Med., 138 (2003), 502-505.
8 S. Daun, J. Rubin, Y. V. Vodovotz, A. Roy, R. S. Parker and G. Clermont, An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats: Results from parameter space reduction, J. Theor. Biol., 253 (2008), 843-853.
9 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 (2006), 237-256.       
10 R. P. Dellinger, M. M. Levy, J. M. Carlet, J. Bion, M. M. Parker, R. Jaeschke, K. Reinhart, D. C. Angus, C. Brun-Buisson, R. Beale, T. Calandra, J. F. Dhainaut, H. Gerlach, M. Harvey, J. J. Marini, J. Marshall, M. Ranieri, G. Ramsay, J. Sevransky, B. T. Thompson, S. Townsend, J. S. Vender, J. L. Zimmerman and J. L. Vincent, Surviving Sepsis Campaign: International guidelines for management of severe sepsis and septic shock: 2008, Crit. Care Med., 36 (2008), 296-327.
11 F. Doyle, L. Jovanovic, D. Seborg, R. S. Parker, B. W. Bequette, A. M. Jeffrey, X. Xia, I. K. Craig and T. McAvoy, A tutorial on biomedical process control, J. Proc. Con., 17 (2007), 571-594.
12 J. A. Florian, Jr., J. L. Eiseman and R. S. Parker, Nonlinear model predictive control for dosing daily anticancer agents using a novel saturating-rate cell-cycle model, Comput. Biol. Med., 38 (2008), 339-347.
13 J. Klastersky and R. Capel, Adreno-corticosteroids in the treatment of bacterial sepsis: A double-blind study with pharmacological doses, Antimicrobial Agents Chemother., 10 (1970), 175-180.
14 R. Kumar, G. Clermont, Y. Vodovotz and C. C. Chow, The dynamics of acute inflammation, J. Theor. Biol., 230 (2004), 145-155.       
15 M. M. Levy, M. P. Fink, J. C. Marshall, E. Abraham, D. Angus, D. Cook, J. Cohen, S. M. Opal, J. L. Vincent and G. Ramsay, 2001 SCCM/ESICM/ACCP/ATS/SIS International Sepsis Definitions Conference, Crit. Care Med., 31 (2003), 250-256.
16 D. Lipiner-Friedman, C. L. Sprung, P. F. Laterre, Y. Weiss, S. V. Goodman, M. Vogeser, J. Briegel, D. Keh, M. Singer, R. Moreno, E. Bellissant and D. Annane, Adrenal function in sepsis: The retrospective Corticus cohort study, Crit. Care Med., 35 (2007), 1012-1018.
17 J. C. Marshall, E. Deitch, L. L. Moldawer, S. Opal, H. Redl and P. T. van Der, Preclinical models of shock and sepsis: What can they tell us?, Shock, 24 (Suppl. 1) (2005), 1-6.
18 B. Ogunnaike and W. Ray, "Process Dynamics, Modeling, and Control," Oxford University Press, New York, 1994.
19 R. S. Parker, F. J. Doyle, III and N. A. Peppas, The intravenous route to blood glucose control, IEEE Eng. Med. Biol. Mag., 20 (2001), 65-73.
20 A. M. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz and B. Ermentrout, A reduced mathematical model of the acute inflammatory response: I Derivation of the model and analysis of anti-inflammation, J. Theor. Biol., 242 (2006), 220-236.       
21 Y. Vodovotz, C. C. Chow, J. Bartels, C. Lagoa, J. M. Prince, R. M. Levy, R. Kumar, J. Day, J. Rubin, G. Constantine, T. R. Billiar, M. P. Fink and G. Clermont, In silico models of acute inflammation in animals, Shock, 26 (2006), 235-244.
22 H. D. Volk, P. Reinke and W. D. Docke, Clinical aspects: From systemic inflammation to 'immunoparalysis', Chem. Immunol., 74 (2000), 162-177.

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