American Institute of Mathematical Sciences

Advanced
2010, 7(4): 739-763. doi: 10.3934/mbe.2010.7.739

Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation

Judy Day 1, , Jonathan Rubin 2, and  Gilles Clermont 3,

1. 

Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Ave, 377 Jennings Hall, Columbus, OH 43210, United States
2. 

Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, United States
3. 

Department of Critical Care Medicine, University of Pittsburgh Medical Center, 3550 Terrace St, Pittsburgh, PA 15261, United States

Received  March 2010 Revised  May 2010 Published  October 2010

Modulation of the inflammatory response has become a key focal point in the treatment of critically ill patients. Much of the computational work in this emerging field has been carried out with the goal of unraveling the primary drivers, interconnections, and dynamics of systemic inflammation. To translate these theoretical efforts into clinical approaches, the proper biological targets and specific manipulations must be identified. In this work, we pursue this goal by implementing a nonlinear model predictive control (NMPC) algorithm in the context of a reduced computational model of the acute inflammatory response to severe infection. In our simulations, NMPC successfully identifies patient-specific therapeutic strategies, based on simulated observations of clinically accessible inflammatory mediators, which outperform standardized therapies, even when the latter are derived using a general optimization routine. These results imply that a combination of computational modeling and NMPC may be of practical use in suggesting novel immuno-modulatory strategies for the treatment of intensive care patients.
Keywords: dosing control., Inflammation, immuno-modulation, nonlinear model predictive control.
Mathematics Subject Classification: Primary: 92C50, 93C15; Secondary: 93C8.
Citation: Judy Day, Jonathan Rubin, Gilles Clermont. Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation. Mathematical Biosciences & Engineering, 2010, 7 (4) : 739-763. doi: 10.3934/mbe.2010.7.739
References:
[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.   Google Scholar

[2]

R. C. Bone, The search for a magic bullet to fight sepsis,, JAMA, 269 (1993), 2266.   Google Scholar

[3]

R. C. Bone, Why sepsis trials fail,, JAMA, 276 (1996), 565.   Google Scholar

[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.   Google Scholar

[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.  doi: doi:10.1097/01.shk.0000168526.97716.f3.  Google Scholar

[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).  doi: doi:10.1016/S0264-410X(99)00230-3.  Google Scholar

[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.   Google Scholar

[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.  doi: doi:10.1016/j.jtbi.2008.04.033.  Google Scholar

[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.  doi: doi:10.1016/j.jtbi.2006.02.015.  Google Scholar

[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.  doi: doi:10.1097/01.CCM.0000298158.12101.41.  Google Scholar

[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.  doi: doi:10.1016/j.jprocont.2007.01.012.  Google Scholar

[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.  doi: doi:10.1016/j.compbiomed.2007.12.003.  Google Scholar

[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.   Google Scholar

[14]

R. Kumar, G. Clermont, Y. Vodovotz and C. C. Chow, The dynamics of acute inflammation,, J. Theor. Biol., 230 (2004), 145.  doi: doi:10.1016/j.jtbi.2004.04.044.  Google Scholar

[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.  doi: doi:10.1097/01.CCM.0000050454.01978.3B.  Google Scholar

[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.  doi: doi:10.1097/01.CCM.0000259465.92018.6E.  Google Scholar

[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.  doi: doi:10.1097/01.shk.0000191383.34066.4b.  Google Scholar

[18]

B. Ogunnaike and W. Ray, "Process Dynamics, Modeling, and Control,", Oxford University Press, (1994).   Google Scholar

[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.  doi: doi:10.1109/51.897829.  Google Scholar

[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.  doi: doi:10.1016/j.jtbi.2006.02.016.  Google Scholar

[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.  doi: doi:10.1097/01.shk.0000225413.13866.fo.  Google Scholar

[22]

H. D. Volk, P. Reinke and W. D. Docke, Clinical aspects: From systemic inflammation to 'immunoparalysis',, Chem. Immunol., 74 (2000), 162.  doi: doi:10.1159/000058753.  Google Scholar

show all references

References:
[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.   Google Scholar

[2]

R. C. Bone, The search for a magic bullet to fight sepsis,, JAMA, 269 (1993), 2266.   Google Scholar

[3]

R. C. Bone, Why sepsis trials fail,, JAMA, 276 (1996), 565.   Google Scholar

[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.   Google Scholar

[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.  doi: doi:10.1097/01.shk.0000168526.97716.f3.  Google Scholar

[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).  doi: doi:10.1016/S0264-410X(99)00230-3.  Google Scholar

[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.   Google Scholar

[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.  doi: doi:10.1016/j.jtbi.2008.04.033.  Google Scholar

[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.  doi: doi:10.1016/j.jtbi.2006.02.015.  Google Scholar

[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.  doi: doi:10.1097/01.CCM.0000298158.12101.41.  Google Scholar

[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.  doi: doi:10.1016/j.jprocont.2007.01.012.  Google Scholar

[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.  doi: doi:10.1016/j.compbiomed.2007.12.003.  Google Scholar

[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.   Google Scholar

[14]

R. Kumar, G. Clermont, Y. Vodovotz and C. C. Chow, The dynamics of acute inflammation,, J. Theor. Biol., 230 (2004), 145.  doi: doi:10.1016/j.jtbi.2004.04.044.  Google Scholar

[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.  doi: doi:10.1097/01.CCM.0000050454.01978.3B.  Google Scholar

[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.  doi: doi:10.1097/01.CCM.0000259465.92018.6E.  Google Scholar

[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.  doi: doi:10.1097/01.shk.0000191383.34066.4b.  Google Scholar

[18]

B. Ogunnaike and W. Ray, "Process Dynamics, Modeling, and Control,", Oxford University Press, (1994).   Google Scholar

[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.  doi: doi:10.1109/51.897829.  Google Scholar

[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.  doi: doi:10.1016/j.jtbi.2006.02.016.  Google Scholar

[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.  doi: doi:10.1097/01.shk.0000225413.13866.fo.  Google Scholar

[22]

H. D. Volk, P. Reinke and W. D. Docke, Clinical aspects: From systemic inflammation to 'immunoparalysis',, Chem. Immunol., 74 (2000), 162.  doi: doi:10.1159/000058753.  Google Scholar

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