Mathematical Biosciences and Engineering, 2015, 12(5): 1127-1139. doi: 10.3934/mbe.2015.12.1127.

Primary: 92C50, 93C15; Secondary: 93C83.

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Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen

1. Department of Mathematics, University of California, Irvine, 340 Rowland Hall, Bldg #400, Irvine, CA 92697-3875
2. Electrical Engineering and Computer Science Department, Masdar Institute of Science and Technology, Masdar City, Abu Dhabi
3. Department of Mathematics, University of Tennessee, 1403 Circle Dr, Ayres Hall 227, Knoxville, TN, 37996-2250

The inflammatory responseaims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen.In cases of acute systemic inflammation, the possibility of collateral tissuedamage arises, which leads to a necessary down-regulation of the response.A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present resultson the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.
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Keywords nonlinear observability.; particle filter; immuno-modulation; nonlinear controllability; Inflammation

Citation: Gregory Zitelli, Seddik M. Djouadi, Judy D. Day. Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen. Mathematical Biosciences and Engineering, 2015, 12(5): 1127-1139. doi: 10.3934/mbe.2015.12.1127

References

  • 1. New Eng J Med, 369 (2013), 840-851.
  • 2. Proceedings of the $52^{nd}$ IEEE Conference on Decision and Control, Florence, Italy, December 10-13 (2013), 3373-3378.
  • 3. Springer-Verlag London, Ltd., London, 1999.
  • 4. American Mathematical Society, Providence, RI, 2007.
  • 5. Math Biosci Eng, 7 (2010), 739-763.
  • 6. J Exp Med, 174 (1991), 1209-1220.
  • 7. Comput. Biol. Med., 38 (2008), 339-347.
  • 8. 9th International Symposium on Dynamics and Control of Process Systems, 9 (2010), 272-277.
  • 9. Springer-Verlag, New York, 1990.
  • 10. J Theor Bio, 242 (2006), 220-236.
  • 11. Wiley-Interscience, Hoboken, NJ, 2006.
  • 12. Oxford University Press, Oxford, 2008.
  • 13. Birkhäuser Boston, Inc, Boston, MA, 1992.

 

This article has been cited by

  • 1. Ouassim Bara, Michel Fliess, Cédric Join, Judy Day, Seddik M. Djouadi, Toward a model-free feedback control synthesis for treating acute inflammation, Journal of Theoretical Biology, 2018, 448, 26, 10.1016/j.jtbi.2018.04.003
  • 2. M. S. Vinogradova, S. B. Tkachev, O. S. Tkacheva, Using an Observer in a Sliding Mode for Modeling Antiangiogenic Therapy, Mathematics and Mathematical Modeling, 2019, 6, 52, 10.24108/mathm.0618.0000165

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Copyright Info: 2015, Gregory Zitelli, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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