Robust Constrained Drug Dosage Regulation of Acute Inflammation Response Under Disturbances

Year 2020, Volume: 8 Issue: 4, 256 - 262, 31.12.2020

Meric Cetin , Selami Beyhan

https://doi.org/10.18100/ijamec.815606

Abstract

Mathematical modelling of the biological processes, diseases and organs are important for the model-based control of diseases. Due to unmodeled dynamics, unknown and external disturbances, the performance of controllers based on these models are degraded for the accurate control. Therefore, robust controllers are need especially for the applications on patients. Inflammation, the cause of many complex biological phenomena and diseases, is a nonlinear process that is difficult to control. In this paper, continuous-time sliding-mode controller has been designed for the control of acute inflammation response (AIR) and antibacterial drug infusion under external disturbances both for septic and aseptic cases. Sliding-mode controller (SMC) is mostly used to control nonlinear systems against external disturbances and parametric uncertainties. Beside the control signal generation, we propose constraints on the control signals based on the clinical experiences such that the applied control signal is suitable for the health and improves the performance of the controller. Due to the multiple equilibrium point on the behavior of the acute inflammation response, it is difficult to design such model-based controllers without input constraints. In the numerical applications, septic death case and aseptic death case with disturbances are controlled and acceptable performances are obtained for future clinical applications.

Keywords

Aseptic and septic cases, Disturbance, Inflammation response, Sliding mode control

References

• R. S. Parker and G. Clermont, “Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges”, Journal of The Royal Society Interface, 7(48):989–1013, 2010.
• 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”, Journal of Theoretical Biology, 242(1):220–236, 2006.
• J. Day, C. Cockrell, R. Namas, R. Zamora, G. An, and Y. Vodovotz, “Inflammation and disease: Modelling and modulation of the inflammatory response to alleviate critical illness”, Current Opinion in Systems Biology, 12:22–29, 2018.
• O. Bara, S.M. Djouadi, J. Day and S. Lenhart, “Immune therapeutic strategies using optimal controls with L1 and L2 type objectives”, Mathematical Biosciences, 290:9–21, 2017.
• I. Ramirez-Zuniga, J. E. Rubin, D. Swigon, and G. Clermont, “Mathematical modeling of energy consumption in the acute inflammatory response”, Journal of Theoretical Biology, 460:101–114, 2019.
• V. Radosavljević, K. Ristovski, and Z. Obradović, “A data mining approach for optimization of acute inflammation therapy”, IEEE International Conference on Bioinformatics and Biomedicine, pages 1–6. IEEE, 2012.
• J. Day, J. Rubin, and G. Clermont, “Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation”, Mathematical Biosciences& Engineering, 7(4):739, 2010.
• G. Rigatos, K. Busawon, and M. Abbaszadeh, “Nonlinear optimal control of the acute inflammatory response”, Biomedical Signal Processing and Control, 55:101631, 2020.
• O. Bara, J. Day, and S. M. Djouadi, “Optimal control of an inflammatory immune response model”, 54th IEEE Conference on Decision and Control, pages 1283–1288. IEEE, 2015.
• J. S. Hogg, G. Clermont, and R. S. Parker. “Acute inflammation treatment via particle filter state estimation and mpc”, IFAC Proceedings Volumes, 43(5):272–277, 2010.
• J.J.E Slotine and W. Li. Applied Nonlinear Control. Prentice-Hall Inc., 1991.
• W. Gao, Y. Wang, and A. Homaifa, “Discrete-time variable structure control systems”, IEEE Transactions on Industrial Electronics, 42(2):117–122, 1995.
• S. Ahmad, N. Ahmed, M. Ilyas, W. Khan, et al. “Super twisting sliding mode control algorithm for developing artificial pancreas in type 1 diabetes patients”, Biomedical Signal Processing and Control, 38:200–211, 2017.
• M. Sharifi and H. Moradi. “Nonlinear robust adaptive sliding mode control of influenza epidemic in the presence of uncertainty”, Journal of Process Control, 56:48–57, 2017.
• M, K, Bera, P, Kumar and R, K, Biswas, “Robust control of hiv infection by antiretroviral therapy: a super-twisting sliding mode control approach”, IET Systems Biology, 13(3):120–128, 2019.
• O. Bara, M. Fliess, C. Join, J. Day, and S. M, Djouadi. “Toward a model-free feedback control synthesis for treating acute inflammation”, Journal of Theoretical Biology, 448:26–37, 2018.
• O. Bara, S. M. Djouadi, and J. Day, “Immune therapy using optimal control with l1 type objective”, American Control Conference, pages 4895–4900. IEEE, 2016.