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Export Reference (APA) 
Zaitri, M. A., Silva, C. J.  & Torres, D. F. M. (2023). An analytic method to determine the optimal time for the induction phase of anesthesia. Axioms. 12 (9)
Export Reference (IEEE) 
Z. M. A. et al.,  "An analytic method to determine the optimal time for the induction phase of anesthesia", in Axioms, vol. 12, no. 9, 2023
Export BibTeX 
@article{a.2023_1716178424765,
	author = "Zaitri, M. A. and Silva, C. J.  and Torres, D. F. M.",
	title = "An analytic method to determine the optimal time for the induction phase of anesthesia",
	journal = "Axioms",
	year = "2023",
	volume = "12",
	number = "9",
	doi = "10.3390/axioms12090867",
	url = "https://www.mdpi.com/2075-1680/12/9/867"
}
Export RIS 
TY  - JOUR
TI  - An analytic method to determine the optimal time for the induction phase of anesthesia
T2  - Axioms
VL  - 12
IS  - 9
AU  - Zaitri, M. A.
AU  - Silva, C. J. 
AU  - Torres, D. F. M.
PY  - 2023
SN  - 2075-1680
DO  - 10.3390/axioms12090867
UR  - https://www.mdpi.com/2075-1680/12/9/867
AB  - We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of anesthesia relies on a pharmacokinetic/pharmacodynamic (PK/PD) model proposed by Bailey and Haddad in 2005 to regulate the infusion of propofol. In order to evaluate our approach and compare it with existing results in the literature, we examine a minimum-time problem for anesthetizing a patient. By applying the Pontryagin minimum principle, we introduce the shooting method as a means to solve the problem at hand. Additionally, we conducted numerical simulations using the MATLAB computing environment. We solve the time-optimal control problem using our newly proposed analytical method and discover that the optimal continuous infusion rate of the anesthetic and the minimum required time for transition from the awake state to an anesthetized state exhibit similarity between the two methods. However, the advantage of our new analytic method lies in its independence from unknown initial conditions for the adjoint variables. 
ER  -