An Approximate Solution for Glucose Model via Parameterization Method in Optimal Control Problems

Document Type : Original Article

Authors

1 Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Applied Mathematics, Islamic Azad University, Damghan Branch, Damghan, Iran

3 Department of Biology, Islamic Azad University, Damghan Branch, Damghan, Iran

Abstract

Glucose tolerance test is advised to detection of pre-diabetics and mild diabetics in the medical practice. Several mathematical models such as glucose model, were proposed for mimicking the blood glucose-insulin interaction. To predict accurate insulin requirement for each glucose concentration, we need to solve optimal control problems. In this model, constraints are linear and nonlinear forms of cost function. Although ordinary methods can be used in glucose model, but non-negative natures of medical variables made them difficult to use. To finding a new approximate solution of glucose model, parameterization method with non-negative coefficients in polynomial was used. In this state parameterization method, we use polynomials that ensure that the control variable is non-negative in this model. And increases the time for the model solution to be non-negative compared to conventional methods. The simplicity, lower requirement for mathematical calculations and more compatibility with variables are positive aspects of our parameterization method.

Keywords

References

1. Erding C., Minghui H., Shandong T., Huihe S., 2013. A new optimal control system design for chemical processes. Chinese Journal of Chemical Engineering. 21(12), 1341-1346.
2. Lenhart S., Workman J.T., 2007. Optimal control applied to biological models. Chapman and Hall/CRC.
3. Moore H., 2018. How to mathematically optimize drug regimens using optimal control. Journal of Pharmacokinetics and Pharmacodynamics. 45(1), 127-137.
4. Ackerman E.,  Rosevar J., Molnar G., 1969. Concepts and models of biomathematics. Dekker, New York, 131-156.
5.  Gatewood L.C., Ackerman E., Rosevear J.W., Molnar G.D., 1970. Modeling blood glucose dynamics. Behavioral science. 15(1), 72-87.
6. MehneH., Hashemi Borzabadi A., 2006. A numerical method for solving optimal control problems using state parameterization. Numerical Algorithms. 42(2), 165-169.
7. Kafash B., Delavarkhalafi  A., Karbassi S.M., 2012. Numerical solution of nonlinear optimal control problems based on state parameterization. Iranian Journal of Science & Technology. 43, 331-340.
8. Kafash B., Delavarkhalafi A., Karbassi S.M., 2012. Application of Chebyshev polynomials to derive efficient algorithms for the solution of optimal control problems. Scientia Iranica. 19(3), 795-805.
 
9. Kafash B., Delavarkhalafi A., Karbassi S.M., Boubaker K., 2014. A numerical approach for solving optimal control problems using the Boubaker polynomials expansion scheme. Journal of Interpolation and Approximation Scientific Computing.
10. Eisen M., 1988. Mathematical Methods and Models in the Biological Sciences. Prentice Hall, Englewood Cliffs, New Jersey.
Journal of Chemical Health Risks
Volume 11, Issue 3
July 2021
Pages 291-298

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History

  • Receive Date: 04 November 2020
  • Revise Date: 30 December 2020
  • Accept Date: 01 January 2021
  • First Publish Date: 26 April 2021

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