Optimal Control in life sciences and medicine

Cover for the slides

Abstract: Optimal Control Applied to Life Sciences

Life Sciences might be seen as the connections between medicine, biology, mathematics, physics, and computer sciences. Further, optimal control might be defined as the extension of static optimization, or even as some comments, the new face of Variational Calculus.

In this talk we present several examples from life sciences analyzed with the support of optimal control. We might apply basically three approaches to optimal control problems, with their own weaknesses and strengthens: the Pontryagin’s Maximum Principle, Dynamic Programming, or Static Optimization. All the problems treated here were analyzed by the Pontryagin’s Maximum Principle.

The problems are solved using numerical schemes implemented in a computer. Topping the bill, we present two cases from a paper on process of publication: phototherapy for infants affected by neonatal jaundice and Feed-Forward Loop Network. We leave as future works comparisons with other approaches such as dynamic programming, or works on constraints on state space. Furthermore, we have concentrated on continuous-deterministic problems.  

 Keywords: Life Sciences, applied optimal control, numerical schemes, Runge-Kutta Method, forward-backward sweep method. 

Full PDF:

Optimal Control applied

 

General Scheme for the numerical simulations

Scheme for the several ways to tackle numerically problems in optimal control theory

flowchart for the algorithms used in the numerical simulations

numerical simulations for the neonatal jaundice photo-therapy using optimal control theory

PS. I was biased mainly by

LENHART, S.; WORKMAN, J. T, Optimal Control Applied to biological models, Chapman & Hall/ CRC, Mathematical and Computational Biology Series, 2007.

See that is also a nice reference: 

Sebastian Anița, Viorel Arnăutu, Vincenzo Capasso, An introduction to optimal control problems in life sciences and economics: from mathematical models to numerical simulation with Matlab®, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, 2011. 

See Suzanne Lenhart homepage for several codes in Matlab. See that the codes are built independently of Matlab, they can be easily adapted to other languages.

 See for a simplified version of the codes used, in Portugal: