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: 

 

On the design of a molecular dynamics based model for studying receptor-receptor interactions: Systems Biology, Molecular Dynamics, and biomechanics

•Content

Introduction

•Methodological procedures

•Theoretical Background

•Receptors

•Dimerization and ligand binding

•Bioinformatics and mathematical modelling

•G-protein-coupled receptor dynamics

•The receptor–dimer cooperativity index

•Single-molecule imaging revealed dynamic GPCR dimerization

•Proposed model

•Conclusions and Final remarks

•References 

Download the full text: PDF.

Introduction

The pharmaceutical industries is likely to be amongst the most important and controversy ones. Issues present on the industries vary from misuse of advances such as not allowing drugs to reach the consumers or even manipulation of results. However, with no doubt , this is an extreme active area. Hot topics at the moment are: Systems Biology, Systems (bio) Medicine, P4 Medicine, and Systems Pharmacology.

The several scale to studying matter, from a physics viewpoint and from a biological viewpoint. For physics what matters is size rather organization. For physics the brain and a stone of the same size and mass is the same thing, but for biology one is a miracle of life and the second is a chunk of matter, useless.

 

The several levels of organization from human to genes, each level can be homeland for modeling, approaches that mixture them are in general called multiscales approaches

Scheme depicting the importance of receptors. A distal region can be controlled due to the concept of ligand and receptors



scheme for the methodology proposed for developing the software. the sphere supposes to represent the cell surface, whereas the dots are the dimers, or even monomers, that is, any clusters that can be considered a point, a node.

Videos used on the talk

  

This video was produced in 2012 in Gdansk as a warming up exercise in Continuous and Discrete simulations, taught by prof. Sergey Kshevetskii
Theoretical Physics Department of Immanuel Kant Russian
State University. The model is simple, just several particles in a box, with a potential between them, they are given an initial kick, there is no dissipation. 

This video was produced in Gdansk, as part of the lesson in classical simulations, by Winczewski Szymon, see Necking (nanowire)