Optimal administration strategies for EPO based on the model for erythropoiesis involving structured population equations

Lippmann, Laura

Optimal administration strategies for EPO based on the model for erythropoiesis involving structured population equations

Files

Lippmann_0-296098.pdf(1.74 MB)

Date

2014

Publication type

Diploma thesis

Abstract

This diploma thesis deals with a hyperbolic partial differential equation (PDE), developed by the Renal Research Institute in New York. It models the population density of CFU-E cells, which depends on time as well as on the maturity attribute of the cells, with respect to external administration of erythropoietin (EPO). CFU-E cells represent one level of development from stem cells to red blood cells and play a role by investigating optimal treatment of dialysis patients, amongst others.
First, the PDE is normalized followed by a discretization of the maturity variable - representing the space variable in this context - which is carried out using Legendre polynomials. This leads to an ordinary differential equation (ODE).
Utilizing a L^2-objective functional an optimal control problem is expressed. Since injections of EPO are only possible at several fixed days the control obtains a discrete nature.
The theoretical background about solvability of the underlying ODE is illuminated and optimality criteria are formulated.
Subsequently, different optimization techniques are examined, including the theta-method for computing the state and the gradient and BFGS method combined with a modified Armijo step size strategy for the optimization process. Next, they are integrated in a model predictive control (MPC) framework. At the end of the thesis, numerical tests - some of which are based on actual problem settings occurring at the treatment of dialysis patients - are executed and results are presented.

Subject (DDC)

510 Mathematics

Keywords

optimal control, model predictive control, erythropoiesis, BFGS method, Cauchy problem, hyperbolic partial differential equation

Cite This

ISO 690

LIPPMANN, Laura, 2014. Optimal administration strategies for EPO based on the model for erythropoiesis involving structured population equations [Master thesis]. Konstanz: Univ.

BibTex

@mastersthesis{Lippmann2014Optim-31586,
  year={2014},
  title={Optimal administration strategies for EPO based on the model for erythropoiesis involving structured population equations},
  address={Konstanz},
  school={Univ.},
  author={Lippmann, Laura},
  note={Diplomarbeit}
}

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University note

Konstanz, Univ., Master thesis, 2014

Comment on publication

Diplomarbeit