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

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2014
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Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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optimal control, model predictive control, erythropoiesis, BFGS method, Cauchy problem, hyperbolic partial differential equation
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ISO 690LIPPMANN, 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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    <dcterms:abstract xml:lang="eng">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.&lt;br /&gt;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).&lt;br /&gt;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.&lt;br /&gt;The theoretical background about solvability of the underlying ODE is illuminated and optimality criteria are formulated.&lt;br /&gt;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.</dcterms:abstract>
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Konstanz, Univ., Masterarbeit/Diplomarbeit, 2014
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