KOPS - Das Institutionelle Repositorium der Universität Konstanz
# Optimal administration strategies for EPO based on the model for erythropoiesis involving structured population equations

- Startseite
- →
- Mathematik und Statistik
- →
- Mathematik und Statistik
- →
- Dokumentanzeige

Publikationstyp: | Masterarbeit/Diplomarbeit |

URI (zitierfähiger Link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-296098 |

Autor/innen: | Lippmann, Laura |

Erscheinungsjahr: | 2014 |

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. |

Hochschulschriftenvermerk: | Konstanz, Univ., Masterarbeit/Diplomarbeit, 2014 |

Fachgebiet (DDC): | 510 Mathematik |

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

Kommentar zur Publikation: | Diplomarbeit |

Link zur Lizenz: | Nutzungsbedingungen |

Prüfsumme:
MD5:7f85083e5a13500b7baa87657bd8ea00

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

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

Lippmann_0-296098.pdf | 245 |