Optimal control for selected cancer chemotherapy ODE models: A view on the potential of optimal schedules and choice of objective function

In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy,...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical biosciences 2011, Vol.229 (1), p.123-134
Main Authors: Engelhart, Michael, Lebiedz, Dirk, Sager, Sebastian
Format: Article
Language:English
Subjects:
Algorithms
Angiogenesis Inhibitors - therapeutic use
Animals
Antineoplastic Agents - administration & dosage
Antineoplastic Agents - therapeutic use
Cancer
Cancer chemotherapy
Computer Simulation
Drug Administration Schedule
Humans
Immunotherapy
Mathematical modeling
Models, Biological
Multiple shooting
Neoplasms - drug therapy
Neoplasms - therapy
Optimal control
Treatment Outcome
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy, anti-angiogenic therapy or combinations of these. Optimal control problem formulations based on these models are proposed, discussed and compared. For different parameter sets, scenarios, and objective functions optimal control problems are solved numerically with Bock’s direct multiple shooting method. In particular, we show that an optimally controlled therapy can be the reason for the difference between a growing and a totally vanishing tumor in comparison to standard treatment schemes and untreated or wrongly treated tumors. Furthermore, we compare different objective functions. Eventually, we propose an optimization-driven indicator for the potential gain of optimal controls. Based on this indicator, we show that there is a high potential for optimization of chemotherapy schedules, although the currently available models are not yet appropriate for transferring the optimal therapies into medical practice due to patient-, cancer-, and therapy-specific components.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2010.11.007