scholarly journals Drug resistance in cancer chemotherapy as an optimal control problem

2006 ◽  
Vol 6 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Urszula Ledzewicz ◽  
◽  
Heinz Schättler ◽  
Keyword(s):  
Optimal Control ◽  
Drug Resistance ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cancer Chemotherapy

scholarly journals Optimal control for a mathematical model for chemotherapy with pharmacometrics

2020 ◽  
Vol 15 ◽  
pp. 69
Author(s):  
Maciej Leszczyński ◽  
Urszula Ledzewicz ◽  
Heinz Schättler
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Drug Effects ◽  
Optimal Controls ◽  
Angiogenic Therapy ◽  
Single Drug ◽  
Qualitative Changes

An optimal control problem for an abstract mathematical model for cancer chemotherapy is considered. The dynamics is for a single drug and includes pharmacodynamic (PD) and pharmacokinetic (PK) models. The aim is to point out qualitative changes in the structures of optimal controls that occur as these pharmacometric models are varied. This concerns (i) changes in the PD-model for the effectiveness of the drug (e.g., between a linear log-kill term and a non-linear Michaelis-Menten type Emax-model) and (ii) the question how the incorporation of a mathematical model for the pharmacokinetics of the drug effects optimal controls. The general results will be illustrated and discussed in the framework of a mathematical model for anti-angiogenic therapy.

scholarly journals Validation of a Mathematical Model of Cancer Incorporating Spontaneous and Induced Evolution to Drug Resistance

2019 ◽  
Author(s):  
Jana L. Gevertz ◽  
James M. Greene ◽  
Eduardo D. Sontag
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Optimal Control ◽  
Drug Resistance ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Additional Data ◽  
Fitting In

AbstractThis paper continues the study of a model which was introduced in earlier work by the authors to study spontaneous and induced evolution to drug resistance under chemotherapy. The model is fit to existing experimental data, and is then validated on additional data that had not been used when fitting. In addition, an optimal control problem is studied numerically.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

Sign in / Sign up

Export Citation Format

Share Document