Qualitative analysis of tumor growth model under antiangiogenic therapy - choosing the effective operating point and design parameters for controller design

Johanna Sápi, Dániel A. Drexler, István Harmati, Z. Sápi, L. Kovács

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Every therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady-state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady-state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady-state tumor volume and the expression for determining the steady-state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed-loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point.

Original languageEnglish
JournalOptimal Control Applications and Methods
DOIs
Publication statusAccepted/In press - 2015

Fingerprint

Tumor Growth
Qualitative Analysis
Growth Model
Parameter Design
Controller Design
Therapy
Tumors
Tumor
Controllers
State Feedback
State feedback
Controller
State Observer
Signal Control
Costs
Positivity
Inhibitor
Closed-loop System
Observer
Cancer

Keywords

  • Linear state feedback
  • LQ optimal control method
  • Pole placement method
  • State observer

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Applied Mathematics
  • Control and Optimization
  • Software

Cite this

@article{2a378033925849c7a5dcdf4b4d354a9b,
title = "Qualitative analysis of tumor growth model under antiangiogenic therapy - choosing the effective operating point and design parameters for controller design",
abstract = "Every therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady-state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady-state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady-state tumor volume and the expression for determining the steady-state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed-loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point.",
keywords = "Linear state feedback, LQ optimal control method, Pole placement method, State observer",
author = "Johanna S{\'a}pi and Drexler, {D{\'a}niel A.} and Istv{\'a}n Harmati and Z. S{\'a}pi and L. Kov{\'a}cs",
year = "2015",
doi = "10.1002/oca.2196",
language = "English",
journal = "Optimal Control Applications and Methods",
issn = "0143-2087",
publisher = "John Wiley and Sons Ltd",

}

TY - JOUR

T1 - Qualitative analysis of tumor growth model under antiangiogenic therapy - choosing the effective operating point and design parameters for controller design

AU - Sápi, Johanna

AU - Drexler, Dániel A.

AU - Harmati, István

AU - Sápi, Z.

AU - Kovács, L.

PY - 2015

Y1 - 2015

N2 - Every therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady-state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady-state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady-state tumor volume and the expression for determining the steady-state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed-loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point.

AB - Every therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady-state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady-state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady-state tumor volume and the expression for determining the steady-state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed-loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point.

KW - Linear state feedback

KW - LQ optimal control method

KW - Pole placement method

KW - State observer

UR - http://www.scopus.com/inward/record.url?scp=84941242625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941242625&partnerID=8YFLogxK

U2 - 10.1002/oca.2196

DO - 10.1002/oca.2196

M3 - Article

AN - SCOPUS:84941242625

JO - Optimal Control Applications and Methods

JF - Optimal Control Applications and Methods

SN - 0143-2087

ER -