Bifurcation analysis on a hybrid systems model of intermittent hormonal therapy for prostate cancer
type: Item
instance of: scholarly article
title: Bifurcation analysis on a hybrid systems model of intermittent hormonal therapy for prostate cancer
zbMATH Open document ID: 1157.37024
author: Gouhei Tanaka
author: Kunichika Tsumoto
author: Shigeki Tsuji
author: Kazuyuki Aihara
published in: Physica D
publication date: 2008-11-28T00:00:00Z
review text: Hybrid systems are widely used to model dynamical phenomena that are characterized by interplay between continuous dynamics and discrete events. An example of biomedical application is modeling of disease progression of prostate cancer under intermittent hormonal therapy, where continuous tumor dynamics is switched by interruption and reinstitution of medication. In the present paper, we study a hybrid systems model representing intermittent androgen suppression (IAS) therapy for advanced prostate cancer. Intermittent medication with switching between on-treatment and off-treatment periods is intended to possibly prevent a prostatic tumor from developing into a hormone-refractory state and is anticipated as a possible strategy for delaying or hopefully averting a cancer relapse which most patients undergo as a result of long-term hormonal suppression. Clinical efficacy of IAS therapy for prostate cancer is still under investigation but at least worth considering in terms of reduction of side effects and economic costs during off-treatment periods. In the model of IAS therapy, it depends on some clinically controllable parameters whether a relapse of prostate cancer occurs or not. Therefore, we examine nonlinear dynamics and bifurcation structure of the model by exploiting a numerical method to clarify bifurcation sets in the hybrid system. Our results suggest that adjustment of the normal androgen level in combination with appropriate medication scheduling could enhance the possibility of relapse prevention. Moreover, a two-dimensional piecewise-linear system reduced from the original model highlights the origin of nonlinear phenomena specific to the hybrid system.
reviewed by: E. Ahmed
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92C60
zbMATH DE Number: 5374945
zbMATH Keywords: hybrid systems
zbMATH Keywords: piecewise linear systems
zbMATH Keywords: grazing bifurcations
zbMATH Keywords: limit cycle
zbMATH Keywords: chaos
zbMATH Keywords: prostate cancer
zbMATH Keywords: intermittent androgen suppression
MaRDI profile type: Publication
full work available at URL: j.physd.2008.03.044
OpenAlex ID: W2016214698
cites work: A mathematical model of prostate tumor growth and androgen-independent relapse
cites work: A stochastic model for prostate-specific antigen levels
cites work: An alternative approach to modelling relapse in cancer with an application to adenocarcinoma of the prostate
cites work: A mathematical model of intermittent androgen suppression for prostate cancer
cites work: An introduction to hybrid dynamical systems
cites work: Switching in systems and control
cites work: Nonsmooth mechanics. Models, dynamics and control.
cites work: Power System Modeling for Inverse Problems
cites work: SIMPLE HYBRID SYSTEMS
cites work: Normal form maps for grazing bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems
cites work: Chaos from a hysteresis and switched circuit
cites work: Bifurcation of switched nonlinear dynamical systems
cites work: SHOOTING METHODS FOR LOCATING GRAZING PHENOMENA IN HYBRID SYSTEMS
cites work: Bifurcation Analysis of Switched Dynamical Systems With Periodically Moving Borders
DOI: 10.1016/J.PHYSD.2008.03.044
description: scientific article; zbMATH DE number 5374945