Controlling a model for bone marrow dynamics in cancer chemotherapy

被引：9

作者：

Ledzewicz, U ^{[1
]}

Schättler, H

机构：

[1] So Illinois Univ, Dept Math & Stat, Edwardsville, IL 62026 USA

[2] Washington Univ, Dept Elect & Syst Engn, St Louis, MO 63130 USA

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2004年 / 1卷 / 01期

关键词：

optimal control; cancer chemotherapy; singular controls; bang-bang controls;

D O I：

10.3934/mbe.2004.1.95

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper analyzes a mathematical model for the growth of bone marrow cells under cell-cycle-specific cancer chemotherapy originally proposed by Fister and Panetta [8]. The model is formulated as an optimal control problem with control representing the drug dosage (respectively its effect) and objective of Bolza type depending on the control linearly, a so-called L-1-objective. We apply the Maximum Principle, followed by high-order necessary conditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics. Singular controls are eliminated as candidates for optimality, and easily verifiable conditions for strong local optimality of bang-bang controls are formulated in the form of transversality conditions at switching surfaces. Numerical simulations are given.

引用

页码：95 / 110

页数：16

共 28 条

[1] Strong optimality or a bang-bang trajectory [J].

Agrachev, AA ;

Stefani, G ;

Zezza, P .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 41 (04) :991-1014

[2] REDUCTION OF CYTO-TOXICITY TO NORMAL-TISSUES BY NEW REGIMENS OF CELL-CYCLE PHASE-SPECIFIC DRUGS [J].

AGUR, Z ;

ARNON, R ;

SCHECHTER, B .

MATHEMATICAL BIOSCIENCES, 1988, 92 (01) :1-15

[3]

Agur Z, 1986, ANN NY ACAD SCI, V504, P274, DOI [DOI 10.1111/J.1749-6632.1987.TB48738.X, 10.1111/j.1749-6632.1987.tb48738.x]

[4]

[Anonymous], 1979, LECT NOTES BIOMATHEM

[5] A THEORETICAL-ANALYSIS OF INTERVAL DRUG DOSING FOR CELL-CYCLE-PHASE-SPECIFIC DRUGS [J].

COJOCARU, L ;

AGUR, Z .

MATHEMATICAL BIOSCIENCES, 1992, 109 (01) :85-97

[6] MATHEMATICAL-MODEL OF CANCER-CHEMOTHERAPY - PERIODIC SCHEDULES OF PHASE-SPECIFIC CYTOTOXIC-AGENT ADMINISTRATION INCREASING THE SELECTIVITY OF THERAPY [J].

DIBROV, BF ;

ZHABOTINSKY, AM ;

NEYFAKH, YA ;

ORLOVA, MP ;

CHURIKOVA, LI .

MATHEMATICAL BIOSCIENCES, 1985, 73 (01) :1-31

[7]

DUDA Z, APPL MATH COMP SCI, V4, P257

[8] Optimal control applied to cell-cycle-specific cancer chemotherapy [J].

Fister, KR ;

Panetta, JC .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 60 (03) :1059-1072

[9]

HAINSWORTH JD, 1994, CANCER, V74, P1377, DOI 10.1002/1097-0142(19940815)74:4<1377::AID-CNCR2820740431>3.0.CO

[10]

2-U

← 1 2 3 →