On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems

Margaret P. Chapman, Eric V. Mazumdar, Ellen Langer, Rosalie Sears, Claire J. Tomlin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Motivated by our prior work on a Triple Negative breast cancer cell line, the focus of this paper is controller synthesis for cancer treatment, through the use of drug scheduling and a switched dynamical system model. Here we study a cyclic schedule of d drugs with maximal waiting times between drug inputs, where each drug is applied once per cycle in any order. We suppose that some of the d drugs are highly toxic to normal cells and that these drugs can shrink the live cancer cell population. The remaining drugs are less toxic to normal cells and can only reduce the growth rate of the live cancer cell population. Also, we assume that waiting time bounds related to toxicity, or to the onset of resistance, are available for each drug. A cancer cell population is said to be stable if the number of live cells tends to zero, as time becomes sufficiently large. In the absence of modeling error, we derive conditions for exponential stability. In the presence of modeling error, we prove exponential stability and derive a settling time, under certain mathematical conditions on the error. We conclude the paper with a numerical example that uses models which were identified on Triple Negative breast cancer cell line data.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3503-3509
Number of pages7
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Oncology
Cancer
Drugs
Dynamical systems
Schedule
Dynamical system
Cells
Cell Population
Asymptotic stability
Cell
Modeling Error
Exponential Stability
Breast Cancer
Waiting Time
Toxicity
Scheduling
Line
Controllers
Tend
Synthesis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Chapman, M. P., Mazumdar, E. V., Langer, E., Sears, R., & Tomlin, C. J. (2019). On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 3503-3509). [8619490] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619490

On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems. / Chapman, Margaret P.; Mazumdar, Eric V.; Langer, Ellen; Sears, Rosalie; Tomlin, Claire J.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 3503-3509 8619490 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chapman, MP, Mazumdar, EV, Langer, E, Sears, R & Tomlin, CJ 2019, On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619490, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 3503-3509, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619490
Chapman MP, Mazumdar EV, Langer E, Sears R, Tomlin CJ. On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 3503-3509. 8619490. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619490
Chapman, Margaret P. ; Mazumdar, Eric V. ; Langer, Ellen ; Sears, Rosalie ; Tomlin, Claire J. / On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 3503-3509 (Proceedings of the IEEE Conference on Decision and Control).
@inproceedings{9df66c2a984843749f43dfb4d026c2b9,
title = "On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems",
abstract = "Motivated by our prior work on a Triple Negative breast cancer cell line, the focus of this paper is controller synthesis for cancer treatment, through the use of drug scheduling and a switched dynamical system model. Here we study a cyclic schedule of d drugs with maximal waiting times between drug inputs, where each drug is applied once per cycle in any order. We suppose that some of the d drugs are highly toxic to normal cells and that these drugs can shrink the live cancer cell population. The remaining drugs are less toxic to normal cells and can only reduce the growth rate of the live cancer cell population. Also, we assume that waiting time bounds related to toxicity, or to the onset of resistance, are available for each drug. A cancer cell population is said to be stable if the number of live cells tends to zero, as time becomes sufficiently large. In the absence of modeling error, we derive conditions for exponential stability. In the presence of modeling error, we prove exponential stability and derive a settling time, under certain mathematical conditions on the error. We conclude the paper with a numerical example that uses models which were identified on Triple Negative breast cancer cell line data.",
author = "Chapman, {Margaret P.} and Mazumdar, {Eric V.} and Ellen Langer and Rosalie Sears and Tomlin, {Claire J.}",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8619490",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "3503--3509",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",

}

TY - GEN

T1 - On the Analysis of Cyclic Drug Schedules for Cancer Treatment using Switched Dynamical Systems

AU - Chapman, Margaret P.

AU - Mazumdar, Eric V.

AU - Langer, Ellen

AU - Sears, Rosalie

AU - Tomlin, Claire J.

PY - 2019/1/18

Y1 - 2019/1/18

N2 - Motivated by our prior work on a Triple Negative breast cancer cell line, the focus of this paper is controller synthesis for cancer treatment, through the use of drug scheduling and a switched dynamical system model. Here we study a cyclic schedule of d drugs with maximal waiting times between drug inputs, where each drug is applied once per cycle in any order. We suppose that some of the d drugs are highly toxic to normal cells and that these drugs can shrink the live cancer cell population. The remaining drugs are less toxic to normal cells and can only reduce the growth rate of the live cancer cell population. Also, we assume that waiting time bounds related to toxicity, or to the onset of resistance, are available for each drug. A cancer cell population is said to be stable if the number of live cells tends to zero, as time becomes sufficiently large. In the absence of modeling error, we derive conditions for exponential stability. In the presence of modeling error, we prove exponential stability and derive a settling time, under certain mathematical conditions on the error. We conclude the paper with a numerical example that uses models which were identified on Triple Negative breast cancer cell line data.

AB - Motivated by our prior work on a Triple Negative breast cancer cell line, the focus of this paper is controller synthesis for cancer treatment, through the use of drug scheduling and a switched dynamical system model. Here we study a cyclic schedule of d drugs with maximal waiting times between drug inputs, where each drug is applied once per cycle in any order. We suppose that some of the d drugs are highly toxic to normal cells and that these drugs can shrink the live cancer cell population. The remaining drugs are less toxic to normal cells and can only reduce the growth rate of the live cancer cell population. Also, we assume that waiting time bounds related to toxicity, or to the onset of resistance, are available for each drug. A cancer cell population is said to be stable if the number of live cells tends to zero, as time becomes sufficiently large. In the absence of modeling error, we derive conditions for exponential stability. In the presence of modeling error, we prove exponential stability and derive a settling time, under certain mathematical conditions on the error. We conclude the paper with a numerical example that uses models which were identified on Triple Negative breast cancer cell line data.

UR - http://www.scopus.com/inward/record.url?scp=85062178247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062178247&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619490

DO - 10.1109/CDC.2018.8619490

M3 - Conference contribution

AN - SCOPUS:85062178247

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3503

EP - 3509

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -