A microenvironment based model of antimitotic therapy of gompertzian tumor growth

Frank Kozusko, Michele Bourdeau, Zeljko Bajzer, David M Dingli

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies-after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter λ, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.

Original languageEnglish (US)
Pages (from-to)1691-1708
Number of pages18
JournalBulletin of Mathematical Biology
Volume69
Issue number5
DOIs
StatePublished - Jul 2007

Fingerprint

Antimitotic Agents
Tumor Growth
tumor
Therapy
Tumors
Tumor
therapeutics
neoplasms
Growth
Dose
Neoplasms
Rate Constant
Cell
Therapeutics
Cell Population
Model
Proliferation
Rate constants
Transfer Function
dosage

Keywords

  • Cell kinetics
  • Chemotherapy
  • Gompertz
  • Proliferation
  • Tumor

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

A microenvironment based model of antimitotic therapy of gompertzian tumor growth. / Kozusko, Frank; Bourdeau, Michele; Bajzer, Zeljko; Dingli, David M.

In: Bulletin of Mathematical Biology, Vol. 69, No. 5, 07.2007, p. 1691-1708.

Research output: Contribution to journalArticle

Kozusko, Frank ; Bourdeau, Michele ; Bajzer, Zeljko ; Dingli, David M. / A microenvironment based model of antimitotic therapy of gompertzian tumor growth. In: Bulletin of Mathematical Biology. 2007 ; Vol. 69, No. 5. pp. 1691-1708.
@article{29ca3eab752545558a038f6452f69461,
title = "A microenvironment based model of antimitotic therapy of gompertzian tumor growth",
abstract = "A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies-after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter λ, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.",
keywords = "Cell kinetics, Chemotherapy, Gompertz, Proliferation, Tumor",
author = "Frank Kozusko and Michele Bourdeau and Zeljko Bajzer and Dingli, {David M}",
year = "2007",
month = "7",
doi = "10.1007/s11538-006-9186-5",
language = "English (US)",
volume = "69",
pages = "1691--1708",
journal = "Bulletin of Mathematical Biology",
issn = "0092-8240",
publisher = "Springer New York",
number = "5",

}

TY - JOUR

T1 - A microenvironment based model of antimitotic therapy of gompertzian tumor growth

AU - Kozusko, Frank

AU - Bourdeau, Michele

AU - Bajzer, Zeljko

AU - Dingli, David M

PY - 2007/7

Y1 - 2007/7

N2 - A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies-after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter λ, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.

AB - A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies-after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter λ, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.

KW - Cell kinetics

KW - Chemotherapy

KW - Gompertz

KW - Proliferation

KW - Tumor

UR - http://www.scopus.com/inward/record.url?scp=34250785124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250785124&partnerID=8YFLogxK

U2 - 10.1007/s11538-006-9186-5

DO - 10.1007/s11538-006-9186-5

M3 - Article

C2 - 17577604

AN - SCOPUS:34250785124

VL - 69

SP - 1691

EP - 1708

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 5

ER -