Computational analysis of tumor angiogenesis patterns using a two-dimensional model

Eun Bo Shim, Young-Guen Kwon, Hyung Jong Ko

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Tumor angiogenesis was simulated using a two-dimensional computational model. The equation that governed angiogenesis comprised a tumor angiogenesis factor (TAF) conservation equation in time and space, which was solved numerically using the Galerkin finite element method. The time derivative in the equation was approximated by a forward Euler scheme. A stochastic process model was used to simulate vessel formation and vessel elongation towards a paracrine site, i.e., tumor-secreted basic fibroblast growth factor (bFGF). In this study, we assumed a two-dimensional model that represented a thin (1.0 mm) slice of the tumor. The growth of the tumor over time was modeled according to the dynamic value of bFGF secreted within the tumor. The data used for the model were based on a previously reported model of a brain tumor in which, four distinct stages (multicellular spherical, first detectable lesion, diagnosis, and death of the virtual patient) were modeled. In our study, computation was not continued beyond the 'diagnosis' time point to avoid the computational complexity of analyzing numerous vascular branches. The numerical solutions revealed that no bFGF remained within the region in which vessels developed, owing to the uptake of bFGF by endothelial cells. Consequently, a sharp declining gradient of bFGF existed near the surface of the tumor. The vascular architecture developed numerous branches close to the tumor surface (the brush-border effect). Asymmetrical tumor growth was associated with a greater degree of branching at the tumor surface.

Original languageEnglish
Pages (from-to)275-283
Number of pages9
JournalYonsei medical journal
Volume46
Issue number2
DOIs
Publication statusPublished - 2005 Apr 30

Fingerprint

Fibroblast Growth Factor 2
Neoplasms
Blood Vessels
Stochastic Processes
Angiogenesis Inducing Agents
Growth
Microvilli
Brain Neoplasms
Endothelial Cells

All Science Journal Classification (ASJC) codes

  • Medicine(all)

Cite this

@article{441b63c626784fcc8cc9166e37f510c4,
title = "Computational analysis of tumor angiogenesis patterns using a two-dimensional model",
abstract = "Tumor angiogenesis was simulated using a two-dimensional computational model. The equation that governed angiogenesis comprised a tumor angiogenesis factor (TAF) conservation equation in time and space, which was solved numerically using the Galerkin finite element method. The time derivative in the equation was approximated by a forward Euler scheme. A stochastic process model was used to simulate vessel formation and vessel elongation towards a paracrine site, i.e., tumor-secreted basic fibroblast growth factor (bFGF). In this study, we assumed a two-dimensional model that represented a thin (1.0 mm) slice of the tumor. The growth of the tumor over time was modeled according to the dynamic value of bFGF secreted within the tumor. The data used for the model were based on a previously reported model of a brain tumor in which, four distinct stages (multicellular spherical, first detectable lesion, diagnosis, and death of the virtual patient) were modeled. In our study, computation was not continued beyond the 'diagnosis' time point to avoid the computational complexity of analyzing numerous vascular branches. The numerical solutions revealed that no bFGF remained within the region in which vessels developed, owing to the uptake of bFGF by endothelial cells. Consequently, a sharp declining gradient of bFGF existed near the surface of the tumor. The vascular architecture developed numerous branches close to the tumor surface (the brush-border effect). Asymmetrical tumor growth was associated with a greater degree of branching at the tumor surface.",
author = "Shim, {Eun Bo} and Young-Guen Kwon and Ko, {Hyung Jong}",
year = "2005",
month = "4",
day = "30",
doi = "10.3349/ymj.2005.46.2.275",
language = "English",
volume = "46",
pages = "275--283",
journal = "Yonsei Medical Journal",
issn = "0513-5796",
publisher = "Yonsei University College of Medicine",
number = "2",

}

Computational analysis of tumor angiogenesis patterns using a two-dimensional model. / Shim, Eun Bo; Kwon, Young-Guen; Ko, Hyung Jong.

In: Yonsei medical journal, Vol. 46, No. 2, 30.04.2005, p. 275-283.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Computational analysis of tumor angiogenesis patterns using a two-dimensional model

AU - Shim, Eun Bo

AU - Kwon, Young-Guen

AU - Ko, Hyung Jong

PY - 2005/4/30

Y1 - 2005/4/30

N2 - Tumor angiogenesis was simulated using a two-dimensional computational model. The equation that governed angiogenesis comprised a tumor angiogenesis factor (TAF) conservation equation in time and space, which was solved numerically using the Galerkin finite element method. The time derivative in the equation was approximated by a forward Euler scheme. A stochastic process model was used to simulate vessel formation and vessel elongation towards a paracrine site, i.e., tumor-secreted basic fibroblast growth factor (bFGF). In this study, we assumed a two-dimensional model that represented a thin (1.0 mm) slice of the tumor. The growth of the tumor over time was modeled according to the dynamic value of bFGF secreted within the tumor. The data used for the model were based on a previously reported model of a brain tumor in which, four distinct stages (multicellular spherical, first detectable lesion, diagnosis, and death of the virtual patient) were modeled. In our study, computation was not continued beyond the 'diagnosis' time point to avoid the computational complexity of analyzing numerous vascular branches. The numerical solutions revealed that no bFGF remained within the region in which vessels developed, owing to the uptake of bFGF by endothelial cells. Consequently, a sharp declining gradient of bFGF existed near the surface of the tumor. The vascular architecture developed numerous branches close to the tumor surface (the brush-border effect). Asymmetrical tumor growth was associated with a greater degree of branching at the tumor surface.

AB - Tumor angiogenesis was simulated using a two-dimensional computational model. The equation that governed angiogenesis comprised a tumor angiogenesis factor (TAF) conservation equation in time and space, which was solved numerically using the Galerkin finite element method. The time derivative in the equation was approximated by a forward Euler scheme. A stochastic process model was used to simulate vessel formation and vessel elongation towards a paracrine site, i.e., tumor-secreted basic fibroblast growth factor (bFGF). In this study, we assumed a two-dimensional model that represented a thin (1.0 mm) slice of the tumor. The growth of the tumor over time was modeled according to the dynamic value of bFGF secreted within the tumor. The data used for the model were based on a previously reported model of a brain tumor in which, four distinct stages (multicellular spherical, first detectable lesion, diagnosis, and death of the virtual patient) were modeled. In our study, computation was not continued beyond the 'diagnosis' time point to avoid the computational complexity of analyzing numerous vascular branches. The numerical solutions revealed that no bFGF remained within the region in which vessels developed, owing to the uptake of bFGF by endothelial cells. Consequently, a sharp declining gradient of bFGF existed near the surface of the tumor. The vascular architecture developed numerous branches close to the tumor surface (the brush-border effect). Asymmetrical tumor growth was associated with a greater degree of branching at the tumor surface.

UR - http://www.scopus.com/inward/record.url?scp=18644361828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18644361828&partnerID=8YFLogxK

U2 - 10.3349/ymj.2005.46.2.275

DO - 10.3349/ymj.2005.46.2.275

M3 - Article

VL - 46

SP - 275

EP - 283

JO - Yonsei Medical Journal

JF - Yonsei Medical Journal

SN - 0513-5796

IS - 2

ER -