Nonlinear behaviors of capillary formation in a deterministic angiogenesis model

Shuyu Sun; Mary F. Wheeler; Mandri Obeyesekere; Charles Patrick

doi:10.1016/j.na.2005.01.066

Nonlinear behaviors of capillary formation in a deterministic angiogenesis model

Shuyu Sun, Mary F. Wheeler, Mandri Obeyesekere, Charles Patrick

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

17 Scopus citations

Abstract

In this paper, we consider a deterministic approach for modeling angiogenesis. The model equations form a nonlinear coupled system of partial and ordinary differential equations. We propose an efficient, accurate and locally conservative numerical method to solve the nonlinear system. Computational results indicate that the model generates the overall dendritic structure and pattern of the capillary network morphologically similar to those observed in vivo. The influence of the capillary network and the growth factor distribution on each other and their interaction are investigated using numerical simulations. © 2005 Elsevier Ltd. All rights reserved.

Original language	English (US)
Title of host publication	Nonlinear Analysis, Theory, Methods and Applications
DOIs	https://doi.org/10.1016/j.na.2005.01.066
State	Published - Nov 30 2005
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-09-21

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.na.2005.01.066

Cite this

@inproceedings{49171b579da74113969eaa2687eebd3f,

title = "Nonlinear behaviors of capillary formation in a deterministic angiogenesis model",

abstract = "In this paper, we consider a deterministic approach for modeling angiogenesis. The model equations form a nonlinear coupled system of partial and ordinary differential equations. We propose an efficient, accurate and locally conservative numerical method to solve the nonlinear system. Computational results indicate that the model generates the overall dendritic structure and pattern of the capillary network morphologically similar to those observed in vivo. The influence of the capillary network and the growth factor distribution on each other and their interaction are investigated using numerical simulations. {\textcopyright} 2005 Elsevier Ltd. All rights reserved.",

author = "Shuyu Sun and Wheeler, {Mary F.} and Mandri Obeyesekere and Charles Patrick",

note = "Generated from Scopus record by KAUST IRTS on 2023-09-21",

year = "2005",

month = nov,

day = "30",

doi = "10.1016/j.na.2005.01.066",

language = "English (US)",

booktitle = "Nonlinear Analysis, Theory, Methods and Applications",

}

TY - GEN

T1 - Nonlinear behaviors of capillary formation in a deterministic angiogenesis model

AU - Sun, Shuyu

AU - Wheeler, Mary F.

AU - Obeyesekere, Mandri

AU - Patrick, Charles

N1 - Generated from Scopus record by KAUST IRTS on 2023-09-21

PY - 2005/11/30

Y1 - 2005/11/30

N2 - In this paper, we consider a deterministic approach for modeling angiogenesis. The model equations form a nonlinear coupled system of partial and ordinary differential equations. We propose an efficient, accurate and locally conservative numerical method to solve the nonlinear system. Computational results indicate that the model generates the overall dendritic structure and pattern of the capillary network morphologically similar to those observed in vivo. The influence of the capillary network and the growth factor distribution on each other and their interaction are investigated using numerical simulations. © 2005 Elsevier Ltd. All rights reserved.

AB - In this paper, we consider a deterministic approach for modeling angiogenesis. The model equations form a nonlinear coupled system of partial and ordinary differential equations. We propose an efficient, accurate and locally conservative numerical method to solve the nonlinear system. Computational results indicate that the model generates the overall dendritic structure and pattern of the capillary network morphologically similar to those observed in vivo. The influence of the capillary network and the growth factor distribution on each other and their interaction are investigated using numerical simulations. © 2005 Elsevier Ltd. All rights reserved.

UR - https://linkinghub.elsevier.com/retrieve/pii/S0362546X05000829

UR - http://www.scopus.com/inward/record.url?scp=28044451781&partnerID=8YFLogxK

U2 - 10.1016/j.na.2005.01.066

DO - 10.1016/j.na.2005.01.066

M3 - Conference contribution

BT - Nonlinear Analysis, Theory, Methods and Applications

ER -

Nonlinear behaviors of capillary formation in a deterministic angiogenesis model

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this