Multicellular model of angiogenesis

Takashi Nakazawa; Sohei Tasaki; Kiyohiko Nakai; Takashi Suzuki; Takashi Nakazawa; Sohei Tasaki; Kiyohiko Nakai; Takashi Suzuki

doi:10.3934/bioeng.2022004

AIMS Bioengineering

2022, Volume 9, Issue 1: 44-60. doi: 10.3934/bioeng.2022004

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Multicellular model of angiogenesis

1.
Center for Mathematical Modelling and Data Science, Osaka University, 1-3, Machikaneyama-cho, Toyonaka-shi, Osaka 560-8531, Japan
2.
Department of Mathematics, Faculty of Science, Hokkaido University, Kita-10, Nishi-8, Kita-ku, Sapporo 060-0810, Japan
3.
Chugai Pharmaceutical Co. Ltd., 2-1-1 Nihonbashi-Muromachi, Chuo-ku, Tokyo 103-8324, Japan

Received: 12 December 2022 Revised: 23 January 2022 Accepted: 25 January 2022 Published: 28 January 2022

This paper presents a mathematical model governing the dynamics of a morphogenetic vascular endothelial cell (EC) during angiogenesis, and vascular growth formed by EC. Especially, we adopt a multiparticle system for modeling these cells. This model does not distinguish a tip cell from a stalk cell. A formed vessel is modeled using phase-field equation to prevent capillary expansion with time stepping in particular. Numerical simulation reveals that all cells are moving in the direction of high concentration of vascular endothelial growth factor (VEGF), and that they are mutually repellent in cases in which they are closer than some threshold.
- angiogenesis,
- multi-agent model,
- reaction–diffusion equation,
- finite element method
Citation: Takashi Nakazawa, Sohei Tasaki, Kiyohiko Nakai, Takashi Suzuki. Multicellular model of angiogenesis[J]. AIMS Bioengineering, 2022, 9(1): 44-60. doi: 10.3934/bioeng.2022004

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Abstract

This paper presents a mathematical model governing the dynamics of a morphogenetic vascular endothelial cell (EC) during angiogenesis, and vascular growth formed by EC. Especially, we adopt a multiparticle system for modeling these cells. This model does not distinguish a tip cell from a stalk cell. A formed vessel is modeled using phase-field equation to prevent capillary expansion with time stepping in particular. Numerical simulation reveals that all cells are moving in the direction of high concentration of vascular endothelial growth factor (VEGF), and that they are mutually repellent in cases in which they are closer than some threshold.

Acknowledgments

This work was supported by JSPS KAKENHI, Grant Number 19K03645, and MEXT KAKENHI, Grant Number 17H06327.

Conflict of interest

The authors declare no conflicts of interest in this paper.

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