Mathematical modeling reveals how the density of initial tumor and its distance to parent vessels alter the growth trend of vascular tumors

Mehran Akbarpour Ghazani; Zahra Nouri; Mohsen Saghafian; Madjid Soltani

doi:10.1111/micc.12584

Mathematical modeling reveals how the density of initial tumor and its distance to parent vessels alter the growth trend of vascular tumors

Microcirculation. 2020 Jan;27(1):e12584. doi: 10.1111/micc.12584. Epub 2019 Sep 6.

Authors

Mehran Akbarpour Ghazani^{1

2}, Zahra Nouri¹, Mohsen Saghafian¹, Madjid Soltani^{3

4

5

6

7}

Affiliations

¹ Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran.
² Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran.
³ Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran.
⁴ Advanced Bioengineering Initiative Center, Computational Medicine Center, K. N. Toosi University of Technology, Tehran, Iran.
⁵ Cancer Biology Research Center, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, Iran.
⁶ Centre for Biotechnology and Bioengineering (CBB), University of Waterloo, Waterloo, ON, Canada.
⁷ Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada.

PMID: 31390104
DOI: 10.1111/micc.12584

Abstract

Objectives: The aim of this study was to investigate the response of a tumor and parent vessels to stimulating factors in the tumor microenvironment in different configurations. How a tumor grows and induces angiogenesis in different distances of a parent vessel is investigated. Moreover, interstitial fluid pressure and its effects on tumor cell phenotype are considered in the model.

Methods: A multiscale continuum-discrete model of a vascular tumor is utilized to simulate the growth of a cluster of tumor cells positioned in different distances of parent vessels. An agent-based probabilistic angiogenesis model is coupled to a discrete tumor model to simulate branching, anastomosis, blood flow, wall shear stress, and interstitial tumor pressure in which tumor cells are divided to necrotic, hypoxic, and proliferative.

Results: Starting the simulations from 9 initial tumor cells, the model proved that tumors grow to a certain size and also reach to a certain distance before being able to induce sprouting. For tumors placed 2 and 2.5 mm away from a parent vessel, initiation of angiogenesis is delayed significantly in comparison with closer distances. For the initial cluster positioned in a distance of 2.5 mm away, first sprout is seen after 47 days. Moreover, dendritic shape of the tumor is seen prior to angiogenesis which is a sign of cells being starved and wandered in the domain to reach the oxygen source. The trend of tumor growth obeys power law function which aligns with the experimental results.

Discussion: The mathematical model revealed the importance of geometry and position of an initial tumor cluster in determining the behavior and final architecture of a vascular tumor. As a tumor cell appears in farther distances from a parent vessel, duration of its growth and inducing angiogenesis becomes longer and the chance of suppressing the tumor in the initial days of growth is higher. Also, the importance of angiogenesis in making tumors devastating is again corroborated by mathematical models.

Keywords: angiogenesis; mathematical oncology; tumor microenvironment; vascular tumor growth.

MeSH terms

Animals
Humans
Models, Cardiovascular*
Neovascularization, Pathologic / physiopathology*
Vascular Neoplasms* / blood supply
Vascular Neoplasms* / physiopathology