Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth, Pre-Existing Vessel Co-Option, Angiogenesis and Blood Perfusion

• Published in: PloS one Vol. 11; no. 3; p. e0150296
• Main Authors: Cai, Yan, Wu, Jie, Li, Zhiyong, Long, Quan
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 02.03.2016; Public Library of Science (PLoS)
• Subjects: Algorithms; Analysis; Angiogenesis; Biodegradation; Biology and Life Sciences; Blood; Blood flow; Blood vessels; Brain; Brain - blood supply; Brain - pathology; Brain - physiopathology; Brain cancer; Brain Neoplasms - blood supply; Brain Neoplasms - pathology; Brain Neoplasms - physiopathology; Brain tumors; Cancer therapies; Care and treatment; Cell migration; Chemotherapy; Civil engineering; Collapse; Computational fluid dynamics; Computer Simulation; Diagnosis; Fluid flow; Glioblastoma; Glioblastoma - blood supply; Glioblastoma - pathology; Glioblastoma - physiopathology; Glioblastomas; Glioma; Health aspects; Hemodynamics; Humans; Hypoxia; Initial conditions; Laboratories; Mathematical analysis; Mathematical models; Matrix methods; Medicine and Health Sciences; Microenvironments; Models, Biological; Motility; Neovascularization; Neovascularization, Pathologic - pathology; Neovascularization, Pathologic - physiopathology; Oxygen; Perfusion; Permeability; Physical Sciences; Remodeling; Research and Analysis Methods; Tumors; Vascular endothelial growth factor; United States
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0150296

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.