The biology and mathematical modelling of glioma invasion: a review

JCL Alfonso, K Talkenberger… - Journal of the …, 2017 - royalsocietypublishing.org
Adult gliomas are aggressive brain tumours associated with low patient survival rates and
limited life expectancy. The most important hallmark of this type of tumour is its invasive …

[HTML][HTML] In vitro biomimetic models for glioblastoma-a promising tool for drug response studies

T Stanković, T Ranđelović, M Dragoj, SS Burić… - Drug Resistance …, 2021 - Elsevier
The poor response of glioblastoma to current treatment protocols is a consequence of its
intrinsic drug resistance. Resistance to chemotherapy is primarily associated with …

The LDL-HDL profile determines the risk of atherosclerosis: a mathematical model

W Hao, A Friedman - PloS one, 2014 - journals.plos.org
Atherosclerosis, the leading death in the United State, is a disease in which a plaque builds
up inside the arteries. As the plaque continues to grow, the shear force of the blood flow …

Spatiotemporal dynamics of a glioma immune interaction model

S Khajanchi, JJ Nieto - Scientific Reports, 2021 - nature.com
We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells,
macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno …

Mathematical models for cell migration: a non-local perspective

L Chen, K Painter, C Surulescu… - … Transactions of the …, 2020 - royalsocietypublishing.org
We provide a review of recent advancements in non-local continuous models for migration,
mainly from the perspective of its involvement in embryonal development and cancer …

A nonlocal model for contact attraction and repulsion in heterogeneous cell populations

KJ Painter, JM Bloomfield, JA Sherratt… - Bulletin of mathematical …, 2015 - Springer
Instructing others to move is fundamental for many populations, whether animal or cellular.
In many instances, these commands are transmitted by contact, such that an instruction is …

Biological modelling with nonlocal advection diffusion equations

KJ Painter, T Hillen, JR Potts - arXiv preprint arXiv:2307.14396, 2023 - arxiv.org
The employment of nonlocal PDE models to describe biological aggregation and other
phenomena has gained considerable traction in recent years. For cell populations, these …

The role of the tumor microenvironment in glioblastoma: A mathematical model

Y Kim, H Jeon, H Othmer - IEEE Transactions on Biomedical …, 2016 - ieeexplore.ieee.org
Glioblastoma multiforme is one of the deadliest human cancers and is characterized by
tumor cells that hijack immune system cells in a deadly symbiotic relationship. Microglia and …

The impact of adhesion on cellular invasion processes in cancer and development

KJ Painter, NJ Armstrong, JA Sherratt - Journal of theoretical biology, 2010 - Elsevier
In this paper we consider a simple continuous model to describe cell invasion, incorporating
the effects of both cell–cell adhesion and cell–matrix adhesion, along with cell growth and …

Mechanistic modeling of the effects of myoferlin on tumor cell invasion

MC Eisenberg, Y Kim, R Li… - Proceedings of the …, 2011 - National Acad Sciences
Myoferlin (MYOF) is a member of the evolutionarily conserved ferlin family of proteins, noted
for their role in a variety of membrane processes, including endocytosis, repair, and …