ArticleBulletin of mathematical biology2012
Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications.
Article in Bulletin of mathematical biology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 41 papers.
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41 citing papers in PubMed, 140 citations in OpenAlex.
- Mimicking tumor hypoxia in a glioblastoma-on-a-chip.Materials today. Bio · 2026Article
- The Size of Glioblastoma Spheroids Influences Patterns of Invasion and Temozolomide Efficacy.Tissue engineering. Part C, Methods · 2026Article
- Time-dependent memory of hypoxia exposure influences tumor invasion dynamics.bioRxiv : the preprint server for biology · 2026Article
- A Phenotype-Structured PDE Framework for Investigating the Role of Hypoxic Memory on Tumor Invasion under Cyclic Hypoxia.Bulletin of mathematical biology · 2026Article
- A phenotype-structured PDE framework for investigating the role of hypoxic memory on tumor invasion under cyclic hypoxia.bioRxiv : the preprint server for biology · 2025Article
- Go-or-grow models in biology: a monster on a leash.Journal of mathematical biology · 2025Review
- Size-dependent invasion and therapeutic phenotype of 42MGBA glioblastoma spheroids.bioRxiv : the preprint server for biology · 2025Article
- Spatiotemporal dynamics of tumor-CAR T-cell interaction following local administration in solid cancers.PLoS computational biology · 2025Article
- Vascular network-inspired diffusible scaffolds for engineering functional midbrain organoids.Cell stem cell · 2025Article
- Mathematical modeling of multicellular tumor spheroids quantifies inter-patient and intra-tumor heterogeneity.NPJ systems biology and applications · 2025Article
- Insights from a multiscale framework on metabolic rate variation driving glioblastoma multiforme growth and invasion.Communications engineering · 2024Article
- Evolution of phenotypic plasticity leads to tumor heterogeneity with implications for therapy.PLoS computational biology · 2024Article
- A Mathematical Modelling Study of Chemotactic Dynamics in Cell Cultures: The Impact of Spatio-temporal Heterogeneity.Bulletin of mathematical biology · 2023Article
- Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model.Communications in nonlinear science & numerical simulation · 2023Article
- The low affinity A2B adenosine receptor enhances migratory and invasive capacityFrontiers in oncology · 2022Article
- Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment.Journal of mathematical biology · 2021Article
- A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors.PLoS computational biology · 2021Article
- Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution.Scientific reports · 2020Article
- Article
- Pretreatment inflammatory indices predict Bevacizumab response in recurrent Glioma.Cancer drug resistance (Alhambra, Calif.) · 2020Article
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4 authors at 2 institutions in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hyperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.
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