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Highly malignant brain tumors such as Glioblastoma Multiforme (GBM) form complex growth patterns in vitro in which invasive cells organize in tenuous branches. Here, we formulate a chemotaxis model for this sort of growth. A key element…

Biological Physics · Physics 2009-11-07 Leonard M. Sander , Thomas S. Deisboeck

In this work, we study the in-vitro dynamics of the most malignant form of the primary brain tumor: Glioblastoma Multiforme. Typically, the growing tumor consists of the inner dense proliferating zone and the outer less dense invasive…

Cell Behavior · Quantitative Biology 2009-11-11 Evgeniy Khain , Leonard M. Sander

In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…

Cell Behavior · Quantitative Biology 2026-02-10 Martina Conte , Sandesh Hiremath , Christina Surulescu

We propose here a multiscale model for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization. The model accounts for the interplay between the different components of the neoplasm and…

Cell Behavior · Quantitative Biology 2026-03-10 Martina Conte , Yvonne Dzierma , Sven Knobe , Christina Surulescu

Glioblastoma multiforme (GBM) is an aggressive form of human brain cancer that is under active study in the field of cancer biology. Its rapid progression and the relative time cost of obtaining molecular data make other readily-available…

Applications · Statistics 2019-11-14 Lorin Crawford , Anthea Monod , Andrew X. Chen , Sayan Mukherjee , Raúl Rabadán

Glioblastoma multiforme (GBM), the most aggressive primary brain tumour, exhibits low survival rates due to its rapid growth, infiltrates surrounding brain tissue, and is highly resistant to treatment. One major challenge is oedema…

We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…

Analysis of PDEs · Mathematics 2017-10-12 Martin Burger , Patricia Friele , Jan-Frederik Pietschmann

Glioblastoma is the most malignant type of central nervous system tumor with GBM subtypes cleaved based on molecular level gene alterations. These alterations are also happened to affect the histology. Thus, it can cause visible changes in…

Quantitative Methods · Quantitative Biology 2020-10-28 Navodini Wijethilake , Mobarakol Islam , Dulani Meedeniya , Charith Chitraranjan , Indika Perera , Hongliang Ren

Glioblastoma Multiforme (GBM) is a highly aggressive brain tumour with limited therapeutic options and poor prognosis. This study presents a mathematical framework to investigate the efficacy of immunotherapy strategies based on cytotoxic…

Populations and Evolution · Quantitative Biology 2025-12-23 Francesca Ballatore , Lorenzo Scolaris , Chiara Giverso

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in…

Machine Learning · Computer Science 2024-08-19 Ray Zirui Zhang , Ivan Ezhov , Michal Balcerak , Andy Zhu , Benedikt Wiestler , Bjoern Menze , John S. Lowengrub

Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding…

Glioblastoma is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mathematical model of GBL…

Image and Video Processing · Electrical Eng. & Systems 2025-06-23 D. Cerrone , D. Riccobelli , S. Gazzoni , P. Vitullo , F. Ballarin , J. Falco , F. Acerbi , A. Manzoni , P. Zunino , P. Ciarletta

Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection-diffusion-reaction…

Cell Behavior · Quantitative Biology 2020-01-16 Christian Engwer , Michael Wenske

Glioblastoma exhibits diverse, infiltrative, and patient-specific growth patterns that are only partially visible on routine MRI, making it difficult to reliably assess true tumor extent and personalize treatment planning and follow-up. We…

Computer Vision and Pattern Recognition · Computer Science 2026-03-06 Valentin Biller , Niklas Bubeck , Lucas Zimmer , Ayhan Can Erdur , Sandeep Nagar , Anke Meyer-Baese , Daniel Rückert , Benedikt Wiestler , Jonas Weidner

Despite ongoing efforts in cancer research, a fully effective treatment for glioblastoma multiforme (GBM) is still unknown. Since adoptive cell transfer immunotherapy is one of the potential cure candidates, efforts have been made to assess…

Tissues and Organs · Quantitative Biology 2025-02-26 Wiktor Jochymczyk , Urszula Foryś

Butterfly tumors are a distinct class of gliomas that span the corpus callosum, producing a characteristic butterfly-shaped appearance on MRI. The distinctive growth pattern of these tumors highlights how white matter fibers and structural…

Alterations in the human gut bacteriome can be associated with human health issues, such as type-2 diabetes and cardiovascular disease. Both external and internal factors can drive changes in the composition and in the interactions of the…

Molecular Networks · Quantitative Biology 2021-07-19 Samitha Somathilaka , Daniel P. Martins , Wiley Barton , Orla O'Sullivan , Paul D. Cotter , Sasitharan Balasubramaniam

Glioblastoma (GBM) exhibits two principal growth phenotypes: infiltrative, characterized by diffuse invasion with minimal mass effect, and proliferative, characterized by pronounced tissue compression. Their quantitative delineation and…

Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumour, it tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumours. Usually, GBMs are detected by magnetic…

Image and Video Processing · Electrical Eng. & Systems 2020-04-21 Matteo Rucco , Lorenzo Falsetti , Giovanna Viticchi
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