A PDE Model of Glioblastoma Progression: The Role of Cell Crowding and Resource Competition in Proliferation and Diffusion

Massimiliano d’Angelo, Federico Papa (), Laura D’Orsi, Simona Panunzi, Marcello Pompa, Giovanni Palombo, Andrea De Gaetano and Alessandro Borri
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Massimiliano d’Angelo: CNR-IASI L’Aquila Research Unit, National Research Council of Italy, 67100 L’Aquila, Italy
Federico Papa: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, 00185 Rome, Italy
Laura D’Orsi: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, 00185 Rome, Italy
Simona Panunzi: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, 00185 Rome, Italy
Marcello Pompa: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, 00185 Rome, Italy
Giovanni Palombo: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, 00185 Rome, Italy
Andrea De Gaetano: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, 00185 Rome, Italy
Alessandro Borri: CNR-IASI L’Aquila Research Unit, National Research Council of Italy, 67100 L’Aquila, Italy

Mathematics, 2025, vol. 13, issue 20, 1-18

Abstract: Glioblastoma is the most aggressive and treatment-resistant form of primary brain tumors, characterized by rapid invasion and a poor prognosis. Its complex behavior continues to challenge both clinical interventions and research efforts. Mathematical modeling provides a valuable approach to unraveling a tumor’s spatiotemporal dynamics and supporting the development of more effective therapies. In this study, we built on the existing literature by refining and adapting mathematical models to better capture glioblastoma infiltration, using a partial differential equation (PDE) framework to simulate how cancer cell density evolves across both time and space. In particular, the role of cell diffusion and growth in tumor progression and their limitations due to cell crowding and competition were investigated. Experimental data of glioblastoma taken from the literature were exploited for the identification of the model parameters. The improved data reproduction when the limitations of cell diffusion and growth were taken into account proves the relevant impact of the considered mechanisms on the spread of the tumor population, which underscores the potential of the proposed framework.

Keywords: tumor modeling; cell growth and diffusion; dynamical systems; numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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