Age-structured mechanical models for tumor growth.

Doron Levy, Hyunah Lim, Antoine Mellet, Maeve Wildes

Abstract read

In one paragraph

Article in Journal of mathematical biology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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1 · What the graph read from it

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4 · The record

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5 · Who and what money

Authors and funding

4 authors.

Doron LevyDepartment of Mathematics, University of Maryland College Park, College Park, MD, 20742, USA.ORCID https://orcid.org/0000-0003-2972-4857

Hyunah LimDepartment of Mathematics, University of Maryland College Park, College Park, MD, 20742, USA.

Antoine MelletDepartment of Mathematics, University of Maryland College Park, College Park, MD, 20742, USA. mellet@umd.edu.ORCID http://orcid.org/0000-0002-9962-9671

Maeve WildesDepartment of Mathematics, University of Maryland College Park, College Park, MD, 20742, USA.

Funding

Directorate for Mathematical and Physical Sciences DMS-2307342

6 · The paper itself

Abstract

In this paper, we introduce and analyze a mechanical model for tumor growth that takes into account the life cycle of a tumor cell. The underlying process for tumor growth is the same as in classical mechanical models: the spatial expansion of the tumor is driven by the proliferation of the cells (mitosis) which is only limited by the pressure inside the tissue. The natural incompressibility of the cells, which leads to a movement of the cells away from regions of high pressure, is taken into account via a nonlinear Darcy's law. Compared to similar models studied recently, we include an additional variable, which represents the age of the cells. The various phases of the life of a cell (growth, mitosis and death) are then dependent on this age variable. We prove the existence of weak solutions and investigate their behavior numerically, focusing on the age distribution of the cells inside the tumor, the convergence to traveling wave solutions and the existence of a threshold for the death rate for expansion/regression of the tumor.

Indexed as

Models, BiologicalNeoplasmsAnimalsBiomechanical PhenomenaCell ProliferationComputer SimulationHumansMathematical ConceptsMitosisNonlinear DynamicsAge-structured modelCross-diffusionExistence of solutionsNonlinear Darcy’s lawTumor growth

Identifiers

PMID41942603

DOI10.1007/s00285-026-02389-z

PMCPMC13053348

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