Deformations of acid-mediated invasive tumors in a model with Allee effect.

Paul Carter, Arjen Doelman, Peter van Heijster, Daniel Levy, Philip Maini, Erin Okey, Paige Yeung

Abstract read

In one paragraph

Article in Journal of mathematical biology, 2025. 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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0citing papers in PubMed

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1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

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3 · Its place in the literature

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0 citing papers in PubMed.

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4 · The record

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5 · Who and what money

Authors and funding

7 authors.

Paul CarterDepartment of Mathematics, University of California, Irvine, CA, USA. pacarter@uci.edu.ORCID 0000-0003-1884-9988

Arjen DoelmanMathematical Institute, Leiden University, Leiden, Netherlands.

Peter van HeijsterMathematical and Statistical Methods-Biometris, Wageningen University & Research, Wageningen, Netherlands.

Daniel LevyProgram in Applied and Computational Mathematics, Princeton University, Princeton, USA.

Philip MainiMathematical Institute, University of Oxford, Oxford, UK.

Erin OkeyDivision of Applied Mathematics, Brown University, Providence, RI, USA.

Paige YeungMassachusetts Institute of Technology, Cambridge, USA.

Funding

Australian Research Council DP190102545Directorate for Mathematical and Physical Sciences DMS-2105816European Research Council 01071417

6 · The paper itself

Abstract

We consider a Gatenby-Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.

Indexed as

Models, BiologicalNeoplasm InvasivenessNeoplasmsAnimalsCell MovementComputer SimulationHumansMathematical Concepts34D1535B3535B3635C0792C50

Identifiers

PMID40323351

DOI10.1007/s00285-025-02209-w

PMCPMC12052936

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.