ArticleBulletin of mathematical biology2014
The impact of cell density and mutations in a model of multidrug resistance in solid tumors.
Article in Bulletin of mathematical biology, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- Reducing phenotype-structured partial differential equations models of cancer evolution to systems of ordinary differential equations: a generalised moment dynamics approach.Journal of mathematical biology · 2025Article
- Estimating treatment sensitivity in synthetic and in vitro tumors using a random differential equation model.NPJ systems biology and applications · 2025Article
- Computational modelling of CAR T-cell therapy: from cellular kinetics to patient-level predictions.EBioMedicine · 2025Review
- Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer.NPJ systems biology and applications · 2022Article
- Mathematical modeling of therapeutic neural stem cell migration in mouse brain with and without brain tumors.Mathematical biosciences and engineering : MBE · 2022Article
- Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation.Journal of mathematical biology · 2022Article
- A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors.CPT: pharmacometrics & systems pharmacology · 2019Review
- Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment.JCO clinical cancer informatics · 2019Article
- Interdependence theory of tissue failure: bulk and boundary effects.Royal Society open science · 2018Article
- Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy.PloS one · 2018Article
- Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases.Mathematical biosciences and engineering : MBE · 2016Article
- Microenvironmental Niches and Sanctuaries: A Route to Acquired Resistance.Advances in experimental medicine and biology · 2016Article
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Authors and funding
4 authors.
Funding
Abstract
In this paper we develop a mathematical framework for describing multidrug resistance in cancer. To reflect the complexity of the underlying interplay between cancer cells and the therapeutic agent, we assume that the resistance level is a continuous parameter. Our model is written as a system of integro-differential equations that are parameterized by the resistance level. This model incorporates the cell density and mutation dependence. Analysis and simulations of the model demonstrate how the dynamics evolves to a selection of one or more traits corresponding to different levels of resistance. The emerging limit distribution with nonzero variance is the desirable modeling outcome as it represents tumor heterogeneity.
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Registered trials
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