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Updated: May 2, 2026

Non-Destructive Evaluation of Regional Cell Density Within Tumor Aggregates Following Drug Treatment
Published on: June 21, 2022
The impact of cell density and mutations in a model of multidrug resistance in solid tumors
James Greene1, Orit Lavi, Michael M Gottesman
1Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742, USA.
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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