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Updated: May 24, 2026

Implementation of In Vitro Drug Resistance Assays: Maximizing the Potential for Uncovering Clinically Relevant Resistance Mechanisms
Published on: December 9, 2015
The dynamics of drug resistance: a mathematical perspective
Orit Lavi1, Michael M Gottesman, Doron Levy
1Laboratory of Cell Biology, National Cancer Institute, National Institutes of Health, Bethesda, MD 20742, USA.
Abstract:
Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.
Insights
Mathematical models offer insights into chemotherapy resistance, particularly multidrug resistance (MDR). Integrating these quantitative approaches with experimental and clinical tools can enhance cancer treatment strategies.
Area of Science:
- Oncology
- Mathematical Biology
- Pharmacology
Background:
- Chemotherapy resistance is a major obstacle in cancer treatment.
- Multidrug resistance (MDR) involves cellular resistance to diverse drugs.
- Mathematical modeling has been applied to various resistance mechanisms.
Purpose of the Study:
- To review mathematically studied aspects of multidrug resistance (MDR).
- To explain the methodological application of mathematics in studying drug resistance.
- To highlight the benefits of integrating mathematical methods into cancer research.
Main Methods:
- Review of existing mathematical models of drug resistance.
- Discussion of quantitative analytical approaches.
- Examination of models for specific biological functions (e.g., ABC transporters, apoptosis).
Main Results:
- Mathematical models address pharmacologic, kinetic, and intracellular resistance mechanisms.
- Quantitative analysis provides insights into drug resistance dynamics.
- Integration of mathematical and experimental methods is crucial.
Conclusions:
- Mathematics offers a powerful framework for understanding chemotherapy resistance.
- Quantitative approaches can complement experimental and clinical studies.
- Integrating analytical methods can advance future cancer treatment strategies.
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