Drug resistance

Physics

Internal medicine

Cancer treatment

Mathematics

Resistance (ecology)

Biology

Microbiology

Cancer

Dynamics (music)

Mathematical analysis

Acoustics

Ecology

Solid tumor

Tumor heterogeneity

Computer science

Computational biology

Differential equation

Ordinary differential equation

Medicine

CPT Pharmacometrics & Systems Pharmacology

Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model-based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model-based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model-based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors