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Open AccessJournal ArticleDOI

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

TLDR
The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.
Abstract
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.

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Treatment-driven tumour heterogeneity and drug resistance: Lessons from solid tumours.

TL;DR: In this paper , the authors focused on tumour heterogeneity and its relation to resistance to targeted-therapy, based on treatment selective pressure across different tumour types, including lung, colorectal, prostate, breast cancer and melanoma.
References
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Computational modeling of the WHO grade II glioma dynamics: principles and applications to management paradigm.

TL;DR: In this paper, WHO grade II glioma will serve as a paradigmatic example to illustrate that computational models allow characterizing tumor dynamics from serial MRIs and the role of these dynamics for both therapeutic management and biological research will be discussed.
Journal ArticleDOI

Impact of genetic dynamics and single-cell heterogeneity on development of nonstandard personalized medicine strategies for cancer.

TL;DR: A mathematical model of personalized cancer therapy incorporating genetic evolutionary dynamics and single-cell heterogeneity is developed, and simulated clinical outcomes are examined, demonstrating that augmented (and sometimes counterintuitive) nonstandard personalized medicine strategies may lead to superior patient outcomes compared with the current personalized medicine approach.
Journal ArticleDOI

Mathematical Modeling of Therapy-induced Cancer Drug Resistance: Connecting Cancer Mechanisms to Population Survival Rates.

TL;DR: A modeling approach was used to connect cellular mechanisms underlying cancer drug resistance to population-level patient survival and developed a set of stochastic differential equations to describe the dynamics of heterogeneous cell populations while taking into account micro-environment adaptations that predicted progression-free survival in cancer patients with metastatic melanoma.
Journal ArticleDOI

Mathematical modelling of prostate cancer growth and its application to hormone therapy

TL;DR: In this paper, the authors presented an extended model of stochastic differential equations and examined how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data.
Journal ArticleDOI

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation☆

TL;DR: Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics.
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