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We study the effect of intratumor heterogeneity in the likelihood of cancer cells moving from a primary tumor to other sites in the human body, generating a metastatic process. We model different scenarios of competition between tumor cells…
Immunotherapies have been proven to have significant therapeutic efficacy in the treatment of cancer. The last decade has seen adoptive cell therapies, such as chimeric antigen receptor T-cell (CART-cell) therapy, gain FDA approval against…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
This paper investigates dynamic behaviors of the tumor-immune system perturbed by environmental noise. The model describes the response of the cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main methods are…
Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is…
There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
Adaptive therapy (AT) is designed to postpone the emergence of drug resistance by exploiting evolutionary competition among tumor subclones. Most mathematical models of AT assume a binary population structure of drug-sensitive and…
Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of…
Phenotypic heterogeneity in cancer cells is widely observed and is often linked to drug resistance. In several cases, such heterogeneity in drug sensitivity of tumors is driven by stochastic and reversible acquisition of a drug tolerant…
In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint…
The majority of cancer treatments end in failure due to Intra-Tumor Heterogeneity (ITH). ITH in cancer is represented by clonal evolution where different sub-clones compete with each other for resources under conditions of Darwinian natural…
We present a theoretical agent-based model of cell evolution under the action of cytotoxic treatments, such as radioteraphy or chemoteraphy. The major features of cell cycle and proliferation, cell damage and repair, and chemical diffusion…
Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of cancer is complex and that individual cancers…
In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…
While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor…
Histopathological evidence supports the idea that the emergence of phenotypic heterogeneity and resistance to cytotoxic drugs can be considered as a process of adaptation, or evolution, in tumor cell populations. In this framework, can we…
We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee…
In here presented in silico study we suggest a way how to implement the evolutionary principles into anti-cancer therapy design. We hypothesize that instead of its ongoing supervised adaptation, the therapy may be constructed as a…
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…