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Adaptive therapy is a recent paradigm in cancer treatment aiming at indefinite, safe containment of the disease when cure is judged unattainable. In modeling this approach, inherent limitations arise due to the structure of the vector…

Dynamical Systems · Mathematics 2025-03-20 Frederik J. Thomsen , Johan L. A. Dubbeldam

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or…

Analysis of PDEs · Mathematics 2012-07-05 Alexander Lorz , Tommaso Lorenzi , Michael E. Hochberg , Jean Clairambault , Benoit Perthame

In the study of therapeutic strategies for the treatment of cancer, eco-evolutionary dynamics are of particular interest, since characteristics of the tumour population, interaction with the environment and effects of the treatment,…

Populations and Evolution · Quantitative Biology 2023-07-19 Giulia Chiari , Giada Fiandaca , Marcello Edoardo Delitala

Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…

Tissues and Organs · Quantitative Biology 2025-12-30 Prithvi Anickode , Fabio Milner

Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are…

Quantitative Methods · Quantitative Biology 2020-08-06 Mark Gluzman , Jacob G. Scott , Alexander Vladimirsky

Resistance to therapy remains a significant challenge in cancer treatment, often due to the presence of a stem-like cell population that drives tumor recurrence post-treatment. Moreover, many anticancer therapies induce plasticity,…

Populations and Evolution · Quantitative Biology 2024-12-25 Chenyu Wu , Einar Bjarki Gunnarsson , Jasmine Foo , Kevin Leder

Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the…

Tissues and Organs · Quantitative Biology 2008-10-28 David Basanta , Andreas Deutsch

Evolutionary therapy (ET) aims to steer tumor evolution by adjusting treatment timing and dosing to control rather than eradicate tumor burden. Clinical use requires reliable monitoring of tumor dynamics to inform mathematical models that…

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…

Molecular Networks · Quantitative Biology 2023-02-10 Viren Shah , Justin Womack , Anthony E. Zamora , Scott S. Terhune , Ranjan K. Dash

The emergence of acquired drug resistance in cancer represents a major barrier to treatment success. While research has traditionally focused on genetic sources of resistance, recent findings suggest that cancer cells can acquire transient…

Populations and Evolution · Quantitative Biology 2020-02-25 Einar Bjarki Gunnarsson , Subhajyoti De , Kevin Leder , Jasmine Foo

Drug resistance and metastasis - the major complications in cancer - both entail adaptation of cancer cells to stress, whether a drug or a lethal new environment. Intriguingly, these adaptive processes share similar features that cannot be…

Molecular Networks · Quantitative Biology 2021-09-28 Aseel Shomar , Omri Barak , Naama Brenner

Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…

Cell Behavior · Quantitative Biology 2020-01-10 Jinzhi Lei

We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…

Tissues and Organs · Quantitative Biology 2020-06-02 Chiara Villa , Mark A. J. Chaplain , Tommaso Lorenzi

The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic…

Populations and Evolution · Quantitative Biology 2009-11-13 Nicola Pizzolato , Davide Valenti , Dominique Persano Adorno , Bernardo Spagnolo

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…

Dynamical Systems · Mathematics 2023-03-21 Marvin Fritz

Any process in which competing solutions replicate with errors and numbers of their copies depend on their respective fitnesses is the evolutionary optimization process. As during carcinogenesis mutated genomes replicate according to their…

Populations and Evolution · Quantitative Biology 2009-12-15 B. Brutovsky , D. Horvath

Evolutionary algorithms have long been used for optimization problems where the appropriate size of solutions is unclear a priori. The applicability of this methodology is here investigated on the problem of designing a nano-particle (NP)…

Neural and Evolutionary Computing · Computer Science 2020-11-11 Michail-Antisthenis Tsompanas , Larry Bull , Andrew Adamatzky , Igor Balaz

Despite recent advances in the field of Oncoimmunology, the success potential of immunomodulatory therapies against cancer remains to be elucidated. One of the reasons is the lack of understanding on the complex interplay between tumor…

Tissues and Organs · Quantitative Biology 2015-07-24 A. I. Reppas , J. C. L. Alfonso , H. Hatzikirou

One of many important features of the tumour microenvironment is that it is a place of active Darwinian selection where different tumour clones become adapted to the variety of ecological niches that make up the microenvironment. These…

Biological Physics · Physics 2019-06-07 Thierry Fredrich , Heiko Rieger , Roberto Chignola , Edoardo Milotti

Working towards the development of an evolvable cancer treatment simulator, the investigation of Differential Evolution was considered, motivated by the high efficiency of variations of this technique in real-valued problems. A basic DE…

Neural and Evolutionary Computing · Computer Science 2020-03-27 Michail-Antisthenis Tsompanas , Larry Bull , Andrew Adamatzky , Igor Balaz
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