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Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given…

Quantitative Methods · Quantitative Biology 2013-12-31 Andrew Dhawan , Kamran Kaveh , Mohammad Kohandel , Siv Sivaloganathan

Cancer progression is an example of a rapid adaptive process where evolving new traits is essential for survival and requires a high mutation rate. Precancerous cells acquire a few key mutations that drive rapid population growth and…

Populations and Evolution · Quantitative Biology 2015-06-18 Christopher McFarland , Leonid Mirny , Kirill S. Korolev

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…

Populations and Evolution · Quantitative Biology 2025-10-28 André Rocha , Claudia Manini , José I López , Annick Laruelle

Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…

Tissues and Organs · Quantitative Biology 2009-11-13 E. A. Reis , L. B. L. Santos , S. T. R. Pinho

To maintain bone mass during bone remodelling, coupling is required between bone resorption and bone formation. This coordination is achieved by a network of autocrine and paracrine signalling molecules between cells of the osteoclast…

Tissues and Organs · Quantitative Biology 2015-02-20 Pascal R. Buenzli , Peter Pivonka , Bruce S. Gardiner , David W. Smith

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…

Molecular Networks · Quantitative Biology 2013-01-14 Andrei Zinovyev , Simon Fourquet , Laurent Tournier , Laurence Calzone , Emmanuel Barillot

The ability of a cancer cell population to achieve heterogeneity in their phenotype distributions offers advantages in tumor invasiveness and drug resistance. Studying the mechanisms behind such observed heterogeneity in mammalian cells…

Cell Behavior · Quantitative Biology 2024-08-20 Simone Scalise , Giorgio Gosti , Giancarlo Ruocco , Giovanna Peruzzi , Mattia Miotto

Collective cell migration governs a range of physiological and pathological processes, from tissue morphogenesis to cancer invasion, in which topological defects arise as an inevitable consequence of frequent cellular rearrangement and…

Soft Condensed Matter · Physics 2026-04-01 Jiusi Zhang , Chung Wing Chan , Bo Li , Rui Zhang

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

Analysis of PDEs · Mathematics 2021-07-07 Luca Scarpa , Andrea Signori

We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…

Numerical Analysis · Mathematics 2016-02-23 Konstantina Trivisa , Franziska Weber

Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…

Tissues and Organs · Quantitative Biology 2026-05-19 Yuhong Zhang , Chenghang Li , Boya Wang , Jinzhi Lei

Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…

Tissues and Organs · Quantitative Biology 2014-07-14 Katrin Böttger , Haralambos Hatzikirou , Anja Voss-Boehme , Miguel A. Herrero , Andreas Deutsch

The homeostasis of epithelial tissue relies on a balance between the self-renewal of stem cell populations, cellular differentiation, and loss. Although this balance needs to be tightly regulated to avoid pathologies, such as tumor growth,…

Biological Physics · Physics 2024-04-10 Johannes C. Krämer , Edouard Hannezo , Gerhard Gompper , Jens Elgeti

We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the…

Analysis of PDEs · Mathematics 2013-10-02 Sebastien Benzekry , Alberto Gandolfi , Philip Hahnfeldt

Assuming that there is feedback between an expanding cancer system and its organ-typical microenvironment, we argue here that such local tumor growth is guided by co-existence rather than competition with the surrounding tissue. We then…

Tissues and Organs · Quantitative Biology 2007-05-23 Thomas S. Deisboeck , Zhihui Wang

Variability in the tumorigenic potential among cancer cells within a tumor population is an unresolved fundamental issue in cancer biology. It is important to know whether cancer cells with higher tumorigenic potential, such as cancer stem…

Molecular Networks · Quantitative Biology 2011-11-30 Subhadip Raychaudhuri

The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their…

Tissues and Organs · Quantitative Biology 2025-01-22 Giorgia Ciavolella , Julien Granet , Jacky Goetz , Nael Osmani , Christèle Etchegaray , Annabelle Collin

Routinely navigating through an ever-changing and unsteady environment, and utilizing chemical energy, molecular motors transport the cell's crucial components, such as neurotransmitters and organelles. They generate force and pull cargo,…

Biological Physics · Physics 2012-09-28 Bartosz Lisowski , Michał Żabicki

Although the lymphatic system is clearly linked to the metastasis of most human carcinomas, the mechanisms by which lymphangiogenesis occurs in response to the presence of carcinoma remain unclear. Hierarchical models are presented to…

Applications · Statistics 2016-02-01 T. R. Fanshawe , C. M. Chapman , T. Crick

Experimental studies of cell motility in culture have shown that under adequate conditions these living organisms possess the ability to organize themselves into complex structures. Such structures may exhibit a synergy that greatly…

Statistical Mechanics · Physics 2021-10-27 G. Nakamura , M. Badoual , E. Fabiani , C. Deroulers
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