English
Related papers

Related papers: A level-set approach for a multi-scale cancer inva…

200 papers

We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be…

Analysis of PDEs · Mathematics 2023-10-27 Montie Avery

In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The…

Analysis of PDEs · Mathematics 2021-09-30 Anna Zhigun , Christina Surulescu

Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor…

Cell Behavior · Quantitative Biology 2022-01-20 Ushasi Roy , Tyler Collins , Mohit K. Jolly , Parag Katira

We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells…

Cell Behavior · Quantitative Biology 2015-06-26 Sergei Fedotov , Alexander Iomin

In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…

Analysis of PDEs · Mathematics 2021-08-31 Xu'an Dou , Jian-Guo Liu , Zhennan Zhou

Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the…

Biological Physics · Physics 2018-06-19 Youness Azimzade , Abbas Ali Saberi , Muhammad Sahimi

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…

Mathematical Physics · Physics 2017-01-20 Andrea Tosin

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must…

Cell Behavior · Quantitative Biology 2015-05-20 Salvatore Torquato

The aim of this chapter is to provide a brief introduction into the basics of a top-down multilevel tumor dynamics modeling method primarily based on discrete entity consideration and manipulation. The method is clinically oriented, one of…

Medical Physics · Physics 2010-09-14 Georgios Stamatakos

Starting from a two-scale description involving receptor binding dynamics and a kinetic transport equation for the evolution of the cell density function under velocity reorientations, we deduce macroscopic models for glioma invasion…

Numerical Analysis · Mathematics 2018-04-04 Gregor Corbin , Alexander Hunt , Florian Schneider , Axel Klar , Christina Surulescu

We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…

Tissues and Organs · Quantitative Biology 2019-11-07 Tommaso Lorenzi , Fiona R. Macfarlane , Chiara Villa

Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…

Tissues and Organs · Quantitative Biology 2007-05-23 Benjamin Ribba , Thierry Colin , Santiago Schnell

For over three decades, the front-capturing level-set method has demonstrated its prowess for the simulation, at the mesoscopic scale, of numerous mechanisms in the context of microstructure evolution occurring during complex…

Computational Engineering, Finance, and Science · Computer Science 2023-10-10 Marc Bernacki

Cancer evolves continuously over time through a complex interplay of genetic, epigenetic, microenvironmental, and phenotypic changes. This dynamic behavior drives uncontrolled cell growth, metastasis, immune evasion, and therapy resistance,…

Quantitative Methods · Quantitative Biology 2025-07-08 Luoting Zhuang , Stephen H. Park , Steven J. Skates , Ashley E. Prosper , Denise R. Aberle , William Hsu

In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…

Cell Behavior · Quantitative Biology 2026-02-10 Martina Conte , Sandesh Hiremath , Christina Surulescu

Heterogeneity within tumour cell populations is associated with an increase in malignancy and appears to play an important role during cancer metastasis. Using in silico experiments, we study the interplay between collective behaviours and…

Tissues and Organs · Quantitative Biology 2015-01-05 Adrien Hallou , Joel Jennings , Alexandre Kabla

We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…

Analysis of PDEs · Mathematics 2015-07-29 Mimi Dai , Eduard Feireisl , Elisabetta Rocca , Giulio Schimperna , Maria Schonbek

In this review we summarize our recent efforts in trying to understand the role of heterogeneity in cancer progression by using neural networks to characterise different aspects of the mapping from a cancer cells genotype and environment to…

Tissues and Organs · Quantitative Biology 2014-04-29 Philip Gerlee , Eunjung Kim , Alexander R. A. Anderson

Cancer is a complex disease that is characterized by uncontrolled growth and division of cells. It involves a complex interplay between genetic and environmental factors that lead to the initiation and progression of tumors. Recent advances…

Biomolecules · Quantitative Biology 2025-02-07 Reza Bozorgpour

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…

Analysis of PDEs · Mathematics 2015-03-31 Donatella Donatelli , Konstantina Trivisa