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Related papers: Reaction-Diffusion Models for Glioma Tumor Growth

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The mathematical modeling of tumor growth has a long history, and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using mathematical tools from statistical…

Statistical Mechanics · Physics 2021-01-08 L. Preziosi , G. Toscani , M. Zanella

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

We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathematical models of tumor growth are largely phenomenological…

Numerical Analysis · Mathematics 2026-02-23 Alexander D. Gilbert , Frances Y. Kuo , Dirk Nuyens , Graham Pash , Ian H. Sloan , Karen E. Willcox

Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions…

Tissues and Organs · Quantitative Biology 2025-08-18 Marcela V. Reale , Gustavo Paccosi , David H. Margarit , Lilia Romanelli

This research presents a mathematical model of glioma growth dynamics with drug resistance, capturing interactions among five cell populations: glial cells, sensitive glioma cells, resistant glioma cells, endothelial cells, and neuron…

Dynamical Systems · Mathematics 2023-08-23 Latifah Hanum , Nanang Susyanto , Dwi Ertiningsih

The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment,…

Tissues and Organs · Quantitative Biology 2017-06-29 Anna Konstorum , Anthony T. Vella , Adam J. Adler , Reinhard Laubenbacher

A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…

Numerical Analysis · Mathematics 2019-02-19 Gopikrishnan C. Remesan

It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study…

Cell Behavior · Quantitative Biology 2009-03-26 Christophe Deroulers , Marine Aubert , Mathilde Badoual , Basil Grammaticos

This paper deals with the cellular biological network analysis of the tumor-growth model, consisting of multiple spaces and time scales. In this paper, we present a model in graph simulation using ABM for tumor growth. In particular, we…

Multiagent Systems · Computer Science 2019-09-05 Ghazal Tashakor , Remo Suppi

In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…

Biological Physics · Physics 2019-01-29 Cristian C. Pérez Águila , Maura Cárdenas G. , J. Fernando Rojas

We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…

Populations and Evolution · Quantitative Biology 2021-02-12 I. Lampropoulos , M. Kavousanakis

In this paper we analyse a differential system related to a Glioblastoma growth. Using numerical simulations, we prove that model captures different kind of growth changing adequately the parameters of the model. Firstly, we make an…

Analysis of PDEs · Mathematics 2021-09-21 A. Fernández-Romero , F. Guillén-González , A. Suárez

Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells…

Dynamical Systems · Mathematics 2022-12-01 Frank Alvarez , Yannick Viossat

Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been…

Biological Physics · Physics 2025-11-07 Mirko Bagnarol , Gianluca Lattanzi , Jan Åström , Mikko Karttunen

The problem of tumor growth prediction is challenging, but promising results have been achieved with both model-driven and statistical methods. In this work, we present a framework for the evaluation of growth predictions that focuses on…

Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in…

Analysis of PDEs · Mathematics 2016-06-06 Harald Garcke , Kei Fong Lam , Emanuel Sitka , Vanessa Styles

In this contribution, the non-local, integro-partial differential system of equations proposed by Hillen et al. (Bull. Math. Biol. 75, 2013, no.1, 161-184) to account for the the tumor growth paradox (or the observation that some incomplete…

Analysis of PDEs · Mathematics 2019-03-13 Isai Padilla , Ramón G. Plaza

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than…

Quantitative Methods · Quantitative Biology 2023-11-07 Navid Mohammad Mirzaei , Leili Shahriyari

Tumor growth is a complex process characterized by uncontrolled cell proliferation and invasion of neighboring tissues. The understanding of these phenomena is of vital importance to establish appropriate diagnosis and therapeutic strategy…

Tissues and Organs · Quantitative Biology 2019-10-23 Miguel Martín-Landrove , Francisco Torres-Hoyos , Antonio Rueda-Toicen

We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the…

Analysis of PDEs · Mathematics 2019-02-06 Anderson L. A. de Araujo , Artur C. Fassoni , Luís F. Salvino