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We introduce here a new diffuse interface thermodynamically consistent non-isothermal model for tumor growth in presence of a nutrient in a domain $\Omega \subset \mathbb{R}^3$. In particular our system describes the growth of a tumor…

Analysis of PDEs · Mathematics 2022-12-19 Erica Ipocoana

We present a phase-space analysis of a mathematical model of tumor growth with an immune responses. We consider mathematical analysis of the model equations with multipoint initial condition regarding to dissipativity, boundedness of…

Dynamical Systems · Mathematics 2019-02-28 Veli Shakhmurov , Rishad Shahmurov

We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…

Cell Behavior · Quantitative Biology 2023-11-14 Giulia L. Celora , Helen M. Byrne , P. G. Kevrekidis

We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may…

Tissues and Organs · Quantitative Biology 2019-09-12 Ana Osojnik , Eamonn A. Gaffney , Michael Davies , James W. T. Yates , Helen M. Byrne

We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion…

Populations and Evolution · Quantitative Biology 2025-09-29 Francesca Ballatore , Xinran Ruan , Chiara Giverso , Tommaso Lorenzi

With the advance of imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high…

Methodology · Statistics 2020-12-10 Qiwei Li , Xinlei Wang , Faming Liang , Guanghua Xiao

The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the…

comp-gas · Physics 2007-05-23 Margarita Voitikova

Accurate interpretation of histopathological images demands integration of information across spatial and semantic scales, from nuclear morphology and cellular textures to global tissue organization and disease-specific patterns. Although…

Computer Vision and Pattern Recognition · Computer Science 2025-10-27 Yating Huang , Qijun Yang , Lintao Xiang , Hujun Yin

Multicellular tumor spheroids are an important {\it in vitro} model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the…

Tissues and Organs · Quantitative Biology 2015-05-20 Edoardo Milotti , Roberto Chignola

Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the…

Analysis of PDEs · Mathematics 2025-07-08 Tommaso Lorenzi , Giulia Pozzi , Andrea Signori

In a previous paper we have introduced a phenomenological model of cell metabolism and of the cell cycle to simulate the behavior of large tumor cell populations (Chignola R and Milotti E, Phys. Biol. 2 (2005) 8-22). Here we describe a…

Biological Physics · Physics 2009-11-13 Roberto Chignola , Alessio Del Fabbro , Chiara Dalla Pellegrina , Edoardo Milotti

In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…

Dynamical Systems · Mathematics 2018-03-15 Veli Shakhmurov , Akif Maharramov , Bunyad Shahmurzada

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

A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…

Biological Physics · Physics 2007-05-23 Roberto Chignola , Edoardo Milotti

We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…

Populations and Evolution · Quantitative Biology 2016-04-18 Martina Baar , Loren Coquille , Hannah Mayer , Michael Hölzel , Meri Rogava , Thomas Tüting , Anton Bovier

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 the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…

Biological Physics · Physics 2023-02-07 Maxim V. Polyakov , Valeria V. Ten

We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the point process setting. The method is based on modelling the…

Methodology · Statistics 2017-10-25 Tuomas Rajala , David Murrell , Sofia Olhede

In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…

Machine Learning · Computer Science 2025-12-18 Kayode Olumoyin , Lamees El Naqa , Katarzyna Rejniak

Mathematical oncology is a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. Tumor-immune interactions play a…

Quantitative Methods · Quantitative Biology 2025-11-05 Chenghang Li , Jinzhi Lei