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Immune cells have evolved to recognize and eliminate pathogens, and the efficiency of this process can be measured in a Petri dish. Yet, even if the cells are time-lapse recorded and tracked with high resolution, it is difficult to judge…

Quantitative Methods · Quantitative Biology 2019-06-21 Claus Metzner

Chemotaxis enables cells to systematically approach distant targets that emit a diffusible guiding substance. However, the visual observation of an encounter between a cell and a target does not necessarily indicate the presence of a…

Quantitative Methods · Quantitative Biology 2021-06-22 Claus Metzner , Franziska Hörsch , Christoph Mark , Tina Czerwinski , Alexander Winterl , Caroline Voskens , Ben Fabry

The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. Although treatment may initially achieve short-term disease control, resistant…

Quantitative Methods · Quantitative Biology 2026-04-03 Nazanin Mokari , Bryce Morsky

The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T…

Tissues and Organs · Quantitative Biology 2025-03-19 Haifeng Zhang , Changjing Zhuge , Jinzhi Lei

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

We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…

Cell Behavior · Quantitative Biology 2026-02-24 Martina Conte , Romina Travaglini

Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally…

Cell Behavior · Quantitative Biology 2019-08-05 Fiona R Macfarlane , Mark AJ Chaplain , Tommaso Lorenzi

In the tumour microenvironment, cancer cells directly interact with both the immune system and the stroma. It is firmly established that the immune system, historically believed to be a major part of the body's defence against tumour…

Tissues and Organs · Quantitative Biology 2017-09-01 R J Seager , Cynthia Hajal , Fabian Spill , Roger D Kamm , Muhammad H Zaman

In chemotaxis, cells are modulating their migration patterns in response to concentration gradients of a guiding substance. Immune cells are believed to use such chemotactic sensing for remotely detecting and homing in on pathogens.…

Cell Behavior · Quantitative Biology 2019-02-28 Claus Metzner

The goal of immunotherapy is to enhance the ability of the immune system to kill cancer cells. Immunotherapy is more effective and, in general, the prognosis is better, when more immune cells infiltrate the tumor. We explore the question of…

Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be…

Cellular immunotherapies are one of the mainstream cancer treatments unveiling the power of the patient's immune system to fight tumors. CAR T-cell therapy, based on genetically engineered T cells, has demonstrated significant potential in…

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

Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors,…

Computational Engineering, Finance, and Science · Computer Science 2012-08-21 Giulio Caravagna , Alex Graudenzi , Marco Antoniotti , Giancarlo Mauri , Alberto d'Onofrio

In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune…

Probability · Mathematics 2025-08-06 Christian Kuehn , Quirin Vogel

Migration of cells can be characterized by two, prototypical types of motion: individual and collective migration. We propose a statistical-inference approach designed to detect the presence of cell-cell interactions that give rise to…

Cell Behavior · Quantitative Biology 2020-03-13 Elena Agliari , Pablo J. Sáez , Adriano Barra , Matthieu Piel , Pablo Vargas , Michele Castellana

In this article a generalized mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate…

Tissues and Organs · Quantitative Biology 2015-11-05 Monika Joanna Piotrowska

We present a spatial hybrid discrete-continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which play a pivotal role in the immune response against tumours. In this framework, tumour cells…

Analysis of PDEs · Mathematics 2022-10-10 Luis Almeida , Chloe Audebert , Emma Leschiera , Tommaso Lorenzi

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

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
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