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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…
Heating of trapped ion clouds by interactions with free electrons crossing the trapping potential was observed. A model describing such process was proposed and discussed. The presented approach predicts two effects: pushing and heating of…
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…
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…
In this paper, we adapt a two-species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction with a third species -- namely immune cells. We run six…
Chimeric antigen receptor T (CAR-T) cell therapy has emerged as a promising treatment for hematological malignancies, offering a targeted approach to cancer treatment. Understanding the complexities of CAR-T cell therapy within solid tumors…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
We present a theoretical agent-based model of cell evolution under the action of cytotoxic treatments, such as radioteraphy or chemoteraphy. The major features of cell cycle and proliferation, cell damage and repair, and chemical diffusion…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
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…
Immunotherapy plays a major role in tumour treatment, in comparison with other methods of dealing with cancer. The Kirschner-Panetta (KP) model of cancer immunotherapy describes the interaction between tumour cells, effector cells and…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
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…
Understanding the impact of tumor biology on the composition of nearby cells often requires characterizing the impact of biologically distinct tumor regions. Biomarkers have been developed to label biologically distinct tumor regions, but…
In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of…
In this paper we consider an optimal control problem arising from a chemotherapeutic drug treatment for tumor cells in a living tissue. The mathematical model for the interaction of chemotherapeutic drug and the normal, tumor and immune…
The ICH E9(R1) addendum provides guidelines on accounting for intercurrent events in clinical trials using the estimands framework. However, there has been limited attention to the estimands framework for meta-analysis. Using treatment…