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This paper is devoted to the analysis of the complex damage of DNA irradiated by ions. The analysis and assessment of complex damage is important because cells in which it occurs are less likely to survive because the DNA repair mechanisms…
A fission decay of highly excited periodically driven compound nuclei is considered in the framework of Langevin approach. We have used residual-time distribution (RTD) as the tool for studying of dynamic features in a presence of periodic…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control…
In this paper, we describe a dataset relating to cellular and physical conditions of patients who are operated upon to remove colorectal tumours. This data provides a unique insight into immunological status at the point of tumour removal,…
Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model is proposed to…
We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its…
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…
We consider a chemo-repulsion model with quadratic production in a bounded domain. Firstly, we obtain global in time weak solutions, and give a regularity criterion (which is satisfied for $1D$ and $2D$ domains) to deduce uniqueness and…
Tumor Necrosis Factor alpha (TNF) initiates a complex series of biochemical events in the cell upon binding to its type R1 receptor (TNF-R1). Recent experimental work has unravelled the molecular regulation of the recruitment of initial…
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…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an `energy model' of the…
We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
We analyze the effect of tumor repopulation on optimal dose delivery in radiation therapy. We are primarily motivated by accelerated tumor repopulation towards the end of radiation treatment, which is believed to play a role in treatment…
In this paper, multivalued data or multiple values variables are defined. They are typical when there is some intrinsic uncertainty in data production, as the result of imprecise measuring instruments, such as in image recognition, in human…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…
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…
Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during treatment, the authors propose a dynamic framework for robust…
We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into…