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Chimeric Antigen Receptor (CAR) T cell therapy has transformed immunotherapy for resistant cancers, yet it faces major limitations such as lack of persistence, toxicity, exhaustion, and antigen-negative relapse. Enhancing CAR T cells with…
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 propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of…
We study the joint effect of thermal bath fluctuations and an external noise tuning activity of cytotoxic cells on the triggered immune response in a growing cancerous tissue. The immune response is assumed to be primarily mediated by…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
In this paper we investigate some stochastic models for tumor-immune systems. To describe these models we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
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…
Heterogeneity is a hallmark of all cancers. Tumor heterogeneity is found at different levels -- interpatient, intrapatient, and intratumor heterogeneity. All of them pose challenges for clinical treatments. The latter two scenarios can also…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
In this paper, a methodology is proposed that enables to analyze the sensitivity of the outcome of a therapy to unavoidable high dispersion of the patient specific parameters on one hand and to the choice of the parameters that define the…
Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…
The transition from the epithelial to mesenchymal phenotype and its reverse (from mesenchymal to epithelial) are crucial processes necessary for the progression and spread of cancer. In this paper, we investigate how phenotypic switching at…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their…