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The tumor microenvironment (TME) significantly impacts cancer prognosis due to its immune composition. While therapies for altering the immune composition, including immunotherapies, have shown exciting results for treating hematological…
The analysis of randomized controlled trials is often complicated by intercurrent events (IEs) -- events that occur after treatment initiation and affect either the interpretation or existence of outcome measurements. Examples include…
In processes such as embryo shaping, wound healing, and malignant cell invasion, epithelial cells transition between dispersed phases, where the cells move independently, and condensed phases, where they aggregate and deform to close gaps,…
The tumor microenvironment (TME) is a spatially heterogeneous ecosystem where cellular interactions shape tumor progression and response to therapy. Multiplexed imaging technologies enable high-resolution spatial characterization of the…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
We propose here a multiscale model for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization. The model accounts for the interplay between the different components of the neoplasm and…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
In this paper, we study the global dynamics of a general reaction-diffusion model based on acid-mediated invasion hypothesis, which is a candidate explanation for the Warburg effect. A key feature of this model is the density-limited tumor…
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the…
Chimeric Antigen Receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed…
We introduce a set of ordinary differential equations (ODE) that qualitatively reproduces delayed responses observed in immune checkpoint blockade therapy (e.g. anti-CTLA-4 Ipilimumab). This type of immunotherapy has been at the forefront…
We present an individual-based model for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes (CTLs) and tumour cells. In this model, every cell is viewed as an individual agent whose phenotypic state is modelled by a discrete…
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…
We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a…
In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting…
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…
Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given…
We discuss the mathematical modelling of two of the main mechanisms which pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation, and between-cell cooperation. In line with the atavistic theory of…