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We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells…
In this review, we discuss recent advances on the plasticity of cancer stem cells and highlight their relevance to understand the metastatic process and to guide therapeutic interventions. Recent results suggest that the strict hierarchical…
In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model addresses the dynamics of tissue growth influenced by…
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed in [A. Hawkins-Daruud, K.G. van der Zee, J.T. Oden, Numerical simulation of a thermodynamically consistent…
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the…
Tumors are defined by their intense proliferation, but sometimes cancer cells turn senescent and stop replicating. In the stochastic cancer model in which all cells are tumorigenic, senescence is seen as the result of random mutations,…
One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical…
In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the…
This paper presents a model for tumor growth using nonlocal velocity. We establish some results on the existence and uniqueness of the solution for a nonlocal tumor growth model. Many experiences show that tumor spheroid can be invariant by…
This paper deals with the cellular biological network analysis of the tumor-growth model, consisting of multiple spaces and time scales. In this paper, we present a model in graph simulation using ABM for tumor growth. In particular, we…
We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…
Cancer is a complex disease that is characterized by uncontrolled growth and division of cells. It involves a complex interplay between genetic and environmental factors that lead to the initiation and progression of tumors. Recent advances…
In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical…
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…
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…
Progress in our knowledge of tumor mechanisms and complexity led to the understanding of the physical parameters of cancer cells and their microenvironment, including the mechanical, thermal, and electrical properties, solid stress, and…
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalization of a phase field…
Computational systems and methods are often being used in biological research, including the understanding of cancer and the development of treatments. Simulations of tumor growth and its response to different drugs are of particular…
We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a…
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for…