Related papers: On a nonlinear model for tumor growth in a cellula…
In this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quir\'os, and V\'azquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of…
Primary tumors infrequently lead to demise of cancer patients; instead, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). It is well-known that malignant tumors induce…
The ability to estimate how a tumor might evolve in the future could have tremendous clinical benefits, from improved treatment decisions to better dose distribution in radiation therapy. Recent work has approached the glioma growth…
Understanding tumor invasion and metastasis is of crucial importance for both fundamental cancer research and clinical practice. In vitro experiments have established that the invasive growth of malignant tumors is characterized by the…
In the present work, we develop a comprehensive and rigorous analytical framework for a non-local phase-field model that describes tumour growth dynamics. The model is derived by coupling a non-local Cahn-Hilliard equation with a parabolic…
The dynamics between healthy and malignant cells at the avascular stage of growth is described by a set of chemical reactions representing the populations of both types of cells. We obtain a generalization of the logistic-Gompertz dynamics…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
Multiple myeloma is a plasma cell cancer that leads to a dysregulated bone remodeling process. We present a partial differential equation model describing the dynamics of bone remodeling with the presence of myeloma tumor cells. The model…
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…
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip…
Tissue self-organization into defined and well-controlled three-dimensional structures is essential during development for the generation of organs. A similar, but highly deranged process might also occur during the aberrant growth of…
Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving 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…
Interstitial fluid flow is a feature of many solid tumours. In vitro Experiments have shown that such fluid flow can direct tumour cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis…
In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may…
Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell-cell adhesion effects are…
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a pressure gradient generated by the death and birth of cells,…
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…
One of many important features of the tumour microenvironment is that it is a place of active Darwinian selection where different tumour clones become adapted to the variety of ecological niches that make up the microenvironment. These…
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…