Publication

Numerical approximation of phase field models for tumor growth

2015
Student Projects

Abstract

In this project, we deal with the numerical approximation of problems described by a phase field model, which is nowadays popular to describe substances sharing sharp interfaces. We present the basis of the theory of mixtures required to introduce the spinodal decomposition and state the Cahn-Hilliard equations. Then, we use a four species model for tumor growth phenomenon, based on the theory of mixtures. Using the finite element method, we characterize the time evolution of a tumor, as well as the concentration of nutrients, in a wide range of scenarios described by a set of parameters.

Official source

https://infoscience.epfl.ch/entities/publication/3aa47da7-5dcc-4725-8734-b98d08a6c2f9

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2015
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3aa47da7-5dcc-4725-8734-b98d08a6c2f9

About this result

Related concepts (32)

Tumor microenvironment

The tumor microenvironment (TME) is the environment around a tumor, including the surrounding blood vessels, immune cells, fibroblasts, signaling molecules and the extracellular matrix (ECM). The tumor and the surrounding microenvironment are closely related and interact constantly. Tumors can influence the microenvironment by releasing extracellular signals, promoting tumor angiogenesis and inducing peripheral immune tolerance, while the immune cells in the microenvironment can affect the growth and evolution of cancerous cells.

Benign tumor

A benign tumor is a mass of cells (tumor) that does not invade neighboring tissue or metastasize (spread throughout the body). Compared to malignant (cancerous) tumors, benign tumors generally have a slower growth rate. Benign tumors have relatively well differentiated cells. They are often surrounded by an outer surface (fibrous sheath of connective tissue) or stay contained within the epithelium. Common examples of benign tumors include moles and uterine fibroids. Some forms of benign tumors may be harmful to health.

Species

In biology, a species (: species) is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. Other ways of defining species include their karyotype, DNA sequence, morphology, behaviour, or ecological niche. In addition, paleontologists use the concept of the chronospecies since fossil reproduction cannot be examined.

Related publications (13)

Numerical approximation of phase field models for tumor growth

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