Traveling waves model tumor invasion

June 25, 2014

Cell migration, which is involved in wound healing, cancer and tumor growth, and embryonic growth and development, has been a topic of interest to mathematicians and biologists for decades.

In a paper published recently in the SIAM Journal on Applied Dynamical Systems, authors Kristen Harley, Peter van Heijster, Robert Marangell, Graeme Pettet, and Martin Wechselberger study a model describing through directional outgrowth or movement in the context of malignant tumors, in particular, melanoma or skin cancer. Tumor cells move up a gradient, based on the presence of a chemical or chemoattractant – this process is called haptotaxis. Receptors on the exterior of cell walls detect and allow passing of the chemoattractant. Based on the locations of these receptors, cells determine the most favorable migration direction.

Continuum mathematical models that describe usually give rise to traveling waves—waves in which the medium moves in the direction of propagation at a constant speed. In this paper, the authors prove the existence and uniqueness of traveling waves to the model of malignant tumor invasion. The model described takes into account the speed of the traveling waves, which corresponds to the rate of invasion of cells, as well as the extracellular matrix concentration (the medium surrounding cells that provides structural and biochemical support to cells). Movement of cells through diffusion is omitted as it is shown to play a relatively small role in the migration process.

Explore further: How do our cells move? Liquid droplets could explain

More information: Existence of Traveling Wave Solutions for a Model of Tumor Invasion SIAM Journal on Applied Dynamical Systems, 13 (1), 366-396

Related Stories

How do our cells move? Liquid droplets could explain

May 1, 2014

Living cells move; not just bacteria, but also cells in our own bodies. EPFL scientists have discovered a new relationship between the three-dimensional shape of the cell and its ability to migrate. The work has important ...

Recommended for you

Sixth sense: How do we sense electric fields?

October 13, 2015

A variety of animals are able to sense and react to electric fields, and living human cells will move along an electric field, for example in wound healing. Now a team lead by Min Zhao at the UC Davis Institute for Regenerative ...

A better way to read the genome

October 9, 2015

UConn researchers have sequenced the RNA of the most complicated gene known in nature, using a hand-held sequencer no bigger than a cell phone.


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.