Spatial models of cancer

I work with M.A. Nowak, I. Bozic, and B. Vogelstein on spatial models of cancer progression. Cancer occurs when enough mutations accumulate to cause uncontrolled cell growth. Along with “driver” mutations that affect the rate of growth/death, many “passenger” mutations occur which initially do ncover12_Martinot confer any fitness advantage but may do so when conditions change, for example, as a result of chemotherapy. I am interested in how growth in space affects genetic diversity of solid tumours, the number of such passenger mutations, and the probability of tumour regrowth. The image to the left shows a simulated tumour in which different colours represent cells with different genetic composition. The more similar the colours, the more mutations the cells have in common.


Recently, we have published a paper in Nature that shows how a combination of four processes: replication, death, local migration, and clonal expansion leads to reduced genetic diversity of tumours. The model is neatly summarized in the picture by Paul Quast (below). If any of these factors is missing, tumours are either very homogeneous or extremely heterogeneous. We also show how ultra-local migration of cells speeds up growth of solid tumours and (see the video below).


© P. Quast- All Rights Reserved.

Our work has attracted some media coverage, see The Science Museum Blog, Edinburgh News, The Indepdendent, and Daily Mail. Noah Baker from Nature has also made this video that excellently summarizes our paper.

My PhD student Chay Paterson works on how cellular migration affects the growth rate and accumulation of mutations in tumours. In this preprint we study a simple mathematical model that works on the same principle as the above model but is analytically solvable. A Mathematica notebook and a file with simulation results accompanying this paper can be found here and here.

Simulation software/visualisation

If you want to simulate your own tumour, I have written this program (Windows only) which has a simple user interface enabling you to set the parameters of the simulation and run the code while displaying the growing tumour in a window. A video below shows how the typical output graphics looks like.

A full version of the code (Windows/Linux/Mac) used in simulations from the Nature paper which however does not have the graphics user interface is available here.

Simulation of a tumour composed of multiple lesions. When treatment begins, most of the tumour dies. This makes space for resistant cells that have occurred through spontaneous mutations during tumour growth and causes the tumour to re-grow. Different colours correspond to cells with different mutations. The more similar the colours are, the more genetically similar the cells are.

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