Philip Maini is one of the most entertaining speakers (entertaining in the good sense, of course) in the European biomathematical community. Prof. Maini is the director of the Centre of Mathematical Biology at Oxford University and gave in Lyon a talk entitled "Modeling aspects of cancerous tumour dynamics".
The modeling aspects he mentions are three different projects:
1) The first project, in which he collaborates with people like Gatenby (Arizona) and Gavaghan (Oxford) studies the acid mediated invasion hypothesis.
According to (my interpretation of) this hypothesis, when tumour cells lack oxygen and start to starve then a mutation might appear that would make some cancer cells switch to what is called glycolitic phenotype. This means that these cells have an alternative metabolism that works without oxygen and that is not as efficient as the regular one. The reason why this alternative phenotype has a chance of success is because the waste produced (galatic acid) can be used to degrade the extra cellular matrix and lead to invasion of other tissue. Gatenby, Gavaghan and Maini came with a model in which tumours contain cells with the glycolitic phenotype. The results is that tumours are not benign and that an possible explanation for the existence of necrotic cores (material generated when cells die disorderly because of starvation) can be the result of too much acidification of the environment, even for acid-resistant glycolitic-type tumour cells.
2) Metabolic changes during carcinogenesis. Also with Gavaghan and Gatenby and referring to research covered by a paper in Nature reviews cancer (vol 4, 891-889, 2004). They study somatic evolution in a system in which tumour cells can be of one of three different types: hyperplastic, glycolitic or acid-resistant. These cells inhabit the space of a 2D lattice in which there is oxygen, glucose and hydrogen that diffuse in a continuous manner. Altering the reach and concentration of these elements leads to different numbers of cells displaying one or the other phenotype.
For me this is a good place in which to see how game theory could be used to study the interactions of different players (cancer cells) using different strategies (the different phenotypes) to maximise their payoff from the environment (O,H,glucose).
3) Together with Benjamin Ribba (Lyon, organiser of the workshop and one guy I am working with as of lately) Maini works on a multiscale model on which to study the differences between the vasculature generated by the normal process of vasculogenesis and the ones generated by tumour cells capable of angiogenesis. One of the conclusions he mentioned: don't trust parameters.