Introducing mathematical oncology to cancer biology and medical students

This Wednesday, as I did last year ago, I am helping with a lecture series entitled Modern Basic Tools of Research at the Moffitt Cancer Center. Last year’s was a pleasurable experience and for 2h we talked about different ways to model growth in tumours. First with growth laws describing population change over time (examples of those laws can be found here), then with more mechanistic models where the dynamics of the tumour growth emerge from the way that different cells interact with each other and with their environment.

This year going that far will be more difficult: my 2h have been reduced to 30m. Thus I am trying to change the focus of the lecture and maybe limit my ambitions. Interestingly this could be a blessing in disguise since I might be forced to try to figure out what is the essence of mathematical modelling of cancer and explain that to smart people that do not have a background (or maybe not even an interesting) in mathematical modelling.

And why 30m this year? Because due to time constraints, the same 2h lecture slot will be used to teach about biostatistics, bioinformatics and mathematical modelling. And that is good: since I have been working in this field every biologist and medical professional I met expected me to be a statistician after describing myself as a mathematical oncologist. This is going to be a great opportunity to explain what we have in common but also the ways in which we work differently.

Hoping to not misrepresent excessively what biostastisticians and bioinformaticians do (expect a line saying UPDATE at the end of this post very soon!), their work is incredibly useful to both cancer biologists and doctors since it allows them to figure out what the data says about a specific biological process or clinical trend. It also allows them to know whether that trend or pattern is meaningful or not or whether they have collected enough experimental points or clinical data to make any statement about it.

The best part is that all that extra information usually comes at very little cost to the experimentalists. Mathematical oncologists on the other hand, we tend to be somewhat more difficult to work with since we need to have an understanding of the biological mechanisms underpinning the cancer we are studying. We, for instance, take a look at the diagram after the first paragraph and think: do all these cell interact with each other? if so how? these tumour cells, are they all the same? where do they come from? do they come alone or together? do they usually arrive in the neighbourhood of the other cells in the diagram? if not, do they sit and wait? Maybe some of the questions would be part of the conversation between experimentalists and but many of them seem to arise when mathematical and computational modellers are involved. When implementing these ideas into a computer, ambiguities are not an option. Ideas that might work in your mind or mine come crashing down when subjected to the cold logic of a computer.

It takes time.

The advantage? We can test new hypotheses, generate novel ones, get molecular, clinical, cellular data and integrate it into the model, we can get all those single cell level measuraments and feed them directly into the model, we can take all these population level experiments and figure out what hypothesis explain them better. We can use that to understand the biology of the cancer, to design new biological experiments, to predict better clinical treatments, to hypothethise how new ones would impact patients in the clinic.

If you are an experimentalist you should know that using mathematical model will require you to work in a different way, to ask different questions and to view of your research with different lenses but it is worth it.
By the way, all the figures in the post have been crafted by our very own +Arturo Araujo .