# Hackathons and a brief history of mathematical oncology

October 28, 2017 2 Comments

It was Friday — two in the morning. And I was busy fine-tuning a model in Mathematica and editing slides for our presentation. My team and I had been running on coffee and snacks all week. Most of us had met each other for the first time on Monday, got an inkling of the problem space we’d be working on, brainstormed, and hacked together a number of equations and a few chunks of code to prototype a solution. In seven hours, we would have to submit our presentation to the judges. Fifty thousand dollars in start-up funding was on the line.

A classic hackathon, except for one key difference: my team wasn’t just the usual mathematicians, programmers, computer & physical scientists. Some of the key members were biologists and clinicians specializing in blood cancers. And we weren’t prototyping a new app. We were trying to predict the risk of relapse for patients with chronic myeloid leukemia, who had stopped receiving imatinib. This was 2013 and I was at the 3rd annual integrated mathematical oncology workshop. It was one of my first exposures to using mathematical and computational tools to study cancer; the field of mathematical oncology.

As you can tell from other posts on TheEGG, I’ve continued thinking about and working on mathematical oncology. The workshops have also continued. The 7th annual IMO workshop — focused on stroma this year — is starting right now. If you’re not in Tampa then you can follow #MoffittIMO on twitter.

Since I’m not attending in person this year, I thought I’d provide a broad overview based on an article I wrote for Oxford Computer Science’s InSPIRED Research (see pg. 20-1 of this pdf for the original) and a paper by Helen Byrne (2010).

Most researchers in the field are familiar with the use of mathematical (and computational) models in the physical sciences. It has been a defining feature of those fields for hundreds of years. Over the last few decades, mathematical modelling has started to play a bigger and bigger role in medicine, including oncology.

It is always hard to find firsts, but a popular candidate for the first mathematical model in oncology is Armitage & Doll’s 1954 multi-stage theory of cancer. They modeled the age distribution of cancer incidence and developed a theory that the prevalence of cancer will increase with a power of age that is one less than the number of changes needed for its progression.

But the biggest push for mathematical models of cancer started in the 1970s. Greenspan (1972,1976) introduced mechanistic models of growth by modelling tumour spheroids. These masses of pure tumour tissue were not overly realistic: the lack of blood vessels in these avascular tumours made many fundamental questions inaccessible. But the tumour spheroids were consistent and reliable in the lab and allowed for a closer coupling of theory and experiment. Around the same time, looking instead to the clinic, Wheldon et al. (1977) introduced an effective theory of the linear-quadratic model for cell death under radiotherapy. This model that is now used to calibrate treatment protocols.

In the late 80s, the first mathematical models of angiogenesis — the recruitment and co-opting of blood-vessels by tumours, were proposed by Balding & McElwain (1985). These were still models based on differential equations and continuum approximations of large numbers of cells. But unlike avascular tumours, the experimental systems for studying angiogenesis were much less consistent and much more chaotic in their dynamics. Whereas avascular tumours looked relatively similar to each other, (mostly differing in the sizes at which they switched from exponential to linear growth and then finally stabilised), the vascularised tumours could look completely different from one to the next. And this heterogeneity between tumours was central to clinically relevant difference, like the rate at which a tumour could invade other tissues (metastasize). It is one of the reasons why your doctor might be more worried about a new mole with irregular boundaries than a circular one.

To address this challenge, the community moved towards explicitly stochastic and discrete agent-based models in the 1990s. These models allowed for easier communication with experimental biologists and parametrising from existing measurements in the literature. But they also forced mathematical oncologists to rely heavily on simulations and parameter sweeps. The many, often implicit, modelling choices that researchers make (researcher degrees of freedom) also allowed for conceptually different models to have very similar observable dynamics. This made the task of model selection very important and encouraged mathematicians and computer scientists to work more closely with biologists and clinicians. By the early 2000s, A.R.A Anderson and colleagues (Anderson & Chaplain, 1998; Anderson, 2005) introduced multi-scale hybrid models that combined discrete cells with continuous diffusion of chemical species like oxygen or growth factors.

To parametrise, these models needed to combine data collected under varying conditions and in different experiments. Modellers also needed to communicate with each other, spurring the development of open source multi-scale tools like CompuCell3D, TU Dresden’s Morpheus, or Oxford’s Cancer, Heart and Soft Tissue Environment (CHASTE). And labs across the world needed to communicate to each through data standards like Systems Biology Markup Language (SBML) and MultiCellDS. And although these complex models of cancer have not made it their way to the clinic, yet, mathematical oncologists look to other computational models in medicine for inspiration. In particular, to computational models of the heart by Denis Noble and his colleagues at Oxford and elsewhere, that are now FDA approved for drug testing.

Breaking through silos, reconciling data, and serving as connectors between different areas of biology became a more integral part of the modeler’s work. This was made possible in part due to large collaborations among computational biologists, mathematicians moving to cancer centres and research institutes, and hybrid-modelers — who wear both the hats of clinical doctors and mathematicians.

The integration continuous today, as a community we are able to quickly absorb mathematical and computational tools and techniques from other disciplines. Through this mathematical oncologists are helping to budge the ingrained paradigm that cancer is a cell-autonomous process, and that the defining properties of a cancer are just properties of individual cells (like their genotypes). By bringing in tools from ecology & evolutionary biology, we can start to view tumours as heterogeneous evolving ecosystems where the cell’s microenvironment can play a determining role in disease progression. For example, David Basanta and colleagues have used evolutionary game theory to reason about the strategies that cancer cells adopt for propagation and survival.

But the biggest contribution of mathematical oncology isn’t any particular model or technique. Our biggest contribution is the dialogue with experimentalists. Theorists help motivate new experiments and hypotheses, propose new measurements. Experimentalists give theorists an endless supply of subtle and complex problems to challenge our tools and understanding.

Mathematicians and computer scientists can clarify and challenge the paradigms in cancer research, and cancer researchers can give us challenges and motivations for new kinds of mathematics and refinements of exiting tools. The field is too young — and most experimental biologists are too uncomfortable with equations — to allow us to rely exclusively on journals for communication. Instead, we flourish when we are brought together into integrated teams that combine experiments, clinical care, and modelling. For this, hackathons like the Integrated Mathematical Oncology Workshop and inter-disciplinary groups are an invaluable resource.

And, although a week-long hackathon or even dozens of carefully-calibrated and validated models won’t cure cancer, the discussions started and contributed to by mathematicians and computer scientists contribute to our progress against this malady.

It was this hackathon back in 2013 that played a central role in exposing me to mathematical oncology and led to my work in the Department of Integrated Mathematical Oncology at the Moffitt Cancer Center. That Friday morning fine-tuning and all the hard work of my teammates didn’t get us the fifty thousand start up funding but helped our team come in second place.

I was hooked.

I returned in the three subsequent years to think about *H. Pylori* and stomach cancer; CAR T-cell therapy for lymphoblastic leukemia; and dark selection in chronic myelomonocytic leukemia. For two of those times, our team even won the start-up grant.

This week, five teams are continuing the competition. Wish them luck and follow along on twitter.

### References

Anderson, A. R., & Chaplain, M. A. J. (1998). Continuous and discrete mathematical models of tumor-induced angiogenesis. *Bulletin of Mathematical Biology*, 60(5): 857-899.

Anderson, A. R. (2005). A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Mathematical medicine and biology: a journal of the IMA, 22(2), 163-186.

Armitage, P., & Doll, R. (1954). The age distribution of cancer and a multi-stage theory of carcinogenesis. *British Journal of Cancer*, 8(1): 1.

Balding, D., & McElwain, D. L. S. (1985). A mathematical model of tumour-induced capillary growth. *Journal of Theoretical Biology*, 114(1): 53-73.

Byrne, H. M. (2010). Dissecting cancer through mathematics: from the cell to the animal model. *Nature Reviews Cancer*, 10(3): 221-230.

Greenspan, H.P. (1972). Models for the growth of a solid tumor by diffusion. *Studies in Applied Mathematics*, 51(4): 317-340.

Greenspan, H.P. (1976). On the growth and stability of cell cultures and solid tumors. *Journal of Theoretical Biology*, 56(1): 229-242.

Wheldon, T. E., Kirk, J., & Orr, J. S. (1977). Optimal radiotherapy of tumour cells following exponential-quadratic survival curves and exponential repopulation kinetics. *The British Journal of Radiology*, 50(597): 681-682.

Before Greenspan, Mayneord in 1932 may have been the first to have combined data and theory to understand the growth law of tumours, see here: http://cancerres.aacrjournals.org/content/16/4/841 . I’ve been using the ideas for years to analyse data in cancer drug development in both xenografts and humans.

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