My vision is clearly not 20/20, otherwise I would have remembered that in a presentation like the one I gave last week, you are meant to devote part of your talk to what you intend to do, science-wise, in the medium/long term.
During the talk I described, once again, my view of cancer as something that cannot be properly undestood in isolation. A small community of cancer researchers, one in which I include myself, thinks that it is better to talk about the ecosystem of cancer [blog post][blog post]. I am interested in understanding how the interacions between the tumour cells (which is a very heterogeneous population of cells), regular non-cancerous cells and the physical microenvironment shapes selection. Here’s our usual picture of how a cancer ecosystem can look like. Bone cancer ecosystem:
One of my colleages at Moffitt, Aga Kasprazak, raised the question of how would I use these ideas to help cancer patients. Very valid question and easy to explain. The main problem with all the treatments we got is that, very often, the tumour evolves resistance to them. Treatments become part of the evolutionary process and strongly select for any tumor phenotype that, on its own or via interactions with the microenvironment, could withstand a little bit better than the others its impact. We then need to understand how evolution, and as part of that, how selection plays a role in treatments. An ecological undestanding of cancer will allow us to guide evolution to a tumour that is less lethal, more treatable. That means that treatments could be designed, not with the aim of killing as many tumour cells as possible, but to transform the tumour: to make it less heterogeneous, less invasive. That will not happen tomorrow but for this to be a reality we need to start rethinking the purpose of the treatments we use.
Thanks to Heiko Enderling, our department has started a programme, which we call HIP-IMO where high school students get to spend the summer at Moffitt working on mathematical models of cancer. So meet Raj Warman, from the Academy at the Lakes, that will spend the next few weeks learning about evolutionary game theory and bone cancer. He looks excited, doesn’t he?
First, a bit of good news: together with the Lynch lab, our group has been awarded a grant from the state of Florida to better understand cancer heterogeneity and Darwinian evolution in bone metastases. We will be using mathematical models, motivated/parameterised/validated in vivo by Conor Lynch, and his group, to figure out how the interactions between heterogeneous cancer cells and bone cells (osteoclasts, osteoblasts, macrophages, etc) shape selection and how the metastasis evolve. Given our partnership with the guys at the GU clinic at Moffitt, there is a good chance that our work will be relevant to patients sooner rather than later.
As a result we can recruit a postdoctoral researcher to help us with this work. It will be a fun ride, do you want to join us?
What are we looking for? a mathematical and/or computational modeler
Do I need to know about cancer? bone metastases? No, but knowing about it is part of the job so if you don’t then you should be happy to learn about it because…
Do I have to care about cancer biology? Yes, we are part of the integrated mathematical oncology department. The ethos of the department and of this group is that experimentalists and mathematical modelers working together can do a lot more than either of us on our own.
What is this Integrated Mathematical Oncology department you speak of? Glad you asked…although I imagine that you are not a regular of these pages.The department is probably the largest and oldest department of mathematical modelers in a cancer research institute. Coincidentally most of us are working on different aspects of and factors on how cancers evolve.
If this integration is so important…who exactly will I be integrating with? On the experimental side, the Lynch lab. Most experimentalists don’t care for/understand the role of mathematical modelling but these guys do! We meet a few times a week, attend their lab meetings, they attend our seminars. They are fun people to work with. On our side the unimitable Arturo Araujo and yours truly.
This looks interesting, but why don’t you give me more details about the specific type of person you are looking for? Because I don’t want to, frankly. I have seen and worked with some very talented mathematical modellers in the past, and buzzwords in the CV are usually a bad metric to tell apart great modellers from good ones.
Today, I’ll show how to simply visualize 3D tumor using MATLAB’s isosurface function combined with a simple blurring technique.
First, we will modify the code from the previous post in order to simulate tumor in 3D. There are only a few changes: redefinition of the domain and the neighborhood; generating permutations on the fly instead of storing them in Pms varaible; and the way in which the initial cell is placed.
Using the above code I simulated two tumors that have different growth characteristics, both with pmig = 5/24 and one with ps = 3/10 and the other one with ps = 5/100. Now we need to visualize them.
Having the whole tumor stored in the L variable we can use isosurface function straight away and plot the tumor as it is. The only thing that we need to do is to remove the cells from the L boundary.
Evolutionary Game Theory (EGT) is an incredibly useful mathematical tool in which to frame how the interactions between different cell types shapes selection and thus the evolutionary dynamics in cancer.
One of the virtues of EGT is its simplicity. This makes it possible to approach complex problems in a qualitative manner without having to make too many assumptions. The drawback is that some times we need to dive in into a specific area of the problem in a way that conventional EGT does not make easy. One such area is space. Space is known to play a role in many key aspects of cancer but conventional EGT treats it only implicitly.
Many people have tried to understand the role of space in various types of games, mainly by letting the players play in a grid. Although a sufficiently adequate solution for many interesting questions, those models are often too complex to be studied analytically. A different approach is to use something like the Ohtsuki-Nowak transform. This would not mean that we can model space explicitly but at least we would have a first-order approximation to it.
Today, the paper that Artem Kaznatcheev, Jacob G. Scott and yours truly started a couple of years ago, is now online at the Royal Society Interface journal [link]. In it we use the ON transform to study how the evolutionary dynamics change when, during tumour growth, tumour cells reach a hard edge like the bone and, in that way, change the number of neighbours with which they will interact in their game.
Artem has done a great job of explaining our work with the ON transform [link] before [link][link][link] so, whatever format you want to use to learn about how we used it, enjoy!.