ESTRO Forum 2013

I'm currently attending the European Society for Radiotherapy & Oncology in Geneva, Switzerland. I feel slightly out of place amongst all radiologists and well-dressed oncologist, not to mention the salesreps trying to sell me massive MRI-machines and devices for brachytherapy (I admit I had to google that one). In any case I've been invited to speak about my work on modelling of metastatic spread and delivered the talk this morning. I focused on my recent work with Jacob Scott et al. from Moffitt on self-seeding, and I believe it was well received (at least I got a bunch of questions and comments).

Principles of Metastasis

I have recently become interested in the dynamics of metastatic spread, and together with colleagues at Moffitt Cancer Center, I have started to work on mechanistic models that look at the impact of the topology of the vascular network (e.g. here and here). When coming into this field I was surprised by the lack of work along these lines, and found that most people were delving deep into the genome of cancer cells to find the answers of why, where and how metastases appear.

I was therefore positively surprised to hear of the work of the late Dr. Leonard Weiss, who did a lot of work on metastases throughout his long career. In his work we find the physical perspective of metastatic spread that is almost completely absent in this gene-centric era. The other day I finally received his book "Principles of Metastases" from 1985, which I still believe to be highly relevant. A review will be posted when I've finished reading it, which should be soon.

The dynamics of cross-feeding

Many functions carried out by microbes, such as degradation of man-made toxic compounds, require the joint metabolic effort of many bacterial species. In such bacterial communities the success of each species depends on the presence or absence of other species and chemical compounds, effectively joining the components of the community into a microbial ecosystem. A common mode of interaction in such ecosystems is cross-feeding or syntrophy, whereby the metabolic output of one species is being used as a nutrient or energy source by another species.

I have together with my colleague Torbjörn Lundh formulated and analysed a mathematical model of cross-feeding dynamics. We show that under certain assumptions about the system (e.g., high flow of nutrients and time scale separation), the governing equations reduce to a second-order series expansion of the replicator equation. By analysing the case of two and three species we derive conditions for co-existence and show under which parameter conditions one can expect an increase in mean fitness.

The paper was recently published in Bulletin of Mathematical Biology:

http://link.springer.com/content/pdf/10.1007%2Fs11538-013-9828-3

Tumour self-seeding

The topic of tumour self-seeding, i.e. the idea that tumour cells leaving the primary via the blood stream come back and boost its growth has been widely debated and investigated (here, here and here to mention a few). I have recently, together with collaborators from Moffitt Cancer Center in Tampa, developed and analysed a model of this phenomenon. Our findings were published the other day in Royal Society Interface although a preprint has been on the arxiv for a while. To summarise: the phenomenon of tumour self-seeding is highly unlikely to contribute to the growth of the primary unless the circulating tumour cells form micrometastases which allow for an expansion in cell number sufficient to balance the severe losses that this hematic round trip incurs.

The model muddle

I've written a Perspective-piece on the basics of cancer modelling that was recently published Cancer Research. It can be found here, or here (if you don'y have access to CR). Enjoy the read!

I left an ansatz in Tampa

Scientific models

In connection to a course on modelling I've been teaching at the Mathematical Sciences, me and my colleague Torbjörn Lundh have written a textbook on scientific models. It has just been published by Studentlitteratur and can be bought online here. The scope of the book is quite broad and our aim is to cover all kinds of model that appear in natural science: from scale models of ships, to animal models of dieases and abstract mathematical equations. The current edition is in Swedish, but we are looking to publish an English version in the near future.