Thursday, 10 March 2016

Travelling wave analysis of a mathematical model of glioblastoma growth

This paper has been on arxiv for a while (and the work dates back to 2011), but it was at last accepted for publication in Mathematical Biosciences after 1.5 years of review. The paper contains an analysis of a PDE-model of brain tumour growth that takes into account phenotypic switching between migratory and proliferative cell types. We derive an approximate analytic expression of the rate of spread of the tumour, and also show (and this is in my view the most intruiging result) that the inverse relationship between wave front steepness and its speed observed for the Fisher equation no longer holds when phenotypic switching is considered. By tuning the switching rates we can obtain steep fronts that move fast and vice versa.

Accepted version: http://arxiv.org/abs/1305.5036 

Wednesday, 30 September 2015

Creative force fields

Yesterday (29th september) I made an appearance as an opponent at a seminar on the topic of mathematical modelling for predicting the spread of culture (Swedish title: "Kan algoritmer ge oss bättre förståelse för kultur och regional utveckling?").

The work that I was reviewing was that of Massimo Buscema at the Semeion Institute in Rome, who has been collaborating with several counties in Sweden in order to make predictions of how culture in the region will grow in the future.

The central tool for this analysis is the 'topological weighted centroid' (TWC) which can be viewed as a generalisation of centre of mass of set of points representing cultural activities.

I am highly critical of the validity and utility of these tools, since it is unclear what the TWC actually represents.

If you want to know more please have a look at the video:

http://bambuser.com/v/5820575

(I make my appearance around 2:20 into the video)

Tuesday, 18 August 2015

Photos of nature

This summer I spent almost two months in a cottage in the Swedish countryside with my family. The cottage is fairly isolated with the closest neighbours a kilometer or so away. This meant living closer to nature than I have ever done, and resulted in me taking an interest in the flora and fauna of the surrounding meadow and forest. The below photos document some of my findings. I will in future post (with the tentative title 'The doubts of a mathematical biologist') write more about my impressions of living close to nature.

Crab spider that has caught a hover fly.

Mini forest

Dragon fly trying to hide

Lady bug

Cloud berry that is slowly ripening

Pine sap (Monotropa hypopitys) is plant without clorophyll that parasitises on fungi

Common self-heal (Prunella vulgaris)

Cross spider (Araneus diadematus)

Poppies

Unknown spider taking a walk on the clothes line

Monday, 17 August 2015

The evolution of carrying capacity in constrained and expanding tumour cell populations

My position at Moffitt Cancer Center certainly payed off in terms of research output. Recently my second paper based on work done at the Integrated Mathematical Oncology group was published. The paper investigates the dynamics of carrying capacity evolution in tumours and was written together with Sandy Anderson. The paper is published in Physical Biology, and was chosen as a "featured article" and is therefore open access for a limited time.

A copy can be found here, and the arxiv-version here (which will remain open access forever).

Illustrating the evolution of carrying capacity (A) and growth rate (B) in a constrained population of tumour cells.

Monday, 29 June 2015

Complexity and stability in growing cancer cell populations

Me and Philipp Altrock recently published a comment on a recent paper by Archetti et al. in PNAS. Their paper was about the dynamics of growth factor production in cancer cells. The study contained some beatiful experimental work, but we had some concerns about the theory presented to explain the data.

Read our comment here, and the response by Archetti et al. here, and judge for yourselves.

Dynamics of tumor growth (1964)


[The tumor] grows as though it were a single organism, rather than as a population of dissociated individual cells, each the progenitor of an independent line of tumor cells, as presumably bacteria and other free cells do when inoculated into a new culture medium. This relation suggests further that the host plus tumor represents a new, integrated system of growth whose nature we do not as yet understand. 
 
Anna Kane Laird, Dynamics of tumor growth, British Journal of Cancer (1964)
 
Now, 50 years on some people still think of cancer cells as independent beings that can be eradicated with toxic enough drugs. I think mathematical modeling can and will aid in pushing the above half-century old perspective on cancer.

Monday, 23 February 2015

Back from the back burner

During my postdoc at the Niels Bohr Institute i started working on a manuscript about asymmetric mutations rates and its implications for the fitness landscape methaphor. I was never able to tie that paper together and it has been lying around for almost 5 years collecting dust. Recently I told Dan Nichol about my unfinished work, and after having read the draft asked me why I never tried to communicate the results. I didn't really have a good answer, so instead I sat down and cleaned up the draft and turned it into something readable.

I'm not quite sure it reaches publication standards so for the moment I've uploaded it to bioarxiv.org. If you have any suggestions for where it can be submitted please let me know.

Directional variation in evolution: consequences for the fitness landscape metaphor.