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.

The Impact of Phenotypic Switching on Glioblastoma Growth and Invasion

Recently we had a paper accepted in PLoS Computational Biology, which introduces and analyses an individual-based model of glioblastoma (brain tumour) growth. From the author summary: In this work, we develop a spatial mathematical model in order to analyse the growth behavior of the brain tumour glioblastoma. Tumours of this type have a diffuse boundary, with considerable local invasion of surrounding brain tissue, making surgery difficult. At the cellular level, the progression of a glioblastoma is known to depend on the balance between cell division (proliferation) and cell movement (migration). Based on recent evidence, our model assumes that each cell in a glioblastoma tumour resides in either of two mutually exclusive states: proliferating or migrating. From a probabilistic model of switching between these two phenotypes, we go on to derive equations that link cellular phenotypes to disease progression. The model has several possible applications. For instance, it could be used to predict the rate of disease progression in an individual patient, and to improve screening methods. And here's the first figure which describes the stochastic switching of cell phenotypes. 

Alan Turing at 100

Nature have published a special issue to commemorate the 100th birthday of Alan Turing. His contributions to mathematics, computer science and biology are unrivaled in the 20th century.

Online issue

Oxford

Last week I went to Oxford to give a talk at the Maths department and to visit my friend Jacob Scott currently studying for his DPhil there. I must say I enjoyed the trip in many different ways: great academic atmosphere, lovely town, live rugby and nice company. Some photos: