Is there any evidence that this is what is actually driving the movement in vivo? Also I am wanting to knw what specifically glioblastoma cells are (hypothetically) moving towards, this is an important part of my model. Thanks.

I would say that cancer cells are not necessarily moving toward something per say, but away from a depleted environment caused by the increased density of cells. But even without a gradient of cells or some substance in vitro, you see cancer cells move, so there is both an external and internal mechanism for invasion. But if you consider the interior of the tumor as "abnormal" and the exterior as "normal", they might move up a gradient of oxygen, nutrients, and growth factors (VEGF, PDGF, TGF) that would be more normally distributed outside of the tumor or be produced by the cancer cells themselves or from the stromal cells. Also, when GBM starts to present with necrotic regions, there are probably both repelling and attracting gradients at these interfaces. 

Indeed Jill, indeed, it's not quite so simple as I would like it to be, sadly.  As a mathematician/medic and not a 'real' biologist, I am seeking to model the behaviour and growth mathematically, so I need to understand the biology so I can model it as neatly as possible.  Oxygen gradient is clearly a factor for when the tumour gets bigger and undergoes necrosis, I guess the compelling question from our end is what is driving the highly motile cells that invade deeply into th brain?  On the boundary of the non-necrotic tumour there will be stress dynamics, haptotaxis, chemotaxis and so on, but the invading cells seem to travel down 'the path of least resistance' i.e. white matter tracts, what is the primary driving force here? 

I'd say that you answered part of it - it's the path of least resistance. The white matter is made of glial cells and myelinated axons that are long, and provide a "highway" for cells to move along. There are also blood vessels that tend to run along the same paths, which help direct movement. The grey matter, on the other hand, is very tortuous so there is more resistance for invasion. But just because there's a pathway doesn't mean that a cell will move along it. There is more to invasion than the anatomy in which cells reside, but it's a start.

Math modeling of GBM is certainly not new, and there are a ton of publications concerning math models of GBM invasion. People have asked this question before, and it's not simple, but like any complex biological modeling effort, you clearly define your question so that you can only include the most significant pieces that affect your precise question. Here's a few related articles.

Grey and white matter invasion model:

http://www.ncbi.nlm.nih.gov/pubmed/11063134

Some reviews on GBM modeling:

http://www.ncbi.nlm.nih.gov/pubmed/17204931

http://www.worldscientific.com/doi/abs/10.1142/S0218202505000960

Biological models on GBM motility:

http://www.ncbi.nlm.nih.gov/pubmed/19428961

http://www.ncbi.nlm.nih.gov/pubmed/16541395

Thanks Jill, we have looked at the mathematical literature surrounding this problem which is, as you say, not new.  It's still pretty hopeless in terms of giving any useful clinical predictions or for planning treatment though.  We do hope to add something different with our approach, as we move toward more detailed models, I will need to know what the latest biology says on the topic to guide the math.  That's the part I haven't read up as fully.  Those biology links are useful, thanks.  I'd read all the math papers already and there is some much more up to date work out there, some of your colleagues at Moffitt have done some good work on this stuff, I have been in communication with some of them while I have been reviewing the existing literature so far.