Also - if you're interested in background on systems biology - there's a broad overview of UCLs biological modelling research group here (http://discovery.ucl.ac.uk/10844/1/10844.pdf [pdf]) - they've got a project modelling the liver / blood-sugar-system.
Apparently the canonical example that has worked pretty well is a computer model of the heart but I think it's a simpler organ in that it's mostly electro-mechanical, without such a complicated chemical system (http://www.sciencemag.org/content/295/5560/1678.abstract - behind Science paywall)
There is actually quite a ways to go before we have high fidelity macro models of the heart in action. (The numerical research I do is closely related). 3D fluid simulations are expensive. Hopefully the quasi-discreteness of the brain reduces the computational requirements for a high fidelity simulation.
Ha, that's funny, that model was the one UCL referenced in their kinda 'This is possible' motivation. I find it all very interesting, but gave up after a year as I felt like a lot of the models were going to be a bit flaky for the next decade and that was a bit of a culture shock (I was a physics student before).
Apparently the canonical example that has worked pretty well is a computer model of the heart but I think it's a simpler organ in that it's mostly electro-mechanical, without such a complicated chemical system (http://www.sciencemag.org/content/295/5560/1678.abstract - behind Science paywall)