What are the constraints when growing an artificial brain?
The comments above are quite relevant -- we are years / decades away from growing functional brains in the lab, so there are probably innumerable constraints that we have likely not even thought of yet.

That being said, you might find this paper interesting: "Adaptive flight control with living neuronal networks on microelectrode arrays" [1]. The authors are able to succesfully culture rat neurons and electrically interface with them in order to control pitch and yaw in the XPlane flight simulation software.  It's a very crude system compared to an actual brain, but it's able to successfully use cells as rudimentary living neural networks. If you consider this to be a successful "artificial brain," then your constraints are all the ones associated with culturing neurons.

[1] DeMarse, et. al 2005