nrz is on the right track with the epilepsy example. One of the limiting factors in the use of our brain is the amount of free molecules of the neurotransmitter glutamate. Having too much free glutamate can cause a phenomenon known as excitotoxicity. This phenomenon is also seen in conditions such as stroke, where damaged cells release their entire load of glutamate due to hypoxic damage.
Once glutamate has been bound with a post-synaptic cell, it must be taken up by neuroglia (supporting cells), which are present in great number in the surrounding milieu, metabolized into glut*amine* (inactivated), and recycled for repackaging and reuse in the neighboring neurons .
In the case of epilepsy (or in the theoretical case of your question, overusing your brain), the glial cells proliferate rapidly, which paradoxically causes a slowing of the transformation of glutamine back into glutamate. This is presumably a homeostatic mechanism.
So, from my own reckoning, it would seem like a rapid increase in function would cause excitotoxic damage in the short term, and lead to a slowdown in the metabolism of fresh transmitter in the long. Granted, there are other transmitters that are active in the cortex, but glutamate is the most abundant.
 Coulter, D.A., Eid, T. (2012) Astrocytic Regulation of Glutamate Homeostasis
in Epilepsy. Glia., 2012 May 16. doi: 10.1002/glia.22341. [Epub ahead of print]