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A lot of articles stress the importance of having to train the brain (By training the brain, I mean the cognitive faculty of the brain for learning things and not brain's normal functions) since the brain is a muscle and training it would improve its cognitive abilities.
Since using anything beyond a limit is detrimental to it, is there a theoretical limit to the use of brain beyond which it would be detrimental to the brain?
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 [1].
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[1].
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.
[1] 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]
Intensive stimuli may trigger epileptic shocks in some individuals. At least prolonged epileptic shocks may damage neurons, I'm not sure about short epileptic shocks. So the answer is yes, using your brain eg. your extended visual system to process excessively intensive visual stimuli may cause epileptic shocks and thus be detrimental to the brain.
However, as far as I know, visual stimuli are not able to cause epileptic shocks to everyone (susceptibility to epilepsy is a requirement), so I'm not sure if there is any proven way how by you could cause brain damage only by brain function (without aid of any voluntary motoric movements) in any individual.
As intensive visual and auditory stimuli are a part of our natural environment - whereas lack of stimuli (sensory deprivation) is an unnatural state - I think triggering epileptic shocks by intensive stimuli can not be considered only as a self-caused way of damaging the brain.
A few thoughts:
A lot of articles stress the importance of having to train the brain
Much of this literature is used to sell computer games and crossword puzzles. In a recent review, Owen et al (2010) concluded that the proposed benefits of brain training lack empirical support. There is a vast literature which suggests that practice is the basis of skill acquisition but that skill acquisition tends to be focused on what is practised. Thus, if you want to get skilled at crossword puzzles, then do crossword puzzles; if you want to get good at a computer game, practice the computer game.
(By training the brain, I mean the cognitive faculty of the brain for learning things and not brain's normal functions)
Learning is a normal function of the brain.
since the brain is a muscle and training it would improve its cognitive > abilities.
As mentioned by @John, brain as muscle is a metaphor. The brain does forget things, and forgetting can be adaptive. Thus, if you want to maintain or develop particular skills, then you should practice them.
Since using anything beyond a limit is detrimental to it, is there a theoretical limit to the use of brain beyond which it would be detrimental to the brain?
This seems like a big question. There is plenty of research on fatigue and stress which would suggest that getting adequate rest is important to maintaining optimal cognitive functioning.
