If you injected human growth hormone, or something like that, into the brain, would it grow
The introduction of certain growth factors into the brain might stimulate something similar to growth, you could potentially get increased branching or sprouting of new terminals. It is dependent on where you inject it and what receptors are or are not there to respondto the agent. This wouldn't be advisable in the normal brain since in the mature state, it is not considered a dynamic system with a lot of growth and rearrangement. For the most part, the neurons you have once you reach maturity are the ones you keep forever (there are exceptions to this, but its not critical to this discussion). Another thing to consider is that there isn't a lot of room in the skull for additional growth. If you start adding on in one region, you will probably compromise the function of another.
The use of growth factors in the "non-normal" brain, ie, diseased or injured, is another issue and is an important focus of research efforts to aid these conditions. The problems in this case are targeting the appropriate growth factors to the region of interest, how to get them in there, how long do they need to be there, etc.
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