Which roman physician took up the theories of hippocrates and extended them with a theory that normal brain functioning is related to a proper balance of four bodily fluids or humors?

I believe the answer is Galen
At that time, Galen was one of the most reknown surgeon in his entire kingdom. Prior to his theory, the majority of people at his society believed the existence of Soul and think that heart is the organ inside our body that controls the activities of other organs.

It would be around the egyptian area.