Don't take these as absolutes, but I've been thinking about how various Socionics functions could be related to the brain. Here are my conclusions:
Te: Related to the prefrontal cortex. The prefrontal cortex is the home of planning and organizing - the "executive functions." The executive functions are in control of goal-oriented behaviour.
Ti: Related to the left hemisphere. The left hemisphere is supposed to be the seat of logic and analysis.
Ne: I think that Ne is the function of the whole brain working together. My reason for thinking this is because there is supposed to be a brain drug that increases creativity, and what it does is increase the functioning of the corpus callosum. Supposedly, this increases the connection between the two hemispheres, and therefore, increases creativity. People who try the drug claim that they are able to generate more ideas when they take it. Now, I'm not saying that I believe the drug is effective, but it provides a theoretical framework for creativity. (And if Ne isn't a function of the whole brain, then I think it would be a function of the right hemisphere, as it is supposedly the seat of holistic thinking.)
Ni: Related to the temporal lobes. The temporal lobes have an interesting relationship with the perception of time. For instance, deja vu is supposedly a temporal lobe phenomenon. Also, I think that the temporal lobes are related to Ni because people with temporal lobe epilepsy become fixated on highly abstract subjects such as religion, philosophy and spirituality.
Fe: Related to the limbic system and the frontal cortex. Supposedly, the frontal cortex is highly related to social knowledge. Also, many emotions are produced by the limbic system and interpreted by the frontal cortex. Therefore, I think the relationship between the two systems produces Fe.
Fi: Related to the limbic system. If I remember correctly, in a lecture in my psychology class, it was mentioned that the amygdala (a structure in the limbic system) is over-active in people who have social anxiety. It seems to me that social anxiety is a function of sensitivity. The limbic system is also supposedly responsible for generating emotions. Therefore, I would associate the limbic system with Fi. (You might say that the frontal cortex could be involved for the same reasons as for Fe, but, in my opinion, the fact that limbic structures are overactive in social anxiety, while the frontal cortex is supposedly good at social skills, points to the notion that Fi is solely a limbic system phenomenon.)
Si and Se: Related to the parietal lobe. From what I understand, the parietal lobe is supposedly the part of the brain that is aware of where your body is located in space, the senations in your body, and sensations that come from outside of your body.
Keep in mind that these are only ideas based on my knowledge of the brain. There is probably more complexity to these functions than that they are simply based on a limited area of the brain. Whole networks of neurons could be involved, using multiple areas of the brain. The pattern or form that some of these networks take could indicate the nature of the functions. However, I don't know enough about the brain to draw any conclusions about this (and perhaps no one knows enough about the brain to explain how it actually corresponds with behaviour).