Imagine that you are in the army and your job is to move several hundred boxes, each weighing 100 pounds, from the dock to the trucks. You are average size so they provide for you an exoskeleton suite. Instead of it requiring your muscles to lift and carry the 100 pounds each time, to you, while using the suite it feels more like 10 pounds. Not so much of a problem moving your several hundred boxes.
In the brain we have neurons. They have many many inputs (dendrites). They have a single output (axon). In most cases the neurons form neural networks in very tight packed formations. But just as your computer has different parts, the brain functions which are formed from these tightly packed networks have outputs which need to go relatively long distances to other large networks with different functions.
It is like any large computer installation. Perhaps you have racks and racks of blade computers. Then you will also have a hugh number of long cables running all over the place to make the whole installation work to accomplish it's function.
The axon (output) of an neuron which goes only a short distance is simply doing it's job floating in the fluid. But if the axon must be long the energy needed to transport information over the long distance would tend to dissipate into the fluid. Welcome the glial (helper) cells! This particular class of glial cell wraps itself around the long axons and much like an exoskeleton makes it much much easier for the output of the neuron to go long distances.
So you come to work one day and they give you the bad news. Exoskeleton down!! But you still need to move all those boxes!!!!
In the areas of the brain where the neurons are tightly packed and need no “exoskeleton” the color is grey. Where a large population of neurons require these “exoskeletons” to to their job the color is white.
In those whose OSA is moderate to severe reductions in white matter in specific areas of the brain have been found[1]. It seems to vary the most consistently with the severity of the O2 desaturations. Also the areas noted are very specific. It is not a whole brain issue, it is more like specific areas of compromised white matter are created.
It seems to affect executive functioning.
[1]
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2491498/