Here is a link to a very thorough and highly researched article by Dr. Stephanie Seneff of MIT discussing the importance of fat and cholesterol, how they work in the brain, why statin use may be counterproductive for people at risk for and dealing with Alzheimer's, the function of beta amyloid and why a high fat diet may be beneficial. I found this especially enlightening in its explanation of how cholesterol is packaged as it is transported throughout the body, and what it is packaged with in LDL particles, for example, may be a surprise.
http://coconutoil.com/the-clue-to-why-low-fat-diet-and-statins-may-cause-alzheimers/
Dr. Seneff has written many other similar articles of great interest to those concerned with cholesterol, statins, Alzheimer's, autism and other neurodegenerative diseases, many of which can be downloaded from her homepage.
http://people.csail.mit.edu/seneff/Labels: Alzheimer's, Apoe4, beta amyloid, cholesterol, high fat diet, ketogenic diet, ketones, statins