Eating a high cholesterol diet is not going to harm your brain but eating a chronic high cholesterol diet can, according to researchers from the Laboratory of Psychiatry and Experimental Alzheimers Research at the Medical University Innsbruck in the journal Molecular Cellular Neuroscience.

Like many things, it can even be implicated in Alzheimer's.    

The researchers studied hypercholesterolemia in adult rats. Male Sprague Dawley rats were fed with normal food in the controls or with a special 5% cholesterol-enriched diet (the hypercholesterolemia part). After 5 months animals were tested for behavioral impairments and the results showed that chronic hypercholesterolemia caused memory impairment, cholinergic dysfunction, inflammation, enhanced cortical beta-amyloid and tau and induced microbleedings, which resemble an Alzheimer's disease-like pathology. 

So they conclude that high fat lipids, including cholesterol, may participate in the development of sporadic Alzheimer's disease.   Alzheimer's disease is a complex heterogenous disease so it can't be concluded that cholesterol alone is responsible for the disease.