hhhhmmmmm......well there is the metaphor of the blind men trying to understand an elephant
http://en.wikipedia.org/wiki/Blind_men_and_an_elephantand often when trying to understand the brain we feel like we are nothing but blind men......
these remarks must be countered with the comment about the trade-offs between complexity and simplicity in a logo design.....
experimentation is always the best way with both approaches, designs favoring simplicity and designs favoring complexity
in terms of spatial layout, graphic side-by-side with name in stacked column of words Brain and Health and Alliance probably will be favored for website banner layout at top of page