Walnuts are often known as a "brain food," not only because of the wrinkled brain-like appearance of their shells, but since they high concentration of omega-3 fats. For your brain cells to function properly, this structural fat needs to be primarily the omega-3 fats found in walnuts and cold-water fish.
The cell membranes of our body including the neurons in our brain are composed of fats. They are the gate keepers to allow certain things and disallow others into the cell. Omega 3 is especially a fluid which makes the whole process a lot easier, thus maximized the cells ability to promote nutrients and eliminating wastes, a good way to keep them away.