Algorithm Space and Time Complexity with Consideration for I/O (eg cache)

Is there an expression of performance for an algorithm or data structure that attempts to consider cache and other hardware concerns?

Context: in my class we're looking at binary trees and it seems like it would be extremely difficult to optimize data retrieval with the structure. I know B-Trees address this problem, but I haven't seen a formal analysis of how much speed is improved considering some amount of cache.