As for the original question - I think most people realize that the big in big data rarely refers to the actual size (volume) of data but rather that we still do not have very efficient techniques for doing certain kinds of data processing when the underlying data simply won't fit into the relational model. A good example is text - there is a reason why Google uses some kind of inverted index and not a relational database in which it stuffs all the web page text.
I don't really know if the medical field has any use for text mining, graph processing and the like. While recommending Hadoop just because the size is in excess of 1 TB looks knee jerk, someone being down-voted for a fairly non-opinionated comment where they suggest exploring use cases before deciding is even more knee jerk.