See, I thought it was related to branches too (think of brachioles - isn't the the branchy part of the lungs?).

The reason I thought that is that one method used has small radioactive sources are attached to the ends of sort-of "wires" (I can't remember the name). (Imagine it kind of like a vacuum cleaner cord, with the plug end being a radioactive source.) The person to be treated has catheters inserted in the treatment area, and for the treatments, the sources are run through the catheters, sit in position next to the cancer (at locations predetermined by your friendly neighbourhood medical physicists) and then retract back into the machine where they spend most of their time.

Anyway, with these branches with sources on the end going into the patient, I thought brachy- made sense. However, there are other types of brachytherapy where (smaller strength) sources are inserted directly and permanently into the patient. No branches involved.