Organizations like RG allowed international researchers to make contact in ways that wasn't imaginable just a few years ago. Since collaborative research is very fruitful and can cover many fields, and since, the required collaborators might not exist in your own institution, looking outside to cover the missing expertise is a natural way to complete your research team. This clearly includes international connections.
However, research requires funding for students, equipment, and more. Especially the capital-intensive fields, such as, medical, make research funding tricky. Are there any organizations that fund international research ? Say, in areas requiring the collaboration of medical and engineering fields?