The ISMRMRD format does not specify specific data storage or database solution, so to your question, there is no standard way of doing it.
That said, it is very easy to store the files on regular network storage systems and you could write a small database application that allows fast lookup of file locations based on some search criteria. Again, no such thing exists at the moment, so you would have to do it yourself. I would use scp or cifs to transfer the files depending on what your network infrastructure allows. I would strongly recommend against the temptation to put the ISMRMRD inside a DICOM container and store them in PACS. The files are huge compared to DICOM images and it will not work well.
Hope this helps,
Michael