I can't find any information on the medium-sized/medium-large RD-1;
what follows deals, however, with a stenosis of LAD (left anterior descending branch of coronary artery)(- but you probably know this or you might have made the term part of your request).

The word order should go like this:
After the branching off of the descending medium-sized RD-1(??), which manifests extreme stenosis, there is ....

Cardiac Investigations and Procedures:
... Dyes will be injected into the coronary arteries (LAD- left anterior descending artery, ... to dilate up the stenosised area to improve the blood flow. ...
home.hkstar.com/~shwan/cardiac&inv.html -

RIVA-Stenose: stenosis of LAD (= left anterior descending branch of coronary artery) (Hexal Dictionary)

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Note added at 2 hrs 18 mins (2005-04-13 22:08:54 GMT)
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Note on what Gerhard has suggested:

\'After branching off\' represents a (reduced) participial clause = \'After it branches off\'

Automatically a comma is asking to be placed here\' , \', the next words being the subject of the sentence.

So: After branching off, the extremely stenosised medium-sized Ramus dexter-1 ... now we need the main verb :

What will it be??

manifests? (we had that recently in a similar context)
indicates?? exhibits??

If we wish to maintain the \'evidence of\', we\'ll need to precede it with \'provides\'; (I don\'t feel \'supplies\'/\'yields\'/\'offers\' would be such a good choice)

So we have:
After branching off, the extremely stenosised medium-sized Ramus dexter-1 indicates a subtotal stenosis of the Ramus interventricularis.

Or:
After branching off, the extremely stenosised medium-sized Ramus dexter-1 shows/provides evidence of a subtotal stenosis of the Ramus interventricularis.

And our thoughts, I feel, should now turn to the poor patient suffering the said condition.