It's an old source (1922), but divides the rhubarb into "leaf stalks", "prominent veins," and "leaves." It states that the leaf stalks are the only edible portion.(1)
In addition, oxalates are in all parts of the plant. But only specifically stated to be in lower quantities in the stalk (2). In fact, people susceptible to kidney stones can be advised to avoid even rhubarb stalks (4). Cooking the leaves can actually INCREASE the toxicity. (3)
Logic would dictate that the veins, being the transition point from stalks to leaves would have a value in between the values in the stalks and leaves. Thus safety indicates one should avoid eating them.
Sources:
1: https://books.google.com/books?id=_GDXAAAAMAAJ&pg=PR3#v=onepage&q&f=false
2: http://www.rhubarbinfo.com/poison
3: http://en.wikipedia.org/wiki/Rhubarb
4: http://www.healwithfood.org/health-benefits/rhubarb-stalks.php