A Walnut Diet Improves Endothelial Function In Hypercholesterolemic Subjects, Circulation, 2004
It compared two diets. Both were a Mediterranean diet - emphasizing vegetables and fish, and limiting red and processed meats, whole-fat dairy foods, and eggs. There was one difference: one diet replaced some olive oil and other sources of monounsaturated fat (olives, avocados) with walnuts.
The walnut diet was better:
"Compared with the Mediterranean diet, the walnut diet improved endothelium-dependent vasodilation and reduced levels of vascular cell adhesion molecule."The benefit of walnuts may go beyond (or act synergistically to) its fatty acid profile. For example, walnuts contain good amounts of the amino acid L-arginine, certainly compared to almost-all-fat olive oil, and L-arginine can lower blood pressure, that is...
"Compared with the Mediterranean diet, the walnut diet produced significant reductions in total cholesterol and LDL cholesterol."
L-arginine is used to make nitric oxide, a compound that helps dilate blood vessels, lowering blood pressure. (L-arginine is good for erectile dysfunction too, for the same blood-vessel-dilating reason). An aside - dark chocolate also increases nitric oxide, and may be partly responsible for its heart benefits.
Just one study.