Suggest you check out the followoing article:  Feldman, The
Scientific
Evidence for a Beneficial Health Relationship Between Walnuts and
Coronary Heart Disease, Journal of Nutrition 2002, 132:1062S-1101S.

Abstract:
The author and four independent experts evaluated the intent and
quality of scientific evidence for a potential beneficial health
relationship between the intake of walnuts and the reduction and
prevention of coronary heart disease. The report also addresses the
supporting evidence for the health benefit of other tree nuts and
selected legumes. Compared to most other nuts, which contain
monounsaturated fatty acids, walnuts are unique because they are rich
in n-6 (linoleate) and n-3 (linolenate) polyunsaturated fatty acids.
Walnuts contain multiple health-beneficial components, such as having
a low lysine:arginine ratio and high levels of arginine, folate,
fiber, tannins, and polyphenols. Though walnuts are energy rich,
clinical dietary intervention studies show that walnut consumption
does not cause a net gain in body weight when eaten as a replacement
food. Five controlled, peer-reviewed, human clinical walnut
intervention trials, involving approximately 200 subjects
representative of the 51% of the adult population in the United States
at risk of coronary heart disease were reviewed. The intervention
trials consistently demonstrated walnuts as part of a heart-healthy
diet, lower blood cholesterol concentrations. None of these studies
were of extended duration that would be essential for evaluation of
the sustainability of the observed outcomes. These results were
supported by several large prospective observational studies in
humans, all demonstrating a dose response-related inverse association
of the relative risk of coronary heart disease with the frequent daily
consumption of small amounts of nuts, including walnuts.

Marilyn