Walnuts (Juglans regia) have the highest total phenolic content, flavonoid content, and antioxidant activity of all nuts commonly consumed in the U.S. Walnuts are a very good source of alpha-linolenic acid (ALA, an omega-3 fatty acid), gamma-tocopherol, and manganese. Walnuts also contain significant levels of magnesium and copper.
Walnuts are also a good source of β-sitosterol, fiber, melatonin, vitamin B6, and zinc, as well as some beta-tocopherol, delta-tocopherol, folate, and selenium. In addition, walnuts are a good source of pedunculagin, an ellagitannin which is hydrolyzed to produce ellagic acid, which is converted by microflora in the gut to urolithin A and other urolithins.
Despite their high caloric and fat content, adding a moderate amount of nuts to the diet has been shown not to result in weight gain. Walnut consumption is associated with reduced risks of coronary vascular disease, type 2 diabetes, and blood clot formation, and has been shown to lower cholesterol and to be neuroprotective. Walnut extract has been shown to reduce the proliferation of liver cancer and colon cancer cells in a dose-dependent manner. Ellagic acid has been found to inhibit cell growth and induce apoptosis (programmed cell death) in cervical cancer cells.

Breast cancer-related effects of consuming walnuts

Walnuts, walnut oil and walnut micronutrient consumption is associated with reduced breast cancer risk. Walnuts are a source of a variety of compounds with anti-cancer activities, including some that have been shown to increase the beneficial effects of breast cancer treatment.

Human study

One 2019 study demonstrated that adding 2 oz. of walnuts per day to the diets of women with breast cancer altered the expression of 456 genes in their tumors during the time between their breast biopsies and lumpectomies approximately two weeks later. The changes were favorable: pathways that promote apoptosis and cell adhesion were activated whereas pathways that promote cell proliferation and migration were inhibited.

Walnut extracts in animal and cell studies

Walnut consumption has been found in several studies to significantly reduce breast tumor incidence and size in laboratory mice. For example, one study reported that a diet including walnuts reduced the size of tumors produced by injecting triple negative (ER-/PR-/HER2-) breast cancer cells into mice. Walnut extracts and walnut compounds have also been shown to inhibit the growth and proliferation of both hormone receptor positive (ER+/PR+) and triple negative breast cancer cells.

Alpha-linolenic acid (ALA)

Consumption of ALA is associated with reduced breast cancer risk. Walnuts are the best source of this plant-derived omega-3 fatty acid. ALA is converted during metabolism into eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), which have been reported to have chemopreventive effects in numerous studies. For example, they have been shown to reduce lung metastasis in a mouse model of breast cancer and to inhibit the early stages of HER2 overexpressing (HER2+) breast cancer.
However, note that the conversion of ALA to EPA and DHA can be blocked in the presence of vegetable oils with high omega-6 fatty acid content (such as corn oil, safflower oil, soybean oil, sunflower oil, and grape seed oil). Therefore, walnuts and walnut oil should be consumed separately from such oils.

Gamma-tocopherol, a form of vitamin E

Vitamin E comprises a group of eight related vitamins, including four tocopherols (α, β, γ, and δ-tocopherol) and four tocotrienols (α, β, γ, and δ-tocotrienol). Alpha-tocopherol (α-tocopherol) is the most abundant form of vitamin E and is the isoform typically found in vitamin E supplements.
As noted above, walnuts are a very good source of gamma-tocopherol (γ-tocopherol), which has greater chemopreventive effects than other forms of vitamin E. Gamma-tocotrienol has been shown to inhibit ER+/PR+ and triple negative breast cancer cell growth in a dose-dependent manner, without affecting normal breast cells.
One study using a mouse model of breast cancer reported that gamma-tocotrienol given as part of the diet suppressed tumor growth. The same study also reported that gamma-tocotrienol inhibited colony formation of both mouse mammary and human breast cancer cell lines. Colony formation refers to the ability of a single cell to grow into a colony consisting of at least 50 cells.
Another study reported different effects for alpha-tocopherol and gamma-tocopherol in combination with docosahexaenoic acid (DHA) (found in fatty fish but also derived from the ALA in walnuts) in triple negative breast cancer cells. DHA alone was shown to induce apoptosis, as expected. The addition of gamma-tocotrienol increased apoptotic events in the cells. However, alpha-tocopherol blocked DHA-induced apoptosis.

Ellagic acid

Ellagic acid has been shown to reduce proliferation of ER+/PR+ breast cancer cells. Ellagic acid has also been found to be effective in the prevention of estrogen-induced mammary tumors in rats. In fact, ellagic acid has been shown to inhibit breast cancer development in a variety of cell and animal studies, in part by inhibiting angiogenesis, the growth of new blood vessels. Angiogenesis is a crucial step that separates preinvasive and dormant forms of cancer from invasive and metastatic malignant growth.
Ellagic acid has also been found to increase the sensitivity of ER+/PR+ breast cancer cells to radiation while reducing damage to normal cells, thereby potentially enhancing the treatment effects of radiotherapy.

Copper

Walnuts should be consumed in moderation since they contain some copper (approximately 0.45 mg per ounce), which can promote angiogenesis. While copper is a vital nutrient, women with breast cancer probably should not exceed the RDA (recommended daily allowance) of approximately 0.9 mg.
Refined walnut oil contains essentially no copper. Cold pressed walnut oil is made from nuts that are dried and then cold-pressed, preserving their nutrient content. However, refined cold pressed oil is best since refining helps eliminate copper. Walnut oil should be stored refrigerated and is best used at room temperature (e.g. in salad dressings) rather than in frying.

Additional comments

Pecans are related to walnuts but have a somewhat less favorable omega-3 fatty acid and phytochemical profile than walnuts.
Below are links to recent studies concerning this food and its components. For a more complete list, including less recent studies, please click on walnuts.