blood count of 4000 or less is called neutropenia
if you are refering to a neutropenic diet then it is given to reduce the chances of infection
You may be told to follow a neutropenic diet. This diet is intended to decrease your exposure to bacteria. A basic neutropenic diet includes:
Avoid all fresh fruits and vegetables. Cooked vegetables and canned fruits and juices are fine. You may eat fruit that you can peel a thick skin off of, such as a banana or an orange.
Avoid raw or rare-cooked meat, fish, and eggs. Meat should be cooked to the "well done" stage. All eggs should be thoroughly cooked (no runny yolks).
Avoid salad bars, fruit bars, and deli counters. Buy vacuum-packed lunch meats rather than freshly sliced meats.
Eat or drink only pasteurized milk, yogurt, cheese or other dairy products.
Avoid soft mold-ripened and blue-veined cheese.
At home, you may use tap water or bottled water. Avoid well water or boil it for 1 minute before using.
however each instituition follows it own diet regimen.
i would advise you to ask your oncologist
about any special recommendation and only then follow the diet under expert dietician follw up
i hope i could help you in your query,
i wish your son a good and speedy recovery