The more radiation that passes through a piece of tissue, the more that spot gets burned. It’s a lot like a sunburn, except that it extends into the flesh instead of stopping in the skin, and can be arbitrarily bad whereas sunburn is limited by how bright the sun is. So if you hit a cancer patient with multiple moderate-strength beams of radiation and angle the beams so they cross inside the cancer, the patient will get minor burns along the path of all the beams and more serious burns where they add together inside the cancer. The burned part of the cancer is destroyed and can’t grow back.
Radiation can cause cancer (just like sunburns can), so that might be why you expect it to make the cancer worse. But it turns out that the amount of radiation it takes to cause on average one cancer would also be enough to kill a person with burns two and a half times over if given all at once. So if you get radiation therapy to cure one cancer that you definitely have right now and give yourself a 20% risk of getting another cancer a few years in the future you’re a lot better off even with the extra cancer risk. A similar risk/benefit calculation is used for some chemotherapy drugs that might eventually cause cancer but definitely help treat the cancer the patient already has (e.g., cisplatin and nitrogen mustards).
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