4. Question 4 Radiation is a useful tool in treating cancerous tumors. In the past few decades, proton beam radiation therapy (PBRT) has been developed as a new option for treating tumors. PBRT accelerates protons in a synchrotron and then delivers them into the body. The main difference between proton therapy and radiation therapy with, for example x-rays, is that the proton loses most of its energy just before it stops. This means that the radiation dose can be dumped at a very specific location; a proton enters the body and emits little radiation until it reaches the tumor and stops, emitting a large amount of radiation to damage the tumor. This is shown in figure1; the peak of radiation dosage at the end of the proton's path is known as the Bragg peak. Currently there are about 40 PBRT treatment centers in the world, with about 25% of them in the US and 25% in Japan. Now imagine you are a doctor and you have three patients with the following types of cancerous tumors: (i) Patie
