You want to treat each patient with some form of radiation therapy. How do you pair the patients with the curves in figure1?

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) Patient 1 has a breast tumor just below her skin.

(ii) Patient 2 has a small brain tumor, a few mm in size, located in the middle of the brain.

(iii) Patient 3 has a brain tumor that is a few cm in size and located in the middle of the brain.

Figure 1: The radiation dosage as a function of depth in tissue. Protons lose most of their energy right before they stop, resulting in the so-called Bragg peak seen in curve (a). The proton beam can be modulated to spread out the Bragg peak, as seen in curve (b). For comparison, an x-ray is shown in curve (c). Source: http://en.wikipedia.org/wiki/File:BraggPeak.png Image Credit: Dr A A Miller, CC BY-SA 3.0

1 \leftrightarrow (c), 2 \leftrightarrow (b), 3 \leftrightarrow (a)1↔(c),2↔(b),3↔(a)

1 \leftrightarrow (a), 2 \leftrightarrow (c), 3 \leftrightarrow (b)1↔(a),2↔(c),3↔(b)

1 \leftrightarrow (b), 2 \leftrightarrow (c), 3 \leftrightarrow (a)1↔(b),2↔(c),3↔(a)

1 \leftrightarrow (c), 2 \leftrightarrow (a), 3 \leftrightarrow (b)1↔(c),2↔(a),3↔(b)