Proton therapy has advanced greatly over the decades. In the present time, methods such as analytical equations and numerical simulation are now able to predict and distinguish different aspects of proton therapy. Cancer treatment is often done by using radiation, such as x-rays or photons that shoot directly at the tumor. The downside of this is that such beams like those mentioned are the beams that don’t care about whether the molecule is the tumor itself, or a part of healthy tissue. The molecules scatter off and leave their energy behind the tumor, and they have to pass through on the way in and out of the patient. This article will tackle the fundamental principles of physics, and how it is applied in proton therapy. This article will also discuss the underlying processes and mathematical methods in applying physics in proton therapy. But before going into the main feature of the article, let us go back in time and define proton therapy.

Proton Therapy

Proton therapy was proposed way back in 1946 by Robert R. Wilson, Ph.D., an American physicist. He proposed to use accelerator-produced beams of protons to treat tumors in humans. His paper, Radiological Use of Fast Protons, attempted to treat patients in nuclear physics facilities, but during that time it was limited for patients as it was just released. Proton therapy is a type of particle therapy that uses a beam of protons to eradicate diseased tissues, such as tumors, which makes it usable for cancer treatment. Compared to traditional radiation therapy, proton therapy is done by using high-energy proton beams, precisely targeted at the tumor itself, leaving the tissues and vital organs around with reduced radiation.

How Does Proton Therapy Work

As I have said earlier, proton therapy is done by using proton beams, targeted at the tumor itself, leaving the tissues with reduced radiation. Usually, proton therapy is also done in sessions, like traditional radiation therapy. A machine called a synchrotron or cyclotron speeds up the protons to create high energy protons. The high energy makes the protons travel to the body, and give a certain radiation dose to the tumor.

Proton therapy has fewer side effects because it doesn’t entirely affect the tissues around the tumor because of the lack of exit dose. Compared to traditional radiation therapy, the beams continue giving radiation doses as it leaves the person’s body, which means it damages the healthy tissues nearby, causing more side effects.

Interactions

Proton therapy has also interactions with the human body, such as side effects. But let’s find out the processes and physics behind proton beam therapy.

Energy loss

Usually, protons lose energy when having a Coulomb interaction with the outer-shell electrons of the exact target atoms. This happens when there is ionization and excitation in the atom, which means ionization is wherein an atom or a certain molecule obtains a charge, whether it is positive or negative, by gaining or losing electrons, resulting in a chemical change. Excitation refers to an addition of a distinct amount of energy to a certain system, such as atoms and molecules, that results from the condition of the lowest energy to higher energy. This usually happens when atoms absorb light or collide with each other, making the atoms “excited”.

Now, let’s go with the mathematical part of this.

The energy loss is given by the Bethe-Bloch equation:

(Figure 1.1)

 This shows that to the first order, -dE/dx is inversely proportional to the square of its speed. Now for the maximum energy transfer to the free electron, the maximum energy transfer is approximate to 4 T meC2/mpc2

Wherein T= 200 MeV

               Tmax =0.4 MeV

               Range » 1.4 mm

Generally, range-energy table and measured depth dose curves are used for practice.

(Figure 1.2)

The figure shows an example of the graph depicting the relative dose deposited in tissue for a variety of commonly used types of proton therapy. If you look closely at the graph, the graph of the plus range gradually increases up to its peak. This peak is called the Bragg peak, wherein the ionization reaches its peak, or just basically there is a rapid loss of energy.

Multiple Scattering

This is one of the causes of energy loss of protons during therapy. Usually, protons scatter due to elastic Coulomb interactions with the target nuclei. This occurs when the proton interacts with the nucleus that causes multiple scatter events. It shows a lot of small-angle deflections. This does affect the lateral margins of the beam, also known as the penumbra. This scatter is insignificant with lesser depth, but the effect increases greatly when getting deeper. This puts up to the lateral dose distribution of the proton beam due to particles that occur due to nuclear reactions.

The equation below is for Passive beam spreading by Bernard Gottschalk:

(Figure 2.1)

 This shows that θ0 is inversely proportional to the proton momentum times the proton speed which is approximate to 1/ (2*T) wherein T<<938 MeV.

The material dependence of θ0 is inversely proportional to the -0.5 power of the target radiation length.

1 g/cm2 of water (LR =36.1 g/cm2) if θ0= 5 mrad for T=200 MeV.

1 g/cm2 of lead (LR =6.37 g/cm2) if θ0= 14 mrad for T= 200 MeV.

(Figure 2.2)

The figure shows an example of a graph of a scatter event. The scatter events cause the proton’s path to drift or deviate from a straight line. Usually, 6 meV photons fall off 6mm at 10 cm depth compared to protons, wherein protons have a lateral fall off 5-8 mm at 10 cm depth.

Conclusion

You might be still skeptical about proton therapy and its effects. But there are a lot of ongoing studies about proton therapy for the advancement of radiation therapy. The physics behind proton therapy is a contributing factor to the medical field. Hoping you have learned something about the mathematical and theoretical aspects of proton therapy. Sooner or later, proton therapy might be a breakthrough not only for cancer treatment but also in the whole medical field.