Free electron production in ion beam cancer therapy

Radiation therapy as a means to treat cancer originates over a century ago, and has proven to be an invaluable tool in the fight against cancer. At the en of the 1950's the first trials with proton beams in the treatment began, but it did not make its way to clinical treatment facilities until 1990. Over time, it has been shown that some certain heavier ions can be used to improve the results, and particularly carbon nuclei have proven to be well suited.

Ion beam cancer therapy

Figure 1 - A beam of carbon ions hit a tumor in the brain of a human. At the microscopic level, one of the carbon ions hits a piece of a DNA strand inside the tumor, knocking loose several electrons, which in turn causes a cascade of subsequent effects leading, in the end, to the death of the cancer cell. The black line illustrates the Bragg curve, which describes the energy deposited by the ion along its trajectory through the tissue.

The technology involved in ion beam cancer therapy (IBCT) has matured, and in recent years the efficiency of IBCT in the treatment of certain types of cancer, e.g. tumors near critical organs, have improved and become more widely accessible. The main difference between IBCT and traditional radiation therapy is the way that the energy of the treatment beam is deposited in the tissue. In traditional radiation therapy, the beam consists of X-ray photons, and the energy deposited is highest in the tissue close to the surface. This means that it is very difficult, and sometimes impossible, to treat deep seated tumors without harming the surrounding tissue. With IBCT, the energy deposition can be controlled much more precisely, since the ions used (typically protons or carbon ions) follow the Bragg curve, which means that most of the energy is deposited around the Bragg peak, which is located at a certain depth inside the tissue, see Fig. 1. The exact depth of the Bragg peak can be controlled by adjusting the initial energy of the beam. This makes it possible to greatly reduce the damage to fragile organs, such as the brain.

It is known that, at the microscopic level, the carbon nuclei from the beam collides with molecules located inside the cancer cells. The main part of the damage caused to the cancer cells originates from secondary electrons which are produced in the collisions, for instance between carbon ions and water molecules. Some of the carbon ions will collide with the DNA inside the cancer cell, and the dynamics of the events following the collisions can be investigated quantum mechanically.

An example of a representative molecule could be a base pair from a strand of DNA, for example consisting of Cytosine and Guanine. An illustration of the explosive collisions that take place can be seen in Fig. 2.

Ion beam cancer therapy

Figure 2 - Video rendition of an explosive collision between a C4+ ion and a cytosine-guanine base pair. The green cloud represents the cloud of electrons that are knocked loose during the collision. The process illustrated is very fast, and lasts only a few hundred attoseconds (as). One attosecond corresponds to 10-18 seconds.

The entire collision takes place over a few hundred attoseconds. The green cloud in Fig. 2 shows the electronic density being delocalized following the collision, representing the electrons knocked loose during the process. These are the electrons that potentially will end up contributing to the cascade of effects leading to cell death.

Ion beam cancer therapy

Figure 3 - The base pair is bombarded from several different angles and from several different points.

The system is investigated systematically by testing collisions at many different angles (denoted by θ in Fig. 3), and at several different projectile trajectories (displacement denoted by d), on top of testing at various initial kinetic energies of the projectile.

Ion beam cancer therapy

Figure 4 - Electronic density change of the CYT+GUA pair. (a) The change in electronic density Δρe around the CYT+GUA pair during collision. Each plot corresponds to a different value of the initial kinetic energy of the C4+ ion, given in units of MeV. The disturbance of the electronic density starts when the C4+ ion approaches the target, and the electronic density surrounding the nucleotide pair starts to drop after the C4+ ion has left the target. The interaction is initiated earlier for lower kinetic energies of the C4+ ion. (b) The change of the electronic densities of the C4+ ion (dots) and the CYT+GUA pair (squares) after the collision is displayed as a function of initial kinetic energy of the projectile. The disturbance of the electronic density during the ion’s passage through the molecule increases for smaller energies. (c) Electronic density corresponding to the free electrons released into the system during collision, i.e., the electronic density not localized around either the CYT+GUA pair or the C4+ ion. The curve peaks at around 1.21 MeV.

The results depicted in Fig. 4 follow the expectations predicted by the Bragg curve. The greatest effect is observed when the carbon ion has a kinetic energy of approximately 1.21 MeV upon collision, which is where the Bragg peak is.

Recent Publications

Quantum mechanical simulations of a carbon ion colliding with a biological target, Andreas Alberg-Fløjborg, Adrian Bøgh Salo, Ilia A. Solov'yov, Journal of Physics B: Atomic, Molecular and Optical Physics, 53, 145202, (2020)
Kvantemekanisk simulering af elektrondynamikken i ionstrålekræftterapi, Adrian Bøgh Salo, Andreas Alberg-Fløjborg, Ilia A. Solov'yov, Kvant, 3, 18-20, (2018)
Free-electron production from nucleotides upon collision with charged carbon ions, Adrian Bøgh Salo, Andreas Alberg-Fløjborg, Ilia A. Solov'yov, Physical Review A, 98, 012702, (2018)