Porcentaje de los tintes para diferentes tonos

The rate at which a charged particle loses energy as it passes through a medium is known as thestopping powerstopping power . The units of stopping power are given as Joules per metre (J m–1 _{) as is usually shown by the term dE/dx —the rate of energy loss with}

distance travelled.

4.3.1

Variation of dE/dX with XVariation of dE/dX with X

A typical graph of dE/dX against distance travelled, X, for a charged particle is shown in Fig. 4.6 Distance d E / d X Fig. 4.6

STOPPING POWER 37

This type of graph is representative of the pattern of energy loss of every charged particle. It is characterized by a relatively low and constant rate of energy loss immediately after entering a medium. However, towards the end of its path, the rate of energy loss rises dramatically and falls to zero. This peak in the curve is known as the Bragg peak, after its discovery by William Henry Bragg in 1903.

The mathematical equation which describes the shape of the curve in Fig. 4.6 is rather complex but there are a few important points which can be clearly stated. The rate of energy loss with distance (dE/dX) is:

◆ Proportional to the square of the charge on the particle . . . so an alpha particle, which

has a charge of +2, will lose energy four times as fast as a proton.

◆ Inversely proportional to the square of velocity of the charged particle . . . as the par-

ticle slows down, the rate of energy loss increases—which agrees with the shape of the graph above.

◆ Independent of the mass of the charged particle —this means that for particles of the

same velocity, the rate of energy loss of a proton is similar to that of an electron as both have a charge of 1 unit.

Fig. 4.7 shows the pattern of absorbed dose from an electron beam and a proton beam. The characteristics appear to be completely different but the energy loss of each particle type is exactly the same as shown above. The reason relates to the relative mass of each particle. Electrons will undergo interactions with other electrons—which are

D o s e D o s e 25 MeV e– 187 MeV p+ 0 5 10 15 20 25 2 4 8 10 11 12 14 Depth in water (cm) Depth in water (cm) Fig. 4.7

ELECTRONS, PROTONS AND NEUTRONS 38

the same mass—and will be easily scattered by the interactions undergone. Many will end up travelling the direction they have come from—hence there is no well defined Bragg peak for the beam as a whole. Protons on the other hand, having a mass nearly 2,000 times greater than an electron are less easily deflected and an obvious Bragg peak is seen. Consider an electron as a ping pong ball and imagine firing a ping pong ball into a collection of other ping pong balls—the srcinal is unlikely to travel through the collection without deflection from its path. If you consider a proton as a ten pin bowling ball and fire that at the same collection of ping pong balls, it is easy to imagine that it would plough through them with minimal path deflection.

4.3.2

Restricted stopping powerRestricted stopping power

It has been shown that charged particles generally lose energy in a large number of small interactions with small energy losses via soft collisions. This has given rise to the descrip- tion of electron motion in terms of a ‘continuous slowing down approximation’ (CSDA). The energy transferred to the medium in this way may be assumed to be absorbed locally, i.e. within a small volume close to the point of interaction. In this case, it is usually safe to assume that the energy lost by the charged particle is the same as that absorbed locally.

Remember δ -rays? These are energetic electrons (and so not really rays) resulting from large energy transfers to an atomic electron via hard collisions. The atomic elec- tron is able to travel a distance and produce ionization far from its point of srcin. Delta-rays may have ranges comparable with those of the primary charged particles which create them.

The concept of restricted stopping power is necessary to draw attention to the energy lost by electrons that is absorbed in close vicinity to the electron path rather than on the total energy dissipated by the electron. The dose deposited by a charged particle in a given area may be overestimated unlessδ -ray equilibrium exists . . . i.e.—for every δ -ray that leaves a small volume of material, a δ -ray enters the volume to replace the energy lost. This is not usually the case. In short, energy lost by a charged particle cannot necessarily be considered to be equal to energy deposited locally . . . and energy deposited per unit mass is what we know as dose.

In radiobiology, restricted stopping power is known aslinear energy transferlinear energy transfer (LET) and represents the stopping power for all collisional interactions, including the production of δ -rays, up to a specified cut off value. Interactions from radiative interactions are

Charged particle 1° 1° Charged particle δ-ray Fig. 4.8

NEUTRONS 39

ignored as it is assumed that the photons produced will interact with another electron a long way from the radiative interaction site.

Ionizing radiation interacts with matter in a similar way but different types of radiation differ in their effectiveness in damaging a biological system. The most important factor that influences the relative biological effectiveness of a type of radiation is the distribution of the ionizations and excitations in its path.

LET is used to describe both excitation and ionization events. Given the shape of the curve shown in Fig. 4.6 above, it can be appreciated that the LET of a particle will change with distance travelled. Commonly, LET values quoted are an average of energy lost with distance. The LET gives the average energy loss of a particle per unit length of travel in terms of keV/micrometre, keV/µ. The variation of energy loss along the track of a charged particle has led to the utility of LET being questioned. However, the fact remains that it is a valuable method of comparing the energy deposition char- acteristics of different radiation modalities.

LET values vary from publication to publication, but the following may be taken as representative. All values quoted are in terms of keV/µ. An electron beam with a kinetic energy of 10keV will have an LET of 2.5, whereas an electron beam with an energy of 1 MeV will have an LET of 0.2. Remember, the greater the energy, the greater the distance travelled, so the average for a given particle type will decrease with increas- ing kinetic energy. Proton beams of energy 10 MeV have an LET of around 5 while those of 100MeV have a value of around 0.5.

Alpha particles are relatively large and slow moving, so they will lose energy more quickly both because of the velocity and charge dependence on dE/dX. A 5.3 MeV alpha particle, such as emitted by Polonium-210 has an LET of almost 50.

Neutrons are not directly ionizing themselves but they may cause a nucleus to break up leading to the production of heavy charged nuclear fragments, with a correspondingly high LET.

The high LET exhibited by alpha particles is the main reason why the absorption of alpha emitting isotopes into the human body is of great concern. They cause a great deal of damage to normal tissues and have been linked with the development of bone tumours.

Radium behaves in a similar way to calcium when ingested, and is readily absorbed by bone where it may sit, irradiating bone marrow and other tissues. In 1917 the U.S. Radium Corporation started producing a radium containing paint called Undark, which as the name may suggest glowed in the dark. The company employed several thousand employees, mainly women, to paint Undark onto the hands and dials of watches. The employees were encouraged to keep the lines and characters they painted sharply defined by licking the tips of their brushes, thus continually ingesting small amounts of radium on a regular basis. Large numbers of the workers developed seri- ous health issues including anaemia and jaw bone necrosis resulting in tooth loss. Significant numbers went on to develop tumours.

4.4

NeutronsNeutrons

Neutrons are not charged and hence are not directly ionizing but they interact quite readily with nuclei and can set protons and other nuclear fragments in motion by

ELECTRONS, PROTONS AND NEUTRONS 40

knock-on collisions. Photon interactions with matter almost always result in the pro- duction of high energy electrons but neutron interactions with matter are not readily categorized. There are several outcomes of neutron interactions but generally two processes are likely.

Elastic scattering. A neutron interacts with a nucleus as whole. The nucleus gains kinetic energy and recoils through the medium. The srcinal neutron loses energy and is deflected from its srcinal path. The transfer of energy is greatest when the target nucleus is lightest i.e. for hydrogen atoms.

Inelastic scattering . Inelastic scattering is considere d to occur when a neu tron is absorbed by a nucleus, rather than scattering off it. This is where things start getting a little complex. The nucleus will be unstable and several different phenomena may occur to return it to a more stable state. It may eject one or more neutrons, which can then go on and interact with other nuclei. It may eject a proton, alpha particle or larger nuclear fragment with high LET, depositing considerable energy and causing consid- erable normal tissue damage in the human body.

The nucleus may also eject a high energy photon in order to return to a lower energy state.

Following some unsuccessful clinical trials in the 1970s and 1980, neutron beams are no longer used. However, clinical photon beams may be contaminated with neutrons. How so?

Clinical photon beams are produced by stopping high energy electron beams. The higher the energy of the electron beam, the higher the energy of the resulting photon beam. As discussed in an earlier chapter, protons and neutrons are bound together in a nucleus and that binding energy is around 8MeV per nucleon. If a photon with energy higher than 8 MeV is absorbed by a nucleus, a neutron can be ejected.

This can be a problem in the radiotherapy department. As highlighted above, it is important for staff safety that treatment rooms containing high energy photon treat- ment units are adequately shielded against neutron leakage. The emission of a high energy photon following neutron absorption does not happen instantaneously. This ‘induced radioactivity’ may persist for several minutes after a high energy photon treatment has finished, meaning that staff entering the treatment room may be exposed to a low intensity high energy photon field, posing a radiation protection issue.

The problem is more evident if a t echnical problem requires disassembly of the treatment head. The induced radioactivity in the vicinity of the linear accelerator target may mean that the commencement of service work may be delayed for several hours so as to allow dose rates to service personnel to reduce to acceptable levels.