# Basic Physics of Nuclear Medicine/Interaction of Radiation with Matter

We have focussed in previous chapters on the source of radiation and the types of radiation. We are now in a position to consider what happens when this radiation interacts with matter. Our main reason for doing this is to find out what happens to the radiation as it passes through matter and also to set ourselves up for considering how it interacts with living tissue and how to detect radiation. Since all radiation detectors are made from some form of matter it is useful to first of all know how radiation interacts so that we can exploit the effects in the design of such detectors in subsequent chapters of this wikibook.
Before we do this let us first remind ourselves of the physical characteristics of the major types of radiation. We have covered this information in some detail earlier and it is summarised in the table below for convenience.
We will now consider the passage of each type of radiation through matter with most attention given to gamma-rays because they are the most common type used in nuclear medicine. One of the main effects that you will notice irrespective of the type of radiation is that ions are produced when radiation interacts with matter. It is for this reason that it is called ionizing radiation.
| Radiation | Mass | Electric Charge | Velocity |
| Alpha Particles | relatively heavy | double positive | relatively slow |
| Beta Particles | about 8,000 times lighter | negative | less than the velocity of light |
| Gamma Rays | None | None | 3 x 10$^8$ m/s in free space |
Before we start though you might find an analogy useful to help you with your thinking. This analogy works on the basis of thinking about matter as an enormous mass of atoms (that is nuclei with orbiting electrons) and that the radiation is a particle/photon passing through this type of environment. So the analogy to think about is a spaceship passing through a meteor storm like you might see in a science-fiction movie where the spaceship represents the radiation and the meteors represent the atoms of the material through which the radiation is passing. One added feature to bring on board however is that our spaceship sometimes has an electric charge depending on the type of radiation it represents.

## Alpha Particles

We can see from the table above that alpha-particles have a double positive charge and we can therefore easily appreciate that they will exert considerable electrostatic attraction on the outer orbital electrons of atoms near which they pass. The result is that some electrons will be attracted away from their parent atoms and that ions will be produced. In other words ionizations occur.
We can also appreciate from the table that alpha-particles are quite massive relative to the other types of radiation and also to the electrons of atoms of the material through which they are passing. As a result they travel in straight lines through matter except for rare direct collisions with nuclei of atoms along their path.
A third feature of relevance here is the energy with which they are emitted. This energy in the case of alpha-particles is always distinct. For example $^{221}$Ra emits an alpha-particle with an energy of 6.71 MeV. Every alpha-particle emitted from this radionuclide has this energy. Another example is $^{230}$U which emits three alpha-particles with energies of 5.66, 5.82, 5.89 MeV.
Finally it is useful to note that alpha-particles are very damaging biologically and this is one reason why they are not used for in-vivo diagnostic studies. We will therefore not be considering them in any great detail in this wikibook.

## Beta Particles

We can see from the table that beta-particles have a negative electric charge. Notice that positrons are not considered here since as we noted in chapter 2 these particles do not last for very long in matter before they are annihilated. Beta-minus particles last considerably longer and are therefore the focus of our attention here.
Because of their negative charge they are attracted by nuclei and repelled by electron clouds as they pass through matter. The result once again without going into great detail is ionization.
The path of beta-particles in matter is often described as being tortuous, since they tend to ricochet from atom to atom.
A final and important point to note is that the energy of beta-particles is never found to be distinct in contrast to the alpha-particles above. The energies of the beta-particles from a radioactive source forms a spectrum up to a maximum energy – see figure below. Notice from the figure that a range of energies is present and features such as the mean energy, E$_{mean}$, or the maximum energy, E$_{max}$, are quoted.
The question we will consider here is: why should a spectrum of energies be seen? Surely if a beta-particle is produced inside a nucleus when a neutron is converted into a proton, a single distinct energy should result. The answer lies in the fact that two particles are actually produced in beta-decay. We did not cover this in our treatment in chapter 2 for fear of complicating things too much at that stage of this wikibook. But we will cover it here briefly for the sake of completeness.
The second particle produced in beta-decay is called a neutrino and was named by Enrico Fermi. It is quite a mysterious particle possessing virtually no mass and carrying no charge, though we are still researching its properties today. The difficulty with them is that they are very hard to detect and this has greatly limited our knowledge about them so far.
The beta-particle energy spectrum can be explained by considering that the energy produced when a neutron is converted to a proton is shared between the beta-particle and the anti-neutrino. Sometimes all the energy is given to the beta-particle and it receives the maximum energy, E$_{max}$. But more often the energy is shared between them so that for example the beta-particle has the mean energy, E$_{mean}$ and the neutrino has the remainder of the energy.
Finally it is useful to note that beta-particles are quite damaging biologically and this is one reason why they are not used for in-vivo diagnostic studies. We will therefore not consider them in any great detail in this wikibook.

## Gamma Rays

Since we have been talking about energies above, let us first note that the energies of gamma-rays emitted from a radioactive source are always distinct. For example $^{99m}$Tc emits gamma-rays which all have an energy of 140 keV and $^{51}$Cr emits gamma-rays which have an energy of 320 keV.
Gamma-rays have many modes of interaction with matter. Those which have little or no relevance to nuclear medicine imaging are:
      * Mössbauer Effect
      * Coherent Scattering
      * Pair Production
and will not be described here.
Those which are very important to nuclear medicine imaging, are the Photoelectric Effect and the Compton Effect. We will consider each of these in turn below. Note that the effects described here are also of relevance to the interaction of X-rays with matter since as we have noted before X-rays and gamma-rays are essentially the same entities. So the treatment below is also of relevance to radiography.

#### Photoelectric Effect

    When a gamma-ray collides with an orbital electron of an atom of the material through which it is passing it can transfer all its energy to the electron and cease to exist – see figure below. On the basis of the Principle of Conservation of Energy we can deduce that the electron will leave the atom with a kinetic energy equal to the energy of the gamma-ray less that of the orbital binding energy. This electron is called a photoelectron.
    Note that an ion results when the photoelectron leaves the atom. Also note that the gamma-ray energy is totally absorbed in the process.
    Two subsequent points should also be noted. Firstly the photoelectron can cause ionisations along its track in a similar manner to a beta-particle. Secondly X-ray emission can occur when the vacancy left by the photoelectron is filled by an electron from an outer shell of the atom. Remember that we came across this type of feature before when we dealt with Electron Capture in chapter 2.

#### Compton Effect

    This type of effect is somewhat akin to a cue ball hitting a coloured ball on a pool table. Here a gamma-ray transfers only part of its energy to a valance electron which is essentially free – see figure below. Notice that the electron leaves the atom and may act like a beta-particle and that the gamma-ray deflects off in a different direction to that with which it approached the atom. This deflected or scattered gamma-ray can undergo further Compton Effects within the material.
    Note that this effect is sometimes called Compton Scattering.
The two effects we have just described give rise to both absorption and scattering of the radiation beam. The overall effect is referred to as attenuation of gamma-rays. We will investigate this feature from an analytical perspective in the following chapter. Before we do so, we'll briefly consider the interaction of radiation with living matter.

## Radiation Biology

It is well known that exposure to ionizing radiation can result in damage to living tissue. We've already described the initial atomic interactions. What's important in radiation biology is that these interactions may trigger complex chains of biomolecular events and consequent biological damage.
We've seen above that the primary means by which ionizing radiations lose their energy in matter is by ejection of orbital electrons. The loss of orbital electrons from the atom leaves it positively charged. Other interaction processes lead to excitation of the atom rather than ionization. Here, an outer valence electron receives sufficient energy to overcome the binding energy of its shell and moves further away from the nucleus to an orbit that is not normally occupied. This type of effect alters the chemical force that binds atoms into molecules and a regrouping of the affected atoms into different molecular structures can result. That is, excitation is an indirect method of inducing chemical change through the modification of individual atomic bonds.
Ionizations and excitations can give rise to unstable chemical species called free radicals. These are atoms and molecules in which there are unpaired electrons. They are chemically very reactive and seek stability by bonding with other atoms and molecules. Changes to nearby molecules can arise because of their production.
But, let's go back to the interactions themselves for the moment.....
In the case of X- and gamma-ray interactions, the energy of the photons is usually transferred by collisions with orbital electrons, e.g. via photoelectric and Compton effects. These radiations are capable of penetrating deeply into tissue since their interactions depend on chance collisions with electrons. Indeed, nuclear medicine imaging is only possible when the energy of the gamma-rays is sufficient for complete emission from the body, but low enough to be detected.
The interaction of charged particles (e.g. alpha and beta particles), on the other hand, can be by collisions with atomic electrons and also via attractive and repulsive electrostatic forces. The rate at which energy is lost along the track of a charged particle depends therefore on the square of the charge on that particle. That is, the greater the particle charge, the greater the probability of it generating ion pairs along its track. In addition, a longer period of time is available for electrostatic forces to act when a charged particle is moving slowly and the ionization probability is therefore increased as a result.
The situation is illustrated in the following figure where tracks of charged particles in water are depicted. Notice that the track of the relatively massive α-particle is a straight line, as we've discussed earlier in this chapter, with a large number of interactions (indicated by the asterisks) per unit length. Notice also that the tracks for electrons are tortuous, as we've also discussed earlier, and that the number of interactions per unit length is considerably less.
The Linear Energy Transfer (LET) is defined as the energy released per unit length of the track of an ionizing particle. A slowly moving, highly charged particle therefore has a substantially higher LET than a fast, singly charged particle. An alpha particle of 5 MeV energy and an electron of 1 MeV energy have LETs, for instance, of 95 and 0.25 keV/μm, respectively. The ionization density and hence the energy deposition pattern associated with the heavier charged particle is very much greater than that arising from electrons, as illustrated in the figure above.
The energy transferred along the track of a charged particle will vary because the velocity of the particle is likely to be continuously decreasing. Each interaction removes a small amount of energy from the particle so that the LET gradually increases along a particle track with a dramatic increase (called the Bragg Peak) occurring just before the particle comes to rest.
The International Commission on Radiation Units and Measurements (ICRU) suggest that lineal energy is a better indicator of relative biological effectiveness (RBE). Although lineal energy has the same units as LET (e.g. keV/μm), it is defined as the:
Since the microscopic deposition of energy may be quite anisotropic, lineal energy should be a more appropriate measure of potential damage than that of LET. The ICRU and the ICRP have accordingly recommended that the radiation effectiveness of a particular radiation type should be based on lineal energy in a 1 μm diameter sphere of tissue. The lineal energy can be calculated for any given radiation type and energy and a Radiation Weighting Factor, (w$_R$) can then be determined based on the integrated values of lineal energy along the radiation track.
All living things on this planet have been exposed to ionizing radiation since the dawn of time. The current situation for humans is summarized in the following table:
Adapted with permission from Applied Imaging Technology. :
| Source | Effective Dose (mSv/year) | Comment |
| Cosmic radiation | ~0.4 | About 100,000 cosmic ray neutrons and 400,000 secondary cosmic rays penetrate our bodies every hour – and it increases with altitude! |
| Terrestrial radiation | ~0.5 | Over 200 million gamma-rays pass through our body every hour from sources such as soil and building materials |
| Internal radiation | ~0.3 | About 15 million $^{40}$K atoms and about 7,000 natural uranium atoms disintegrate inside our bodies every hour, primarily from our diet |
| Radon and other gases | ~1.3 | About 30,000 atoms disintegrate inside our lungs every hour as a result of breathing |
The sum total of this Natural Background Radiation is about 2.5 mSv per year, with large variations depending on altitude and dietary intake as well as geological and geographical location.
Its generally considered that repair mechanisms exist in living matter and that these can be invoked following radiation damage at the biomolecular level. These mechanisms are likely to have an evolutionary basis arising as a response to radiation fluxes generated by natural background sources over the aeons. Its also known that quite considerable damage to tissues can arise at quite higher radiation fluxes, even at medical exposures. Cell death and transformations to malignant states can result leading to latent periods of many years before clinical signs of cancer or leukemia, for instance, become manifest. Further treatment of this vast field of radiation biology however is beyond our scope here.

## Practical Radiation Safety

Radiation hazards arise since nuclear medicine involves the handling of radioactive materials. Although this risk may be small, it remains important to keep occupational exposures as low as reasonably achievable. Essential practices for achieving this aim include:
Administration
      * Maintaining a comprehensive record of all radioactive source purchases, usage, movement and storage.
      * Ensuring that any Codes of Safe Practice are adhered to and develop sensible written protocols and working rules for handling radioisotopes.
      * Protocols for dealing with minor contamination incidents of the environment or of staff members must be established. Remember that no matter how good work practices are, minor accidents or incidents involving spillage of radioisotopes can take place.
Facility
      * Storage of radioactive sources in a secure shielded environment. Specially dedicated facilities are required for the storage, safe handling, manipulation and dispensing of unsealed radioactive sources. Storage areas should be designed for both bulk radioisotope and radioactive waste. Furthermore, radioactive patients should be regarded as unsealed sources.
      * Adequate ventilation of any work area. This is particularly important to minimize the inhalation of Technigas and potentially volatile radioisotopes such as I-125 and I-131. It is preferable to use fume hoods when working with volatile materials.
      * Benches should be manufactured with smooth, hard impervious surfaces with appropriate splash-backs to allow ready decontamination following any spillage of radioisotopes. Laboratory work should be performed in stainless steel trays lined with absorbent paper.
      * Excretion of radioactive materials by patients may be via faeces, urine, saliva, blood, exhaled breath or the skin. Provision to deal with any or all of these potential pathways for contamination must be made.
      * Provision for collection and possible storage of both liquid and solid radioactive waste may be necessary in some circumstances. Most short-lived, water soluble liquid waste can be flushed into the sewers but longer lived isotopes such as I-131 may have to be stored for decay. Such waste must be adequately contained and labelled during storage.
Equipment
      * Ensure that appropriate survey monitors are available to determine if any contamination has occurred and to assist in decontamination procedures. Routine monitoring of potentially contaminated areas must be performed.
      * Ensure that all potentially exposed staff are issued with individual personnel monitors.
      * Protective clothing such as gowns, smocks, overboots and gloves should be provided and worn to prevent contamination of the personnel handling the radioactivity. In particular, gloves must be worn when administering radioactive materials orally or intravenously to patients. It should be noted that penetration of gloves may occur when handling some iodine compounds so that wearing a second pair of gloves is recommended. In any event, gloves should be changed frequently and discarded ones treated as radioactive waste.
Behaviours
      * Eating and drinking of food, smoking, and the application of cosmetics is prohibited in laboratories in which unsealed sources are utilized.
      * Mouth pipetting of any radioactive substance is totally prohibited.
      * Precautions should be taken to avoid punctures, cuts, abrasions and any other open skin wounds which otherwise might allow egress of radiopharmaceuticals into the blood stream.
Optimization
      * Always ensure that there is a net benefit resulting from the patient procedure. Can the diagnosis or treatment be made by recourse to an alternative means using non ionizing radiation?
      * Ensure that all staff, including physicians, technologists, nurses and interns and other students, who are involved in the practice of nuclear medicine receive the relevant level of training and education appropriate to their assigned tasks. The training program could be in the form of seminars, refresher courses and informal tutorials.
      * A substantive Quality Assurance (QA) program should be implemented to ensure that the function of the Dose Calibrator, Gamma Camera, computer and other ancillary equipment is optimized.
The potential hazards to staff in a nuclear medicine environment include:
      * Milking the $^{99m}$Tc generator, drawing up and measuring the quantity of radioisotope prior to administration.
      * Delivering the activity to the patient by injection or other means and positioning the now radioactive patient in the imaging device.
      * Removing the patients from the imaging device and returning them to the ward where they may continue to represent a radiation hazard for some time. For Tc-99m, a short-lived radionuclide the hazard period will be only a few hours but for therapeutic isotopes the hazardous period may be several days.
      * Disposal of radioactive waste including body fluids, such as blood and urine, but also swabs, syringes, needles, paper towels etc.
      * Cleaning up the imaging area after the procedure.
      * Contamination.
The table below lists the dose rates from patients having nuclear medicine examinations. In general, the hazards from handling or dealing with radioactive patients arise in two parts:
      * External hazard: This will be the case when the radioisotope emits penetrating gamma-rays. Usually, this hazard can be minimised by employing shielding and sensible work practices.
      * Radioactive contamination: This is potentially of more concern as it may lead to the inhalation or ingestion of radioactive material by staff. Possible sources of contamination are radioactive blood, urine and saliva, emanating from a patient, or airborne radioactive vapour. Sensible work practices, which involve high levels of personal hygiene, should ensure that contamination is not a major issue.
One of the most common nuclear medicine diagnostic procedures is the bone scan using the isotope Tc-99m. The exposure rate at 1 metre from a typical patient will peak at approximately 3 μSv per hour immediately after injection dropping steadily because of radioactivity decay and through excretion so that after 2 hours it will be about 1.5 μSv per hour. Neglecting any further excretion, the total exposure received by an individual, should that person stand one meter from the patient for the whole of the first 24 hours, would be ~17 μSv. For a person at 3 meters from the patient this number would reduce to 1.7 μSv and for a distance of 5 metres it would be ~0.7 μSv. These values have been estimated on the basis of the inverse square law.
Patients should be encouraged to drink substantial quantities of liquid following their scan, as this will improve excretion and aid in minimizing not only their radiation dose but also that of nursing staff.