Radiophysics

Interactions of radiation with matter and radioactivity

 

Matter and radiation

The smallest unit of radiation, a photon or a quantum, arises in matter, when a nucleus, an atom or electrons of an atom, is affected by a disturbance coming from outside. In order to understand the physical principles of imaging methods and the technical aspect of devices, one must have knowledge of the atomic structure of matter and of those changes which occur when an atomic microsystem is disturbed (e.g. a tungsten nucleus in an X-ray tube). 

Figure 1. Energy level-diagram of the electrons of a tungsten atom. The binding energy of each shell is shown. This is the minimum energy, which an incoming electron or gamma quantum must have to be able to ionize the atom. Excitation with a smaller amount of energy only raises an electron to one of the higher levels provided that a vacancy exists. Two characteristic X-ray quanta are also shown.

Fig. 1 shows the orbits or shells K, L, M etc. of tungsten. These shells are saturated with electrons up to the N-shell and even O- and P-shells are partly filled. It is normal for electrons to be situated in the lowest available orbits, in other words that their energy be as small as possible. The situation is different at higher temperatures, in radioactive substances and generally, when an atomic microsystem is disturbed. This happens for instance when an incoming electron crashes into the anode of an X-ray tube or light is produced from the heated filament of a light bulb. Microsystems become ionized or excited in these ways.

Once excited, an electron is raised from a low energy shell (e.g. the K-shell) to a higher energy shell. An excitation state is discharged by the emission of characteristic X -radiation, when simultaneously an electron from the L-shell, or less likely the M-shell, falls down to the K-shell. The energy difference between these shells in question (59 keV K_α or 67 keV K_ß) is liberated as a monochromatic quantum. This filling up of an electron hole in a shell is followed by a series of similar events in higher orbits with smaller and smaller energy transfers until the system is returned to its stable state. All this happens very quickly, in a considerably shorter time period than a milliardth of a second.

Radiation is divided into two principal components:
1. particle radiation, of which only the electron (and positron, the positive electron) has importance in imaging methods, and
2. electromagnetic (em-) radiation. Its basic quantity, a quantum or a photon moves with the speed of light and lacks mass.

It is accepted in modem physics that a photon can behave as a particle or as a wave. The properties of radiation can therefore be characterized with three concepts; energy (unit being an electron volt eV, keV etc.), frequency (Hz, MHz etc.) and wavelength (cm etc.). Frequency is directly proportional and wavelength inversely proportional to energy.

When an X-ray spectrum is generated in an X-ray tube the penetrating properties and to a lesser extent the intensity of radiation are determined by the high voltage (kilovolt kV or kVp). Em-radiation varies from very low-energies (low frequency or high wavelength) to high energies. Due to historical reasons different names for separate domains of the em-spectrum are in use, but in fact they refer to the same phenomenon, i.e. electromagnetic radiation:
- X-ray, ultraviolet- and visible light arise from changes in electron shells,
- infrared radiation is a consequence of heat liberated by the motion of atoms and molecules,
- radio waves arise from the motion of electrons in a conductor and also from changes in nuclear orbit and spin, etc.,
- gamma radiation originates as a consequence of changes in the excitation of a nucleus

The different ways with which a photon interacts with matter are greatly dependent on energy. Different photon energies are utilized in imaging

Figure 2. X-ray quanta are absorbed heterogeneously in different tissues, most occurs in bone and contrast media and least occurs in air-containing spaces like lungs (Fig. 9). The transmitted primary quanta and a significant part of the scattered, through lead grid penetrated quanta, expose the film. Details of the object are seen in the image if large enough intensity differences (contrast, Fig. 10) have been produced by the distribution of X-rays.

methods to get information from tissues, but the direct in vivo utilization of particle radiation (electrons) in medicine happens only in radiotherapy. On the other hand, ultrasound means vibration in matter. It is transmitted through tissues at the speed of sound (compared with the much higher velocity of light). Ultrasound is not radiation.

Interactions of X-rays and gamma rays with matter

X-ray imaging is the imaging of shadows (see Fig. 2). Different tissues allow the transmission of different amounts of quanta, which are projected onto the image plane. This is either a screen-film-combination, an image intensifier or a sensor, for instance in a CT unit. Radiation must therefore possess two properties for the formation of a radiograph or an X-ray image:
1. Photons must penetrate tissues to a sufficient degree (resulting in a radiation dose).
2. Quanta should be attenuated differently in different tissues (resulting
in image contrast).

When X-rays are used, external radiation penetrates tissues and the quanta are detected on the other side of the patient. In nuclear medicine imaging, photons from activity distributions within body tissues are emitted.

Figure 3. The interactions of photons and electrons with matter. Pair production is possible only at higher energies than 1.022 MeV. It has no importance in X-ray and nuclear medicine imaging, but plays an important role in radiotherapy.

In the latter case, there is a prerequisite that the target object has collected more (or less) activity than organs in the background.

The interactions of X-rays and gamma rays with tissues are the same. Their mode of production is, however, different. A gamma quantum comes from de-excitation of a nucleus and its energy therefore has a specific value. In other words, gamma radiation is monochromatic (different nuclei decay of course with quanta of different energies). On the other hand, an X-ray spectrum consists of quanta with energies between a maximum and minimum value (polychromatic radiation). These limits are determined by the high voltage and filtration of the tube (see X-ray Generator and X-ray tube and Fig. 5).

In the other types of em-radiation quanta have similar interaction properties. Light and infrared radiation for instance penetrate tissues only in small amounts. Infrared radiation, as well as high frequency radiation, penetrates matter to a certain degree, but high spatial resolution is not possible. With infrared radiation it is possible to detect heat producing phenomena only in the vicinity of the skin surface. The situation is somewhat different in magnetic resonance imaging, where tissues are stimulated with radio waves in a strong external magnetic field.
Fig. 3 shows the interactions of photons with matter in the energy domains utilized in X-ray and nuclear medicine imaging, as well as in radiotherapy. The figure also shows the interactions of electrons. All phenomena

Figure 4. Probabilities for photoelectric absorption and Compton scattering, (these phenomena are schematically inserted in the figure with the diameters of an average atom and a nucleus) in various elements and at various energies. On the line in the picture the probabilities are equal. Scattering occurs therefore very frequently in soft tissues (atomic number approximately 7,5). Egamma' Ebind and Ekin mean the energy of the incoming quantum, the binding energy of the shell and the kinetic energy of the electron.

described in the figure are simultaneously possible with different probabilities, except pair production (which occurs in radiotherapy) which requires a minimum energy. Each interaction of a photon gives energy to one or more electrons. High-energy electrons are then able to ionize and excite atoms and dissociate tissue molecules. Radiation dose, so characteristic of ionizing radiation is closely connected to these so called secondary electrons.

Photoelectric absorption and Compton scattering are the important photon interaction phenomena in the diagnostic energy domain of 15-500 keV (Fig. 4). In X-ray and isotope examinations, so-called coherence scattering is of little importance and does not need to be considered. The former phenomenon is an absorption event, at which a photon gives all its energy to an electron, frequently in one of the inner atom shells. This photoelectron is slung from the atom with kinetic energy equal to the original energy of quantum reduced with the binding energy of the shell.

In Compton scattering a photon scatters (changes its direction) with a reduction in energy caused by giving part of its energy to an electron. The relationship between photoelectric and Compton phenomena varies so that in low atomic weight substances, such as soft tissues (and in all matter at high energies), scattering happens much more often than photoelectric absorption (Fig. 4). The frequency of occurrence of these two phenomena is the reverse at low energies and particularly in heavy substances (i.e. in protective layers like lead apron), where quanta are almost entirely absorbed.

Depending on the thickness of the object, a fraction of the number of primary photons is able to penetrate through tissue in the original direction. The remainder is stopped in tissue. Effects of radiation in tissues are later described incorporating such concepts as absorbed dose and dose equivalent (Radiation protection and patient dose).

Fig. 3 shows one photon and its path through matter. But in an X-ray examination nearly parallel quanta are coming in very great quantities from the focus of the X-ray tube. The number of quanta, i.e. the intensity of radiation (quantalcm2 s) diminishes as the radiation penetrates more deeply through matter. In addition to the previous description of absorption and scattering phenomena, the effects of radiation can also be described statistically as a great number of quanta (the magnitude of 1012 quanta hit the patient's skin during the creation of an X-ray image). It is therefore postulated that radiation is attenuated which implies two things;
1. photons are absorbed in electron shells, and
2. photons are deviated from their original direction i.e. they are scattered.

Attenuation follows the exponential function I = I_o exp ^-xm, here I_o is the incoming and I the transmitted intensity of radiation, x is the thickness of the tissue and is a coefficient of attenuation. m is a constant and characteristic of every element and every combination of elements, in other words characteristic of substances and tissues. It depends strongly on radiation energy and other factors.

Interactions of electron; X-ray spectrum from X-ray tube

Fig. 3 shows that an electron with kinetic energy excites and ionizes atoms and dissociates molecules in matter. When kinetic energy increases, this also increases the probability of a braking radiation interaction. This

Figure 5. Braking radiation is generated in the anode of an x-ray tube. In medical imaging the energy of the incoming electron may vary between 15-200 keV (see also text of Fig. 8).

phenomenon means that when a negatively charged electron passes a positively charged nucleus, the former changes direction and loses part of its energy as an em-radiation quantum (Fig. 5). The nearer the electron comes to the nucleus, the greater the change in direction and hence the greater the amount of energy loss. The quantum can gain any amount of energy from the maximal energy of electron (a straight hit) to the energy of a light photon or infrared photon (that is in the range of a few e V). The latter events are the most common. Therefore, the number of low-energy photons inside the anode is greater than the number of high-energy photons (the upper curve in Fig. 5). This makes the anode surface glow, and there is a risk that the anode can even melt under excessively long exposures.

The lower curve in Fig. 5 depicts the quantum radiation spectrum used in patient examinations. It is worth remembering that the secondary electron set in motion by a quantum is particularly important when considering radiation biology and patient dose.

Interactions in a magnetic field

In a magnetic examination a patient on the examination table is exposed to a strong and very homogeneous magnetic field. The field strength can be between 0.04-2 T, (400-20 000 gauss), which is much bigger than the magnetic field of the earth. In the Nordic Countries this is approximately 0.6 gauss. This static magnetic field changes the direction of all of the spinning hydrogen nuclei, (i.e. protons), so that they are aligned parallel to the direction of the field. Radio frequency (rf-) radiation is then applied to tissues where energy quanta are absorbed by some of the protons. These become excited as a result and while decaying send quanta of em-radiation to the environment. These photons are detectable and slice images are reconstructed from the resultant interference pattern (magnetic imaging). During this procedure, magnetic field gradients are utilized to extract three-dimensional information.

The photons which make up the radio-frequency interference pattern have such a low energy that they are not able to ionize matter. Magnetic resonance imaging, however, combines strong static and quickly varying magnetic fields, as well as quickly varying rf-pulses which can cause eddy currents. These eddy currents can generate heat in metallic foreign bodies, if such exist in tissue. The theory and practice of magnetic resonance imaging are described more closely in the chapter on Modalities, with possible biological effects and contraindications.

Interactions of ultrasound

A vibrating ultrasound crystal in contact with skin (using a gel coupling medium for good transmission of vibration energy) forces tissues to move synchronously with the crystal's characteristic frequency, which may vary between 2 and 20 MHz in medical ultrasound examinations. This phenomenon can not be used in a vacuum like em-radiation, it always needs matter. In soft tissues vibrations occur back and forth in the examined cone of tissues the dimensions of which are fixed by the characteristics of the crystal. Motion amplitudes are small, but even so dynamic (changing in time) areas of compression and rarefaction are generated in matter. The resolution of ultrasound imaging (something between 0.8-0.08 mm) is determined by the wave characteristics of the transmitted beam.

Matter is composed of molecules bound to one another with varying degrees of elasticity. Matter is somewhat slow to set in motion, and it opposes the genesis and propagation of motion. Translation speed in soft tissues varies between 1460-1580 m/s (approximately five times faster than in air) and in bone between 2500-4700 m/s. Ultrasound advances straight in homogeneous matter and it behaves very much like light; it is reflected, refracted, absorbed and scattered. This means that energy diminishes

Figure 6. Ultrasound is reflected at all boundary surfaces according to the coefficient of reflection R. Calculated values of vibration intensity in the figure are given in percentages of the incoming intensity. Boundary surfaces are seldom perpendicular to the ultrasound ray, therefore according to the reflection law a considerable share of vibration energy is lost from the main direction (this also causes artefacts). Vibration energy is scattered and absorbed everywhere in matter, in other words energy is attenuated on its way into tissues and on its way back to the crystal.

continuously in the cone of tissues in the direction of the motion (and also after reflection while returning back towards the crystal), in other words vibration is attenuated.

The ultrasound image is constructed with that part of the vibration energy which is reflected back towards to the crystal at each boundary surface or tissue interface. The amount of reflected energy depends on the characteristics of the tissue, its acoustic impedance (= ultrasound's translation speed multiplied by the density of tissue), the frequency of the beam, the orientation of the reflecting surface in relation to the direction of the applied ultrasound cone, as well as the interface structure and "roughness" compared with the wavelength of the applied beam (Fig. 6).

From an even surface ultrasound is reflected in the same way as light from an even metal surface; the angle of reflection equals the angle of incidence. Reflected energy is determined by the coefficient of reflexion R. At the boundary surface between soft tissue and air almost all energy is reflected (it is almost impossible to examine lung) and very little at the boundary surface between two tissues with approximately the same value of acoustic impedance. Vibration energy is scattered in all directions particularly at surfaces with rough structure compared with the wavelength. This is the reason that inclined tissue surfaces can not well be imaged. Ultrasound imaging method and applications are described in the chapter on Modalities.

Radioisotopes and radiopharmaceuticals

An organ can be visualised by measuring the emission of gamma radiation from a radioisotope with which a physiological or metabolic agent is labelled. Such an agent (a "radiopharmaceutical"), is introduced into the body by intravenous injection or oral ingestion. The imaging or measurement of a patient is performed with a gamma camera or a PET -camera (see chapter on Modalities).

In contrast to X-ray imaging, radioisotopes emit radiation from their nuclei. In nature almost one hundred elements can be found, whereas the number of known elements is greater than this. Every element (with a fixed number of protons) has several isotopes, which differ from each other by the number of neutrons. An isotope is stable if the ratio between the number of protons and neutrons is in "balance"; in light elements the number of neutrons is approximately the same as the number of protons, in heavy elements there are more neutrons. Most of known isotopes are radioactive, which means that they are in an excited state. Radioisotopes for medical purposes are produced artificially in a nuclear reactor or a particle accelerator.

The energy of a radioactive isotope is released by the emission of emradiation (a monochromatic gamma quantum) and also by the emission of particle radiation (an electron = beta-minus particle, a positron = positively charged electron = beta-plus particle, an alpha particle, etc.). In these latter cases an element is simultaneously transformed to another substance. Radionuclides which emit only gamma radiation are most commonly utilized in diagnostic nuclear medicine, because only em-radiation with suitable energy (60-600 keV) has the capacity to travel from tissues to a gamma camera. Fast electrons with kinetic energy lose this energy in tissues and contribute only to the radiation dose.

Table 1. Clinically important radionuclides (with type of emission and half-life) and with them labelled examination substances, so-called radiopharmaceuticals, which are often produced in hospitals by the injection of Tc solution into a so-called "kit"-bottle. The notation 2 x 511 keV implies that two photons of 511 keV are simultaneously emitted by the nuclide concerned.

Nuclide Domain	Emission  keV	Half-life	Application
Carbon-11	2 x 511	20 min	Glucose metabolism
Nitrogen-13	2 x 511	10 min	Amino acid metabolism
Oxygen-15	2 x 511	2 min	02, CO, C02
Fluorine-18	2 x 511	110 min	Receptor imaging
Gallium-67	92, 182	72h	Malignancy, infection
Technetium-99m	140	6h	Majority of examinations
Indium-111	173,247	2,8 d	Components of blood
lodine-123	160	13 h	Kidney
lodine-131	360	8 d	Thyroid
Xenon-133	81	5.3 d	Lung embolus
Thallium-201	80	73 h	Heart infarct, ischemia

An excellent example of a pure gamma radiation emitter is 99mTc which has a gamma quantum of 140 keV and a half-life of 6 hours (that time, after which half of the original nuclides are in existence). 99mTc is used in most nuclear medicine examinations. Table l shows clinically important radionuclides and some of their areas of application.

The parent substance of technetium is molybdenum 99Mo with a half-life of 66 hours. This so-called Mo-Te-generator is transported to hospital once or two times in a week. It is "milked", that is rinsed with saline, to produce sterile sodiumpertechnetate solution which is used to label different examination agents. The labelling happens by injecting some of the solution into a sterilized vial, containing freeze dried physiologically or metabolically active agent. The product is then normally ready to be injected to patient. Typically, the amount of effective radioactive labelled substance is extremely small (the agent can even be poisonous) and it is always dissolved in some millilitres of saline.

The number of decaying radioisotope nuclei per unit time is described as activity A. Its unit is one decay event/s = one Becquerel, Bq. The older unit is the curie, Ci, = 3,7 x 1010 decay events/s. Thus, a typical in vivopatient dose of 99mTc is 370 MBq = 10 mCi. If the mass and volume of radiopharmaceutical agents are also taken into account, the concepts of mass and volume specific activity (Bq/kg and correspondingly Bq/m3) can be used.

Radioactive decay follows the exponential function A = Ao exp-lambda x t where lambda is the constant of disintegration or decay (characteristic to each radioactive nuclide) and t is time. The decay constant and half-life have the following relationship: half-life = 0.693/decay constant. In addition to the physical half-life, the concept of the biological half-life is also used. The combination of these terms is called the effective half-life.

 

Aaro Kiuru