# Basic Physics of Digital Radiography/The Patient

There are many aspects of patient care to be considered when taking an X-ray given the individuality and uniqueness of each patient and each examination. Physical and biological aspects of the interaction of the radiation with the patient's anatomy are addressed in this chapter. Our purpose is to develop an understanding of the mechanisms and consequences of the absorption and scattering of radiant energy in the image formation process and in radiation dosimetry.

## Interaction Processes

The attenuation of X-rays by materials used for radiation detection has been discussed in an earlier chapter. Instead of considering gross electron behavior as in the Energy Band Theory, we will return in this chapter to considering what happens at the level of an individual atom. We will see that the energy loss by X-ray photons in different materials is characterised by ionizations. In addition, excitations can occur where electrons in the material are raised to higher energy levels.

#### Photoelectric Effect

There’s basically three major processes we need consider. Firstly, there’s the Photoelectric Effect - which is illustrated in Figure 3.1. An incoming X-ray collides with, is totally absorbed by and ejects a K-shell electron, for instance, as in panel (a). The ejected electron is called a photoelectron. The resultant vacancy in the K-shell can be filled by an electron from another shell and a K-fluorescent X-ray is generated from the transition - panel (b).
Fig. 3.1: The Photoelectric Effect - (a) photon absorption and electron ejection and (b) fluorescent X-ray emission.
The probability of a Photoelectric Effect occurring is found to be dependent on three major considerations:
• the incoming X-ray photon must have an energy greater than the binding energy of the inner shell so that it can eject a tightly-bound electron,
• once the incoming X-ray photon has an energy greater than the binding energy, then the interaction probability is at a maximum and reduces approximately with the cubed root of the photon energy, E,
• the interaction probability is greatest when the electron is very tightly bound, i.e. the greater the atomic number of the atom, the greater the probability of the photoelectric effect. This probability is very approximately proportional to the cube of the atomic number, Z.
We can therefore infer that the probability of the Photoelectric Effect is approximately dependent on:
Z3 / E3.
The Photoelectric Effect is of fundamental importance in diagnostic radiography since it is the primary method by which contrast is developed in radiographs. Since its probability is proportional to Z3, the absorption in bone, for instance, is amplified relative to that in the surrounding tissue. It can also be used to amplify absorption differences between soft tissues. However the extent of this difference is also seen to be inversely proportional to the X-ray energy, so that the absorption difference between bone and tissue is greatly reduced. It can therefore be inferred that contrast between bone and tissue in radiographs should increase at lower kilo-voltages (kV). However it can also be inferred that the lower kV will increase the patient absorbed dose since the Photoelectric Effect results in the total absorption of the energy of the incoming X-ray photon.

#### Compton Effect

The second process of interest is called the Compton Effect. It is a radiation scattering event where the incoming X-ray gets scattered by an outer atomic electron - as illustrated in Figure 3.2. Here we can see an incoming X-ray which glances off and ejects an outer-shell electron. This outer-shell electron is considered to be essentially free of the atom because its binding energy is so low, which is the case in high atomic number materials. However, in low atomic number materials, such as soft tissues, all atomic electrons can be considered to be essentially free because the binding energy of all electron shells is less than 1 keV.
Fig. 3.2: The Compton Effect - (a) photon scattering and electron ejection leading to (b) an ionized atom.
We refer to the ejected electron as a Recoil Electron. The situation is somewhat similar to a billiard-ball collision and we use the angle, θ, to express the extent of the scattering process.
The energy of the scattered X-ray is given by:
${\displaystyle E'={\frac {E}{1+E(1-\cos \theta )/mc^{2}}}}$
where E is the energy of the incoming photon, m is the rest mass of the electron and c, the velocity of electromagnetic radiation. This is called the Klein-Nishina Formula. The angle, θ, can be in any direction, although it is found that there is a preference for scatter in the forwards direction at higher X-ray energies. We can infer on the basis of this equation that the energy of scattered X-ray photons reduces as the scattering angle increases, and that this reduction increases with photon energy.
This is illustrated in Figure 3.3, which shows a plot of the energy of the scattered photons versus angle, as a function of the energy of the incident X-rays.
The probability of a Compton Effect is found to be dependent on the number of electrons in the absorbing material. This number depends on the density of the absorber and the number of electrons per unit mass. Since, for almost all elements, the number of electrons per unit mass is approximately the same, it can be concluded that the probability of a Compton Effect is independent of the atomic number (Z) of the absorber. It is also found that in the range of energies used in diagnostic radiography, the probability of occurrence is more or less independent of X-ray energy.
Fig. 3.3: The energy of X-ray photons scattered at different angles, as predicted by the Klein-Nishina equation.

It is important to appreciate that the Compton Effect gives rise to radiation being scattered in all directions. When an X-ray beam strikes a patient, for instance, the scattering is such that X-rays are redirected quasi-isotropically around the irradiated area. These X-rays may then proceed to generate further interactions both inside and outside the patient. From a radiation protection perspective, scattered photons may strike anyone who might be close to the patient during the exposure.
Note that radiation scattered in a backwards direction is referred to as Backscatter and occurs following maximal energy transfer from an X-ray photon to a recoiling electron. As the scattering angle decreases, the energy retained by the scattered photons increases and the energy transferred to the recoil electrons decreases, as might be expected.
The scattered X-rays which reach the image receptor add a patient-specific, background haze to radiographs which obscure small absorption differences between tissues and generate blurred representations of borders between tissues. They are a considerable hindrance to the recording of sharp radiographic images and a number of methods are commonly used to counteract their effects, which we will consider later.
Note that electrons released in both the Compton and photoelectric interactions can lose energy by collisions with electrons in adjacent atoms and thereby produce additional ionizations. Typically about a thousand such ionizations can occur when a single 30 keV X-ray photon is completely absorbed, for instance.

#### Coherent Scatter

The third process of interest in terms of the interaction of X-rays with matter is Coherent Scatter. Here, an incoming X-ray photon causes an electron to vibrate. The electron subsequently emits an X-ray photon of an equivalent energy in a forward direction but its atom is otherwise left unchanged.
Note that the ionizations that occur in photoelectric absorption and Compton scatter do not happen with coherent scattering. The process mainly occurs at low X-ray energies and, at diagnostic energies, is always a small percentage of the overall total interactions. It is therefore of little consideration in diagnostic radiography.
Fig. 3.4: Simplified illustration of the consequences of irradiation at diagnostic X-ray energies.

The effect of the two major interaction processes is illustrated in Figure 3.4. Photoelectric absorption of the incident photons gives rise to the generation of a photoelectrons and fluorescent X-rays, while Compton scattering generates scattered photons and recoil electrons. The transmitted photons proceed through the patient and strike the image receptor to form an image. Scattered photons can also reach the receptor - and can also be scattered in any direction around the absorber. Furthermore, some scattered photons in addition to the photoelectrons, recoil electrons and fluorescent photons loose their energy in the absorber. It is this energy loss that constitutes what is referred to as the Absorbed Dose, which we will consider in a later section of this chapter.

We have just considered the interactions of X-rays with matter at the atomic level. When living matter is the attenuating material, ionizations caused primarily by photoelectrons and Compton recoil electrons can lead to chemical, molecular and, ultimately, biological changes. Note that both the X-ray and electron energies involved are sufficient to break chemical bonds in the organic material. Excitation processes can also occur where valence electrons are raised to atomic shells that are not normally occupied. These electron changes may alter the chemical forces which bind atoms together inside molecules and cause the creation of different molecular species.

#### Biomolecular Damage

From a chemical perspective, ionizations can give rise to the production of free radicals. These consist of atoms which have an electron orbit with a single unpaired electron. They can easily bind with orbital electrons of neighbouring molecules and are therefore highly reactive chemically. In addition, they can diffuse through the medium before reacting and can thereby affect distant molecules. Alternatively, chain reactions can occur where a free radical binds with a neighbouring molecule and as a result generates another free radical. This process can be repeated through groups of molecules and critical changes in the organic material may result.
Fig. 3.5: DNA damage pathway.
Radiation damage to organic molecules occurs almost exclusively by free-radical interactions. Ionizing radiation exposure can produce free radicals in abundance through excitation processes. In cells, water is the most abundant source of radiation-produced hydrogen and hydroxyl free radicals. These can interact with molecules involved in cellular metabolism, for instance, and the normal function of the cell may become impaired. They can also interact with nucleic acid molecules which can result in cellular mutations or even cell death - see Figure 3.5. A broad range of damage can occur in genes and DNA double-strand breaks (DSBs) are considered to be the most likely trigger for cell killing, chromosome aberration formation and cancer induction. DSBs have been observed using immunofluorescence-based bioassays of venous blood samples taken from patients undergoing computed tomography (CT)[1] and percutaneous transluminal angioplasty (PTA)[2]. In addition, the use of contrast media has been found to enhance radiation damage to lymphocytes during CT[3].

#### Tissue Damage

At the tissue level, disruption to the nervous system, to the bone marrow and to the digestive tract, for example, can occur as well as the induction of cancer. Additionally, such changes can lead to genetic damage and to the death of the irradiated person. At the population level, such changes could ultimately lead to changes in the gene pool. Furthermore, the risk of cancer induction from diagnostic X-ray exposures although small is nevertheless estimated to represent ~1% of cancers which arise spontaneously among the population[4].

#### Health Risks

At the level of the individual, the radiation damage can be classified as either Deterministic or Stochastic. Deterministic damage generally refers to the killing of cells, while stochastic damage generally refers to cell modifications which do not impair the cell's capacity to reproduce.
Cell death and replacement are natural processes which occur in tissue all the time. It can therefore be inferred that deterministic radiation damage is only of concern when the amount of cell death exceeds the replacement capacity of the tissue. Such damage can, as a result, be considered to occur only above a threshold dose. The value of this threshold has been found to be dependent on the type of tissue involved, ranging from red blood cells (relatively low radio-sensitivity), through to oesophageal epithelium and gastric mucosa (relatively high radio-sensitivity) to lymphocytes and ovarian follicular cells (very high sensitivity), for example. As a general guide, radio-sensitivity is dependent on the number of actively proliferating cells in the tissue and the length of the mitotic phase in the cell cycle. Furthermore, the degree of differentiation of the cells is inversely related to their radio-sensitivity. The severity of deterministic effects has been found to increase with radiation dose once this threshold has been exceeded. It should be noted, however, that these thresholds are rarely exceeded in well-managed clinical environments.
In contrast, stochastic effects have no threshold dose. Here the probability, and not the severity, of damage is found to increase with dose. The onset of resultant diseases, e.g. leukaemia, solid tumour formation, caused by stochastic effects have been found to occur only after a latency period of several years or decades. Stochastic health risk is therefore substantially higher for paediatric radiography examinations than it is for the radiography of aged people, for example.
The difference between the two effects can be considered to result because changes in single cells are sufficient to cause stochastic damage while changes in many cells are needed for deterministic effects to occur. Note that this implies that any dose of X-rays has a theoretical potential to cause cancer and that thresholds need to be exceeded before deterministic effects can occur.

## Tissue Attenuation

The combined effects of the photoelectric effect, Compton effect and coherent scattering are now considered. Specifically the dependence of each on the energy of the irradiating X-rays in different materials of medical interest. Our purpose is to describe how X-ray shadows are formed from an atomic physics perspective. We will return to the topic of radiation dose later in this chapter.

#### Soft Tissue

Let's first consider the attenuation situation for muscle tissue, as shown in Figure 3.6, where its Mass Attenuation Coefficient is plotted against X-ray energy[6]. This coefficient is a measure of the attenuating ability of a material, where ‘attenuation’ is the term used to express the effects of both absorption and scattering processes.
Fig. 3.6: The energy dependence of the Mass Attenuation Coefficient of muscle tissue.
The attenuation due to the photoelectric effect is seen to decrease almost linearly with X-ray energy and becomes less than that of the Compton effect above about 25 keV. The Compton effect itself is seen to be relatively constant at all X-ray energies at about 0.2 cm2/g. And finally, coherent scatter is seen to have a relatively low value and to decrease with X-ray energy. We can therefore conclude that, for muscle, the major interaction process is the photoelectric effect at low X-ray energies and the Compton effect becomes dominant at higher energies.

#### Bone

In contrast to muscle, the situation for cortical bone is shown in Figure 3.7. Note first that the total attenuation is greater than for muscle, at all except the higher X-ray energies. Secondly, note that attenuation due to the photoelectric effect decreases, once again, almost linearly with energy and becomes less dominant than Compton scatter above about 40 keV. And thirdly, note that attenuation due to the Compton effect is reasonably constant over the energy range at, once again, ~0.2 cm2/g, while coherent scatter is quite a small percentage of the total attenuation.
Fig. 3.7: The energy dependence of the Mass Attenuation Coefficient of cortical bone.
These conclusions are in line with our earlier discussion of the energy dependence of the three interaction processes. We can conclude that lower energy X-rays should enhance the attenuation differences between bone and muscle and that scattered radiation may become problematic at the higher X-ray energies.

#### K-Edge Effect

A final material to consider is sodium iodide - see Figure 3.8. This material is widely used in radiation detectors and its attenuating properties are quite similar to those of iodinated contrast media. This material is also of interest because it demonstrates an interesting absorption phenomenon, that of a K-absorption edge. This happens when the energy of the incoming X-rays exceeds that of the K-shell of the iodine atoms, so that these electrons can now be ejected from the atom.
Fig. 3.8: The energy dependence of the Mass Attenuation Coefficient of sodium iodide.
The Photoelectric Effect is again seen to decrease with X-ray energy, but this time with an absorption edge at about 33 keV. The Compton Effect is again seen to be constant at ~0.2 cm2/g, while Coherent Scatter, although more prominent, once again falls off with increasing X-ray energy.
Note also that the total attenuation in sodium iodide is about 10 times greater than cortical bone at low X-ray energies while it is about 30 times greater (and about 300 times that of muscle) at just above the K-absorption edge. This characteristic has made this material suitable as a radiation detector. It is also one of the reasons why contrast media containing iodine are used to distinguish blood vessels from surrounding tissues in angiography.
A final point to note is that numerous materials have been found which have K-absorption edges in the diagnostic energy region. These include cesium iodide, where in addition to the iodine K-edge, there’s a second one at 36 keV due to the cesium atoms. Lanthanum, as another example, has a K-edge at 39 keV - and we saw its effect on the X-ray energy spectrum earlier. These materials have found application in intensifying screens because of this absorption feature.
Another example is barium, which has a K-edge at 37 keV. This characteristic has found application in barium contrast media used, for example, to distinguish the digestive tract from the surrounding tissue in the Barium Meal. It has also found application in computed radiography (CR) where the photostimulable material is made from barium fluorohalide.
Fig. 3.9: Histogram of transmittance values for a chest radiograph.

The overall effect of tissue attenuation is illustrated in the Figure 3.9 for the case of a chest radiograph. The exposed area of the patient consists in simplistic terms of air, tissues and bone and is surrounded by the rectangular collimator leaves. The air provides relatively negligible attenuation, while the bone provides substantial attenuation - and tissues provide an intermediate amount. As a result, bone can generate relatively high attenuation at lower X-ray energies and their X-rays shadows can interfere with the visualisation of the lung fields. Increasing the X-ray energy, by increasing the kV, will increase bone penetrability and reduce their shadowing effect. The overall result is a change in the prominence of features associated with different regions in the image histogram.

Fig. 3.10: A radiograph of the hand.

Besides observing X-ray shadows of parts of the human body cast on a barium plantinocynanide-coated cardboard screen, Wilhelm Röntgen also recorded these shadows using photographic film. It was soon found that short X-ray exposures could be used when a intensifying screen/film combination was used, which could be further shortened when two screens were used to sandwich a sheet of double emulsion film. These short exposures facilitated the recording of snapshot images of moving internal parts of the body and reduced the effects of motion artifacts in radiographs. Today we use screens with digital image receptors for the same purpose.

A typical image is shown in Figure 3.10. It can be seen that bone has a brighter shade of grey than that of the enveloping tissue and is brighter still than the surrounding air. This is the conventional method of displaying a radiograph such that higher photon attenuation is encoded as a brighter shade of grey.

From our earlier discussion, we can expect bone to absorb X-rays preferentially relative to the surrounding tissue and that the energy of these X-rays should have a strong influence on this absorption difference. It is this difference which generates contrast in radiographic images, and we can therefore expect contrast to reduce with increasing X-ray energy. We can also expect that the influence of scatter should be apparent at all X-rays energies.

It might be thought that such absorption differences could be used in determining, for instance, the physical density of bone, or indeed the density of tissue. However the presence of scattered radiation has a strong, detrimental effect on such densitometric measurements, as we will see later.

#### Imaging Geometry

The physical characteristics of the human body allow radiographs to be recorded at diagnostic X-ray energies and many anatomical structures to be examined. The spatial resolution of such images is found to be highly dependent on the size of the source of X-rays. We have already seen that X-rays can be generated by a tungsten anode, for instance. What we haven’t considered is the size of this source.
It is found that the smaller this source, the better is the spatial resolution in the recorded radiograph. The reason can be appreciated from Figure 3.11, where it is seen that a focal spot of finite size, f, on the anode target of the X-ray tube (XRT) is used to expose the edge of a opaque object. The image of the edge is seen to be spread out into a penumbra, p, of dimensions depending on the ratio of the distance from the X-ray source to the image (the SID) and the distance from the X-ray source to the object. This ratio is called the Geometric Magnification, m. It is equivalent, on the basis of considering the geometry of this arrangement, to the image size divided by the object size.
An assumption in deriving the mathematical relationships in the diagram is that the focal spot, f, is indeed parallel with the image plane. This is generally not the case and for technical reasons it is angled, as we will saw earlier.
Since the size of the penumbra, p, is nevertheless greater than the focal spot size to an extent dependent on the magnification, it can be reduced by any or all of the following:
• reducing the focal spot size, f;
• increasing the source-to-object distance, h1;
• decreasing the object-to-image distance, h2.
Fig. 3.11: Penumbra generation when imaging an opaque edge with a focal spot of finite size and approximate geometrical relationships.
The first option for reducing the focal spot size is limited by the properties of the XRT anode and is generally about 0.5 to 1 mm depending on the application. Its even smaller in Mammography where fine focal spots of 0.1-0.3 mm are common because of the requirement to image microcalcifications.
The second option gives rise to source-to-image distances (SID) of up to one meter or more being used in diagnostic radiography. The final option is generally applied by placing the part of the body being irradiated as close to the image receptor as possible. However, unity magnification is never achieved because of the finite thickness of the cover of the cassette containing the image receptor and, more importantly, because of the finite thickness of the body part. The posterior surface of the part will receive the smallest magnification, while the anterior surface will be magnified to a greater extent. Intermediate structures will be magnified to an intermediate extent depending on their distance from the image receptor. Additionally, images of these intermediate structures, e.g. bones, can be displaced relative to each other, which can lead to problems in determining their exact anatomical size, shape and location.

#### Image Distortion

The imaging of a flat, opaque object of dimension, o, is considered in Figure 3.12. It can be appreciated that the finite-sized focal spot will now generate penumbra on each side of the umbra, u, of the object. It can also be seen that the penumbra will be of different sizes, p and p’, depending on the angle of the focal spot. Note that the size of the image of the object will be magnified by the geometric magnification as well as a factor depending on the ratio of the focal spot to object sizes. Also note that, at an extreme, as the object’s dimension becomes smaller than the focal spot, the magnification increases rapidly and the penumbral blur can be substantially larger than the umbra itself. In essence, the ability to resolve fine detail will be compromised by the focal spot size.
Fig. 3.12: Penumbra generation when imaging an opaque disk and approximate geometrical relationships.
Fig. 3.13: Radiographic distortion in the imaging of two spheres.
On the basis of this discussion, it can be concluded that finer resolution radiographs can be obtained with a smaller focal spot, a large source-to-image distance (SID) and a minimal distance between the body part and the image receptor.
Fig. 3.14: Illustration of the spatial distortion involved in wrist/hand radiography.
It should also be appreciated that the beam emerging from a focal spot is shaped by rectangular collimators so that a divergent, rectangular radiation field strikes the patient. We can therefore infer that objects in the peripheral regions of the field will experience a greater magnification and resultant distortions in shape relative to those in the beam’s centre. We can also infer that these effects should increase as we move from the centre of the field to the periphery of the radiation field.
The unequal magnification effects are illustrated in Figure 3.13. The divergent nature of the X-ray beam can be seen to cause shadows of peripheral disk-shaped objects to become broadened and distorted. The situation in wrist radiography is illustrated in Figure 3.14. Here, the ‘Central Ray’ of the X-ray beam was centered near the trapezium bone and the image represents differences between true anatomical locations and those imaged. It is seen that the best match occurs, as expected, in the region of the Central Ray and that the mismatch increases as we move towards the more peripheral regions of the body part.

## Subject Contrast

The term contrast is used to express how well the X-ray opacity of an area in a patient’s radiograph differs from its surroundings. It could refer to how well a calculus, for instance, stands out from the surrounding renal tissues in a radiograph of the kidneys, or a lung lesion in a chest radiograph. The Subject Contrast is a term which expresses these differences in terms of X-ray intensities emerging from the patient, whereas the term Image Contrast expresses these differences as recorded on the radiograph.

Subject contrast is developed mainly because of differences in the extent of photoelectric absorption in different tissues. Greater absorption occurs in bone relative to tissue, for instance, as we have previously described. This absorption completely removes X-ray photons from the beam so that what emerges from the patient and what is recorded by the image receptor are differences in X-ray attenuation.

There are numerous ways in which subject contrast can be expressed mathematically. For our purposes here we will define it as follows:

C = ln IA - ln IB

where IA and IB are the transmitted X-ray intensities through two segments of tissue - see Figure 3.15, for an example. Our discussion here assumes for simplicity that the incident radiation consists of single energy photons, i.e. they are monoenergetic, and that only photoelectric effects occur in bone and tissue, i.e. no Compton nor coherent scattering occurs. We also assume an ideal imaging system, i.e. one that does not influence the contrast in any way - a gross over-simplification as we will see in the next chapter!

Before proceeding, note that while some textbooks define the subject contrast as:

C = (IA - IB)/IA

their equation is a derivation of the logarithmic difference equation solely for application in low contrast situations.

Fig. 3.15: Attenuation of an incident X-ray beam, of intensity I0, by bone and tissue.

It is apparent from our earlier discussion about X-ray attenuation that both IA and IB are the result of exponential attenuation in the pure tissue and in the bone-plus-tissue regions, respectively. It is therefore apparent that the subject contrast depends on differences in thickness, density and/or effective atomic number of the anatomy being irradiated. The effective atomic numbers of bone and tissue are roughly 12.3 and 6.5, respectively, and the cubic dependence can give great contrast between these materials.

The contrast can therefore be re-expressed as:

C = (μb - μa) xb

where μa and μb are the linear attenuation coefficients of the tissue and bone, respectively and xb is the bone thickness. This equation indicates that the contrast is directly proportional to bone thickness with a constant of proportionality equal to the difference in linear attenuation coefficient between bone and tissue. It is apparent that contrast increases linearly with bone thickness in this idealized situation, which suggests that estimates of bone thickness could in principle be obtained from a contrast measurement. Scatter, as we will see, makes this virtually impossible, however.

From an X-ray energy perspective, it is clear that there should be a strong influence of energy on these differences, and hence the contrast between anatomical regions. We can therefore expect that subject contrast should decrease with increasing kV, and that lowering the kV should improve contrast substantially in images. It should be appreciated that this improved contrast will however increase the patient’s radiation dose, because of the increased photoelectric absorption in both bone and tissue.

Note that the definition of contrast used in this discussion which is based on the logarithmic difference in signal intensity reduces to the expression (IA - IB)/IA in low contrast situations, as might be encountered in mammography, for instance.

We are now in a position to be able to relax one of our simplifying assumptions to include effects generated by scattered radiation. Scatter can be considered to add a background haze, S, to radiation intensities so that the contrast is reduced to:
C = ln (IA+S) - ln (IB+S).
Fig. 3.16: Radiographic images of three small plastic disks. The scatter component is three times higher in (a) than in (b).
Here it is assumed that the scatter contributing to the two regions is the same, although it should be appreciated that this is rarely the case, with S being more akin to a background which varies slowly and weakly within an image in loose synchrony with the patient’s anatomy.
The reduction in contrast due to scatter can be appreciated from the images in Figure 3.16. Here, two radiographs are seen of three small, thin and circular plastic disks, which are intended to mimic subtle lesions in images. The image in panel (a) was acquired with a level of scatter representative of clinical imaging conditions. The image in panel (b) was generated using a computerized scatter reduction method which reduced the scatter to about a third. It is clear from the figure that scatter can greatly reduce image contrast to the extent that subtle opacities may not be visualized.
The extent of this contrast reduction can be estimated on the basis of the expression for contrast we developed above to be given by:
${\displaystyle C=\ln {\frac {1+SPR}{\exp -(\mu _{b}-\mu _{a})t_{b}+SPR}}}$
where SPR is the ratio of the scattered to primary radiation intensities - the so-called Scatter-to-Primary Ratio. Note that the simple, non-scatter, linear relationship can be obtained when the SPR is set to zero in the above equation.
Fig. 3.17: Impact of scatter on subject contrast for two bone thicknesses.
The issue is the magnitude of the SPR. Experimental measurements reported in the literature indicate that the SPR ranges:
• from about 1.2 in the lung fields to ~10 in the mediastinum of a chest phantom at 120 kVp[7]; and
• from about 2 in the lung fields to ~19 in the mediastinum on average in CR chest radiography of 102 patients at 95 kVp[8].
The SPR can therefore be considered to be reasonably large in many clinical radiographs to an extent that scatter can be considerably higher in intensity than that of the transmitted primary beam which contains the radiographic attenuation information. Another perspective on this situation is shown in Figure 3.17. Here, the influence of SPR on the subject contrast of two thicknesses of bone are shown. It is seen that the even a small amount of scatter can have a significant effect on contrast. For instance, the contrast of a 2 cm thickness of bone is seen to be reduced by 50% when the SPR is just 0.6 and by about 90% when the SPR is equal to 2. We can therefore infer that even an SPR of just 2, as has been measured in the lung fields in CR chest radiography, can have a substantial influence on the contrast of attenuating lesions within those fields. It can therefore be concluded that contrast in radiographic images can be improved substantially when scattered radiation is reduced, i.e. when the SPR is improved.

#### Scatter Reduction

SPR reduction can be achieved by decreasing the kV and thereby increasing the likelihood of the Photoelectric Effect - see the discussion above. It can also be reduced by:
• reducing the field size, using tight beam collimation, for instance,
• decreasing the part thickness through compression, as used in Intravenous Pyelography (IVP) and Mammography, for example,
• increasing the patient-to-image distance, using an air gap, and
• using a radiographic grid placed between the patient and the image receptor.
Fig. 3.17.5: The dependence of the scatter-to-primary ratio, SPR, on tissue thickness for different field sizes and air gaps, predicted by a broad-beam analytical model.
The first three methods can be readily understood on the basis that the more absorber atoms that are presented to the incoming X-ray beam, the greater the likelihood of scattering events. This is illustrated in Figure 3.17.5 which shows the predictions of a broad-beam analytical model[9] of the SPR dependence on imaging geometry factors for different thickness of soft tissue which includes multiple-scattering events. It can be seen that the estimated SPR increases rapidly with increasing tissue thickness for increases in the field size and reductions in the size of the air gap between the patient and image receptor. The consequent subject contrast is therefore highly dependent on these factors. It can also be seen in the figure that the SPR is greater than 1 for most geometrical conditions - even for imaging just 5 cm of tissue. The intensity of scattered radiation can therefore be assumed to dominate the primary intensity for almost all radiographic examinations. Methods of scatter eduction can therefore greatly improve subject contrast. Note, however, that introducing an air gap can increase image magnification, and that reducing the field size through tight beam collimation is therefore the most applicable of these methods in many clinical imaging situations.

The fourth SPR reduction method of using a radiographic grid was first introduced to diagnostic radiography by Gustav Bucky in 1913. The grid consists of a thin arrangement of lead strips, tightly packed together, with a low atomic number interspace material between them[10] which is placed between the patient and image receptor - see Figure 3.18. Obliquely incident X-rays, e.g. from scattering processes, are absorbed by the lead strips preferentially relative to X-rays which pass straight through, i.e. primary radiation - somewhat like the action of a venetian blind. Grids can be:
• Parallel, with the lead strips arranged parallel to each other and perpendicular to the incident radiation beam,
• Focused, with the lead strips angled obliquely so that a line focus is obtained at a specific distance,
• Crossed, using two layers of parallel or focused strips at right angles to each other, and
• Moving, where the grid is moved reciprocally to remove any shadows generated by the grid lines during the X-ray exposure.
Note that the moving grid, while having been introduced by Hollis Potter in 1920, is generally referred to in diagnostic radiography as a Bucky.
Fig. 3.18: Cross-sectional view through a grid with definitions for the grid ratio, r, and pitch, N.
Figure 3.18 allows a number of parameters which characterize a grid to be defined. The first is the Grid Ratio, r, which is defined as the ratio of the height of a strip to the width of the interspace material. Therefore, the greater the Grid Ratio, the greater the SPR improvement. Grid Ratios of between 4 and 16 are in common use in diagnostic radiography, depending on the clinical application.

The second parameter used to describe radiographic grids is the Pitch, i.e. the number of lines per unit distance, N. The greater the pitch, the greater the SPR improvement, and typical grids have values of between 20 and 80 lines/cm depending on the clinical application.
The third parameter is the Bucky Factor, which expresses the exposure (i.e. the mAs) increase required because of X-ray absorption by the grid materials. Typical values are between about 4 and 10, depending on the grid and its clinical application. It can therefore be concluded that the use of a grid should increase patient absorbed dose and that a balance must be achieved between the resultant contrast improvement and the consequent increase in patient dose.
In clinical practice, focussed grid lines should be aligned in the correct orientation and are generally marked with a label such as Tube-Side - otherwise a phenomenon referred to as Grid Cut-Off can result and the radiograph may need to be retaken and the patient re-exposed. In addition focussed grids need to be positioned precisely parallel with the image receptor - to within ~3% - otherwise an unwarranted exposure increase will result when Automatic Exposure Control (AEC) is in use.

We have seen that the generation of subject contrast is related to attenuation differences between different materials in the body. We can therefore infer that X-ray dose is dependent on the number of photons striking a tissue and their energy, as well as on the Linear Attenuation Coefficient of the tissues involved. Dose can therefore be considered to result from the deposition of radiant energy in a tissue. The amount of energy deposited is given by the absorbed dose, D, which is defined, in SI units, as the absorption of 1 joule per kilogram of attenuating material - and which is referred to as the absorption of 1 gray (Gy). This energy is equivalent to that of ~1017 X-ray photons at 60 keV and therefore represents a relatively large exposure.

Ionization chambers have traditionally been used to measure the Exposure of X-ray beams. This quantity was measured in roentgens (R), where 1 R is defined as an exposure which generates 2.58x10-4 C/kg of air (at STP). It is an empirically-derived quantity and has consequently fallen into disuse to be replaced by the quantity, Kinetic Energy Released in Matter (Kerma), which has a more theoretical foundation. Kerma is measured in grays (Gy) and is equivalent to absorbed dose in many situations. Its use to measure exposure in an X-ray beam is referred to as the Air Kerma because the beam is travelling through air, and is generally measured using an Ionization Chamber. When the area of the X-ray beam is also taken into account, Ionization Chambers can be used to measure the Kerma-Area Product (KAP), also known as the Dose-Area Product (DAP). At diagnostic X-ray energies, the difference between air kerma and absorbed dose is less than 7%.

It can be expected that the absorbed dose in diagnostic radiography should be higher at the skin entrance than below the skin surface. Further, the actual distribution of absorbed dose within the patient's body can be expected to be dependent on the amount of X-ray scattering to non-exposed regions.

Note that the absorbed dose on its own does not provide a direct predictor of the severity nor the probability of a biological effect. Other factors need to be accounted for, not least being the spatial variations of the energy depositions within a tissue or organ at the microscopic level. The biological effectiveness of ionizing radiation is expressed by the term Equivalent Dose, H which is given by:

H = WR D,

where WR is the Radiation Weighting Factor - which for X-rays has a value of unity, although its higher for other types of ionising radiation. Equivalent doses have their measurement units expressed in sieverts (Sv).

#### Effective Dose

To account for the different radio-sensities of different tissues, the Effective Dose, E, can be defined as follows:
E = WT H,
where WT is called the Tissue Weighting Factor - see the following table. Effective dose can therefore can estimated by weighting the equivalent dose by WT and summing over all tissues. Results are generally expressed in sieverts (Sv). A uniform whole body absorbed dose of 1 Gy from X-ray exposure is therefore equivalent to an effective dose of 1 Sv. It is important to appreciate that effective dose is a calculated quantity and is not directly measured. It is generally estimated from measurements such as the skin entrance air kerma and calculated using computer software.
Tissue Weighting Factors recommended by the ICRP[11]
Tissue Weighting Factor
Bone marrow, colon, lung, breast, stomach, remainder
0.12
0.08
0.04
Bone surfaces, brain, salivary glands, skin
0.01
It is seen in the table that the more radio-sensitive tissues are red bone marrow, colon, lung, breast and stomach. The remainder tissues listed include the adrenal glands, gall bladder, heart, kidneys, pancreas, prostate gland, small intestine, spleen, thymus and uterus/cervix. Skin is seen to be one of the tissues with lower sensitivity.
Note that traditional radiation units are still in use in some parts of the world. Here the unit of absorbed dose is the rad, where

and that of equivalent dose is the rem, where

1 rem = 0.01 Sv.
This general approach allows doses from different X-ray examinations to be compared and to be contrasted with doses from other sources of ionising radiation. It should be noted, however, that "Effective dose is calculated for a Reference Person and not for an individual"[12] and that "the risk coefficients underlying effective dose... do not apply to individual risk and do not predict future risk of cancer or hereditary damage" [13].
We can nevertheless attempt to use these units to try to estimate radiation damage - purely for illustrative (as opposed to scientific) purposes. For example, it has been found that skin erythema can occur above 250 mSv and haematopoiesis impairment above 1 Sv. Still higher doses are known to cause damage to the mucosa of the alimentary canal, with symptoms of diarrhoea and nausea. In addition, whole-body doses above 4 Sv are known to be lethal and above 20 Sv are known to cause instantaneous death.
Other non-cancerous damage to the body, such as alterations in fibrotic tissue, cataracts and infertility can also occur. For example, an annual dose limit of 20 mSv is applied in the case of the lens of the eye of radiation workers by international recommendation. It should be appreciated that survivors of deterministic effects also carry a dose-dependent increase in their risk from stochastic effects.

Effective doses in diagnostic radiography are substantially lower than those quoted above - see the following table for examples. Only stochastic effects are relevant at these relatively low doses, but given the latency periods involved it is virtually impossible to establish a causal link between such doses and cancer induction.
Examination Entrance Skin Dose (mGy) Effective Dose (mSv)
Chest, PA
0.14
0.017
Abdomen, AP
5.0
0.7
Pelvis, AP
4.0
0.66
Thoracic Spine, AP
3.3
0.4
Lumbar Spine, AP
5.2
0.69
Lumbar Spine, LAT
13.0
0.29
Note that the effective doses in the table arise as a result of the types of tissues included in a particular X-ray examination, e.g. the gonads and bladder are not directly exposed in PA (posterior-anterior) chest radiography. Further, anterior-posterior (AP) chest X-rays can therefore be considered to generate a higher effective dose than PA views because of the location of the breasts closer to the XRT and the consequent increase in their absorbed dose.
Note also that this data is reflective of practice in the era of film/screen technology and is used here solely to illustrate the relationship between the entrance skin dose and the effective dose. Revisions to the data in the above table are provided in Wall & Hart (1997)[15] and more extensive, and recent, data is provided in Mettler et al. (2008)[16]. In addition, its of interest to note that significant exposure reductions have been observed since the 1980s in both radiography and fluoroscopy[17].
It is important to appreciate that obese patients receive larger effective doses from the same radiographic examination than do lean patients, e.g. the dose increase can reach factors of 70–80 for extremely obese patients[18]. It has been found that doses for such patients can be reduced by orienting the patient so that the thickest body fat layer is closest to the XRT and by increasing the kV for such examinations.

#### Epidemiology Studies

Epidemiological studies have been used to explore possible links between radiation dose and cancer induction[19]. These studies compare cancer incidence in groups of exposed and unexposed people. Here the main source of information is that provided by atomic bomb survivors in Hiroshima and Nagasaki. It has been found, for instance, that statistically significant cancer risks from radiation exposure can be demonstrated only at organ doses above 50-100 mSv. Other epidemiological studies have demonstrated links between leukaemia and cancer induction in patient's exposed for medical treatment and monitoring purposes - and, more recently, for diagnostic purposes [20] - albeit with caveats. Additional evidence has been provided by studies of workers such as uranium and other miners, radium-dial painters, nuclear energy workers[21]. as well as radiographers and radiologists[22]. An increased incidence of leukaemia and lung cancer, for example, has been observed in radiation workers exposed to doses as low as 20 mSv accumulated over their working lives[23]. An interesting insight to doses for radiographers in the early days, by the way, is given by Kotre & Little (2006)[24].
It should be noted that much of this data is based on estimates of the absorbed dose sometime following the actual exposures. It therefore seems clear that no definitive link has been established between routine diagnostic exposures and cancer induction in these epidemiological studies and that future investigations be should based on accurate dose measurements prior to patient follow-up[25]

Epidemiological results can theoretically be used to extrapolate health risks from lower doses. The question is the method of extrapolation. The International Commission on Radiological Protection (ICRP) has recommended the assumption of a linear relationship between dose and cancer risk - the so-called Linear No-Threshold (LNT) hypothesis. The influence of repair mechanisms is not taken into consideration. It is of relevance to note that the increase in thyroid cancer observed in children exposed following the nuclear accident at Chernobyl, for example, is broadly in line with ICRP expectations. In addition, it has been suggested that a Systems Biology approach could assist further development of the modelling of epidemiological extrapolations[26].
It is important to appreciate that epidemiological studies are used by the ICRP for estimating the Tissue Weighting Factor, WT, for individual organs. In addition, the development of such weighting factors has been for general radiological protection purposes, and not specifically for the case of partial body exposures, as in diagnostic radiography[27]. In addition, WT for an individual organ does not take into account any radio-sensitivity changes resulting from pathology, for example. The factors and their application should therefore be interpreted as only a crude indicator of an estimate of health risk. It can nevertheless be useful as a conceptual framework which provides a foundation for future developments in our understanding.

Finally, it can be helpful to compare risks from medical exposure to those of other everyday hazards. For instance, everyone on the planet is exposed to background radiation, including from internal body sources, with a worldwide average annual effective dose of 2.4 mSv (with substantial variation globally). Airline crews on long-haul flights experience a higher level of cosmic radiation and can receive doses of 4-5 μSv each hour, for instance [28], so that one flight may result in the equivalent of a number of chest X-rays for them and their passengers. The annual effective doses for aircrew are typically on average 1–2 mSv for those employed on short-haul flights and 3–5 mSv for those on long-haul flights[29].

Three fundamental principles for radiation protection have been developed by the ICRP for any exposure to ionizing radiation:

• Justification of exposure;
• Optimization of protection;
• Application of Dose Limits.

The first two principles apply to all individuals and to all exposures. The third principle does not apply in the case of medical exposures.

#### Justification

The principle of justification is that a radiation exposure should do more good than harm. In other words, any new exposure of an individual or any changes in their existing or potential exposures should benefit them to an extent that it offsets any resultant detriment. A medical exposure should therefore only be performed when it is appropriate for a particular person with a particular medical condition, i.e. when the expected health benefit exceeds any expected negative consequences. Health benefits include increased life expectancy, relief of pain, improved well-being and reduction in anxieties, while negative consequences, for example, include reduced life expectancy, pain produced by the examination, time off work and the consequences of inaccurate diagnoses. Ethical features implicit in the ICRP's adoption of the Linear No-Threshold model are considered in Malone & Zölzer (2016)[30].

#### Optimization

An implication of the principle of optimization is that all exposures should be kept as low as reasonably achievable (ALARA). This should be applied with both economic and societal factors taken into account which implies that the level of protection should be the best available given the circumstances. The fundamental tenets of radiation protection are:
• Time - exposure periods to be kept as short as possible;
• Distance - exploit the inverse square law; and
• Shielding - use materials of high atomic number such as lead.
In diagnostic radiography, the optimization principle is applied in specific designs for X-ray facilities and equipment, and in that equipment’s appropriate application, details of which we will consider later. For the moment, we can conclude that a patient’s exposure should be sufficient for the medical purpose and that any unnecessary exposure should be avoided. It should be appreciated however that use of too low an exposure may affect the diagnostic quality of radiographs. For this reason, exam-specific Reference Levels have been introduced which provide values of the typical dose for an average patient - see the following table for examples:
Diagnostic Reference (Guidance) Levels for Common X-Ray Examinations[31]
Chest, PA
0.2
Abdomen, AP
5
Pelvis, AP
5
Thoracic Spine, AP
3.5
Lumbar Spine, AP
5
Lumbar Spine, LAT
15
Note that reference levels generally refer to the Entrance Skin Dose (ESD). This quantity can be measured directly using TLDs, for instance, or indirectly by repeating the radiographic exposure using a radiation detector and correcting for backscatter and other factors. Dose-Area Product can also be used to express reference levels. A comprehensive survey in the United Kingdom was used as the basis for establishing national reference levels[32]. Reference levels were based on the third quartile values of dose distributions for over 30 types of diagnostic X-ray examination generated by over a quarter of a million measurements at 316 hospitals over a 5-year period to the end of 2005, and are ~15-30% lower than those listed in the table above. It is important to appreciate that the reference level concept was developed by the ICRP for dose management purposes in regional, national or local environments and was not designed to be used for comparisons with individual patient doses[33].
A critique of the use of patient shielding in diagnostic radiology is provided by Marsh and Silosky (2019)[34] where it is argued that the practice should be abandoned. The American Association of Physicists in Medicine (AAPM) has developed a position statement on this basis of this work.

#### Dose Limits

The dose limits principle does not apply to medical exposures since such limits may interfere with a patient's medical treatment. Different dose limits are nevertheless applied to members of the general public than to those who are exposed occupationally, e.g. X-ray personnel. For example, annual effective dose limits of 20 mSv for occupationally-exposed people (averaged over 5 years, with an annual limit of 50 mSv in any single year) and of 1 mSv for the public are recommended by the ICRP - along with additional limits for the skin, the hands and feet, and the lens of the eye and for pregnant workers. Personal dose monitors are therefore worn by radiation workers to ensure that doses are below the annual limits and to assess their radiation safety practices. Annual staff doses are of the order of 0.25 mSv for radiographers, 0.75 mSv for radiologists and 2.5 mSv for interventionists. It is important to realize that the dose limits should not be considered as acceptable levels, but rather as maximum values which should not be exceeded.
The requirement to have two sets of limits, one for workers and one for the public, arises because the general population, including children, may be more radiosensitive than the limited population of radiation workers. Children in particular have a longer time following exposure for any deleterious effects to develop. In addition, radiation workers are generally more aware of the sources of risk and can take precautions to minimize them. The public is generally unaware of radiation hazards. Furthermore, people need protection in the form of suitable shielding should they, for instance, walk nearby or sit in the waiting room of an X-ray facility. On this basis, the provision of dose limits for members of the public has to be taken into account when designing new X-ray rooms. Inside the room, additional devices are available to suit the individual examination both for the patient and radiation workers[35]. The Image Wisely (for adults) and the Image Gently (for children) campaigns represent efforts to improve existing optimization methods.

#### Dose Reduction

The referral of a patient for diagnostic radiography is generally the initial occasion for optimization issues to arise[36]. The benefit of the examination to the patient’s health management and the availability of other forms of imaging which use non-ionizing radiation (e.g. ultrasound and MRI) should be considered. Since there is always a small but finite health risk from X-ray examinations, dose reduction strategies should always be considered. It is also reasonable to assume that when patient radiation doses are kept to a minimum, then staff radiation doses are also reduced to a minimum.
Strategies for patient dose reduction in General Radiography include:
• Limiting the area of the patient which is exposed to the primary X-ray beam - this should also improve contrast through the reduction in scattered radiation.
• Filtering the primary beam appropriately - generally such filtration should equivalent to 2.5 mm Al or greater for exposures greater than 70 kV.
• Applying the maximum kV that is compatible with adequate image contrast.
• Using a source-to-skin distance generally no less than 30 cm for mobile radiography and 45 cm for fixed radiography.
• Using fixed X-ray equipment as opposed to mobile radiography, when appropriate - radiography rooms generally offer a wider choice of exposure factors and patient positioning options while also providing automatic exposure control (AEC) and better protection for radiation workers and other patients.
• Using X-ray grids only in appropriate examinations, i.e. when improved subject contrast is warranted.
• Using image receptor cassettes and patient tables with low attenuating properties, e.g. carbon-fiber.
• Compressing the body part, if appropriate, e.g. in intravenous pyelography and mammography.
• Establishing a quality assurance system for the radiographic equipment which ensures optimization, minimizes retake and repeat examinations and maintains image quality.

Note that there are additional strategies to be applied in fluoroscopy and angiography which we will consider in the next chapter. Note also that numerous additional considerations are required for radiography of children and pregnant patients.

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