Imaging Physics - Clinical Tree

X-Ray Physics

Production of X-Rays

X-Ray Tube ( Fig. 14.1 )

An x-ray tube is an energy converter receiving electrical energy and producing heat and X-rays. For a diagnostic x-ray tube operating at 100 peak kilovoltage (kVp), the production of heat and X-rays is:

Heat, 99%
X-rays, 1%
- Electron deceleration (Bremsstrahlung), 0.9%
- Characteristic radiation through ionization, 0.1%

X-ray tubes are designed to minimize heat production and maximize x-ray output. Tubes consist of two main elements: a cathode (for electron production) and an anode (for conversion of electron energy into X-rays). During the process of x-ray generation, x-ray beams are generated in all directions; however, the useful beam is composed only of those X-rays leaving the lead (Pb)-shielded tube . All electrical components in an x-ray tube are in a vacuum. The vacuum prevents dispersion of the electrons and ionization, which could damage the filament.

Cathode

Cathodes produce the electrons necessary for x-ray generation. Cathodes typically consist of a tungsten (W) filament that is heated to >2200° C. The filament is surrounded at its cathode end by a negatively charged focusing cup to direct the electrons in a small beam toward the anode.

Anode

The anode has two functions: to convert electron energy into X-rays and to dissipate heat. Heat dissipation is achieved by rotating the angulated target (at approximately 3600 rpm, or 60 cycles/s). The amount of X-rays produced depends on the atomic number (Z) of the anode material and the energy of electrons. Common anode materials include W (Z = 74) and W/rhenium (Re) alloys (90%/10%). These materials are used because of their high melting point and the high yield of X-rays. Mammography units frequently use different anode materials (e.g., molybdenum [Mo]).

The focal spot (FS) is the small area on the anode in which X-rays are produced. The size of the FS is determined by the dimensions of the electron beam and the anode angulation. Typical angles are 12–20 degrees; however, smaller angles (6 degrees) are used for neuroangiography. Tubes with smaller FS size are used when high image quality is essential.

X-Ray Tube Output ( Fig. 14.2 )

Exposure delivered by an x-ray generator is controlled by selecting appropriate values for milliampere (mA), kVp, and exposure time. The output of an x-ray tube increases:

Linearly with mA
Linearly with Z (number of protons) of the target element
As the square of kVp

Milliampere (mA)

The mA is a measure of current referring to the number of electrons flowing per second (1 A corresponds to 6.25 × 10 ¹⁸ electrons). The higher the mA, the higher the electron flux and the higher the x-ray production. An increase in mA changes only the amount of X-rays (i.e., the intensity or exposure rate), not the maximum energy of the X-rays produced. Typical mA values range from 25 to 500 on a given x-ray unit. The use of small FS sizes (for high resolution) also limits the number of mAs that can be used. General rules for selecting mA include:

Use lower mA for smaller FS when image detail is important.
Select high mA to reduce exposure time (i.e., to limit motion blurring).
Select high mA and reduced kVp when high image contrast is desired.

Voltage

The voltage of an x-ray tube is measured in kVp (peak kilovoltage). The kVp determines the maximum energy of the X-rays produced. 100 kVp means that the maximum (peak) voltage across the tube causing electron acceleration is 100,000 V. The term kiloelectron volt (keV) refers to the energy of any individual electron in the beam. When an x-ray tube is operated at 100 kVp, only a few electrons will acquire kinetic energy of 100 keV because the applied voltage usually pulsates between lower values and the maximum (peak) selected. The mean energy of an x-ray beam is approximately one-third of its peak energy. For 100 kVp, the mean energy would be 33–40 keV. An increase in kVp translates into:

Increased photon frequency
Increased photon penetration
Shortening of photon wavelength
Increased anode heat production
Decreased skin dose
Decreased contrast

Film exposure is more sensitive to changes in kVp than to changes in mA or exposure time. General rules for selecting kVp include:

A 15% increase in kVp doubles exposure at the recording system (e.g., film) and has the same effect on film density as a 100% increase in mA.
An increase in kVp of 15% will decrease the contrast, so that doubling of mA is usually preferred.
mA generally needs to be at least doubled when changing from a nongrid to a grid technique (depending on field size and patient thickness).

Exposure Time

Exposure times are set either by the operator (setting of a timer) or by a circuit that terminates the exposure after a selected amount of X-rays have reached the patient. General rules for selecting exposure time include:

Short exposure time minimizes blurring.
Long exposure times can be used to reduce either mA or kVp when motion is not a problem.

Heat Unit ( Fig. 14.3 )

Heat is the factor that limits the uninterrupted use of x-ray generators. Heat units are calculated as:

Heat unit = Voltage (kVp) \times Current (mA) \times Time (s)

$Heat unit = Voltage (kVp) \times Current (mA) \times Time (s)$

This formula holds true only for single-phase generators. For three-phase generators, the heat unit has to be multiplied by 1.35.

Rating Charts ( Fig. 14.4 )

The safe limit within which an x-ray tube can be operated for a single exposure can be determined by the tube rating chart. Always convert mA into mA and time (mAs) before reading the charts.

Example

What is the maximum safe kVp for a 500-mA exposure at 0.1 s?

Answer

Approximately 100 kVp (see Fig. 14.4 ).

Focal Spot (FS)

The FS is the small area on the anode in which X-rays are produced. In mammography, FS of 0.3 mm and 0.1 mm are used. In general radiography, FSs of 0.6 mm and 1.2 mm are used. National Electrical Manufacturers Association (NEMA) specifications require that FSs of <0.3 mm have to be measured with the line pair resolution test (star pattern) and that larger FSs can be measured with a pinhole camera. The apparent FS increases with:

Increase in mA (“blooming effect”)
Increase in target angle
Decrease in kVp

Focal Spot Sizes

FS (mm)	Application
0.1	Magnification X-ray
0.3 ^a	Mammography
0.6	Typical small FS size
1.2	Typical large FS size
1.7 × 2.4	Maximum size of 1.2-mm FS by NEMA standards

FS , Focal spot; NEMA , National Electrical Manufacturers Association.

a NEMA standards allow a 0.3-mm FS to have a tolerance of −0% and +50% (i.e., a maximum of 0.45 mm).

FS and Resolution

Resolution is related to the size of the FS, the FS–object distance (FOD), and the object-detector distance (ODD):

Resolution (lines / mm) = \frac{1.1 FOD}{FS (mm) \times ODD}

$Resolution (lines / mm) = \frac{1.1 FOD}{FS (mm) \times ODD}$

From this equation it is evident that:

The smaller the FS, the better the resolution.
The shorter the ODD, the better the resolution.
The longer the FOD distance, the better the resolution.

Measurement of FS Size

Two methods are used to determine the FS size: pinhole method (determines the actual FS size) and star test pattern (determines effective blur size).

Pinhole Method

A pinhole is placed halfway between the FS and the detector. The image of the FS on the exposed film will be the same size as the actual physical dimension of the FS. Pinholes are usually 0.03 mm in diameter.

Star Test Pattern

A star test pattern is positioned midway between FS and detector. An image is then obtained in which there is a zone of blurring at some distance from the center of the object. The FS is calculated as:

FS = \frac{(δ \times D \times π)}{(180 (M - 1))}

$FS = \frac{(δ \times D \times π)}{(180 (M - 1))}$

where δ = angle of one test pattern segment, D = diameter of the blur circle, and M = magnification factor.

Magnification ( Fig. 14.5 )

The true magnification (M) for a point source is:

M = \frac{Film distance (a + b)}{Object distance (a)}

$M = \frac{Film distance (a + b)}{Object distance (a)}$

In Fig. 14.5 , the magnification would be (36 + 4)/36 = 1.11 (equivalent to 11% magnification). However, because FSs are not true point sources, the real magnification of images (including penumbra) depends on the size of the FS and is given by:

M = m + (m - 1) (f / d)

$M = m + (m - 1) (f / d)$

where m = geometric magnification (a + b)/a, f = FS size, and d = object size. For this example, the true magnification would thus be:

\begin{matrix} M = 1.11 + (1.11 - 1) (0.6 / 0.2) \\ = 1.44 (equivalent to 44 % magnification) \end{matrix}

$\begin{matrix} M = 1.11 + (1.11 - 1) (0.6 / 0.2) \\ = 1.44 (equivalent to 44 % magnification) \end{matrix}$

Penumbra: zone of geometric unsharpness (edge gradient) that surrounds the umbra (complete shadow).

Unsharpness

Unsharpness = FS size \times (Magnification - 1)

$Unsharpness = FS size \times (Magnification - 1)$

Geometric unsharpness is highest with:

Large FS
Short focus object distance

Other sources of unsharpness are:

Intensifying screen (i.e., slow single-screen films)
Motion

Radiation Exposure and Distance

X-ray exposure to a patient increases as the square of the focus-film distance.

Example

What is the increase in exposure when the focus-film distance is changed from 50 to 75 cm?

Answer

\begin{matrix} {Exposure}_{new} / {Exposure}_{old} \\ = {({Distance}_{new} / {Distance}_{old})}^{2} \\ = {(75 / 50)}^{2} = 2.25 -fold increase \end{matrix}

$\begin{matrix} {Exposure}_{new} / {Exposure}_{old} \\ = {({Distance}_{new} / {Distance}_{old})}^{2} \\ = {(75 / 50)}^{2} = 2.25 -fold increase \end{matrix}$

Spectrum of X-Rays

X-rays are generated by two different processes:

Bremsstrahlung: produces a continuum of photon energy radiation
Characteristic radiation: produces defined peaks of photon energy

Bremsstrahlung ( Fig. 14.6 )

Bremsstrahlung refers to the process by which electrons, when slowed down near the nucleus of a target, give off a photon of radiation. The energy of a photon (E) is inversely proportional to its wavelength:

E (in keV) = \frac{12.4}{Wavelength (Å)}

$E (in keV) = \frac{12.4}{Wavelength (Å)}$

For 100 kVp, the maximum energy of an electron would be 100 keV, and its minimum wavelength would therefore be 12.4/100 keV = 0.124 Å. The maximum wavelength of a photon is open ended and only determined by the absorption through glass or filters.

Characteristic Radiation ( Fig. 14.7 )

Characteristic radiation results when bombarding electrons eject a target electron from the inner orbits of a specific target atom. Characteristic energies from a W target are:

α ₁ peak: 59.3 keV (L shell to K shell)
α ₂ peak: 57.9 keV (L shell to K shell)
β ₁ peak: 67.2 keV (M shell to K shell)
β ₂ peak: 69 keV (N shell to K shell)

The higher the atomic number of the target atom, the greater the efficiency of x-ray production. The fraction of energy (f) released as X-rays by electrons of energy (E) in a material with atomic number (Z) is given by:

f = \frac{Z \times E (meV)}{800}

$f = \frac{Z \times E (meV)}{800}$

For example, in an x-ray tube with a W target (Z = 74) and 100 keV, only 0.92% of total energy is converted into X-rays.

Heel Effect ( Fig. 14.8 )

The intensity of an x-ray beam that leaves the tube is not uniform across all portions of the beam (heel effect): the intensity on the anode side is always considerably less and is close to zero for X-rays emitted along the inclined surface of the anode (cutoff). Implications of heel effect include:

Thicker parts of the patient should be placed toward the cathode side of the tube (e.g., mammography is performed with the thicker portion of the breast and chest wall aligned with the cathode).
Heel effect is less when large distances are used (see Fig. 14.8 ).
Heel effect is less pronounced if smaller films are used.
Heel effect is less with larger anode angle (the tradeoff is a larger FS).

X-Ray Generators

Transformer ( Fig. 14.9 )

A transformer consists of two wire coils wound around an iron ring. When current flows through the primary coil, a magnetic field is created within the iron ring. The magnetic field will then create a momentary current in the secondary coil. Current flows through the secondary coil only when the magnetic field is changing (i.e., when it is switched either on or off). For this reason, direct current (DC) cannot be used in the primary coil to create a steady current in the secondary coil (see Fig. 14.9 ). Rather, an alternating current (AC) has to be used in the primary coil. The voltage (V) in the two circuits is proportional to the number of turns (N) in the two coils:

N_{primary} / N_{secondary} = V_{primary} / V_{secondary}

$N_{primary} / N_{secondary} = V_{primary} / V_{secondary}$

A transformer with more windings in the primary than in the secondary coil is called a step-down transformer, and a transformer with more windings in the secondary coil is called a step-up transformer. The product of the voltage (V) and current (I) (which is power [W]: W = V × I) is always equal in both circuits:

V_{primary} \times I_{primary} = V_{secondary} \times I_{secondary}

$V_{primary} \times I_{primary} = V_{secondary} \times I_{secondary}$

Circuits of X-Ray Generators ( Fig. 14.10 )

X-ray units have two principal circuits: a high-voltage circuit (consisting of autotransformer, timer, and high-voltage transformer) and a low-voltage filament circuit.

Autotransformer

This transformer is the kVp selector. The voltage across the primary coil can be varied by changing the number of coils in the autotransformer.

High-Voltage Transformer

This transformer is a step-up transformer, increasing the voltage by a factor of about 600 by having about 600 times more windings in the secondary than in the primary coil. Because the potential of the step-up transformer is up to 150,000 V, the whole transformer is immersed in oil.

Timer

Controls the exposure time.

Rectifier ( Fig. 14.11 )

The function of the rectifier is to change AC into DC flowing in only one direction at all times. Modern rectifiers use full-wave rectification requiring four rectifiers.

Filament Circuit

Consists of a step-down transformer used to produce approximately 10 V and 3–5 A to heat the x-ray tube filament. The amount of current is controlled by a resistor. The more current, the hotter the filament, and the more electrons are emitted.

Types of Generators

Three-Phase Generators ( Fig. 14.12 )

Three-phase generators produce an almost constant potential difference across an x-ray tube. The three phases lag behind each other by 120 degrees, so that there are no deep valleys between the peaks. Ripple refers to the fluctuations of the voltage across the x-ray tube (expressed as a percentage of maximum value). The theoretical ripple factor is:

Single-phase generator: 100%
6-pulse, three-phase generator: 13%
12-pulse, three-phase generator: 3%

Advantages of Three-Phase Generators

Higher average beam energy, less exposure for patient because unnecessary low-level radiation is reduced (higher average dose rate per time unit)
Shorter exposure time
Higher tube rating

Mobile Generators ( Fig. 14.13 )

Most portable x-ray machines are battery powered, whereas others operate directly from a single-phase 60-Hz power outlet. The DC supply in battery-powered units is converted to AC with 60-Hz or higher kilohertz frequency. The high voltage is generated by the usual transformer-rectifier system. A capacitor discharge system is sometimes used for x-ray tube operation.

Capacitor Discharge Generators

The capacitor stores the electrical charge received through rectifiers from a step-up transformer. When a certain potential is achieved, the capacitor is discharged through an x-ray tube. During this discharge both the tube kV and the tube mA fall exponentially.

Phototimers

Phototimers are used to terminate unnecessary x-ray generation after optimum exposure has been achieved. In older equipment, photomultiplier (PM) tubes were located behind the cassette. Modern x-ray equipment uses radiolucent ionization chambers placed in front of the cassette. Ionization chambers are frequently used in triplets to sample several areas of the radiographic field. A detector then averages the recorded exposure from the three chambers.

Interaction Between X-Rays and Matter

There are five basic ways in which an X-ray or a gamma ray interacts with matter:

Coherent scattering
Photoelectric effect (PE)
Compton scattering
Pair production
Photodisintegration

Coherent Scattering ( Fig. 14.14 )

Coherent scattering refers to radiation that undergoes a change in direction without a change in wavelength. It is the only type of interaction that does not cause ionization. Coherent scattering usually represents less than 5% of x-ray matter interaction and does not play a major role in radiology.

Photoelectric Effect ( Fig. 14.15 )

An incident photon ejects an electron from its orbit. An electron from an outer shell then fills the gap in the K shell, and characteristic radiation (with wavelength specific for that element) is emitted. For x-ray emission to occur, the orbit must usually be in the K shell. The end result of the PE is:

Characteristic radiation
A photoelectron
A positively charged ion

The probability of the PE's occurrence depends on the following:

The incident photon must have sufficient energy to overcome the binding energy (BE) of the electron.
A PE is most likely to occur when the photon energy and electron BE are similar.
The more tightly an electron is bound in its orbit, the more likely it is to be involved in a photoelectric reaction. Electrons are more tightly bound in elements with high atomic numbers.

Electron Binding Energy

Atomic Number	Atom	K-shell Binding Energy (keV)
6	Carbon	0.28
8	Oxygen	0.54
20	Calcium	4
53	Iodine	33.2
82	Lead	88

keV , Kiloelectron volt.

The statistical probability of the PE occurring per unit mass of a given element is proportional to the atomic number (Z) and inversely proportional to the energy (E) of the X-ray:

PE \approx \frac{Z^{3}}{E^{3}}

$PE \approx \frac{Z^{3}}{E^{3}}$

Pearls

More tightly bound electrons are more likely to interact in the PE (K > L > M).
Electrons in the K shell are at a higher energy level than electrons in the L shell.
Characteristic radiation is produced by the PE by exactly the same process as discussed in the section on production of X-rays; the only difference is the method of ejecting the inner shell electron.
Advantages of PE:
- Does not produce scatter radiation
- Enhances natural tissue contrast by magnifying the difference between tissues composed of different elements
Disadvantage of PE:
- Patients receive more radiation from each photoelectric reaction than from any other type of interaction.
If Pb (K-shell BE of 88 keV) is irradiated with 1-megaelectron volt (MeV) photons, the emitted photoelectrons will have a minimum energy of 912 keV.

Compton Scattering ( Fig. 14.16 )

A photon is deflected by an electron so that it assumes a new direction as scattered radiation. The initial photon always retains part of its original energy. Note that the recoil electron is always directed forward, but scatter of X-rays may occur in any direction. Two factors determine the amount of energy that the photon retains:

Its initial energy
Angle of deflection from the original photon direction

Calculation of the change in wavelength of a scattered photon:

λ^{'} - λ = \frac{h}{m_{e} c} (1 - \cos θ)

$λ^{'} - λ = \frac{h}{m_{e} c} (1 - \cos θ)$

Where θ is the scattered angle, h is the Planck constant, m _e is the electron rest mass, and c is the speed of light. The maximum energy of a Compton electron in keV is given by:

E_{\max} = E_{incident} \times \frac{2 a}{(1 + 2 a)}

$E_{\max} = E_{incident} \times \frac{2 a}{(1 + 2 a)}$

where a = \frac{E_{incident}}{511 KeV}

$where a = \frac{E_{incident}}{511 KeV}$

At very high energies (e.g., 1 MeV), most photons are scattered in a forward direction. With lower-energy radiation, fewer photons scatter forward and more scatter at an angle greater than 90 degrees. Therefore the distribution of scattered photons (e.g., 100 keV) assumes a probability curve as shown in the diagram (blue shading) ( Fig. 14.17 ).

Probability of Compton Scatter

The probability does not depend on atomic number (unlike PE and pair production).
The probability is inversely proportional to photon energy (although its probability relative to the PE increases with increasing energy since probability of PE ≈ 1/E ³ ).
The probability increases with electron density (electrons/cm ³ ) and physical density of material.
The probability increases with field size and patient thickness.
The probability does not depend on mA or FS size.

Pearls

Almost all the scatter in diagnostic radiology is a result of Compton scatter.
Scatter radiation from Compton reactions is a major safety hazard: a photon that is deflected 90 degrees still retains most of its original energy in the diagnostic range.

Other Types of Interactions

Pair Production

Occurs only with photons whose energy is >1.02 MeV. The photon interacts with the electric field around the nucleus, and its energy is converted into one electron and one positron. Pair production is the dominant mode of interaction of radiation with tissue >10 MeV.

Photodisintegration

Occurs only with photons whose energy is >7 MeV. In photodisintegration, part of the nucleus is ejected. The ejected portion may be a neutron, a proton, an alpha particle, or a cluster of particles.

Comparison of Interaction ( Fig. 14.18 )

Only two interactions are important to diagnostic radiology: Compton scatter and the PE. Compton scattering is the dominant interaction except at very low energies (20–30 keV).

Pearls

High keV (chest radiographs [CXRs]): Compton effect predominates (determined by electron density), lower bone contrast
Low keV (mammography): PE predominates (determined by Z ³ and E ⁻³ ), high calcification contrast
Iodine (I) contrast material: PE predominates for photons of energy >33.2 keV (k-edge of I)

Attenuation

Attenuation refers to the reduction in intensity of an x-ray beam as it traverses matter, either by absorption or by deflection. The amount of attenuation depends on:

Energy of the beam (high-energy beams have increased transmission)
Characteristics of absorber (high Z number material results in decreased transmission)
- Atomic number (the higher the number, the larger the percentage of photoelectric absorption)
- Density of absorber
- Electrons per gram (6 × 10 ²³ × Z/atomic weight). The number of electrons per gram of substance is almost the same for all materials except hydrogen (which is approximately twice that of other elements).

Attenuation Coefficients

Linear Attenuation Coefficient (cm ⁻¹ )

This coefficient represents the actual fraction of photons interacting per unit thickness of an absorber and is expressed as the fraction of attenuated photons per centimeter.

Mass Attenuation Coefficient

This coefficient equals the linear attenuation coefficient but is scaled per gram of tissue (cm ² /g) to reflect the attenuation of materials independent of their physical state. For example, the mass attenuation coefficient of ice, water, and vapor is the same, whereas the linear attenuation coefficient is not.

Density

Material	Effective Atomic Number (Z)	Density (g/cm ³ )
Water	7.41	1.0
Muscle	7.5	1.0
Fat	5.9	0.9
Air	7.6	0.00129
Calcium	20.0	1.5
Iodine	53.0	4.9
Barium	56.0	3.5

Monochromatic Radiation

Monochromatic means that all photons have exactly the same energy (i.e., wavelength). The attenuation of monochromatic radiation is exponential:

N = N_{0} \times e^{- μ x}

$N = N_{0} \times e^{- μ x}$

where N = number of transmitted photons, N ₀ = number of incident photons, µ = linear attenuation coefficient, and x = absorber thickness (cm). At small values of x, µ can be approximated to reflect the fractional rate of photon absorption from a beam per centimeter (e.g., µ = 0.1 cm ⁻¹ means 10% absorption per centimeter). The half-value layer (HVL) refers to the absorber thickness required to reduce the intensity of the beam to 50% (n = number of HVL):

HVL = 0.693/µ
Fraction transmitted = e ^−0.693n where n = thickness/HVL
Fraction transmitted = (0.5) ^{thickness/HVL}
Fraction absorbed = 1-fraction transmitted
The typical HVL in mm of aluminum (Al) for film-screen mammography is approximately kVp/100. For example, if kVp is 27, then the HVL of the beam is roughly 0.27 mm Al.

Example

The HVL of a 140-keV beam through a given material is 0.3 cm. What is the percentage of X-rays transmitted through 1.2 cm?

Answer

Fraction transmitted = {(0.5)}^{1.2 / 0.3} = 0.0625 = 6.25 %

$Fraction transmitted = {(0.5)}^{1.2 / 0.3} = 0.0625 = 6.25 %$

K-Edge ( Fig. 14.19 )

K-edge refers to a sharp increase in the attenuation coefficient depending on the material and photon energy, which occurs at the BE of the K-shell electron being ejected at that specific photon energy (e.g., 29 keV for tin [Sn], 88 keV for Pb). There are also increases at the BE for other shells (e.g., the L shell), which occur at lower energies. The adjacent graph indicates that on a gram-for-gram basis, Sn ²⁺ is a better absorber of X-rays than Pb (between 29 and 88 keV).

Polychromatic (Typical X-Ray) Radiation ( Fig. 14.20 )

Polychromatic radiation consists of a spectrum of photons with different energies. Unlike attenuation of monochromatic radiation, attenuation of polychromatic radiation is not exponential. In polychromatic radiation, a large percentage of low-energy photons is absorbed throughout the absorber so that the mean energy of remaining photons increases.

Factors that affect scatter radiation in radiographic images are:

Field size (most important): the larger the field size, the more scatter
Part thickness
Kilovoltage (not as important as the other two factors). At low kV (<30 keV) there is little scatter because the PE predominates; as radiation energy increases, the percentage contribution of Compton scatter increases.

Example

Fetus receives the hypothetical X-ray dose of 1 rem. What is the maternal skin entrance dose, assuming a monochromatic beam, µ = 0.2 cm ^-1 and the fetus is 5 cm below the skin surface?

Answer

Implementing the attenuation formula for monochromatic radiation, N = N ₀ × e ^−μx

1 = N_{0} \times e^{- (0.2 \times 5)}

$1 = N_{0} \times e^{- (0.2 \times 5)}$

N_{0} = \frac{1}{e^{- 1}}

$N_{0} = \frac{1}{e^{- 1}}$

N_{0} = 2.7

$N_{0} = 2.7$

To obtain 1 rem to the fetus, the incident ray has to be 2.7 rem.

Filters

Filters are sheets of metal placed in the path of an x-ray beam near the tube to absorb low-energy radiation before it reaches the patient. The function of a filter is to protect the patient from absorption of unnecessary low-energy radiation, reducing the skin dose by as much as 80%. Use of filters typically must be compensated for by longer exposure times. Generally, one of two filter types is used:

Al filter: good filter for low energies. National Council of Radiation Protection (NCRP) recommendations:
- <50 keV: 0.5 mm Al
- 50–70 keV: 1.5 mm Al
- >70 keV: 2.5 mm Al
Copper (Cu) filter: better filter for high energies. Typically, about 0.25 mm thick and backed with 1.0 mm Al to filter out the low-energy scatter and characteristic X-rays from the Cu.

Restrictors ( Fig. 14.21 )

The basic function of a restrictor is to regulate the size and shape of the x-ray beam. Well-collimated beams generate less scatter and thus improve image quality. Three types of x-ray restrictors include:

Aperture diaphragms
Cones
Collimators

The collimator is the best all-round x-ray beam restrictor. Federal regulations require automatic collimators on all new x-ray equipment. To calculate the geometry of the aperture:

a / b = A / B

$a / b = A / B$

Grids

Grids consist of Pb strips separated by plastic spacers. Grids are used to absorb scatter and to improve radiographic image contrast.

Grid Ratio ( Fig. 14.22 )

The grid ratio is defined as the ratio of the height of the Pb strips (H) to the distance between them (D):

Grid ratio = H : D

$Grid ratio = H : D$

The thickness of the Pb strip (d) does not affect the grid ratio, although it does affect the Bucky factor (BF). The higher the grid ratio:

The better the image contrast
The higher the patient exposure
The better the grid function (more scatter absorbed)

Comparison of Grids

Parameter	12 : 1 Grid	8 : 1 Grid
Contrast	Better	Worse
Patient exposure	Higher	Lower
Lateral decentering artifact ^a	More prominent	Less prominent
Scatter	Lower	Higher

a Loss of density across the image.

Rules of thumb regarding grids:

<90 kVp X-ray: use 8 : 1 grid
>90 kVp X-ray: use 12 : 1 grid
Mammography: carbon fiber grids, 4 : 1 ratio, 150 lines/inch (i.e., 60 lines/cm)
Mobile units: 6 : 1 ratio grid, 110 lines/inch
Common reciprocating Bucky: 12 : 1 ratio grid, 80 lines/inch
High line density for stationary grids

Types of Grids ( Fig. 14.23 )

Linear Grid

Pb strips are parallel to each other. Advantage: angle of x-ray tube can be adjusted along the length of the grid without cutoff.

Crossed Grid

Made up of two superimposed linear grids. Cannot be used with oblique techniques (disadvantage). Only used when there is a great deal of scatter (e.g., in biplane cerebral angiography).

Focused (Convergent) Grid

Pb strips are angulated so that they focus in space (the convergent line). The focal distance is the distance between the grid and the convergent line or point and should be close to the focus-film distance in use.

Moving Grid (Bucky Grid)

If grids are moved during x-ray exposure, the shadow casts produced by Pb trips (grid lines) can be blurred out and the image quality can thus be improved. Although it is advantageous to use moving grids, there are certain disadvantages:

Moving grids increase the patient's radiation dose for two reasons:
- Lateral decentering (see Fig. 14.25 )
- Exposure is spread out over the entire surface of film
Longer exposure times are needed (because of lateral decentering)
Higher cost (because of film advancement mechanism)

A grid-controlled x-ray tube is a tube in which a large negative voltage can be applied to a third electrode near the cathode. This negative voltage repels electrons before they reach the target and prevents x-ray production. Using this method, the x-ray beam can be rapidly switched on and off. When the grid voltage is synchronized with exposures, this tube is suitable for rapid cinefluoroscopy (e.g., cardiac fluoroscopy).

Grid Performance ( Fig. 14.24 )

Grid performance is usually measured by one of three parameters:

Contrast improvement factor
BF
Primary transmission

Contrast Improvement Factor

Measurement of a grid's ability to improve contrast. High-ratio grids with a high Pb content have a high contrast improvement factor (K).

K = \frac{Contrast with grid}{Contrast without grid}

$K = \frac{Contrast with grid}{Contrast without grid}$

A disadvantage of this parameter is that it depends on kVp, field size, and phantom thickness, the three classic parameters that determine the amount of scatter. The contrast improvement factor is usually determined at 100 kVp with a large field and a phantom thickness of 20 cm.

Bucky Factor (BF)

Related to the fraction of the total radiation (primary radiation and scatter) absorbed by a grid. BFs usually range from 3 to 7, depending on the grid ratio. The BF indicates:

How much exposure factor must be increased because of use of a grid
How much extra radiation the patient receives
- The BF is calculated as follows:
  
  $BF = \frac{Incident radiation}{Transmitted radiation}$ $BF = \frac{Incident radiation}{Transmitted radiation}$

Bucky Factor by Grid Ratio

Grid Ratio	BF at 70 kVp	B at 120 kVp
No grid	1	1
5 : 1	3	3
8 : 1	3.5	4
12 : 1	4	5
16 : 1	4.5	6

BF , Bucky factor; kVp , peak kilovoltage.

Pearls

The BF increases as the grid ratio increases.
The BF increases with the thickness of the patient.
Although a high BF is desirable (good film quality), it has the disadvantage of a higher exposure to the patient.

Primary Transmission

Measurement of the primary radiation (scatter excluded) transmitted through a grid. The scatter is excluded in the experimental setup by the use of a Pb diaphragm and placing the phantom a long distance from the grid. The observed transmission is always lower (60%–70%) than calculated transmission (80%–90%) partly because the spacer absorbs some primary beam. The transmission (T) can be calculated by:

where D = thickness of the spacer and d = thickness of the Pb strip.

Grid Artifacts ( Fig. 14.25 )

Upside-Down Focused Grid

All grids have a tube side, which is marked as such. If the grid is inadvertently inserted the other way around, one will see a central area of exposure with peripheral underexposure. One may get the same sort of artifact in two other scenarios:

A parallel grid is used (i.e., Pb strips are not convergent)
Focus-grid decentering (i.e., x-ray tube is too close or too far from convergent line)

Focus-Grid Distance Decentering

The x-ray tube focus is above (far) or below (near) the convergent line. The artifact is the same as with an upside-down grid.

Lateral Decentering

The more lateral the misalignment of a grid and x-ray focus, the more severe this artifact. The artifact consists of a homogeneous underexposure of the entire film. This artifact is probably the most difficult to recognize. The loss of primary radiation (in %) because of lateral decentering is given by:

Loss = \frac{Grid ratio \times Lateral decentering (cm)}{Focal distance (cm)} \times 100

$Loss = \frac{Grid ratio \times Lateral decentering (cm)}{Focal distance (cm)} \times 100$

When exact centering is not possible (as in portable films), low ratio grids and long focal distances should be used.

Combined Lateral and Focus-Grid Distance Decentering

Probably the most commonly recognized artifact. Causes uneven exposure, resulting in a film that is light on one side and dark on the other side.

Air Gap Techniques ( Fig. 14.26 )

Air gap techniques are an alternative method of eliminating scatter with large radiographic fields. This method is often employed for CXRs. Patient exposure is usually lower with this technique than with grids. The intensity of scatter is maximal at the patient's exit surface and diminishes rapidly at increasing distance from the surface. If the film is placed at a distance (gap), most scatter misses the film. Focal film distance is increased in an attempt to maintain image sharpness. As a result, x-ray exposure factors (mAs) are usually greater than with grid techniques.

Screens ( Figs. 14.27 – 14.28 )

Much of modern radiography has transitioned to digital radiography, but discussion of intensifying screens is included for historical purposes. Intensifying screens are thin sheets of fluorescent material that surround radiographic film within the cassette or film changer. Screens are used because light is approximately 100 times more sensitive in exposing film than is radiation. Almost all x-ray absorption in the screen is caused by the PE (high atomic number). Implications of using screens include:

Reduces the x-ray dose to the patient
Allows lowering of mAs, which results in shorter exposure times and fewer motion artifacts
Main disadvantage is that they cause blurring of film

A variety of intensification screens are available. Calcium tungstate (CaWO ₄ ) screens were used until the 1970s before being replaced by rare earth (such as gadolinium [Ga] and lanthanum [La]) screens.

Digital Radiography (DR)

Modern radiography has largely transitioned to DR which allows for efficient archiving and convenient dynamic postprocessing of images. Two main types of DR exist:

1
Computed radiography (CR) ( Fig. 14.29 )
- A cassette is used as the detector (analog to film cassette in conventional analog radiography).
- Photostimulable phosphor plate (europium containing barium fluorohalides) within the cassette stores exposure which can be subsequently read out by a scanner to generate a digital image.
  - Europium (Eu) ²⁺ is ionized to Eu ³⁺ following x-ray strike. Liberated electron is trapped by the halide which maintains a metastable state
  - Scanning laser releases trapped electron which is recaptured by Eu resulting in the emission of visible light (photostimuable luminescence) ( Fig. 14.30 ).
  - The luminescence of Eu:BaFX (barium fluorohalide) decays exponentially as soon as the reading light is turned off (half-luminescence time is 0.8 µs) ( Fig. 14.31 ).
  - Fading refers to loss of the stored x-ray information in the image plate with time. As a rule of thumb, light emission will decrease about 25% within 8 hours after acquisition of the X-ray.
  - The image plate is also sensitive to other forms of radiation, including gamma rays, alpha rays, beta rays, etc. Therefore the cassettes should be kept away from other sources of radiation.
2
DR
- No cassette needed and faster than conventional film or CR radiolography
- Flat panel detectors used to automatically generate a digital image. This process can be direct (x-ray exposure converted directly into electrical charge) or indirect (phosphor screen scintillator converts X-rays into light which is then converted into electrical charge).
- Indirect DR
  - Utilizes a scintillator (thallium-doped cesium iodide) which emits light after absorption of X-ray
  - Emitted light is converted to electrical charge via a photodiode which is then read out by a digital array
  - Indirect methods are susceptible to lateral dispersion
- Direct DR
  - Uses photoconductor (amorphous selenium) to directly convert X-ray to electrical charge
  - No lateral dispersion
  - Direct DR systems have a higher fill factor (more efficient detector) compared with CR or indirect DR systems.

Quantum Mottle

Quantum mottle is due to statistical fluctuation of photons in an x-ray beam. The more photons that are used, the less mottle there is.

Quantum Mottle

Source of Mottle	Ways to Reduce Quantum Mottle (i.e., Less Noisy Image)
X-Ray Tube
mA	Increase the mA (generates more photons)
kVp	Increase the kVp (generates more photons)
Dose	Increase the dose (generates more photons)
Contrast	Decrease the contrast
CT slice thickness	Increase the slice thickness

CT , Computed tomography; kVp , peak kilovoltage; mA , milliampere.

Image Quality

Quality of an X-ray is primarily determined by contrast, resolution, and noise (quantum mottle). The higher the contrast-to-noise ratio, the better the image.

Contrast

Radiographic contrast describes the degree of density difference in two areas and depends on:

Inherent subject contrast
Scatter

Subject contrast refers to the difference in x-ray intensity transmitted through one part of the subject as compared with another. Subject contrast depends on:

Thickness of different portions of the subject (the thicker the subject part, the higher the absorption)
Density difference (mass per unit volume [i.e., g/cm ³ ]); the greater the difference, the higher the absorption
Atomic number difference (photoelectric absorption increases with high atomic numbers)
Radiation quality (kVp); low kVp will produce high contrast (mammography), provided the kVp is high enough to penetrate the part being examined.

Scatter (especially Compton scatter) is undesirable because it decreases radiographic contrast. Noise in DR largely arises from a combination of quantum mottle and intrinsic noise in the digital detector system.

Line Spread Function ( Fig. 14.32 )

Parameter of image quality. Tested with a vertical 10-µm collimated x-ray beam, which exposes a film-screen combination or digital detector. The “observed” width of the image (usually the full width at half maximum [FWHM]) is greater than 10 µm and depends on the film-screen combination or response function of the detector.

Modulation Transfer Function (MTF) ( Figs. 14.33 – 14.34 )

Parameter of image quality. The MTF can be expressed as the ratio of the diagnostic information recorded on film/detector divided by the total information available presented as a function of spatial frequency (e.g., line-pairs per millimeter). A ratio of 1 indicates perfect use of information. The lower the ratio, the more information is lost in the recording process. The individual MTF factors of the x-ray detector, x-ray film, intensifying screen, and x-ray tube can be multiplied to result in the total MTF of the x-ray system.

MTF = \frac{Contrast output}{Contrast input} = \frac{I'_{max} - I'_{min}}{I_{max} - I_{min}}

$MTF = \frac{Contrast output}{Contrast input} = \frac{I'_{max} - I'_{min}}{I_{max} - I_{min}}$

where I = intensity

Contrast output = \frac{I'_{max} - I'_{min}}{I_{max} + I_{min}}

$Contrast output = \frac{I'_{max} - I'_{min}}{I_{max} + I_{min}}$

Contrast input = \frac{I_{max} - I_{min}}{I_{max} - I_{min}}

$Contrast input = \frac{I_{max} - I_{min}}{I_{max} - I_{min}}$

Fluoroscopy

Fluoroscopes produce immediate and continuous images. Historically, flat fluorescent screens were used to intercept and visualize x-ray beams as they left the patient. As technology improved, image intensifier tubes were used, which greatly improved image quality by amplifying x-ray beams. Modern day fluoroscopy units have digital flat panel detectors which has resulted in significant improvements in sensitivity, temporal resolution, and contrast resolution. Spatial resolution of modern digital detectors is equivalent to their analog counterparts.

Image Intensifier ( Fig. 14.35 ) (Included for Historical Purposes)

An image intensifier is an electronic vacuum tube that converts an incident x-ray image into a light image of small size and high brightness.

Image intensifiers are required to amplify the x-ray signal to the light level needed for photopic (cone) vision. The individual components of an image intensifier consist of:

Input phosphor: absorbs X-ray and converts it to light photons
Photocathode: light photons strike photocathode, and electrons are emitted.
Accelerating anode: electron stream is focused by lens system onto a small area (e.g., 1-inch diameter) and accelerated to anode. Anode-cathode potential is 25 kV; because electrons are accelerated, they produce more light on the output phosphor (50-fold increase).
Output phosphor: converts electron stream to light
A video camera is usually used to record the small image at the end of the intensifier tube.

Input Phosphor and Photocathode ( Fig. 14.36 )

Input phosphor: thin layer of cesium iodide (CsI)
Photocathode composed of antimony and cesium compounds
Output phosphor composed of silver (Ag)-activated zinc-cadmium sulfide

Brightness Gain

The brightness gain of an image intensifier is measured by the conversion factor: candela per square meter (cd/m ² ) at the output phosphor divided by milliroentgen/second (mR/s) input exposure. The brightness gain deteriorates as the image intensifier ages (approximately 10% per year). Flux gain refers to the increase in number of output screen light photons relative to the input screen light photons.

Brightness gain = Minification gain \times Flux gain

$Brightness gain = Minification gain \times Flux gain$

Example

What is the brightness gain with an input screen of 6 inches, an output screen of 0.5 inch, and a 50-fold light flux gain?

Answer

Gain = {(6 / 0.5)}^{2} \times 50 = 7200 times

$Gain = {(6 / 0.5)}^{2} \times 50 = 7200 times$

Minification Gain

Minification gain = \frac{{Diameter input screen}^{2}}{{Diameter output screen}^{2}}

$Minification gain = \frac{{Diameter input screen}^{2}}{{Diameter output screen}^{2}}$

Because the output screen is usually 1 inch in diameter, the minification gain is usually the square of the image intensifier diameter (e.g., 81 for a 9-inch intensifier).

Example

What are the consequences when a 9-inch diameter image intensifier is switched to intensify a 6-inch diameter image?

Answer

First, the exposure to the patient will increase to maintain the same image brightness. Second, the new image will be magnified at the ratio of 9 : 6.

Resolution of Intensifiers

1–2 line-pairs/mm for old zinc-cadmium intensifiers (similar to old direct fluoroscopic screens with red light adaptation)
4 line-pairs/mm for modern CsI intensifiers

Distortion of Intensifiers

Refers to nonuniform electron-beam focusing
Distortion is most severe at the periphery of the intensifier.
Distortion is always more severe with large intensifiers.
Fall-off in brightness toward the periphery of the image is called vignetting .

Mammography

Key Differences From Traditional Radiography

Lower-energy x-ray beam is required in mammography because of the small difference in attenuation between normal breast tissue and breast cancer (recall that the probability of PE is proportional to 1/E ³ ).
Mammography also requires higher spatial resolution in order to see microcalcifications.
X-ray tube uses beryllium windows (in contrast to pyrex glass in diagnostic radiography tubes)

Target Filter Combinations

Mo or rhodium (Rh) is used as anode material for mammography because the lower-energy characteristic X-rays (17.5 and 19 keV for Mo) are more desirable for maximum subject contrast. A K-edge filter is used to filter out x-ray photons above and below the characteristic K-edge value (~20 keV for Mo filter) to generate a near monoenergetic beam. An Mo filter with a Rh target (Rh/Mo) should never be used as the higher keV emissions from the Rh target (20 keV and 22.7 keV) would be attenuated significantly by the Mo filter. Other target/filter combinations for mammography include:

Target Filter Combinations

Target	Filter
Molybdenum	Molybdenum
Tungsten with beryllium window	Variety of filters available. Allows for higher energy spectra and higher power loading.
Rhodium	Rhodium (higher energy beam for larger or denser breasts)
Molybdenum	Rhodium (generates intermediate energy beam)

Technical Requirements of Mammography

A small FS (~0.3–0.4 mm) is required for high resolution (the larger the FS, the worse the geometric unsharpness). Mammography units should also have 0.1-mm normal FS for magnification views.
Small FS limits how high you can go on mA meaning longer exposures relative to traditional radiography
Low kVp (24–25) to obtain good soft tissue contrast
Long distance of tube to object (65 cm) for high resolution
Short imaging time to reduce motion and dose
Scatter is best reduced by breast compression and the use of a grid; a grid of 5 : 1 should be used when compressed breast is >6 cm.
Compression decreases dose owing to thinner tissue plane, shorter exposure, and separation of overlapping structures.
Phototiming (automatic exposure control)

Digital Mammography

Digital mammography has largely supplanted analog film
- Various systems exist for digital detectors similar to other forms of diagnostic radiography (e.g., direct vs. indirect capture).
Digital systems have lower spatial resolution compared with analog film
Advantages of digital mammography include improved efficiency of x-ray photon absorption, increased dynamic range, decreased dose, ability for easy and rapid postprocessing, as well as efficient archiving.

Tomography/Tomosynthesis ( Fig. 14.37 )

Tomography is an x-ray technique that allows for separation of superimposed structures by a moving x-ray tube around the object. Tomosynthesis specifically refers to implementing tomography at limited angles (<360 degrees) to achieve this. Traditional analog tomography using film cassettes has been replaced by digital detectors for performing digital breast tomosynthesis. Historically, there are two basic types of tomography: linear and nonlinear. In both techniques, the tube moves in one direction while the film cassette/detector moves in the opposite direction, with both motions centered around a fulcrum. Modern day digital breast tomography systems acquire multiple projections in an arc which are then used to reconstruct a three-dimensional (3D) image. Modern systems typically use a direct x-ray photon detector with a layer of amorphous selenium (a-Se).

Linear Versus Nonlinear Tomography

Parameter	Linear Tomography	Circular Tomography
Cost	Inexpensive	Expensive
Blur margins	Indistinct	Distinct
Objects outside plane	May be visible (parasite streaks)	No parasite streaks
Phantom images	No	Yes (narrow-angle tomography)
Section thickness	Not uniform	Uniform

The amount of blurring depends on the following factors:

Amplitude of tube travel (more blur with wide-angle motion)
Distance from focal plane (more blur at long object–focal plane distances)
Distance from film (more blur at long object–film distances)
Orientation of tube travel: object needs to be oriented perpendicular to motion
Blurring is unrelated to size of the object.

The amplitude of tube traveling is measured in degrees (tomographic angle).

The wider the angle, the thinner the section.
The narrower the angle, the thicker the section.

Wide-Angle Versus Narrow-Angle Tomography

Parameter	Wide-Angle Tomography	Narrow-Angle Tomography
Angle	30–50 degrees	<10 degrees
Section thickness	Thin	Thick
Blurring	Maximum	Minimum
Use	Tissue with high contrast (bone)	Tissue with low contrast (lung)
Type of tomography	Linear or circular	Circular only
Phantom images	Unlikely	Yes
Exposure times	Long	Short

Disadvantages of Tomography

High patient dose with multiple cuts
High cost of circular tomography
Long exposure times (exposure time determined by time it takes to move the tube 3–6 seconds)
Motion artifacts with long exposure times are more common.

Stereoscopy ( Fig. 14.38 )

Stereoscopy is now rarely used and this section is included for historical purposes. Currently, stereoscopy is only used in the setting of stereotactic breast biopsies. Stereoscopic imaging techniques require the exposure of two films (one for each eye), with the x-ray tube minimally shifted between exposures. The original advantage of stereoscopy was that confusing shadows could be “untangled” when tomosynthesis and magnetic resonance imaging (MRI) were not available. However, there are many disadvantages to stereoscopy:

Twice as much patient exposure
Patient has to hold absolutely still

Computed Tomography (CT) (Helical, Multislice) ( Fig. 14.39 )

Overview

In CT a thin fan-shaped x-ray beam is projected through a slice of the body to be imaged. Penetrating radiation (or attenuation µ) is then measured by a detector. Images are reconstructed from multiple “views” obtained at different angles as the x-ray beam rotates around the patient.

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X-Ray Physics

Production of X-Rays

X-Ray Tube ( Fig. 14.1 )

Cathode

Anode

X-Ray Tube Output ( Fig. 14.2 )

Milliampere (mA)

Voltage

Exposure Time

Heat Unit ( Fig. 14.3 )

Rating Charts ( Fig. 14.4 )

Example

Answer

Focal Spot (FS)

FS and Resolution

Measurement of FS Size

Pinhole Method

Star Test Pattern

Magnification ( Fig. 14.5 )

Unsharpness

Radiation Exposure and Distance

Example

Answer

Spectrum of X-Rays

Bremsstrahlung ( Fig. 14.6 )

Characteristic Radiation ( Fig. 14.7 )

Heel Effect ( Fig. 14.8 )

X-Ray Generators

Transformer ( Fig. 14.9 )

Circuits of X-Ray Generators ( Fig. 14.10 )

Autotransformer

High-Voltage Transformer

Timer

Rectifier ( Fig. 14.11 )

Filament Circuit

Types of Generators

Three-Phase Generators ( Fig. 14.12 )

Advantages of Three-Phase Generators

Mobile Generators ( Fig. 14.13 )

Capacitor Discharge Generators

Phototimers

Interaction Between X-Rays and Matter

Coherent Scattering ( Fig. 14.14 )

Photoelectric Effect ( Fig. 14.15 )

Pearls

Compton Scattering ( Fig. 14.16 )

Probability of Compton Scatter

Pearls

Other Types of Interactions

Pair Production

Photodisintegration

Comparison of Interaction ( Fig. 14.18 )

Pearls

Attenuation

Attenuation Coefficients

Linear Attenuation Coefficient (cm −1 )

Mass Attenuation Coefficient

Monochromatic Radiation

Example

Answer

K-Edge ( Fig. 14.19 )

Polychromatic (Typical X-Ray) Radiation ( Fig. 14.20 )

Example

Answer

Filters

Restrictors ( Fig. 14.21 )

Grids

Grid Ratio ( Fig. 14.22 )

Types of Grids ( Fig. 14.23 )

Linear Grid

Crossed Grid

Focused (Convergent) Grid

Moving Grid (Bucky Grid)

Grid Performance ( Fig. 14.24 )

Contrast Improvement Factor

Bucky Factor (BF)

Pearls

Primary Transmission

Grid Artifacts ( Fig. 14.25 )

Upside-Down Focused Grid

Linear Attenuation Coefficient (cm ⁻¹ )