3A Projection Radiography

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3A – Projection Radiography

Projection radiography, or x-ray imaging, is the most widely used imag-ing modality because it is low cost, fast and simple. It is particularly useful for imaging bony tissues and is still the method of choice for breast cancer screening.

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Electromagnetic Radiation

- Electromagnetic radiation has no rest mass and no charge, and can act like a wave or a particle.

- When treated as a wave, the wavelength λ (m) and frequency ν (Hz) are related as

λ = c/ν (1)

where c = 3.0 × 108 m/s is the speed of light.

- When treated as a particle, electromagnetic radiation is conceptual-ized as packets of energy (photons). The energy of a photon, given in Joules (J), is

E = hν = hc

λ (2)

where h = 6.626 × 10−34 J-s is Planck’s constant.

- The energy of a photon, given in electron volts (eV), is

E (keV) = 1.24

λ (nm) (3)

Note: 1 keV = 1.6021 × 10−16 J.

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Imaging Setup

- X-rays are generated by the interaction of accelerated electrons with a target material in the x-ray tube.

- The tube is placed at a distance of one or more meters from the patient.

- The radiograph may be a photosensitive ﬁlm or solid-state detector. - The image indicates the number of photons reaching the ﬁlm or detector; the greater the number of photons incident at a point, the darker the radiograph at that point.

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Measures of Beam Strength

The flow of x-ray photons is measured by quantities such as fluence, flux and energy fluence.

Fluence (unit m−2_{), or photon ﬂuence, is the number of photons, N, per}

unit area A:

Φ = N

A (4)

where the area is oriented at right angle to the direction of the radiation beam propagation.

Flux (unit m−2 s−1), or photon ﬂux, is the ﬂuence rate, i.e, the rate at which the photons pass though a unit area over an interval Δt:

φ = N

AΔt (5)

Energy ﬂuence is the amount of energy delivered per unit area. For a

monoenergetic beam of photons, the energy ﬂuence, Ψ is the product of the ﬂuence (Φ) and the energy per photon (E):

Ψ = Φ× E (6)

= N

A × E (7)

= Nhν

A (8)

The unit of Ψ is energy per unit area, e.g., J/m2.

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For a polyenergetic x-ray beam, the energy ﬂuence is obtained by mul-tiplying the number of photons at each energy by that energy, and sum-ming the individual contributions:

Ψ = Φ1 × E1+ Φ2 × E2 + . . . (9)

=

i Φi× Ei (10)

Energy ﬂux or intensity, I, is the power delivered per unit area. The

unit of I is energy per unit area per unit time (or power per unit area), e.g., W/m2. For a monoenergetic x-ray beam,

I = φ × E = Nhν

AΔt (11)

For a polyenergetic x-ray beam,

I =

i φiEi (12)

Summary

Fluence: number of photons per unit area m−2 Flux: number of photons per unit area per unit time m−2 s−1 Energy ﬂuence: energy per unit area J/m2

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Example

An x-ray beam comprises dual-energy photons: 40 keV at a ﬂux of 2× 1013 photons/m2-s, and 50 keV at a ﬂux of 3× 1013 photons/m2-s. The beam intensity is

I =

i=1,2φiEi = φ1E1 + φ2E2

= 2× 1013 photons/m2-s× 40 keV+3× 1013 photons/m2-s× 50 keV = 230× 1013 keV/m2-s

= 0.37 W/m2

The beam intensity is also given by

I = φt × ¯E

where φt is the total beam ﬂux and ¯E is the average photon energy. We

have φt = 2× 1013 + 3 × 1013 = 5× 1013 photons/m2-s ¯ E = (2× 40) + (3 × 50) 2 + 3 = 46 keV Thus, I = 5 × 1013 photons/m2-s × 46 keV = 230× 1013 keV/m2-s = 0.37 W/m2 6

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Example

Consider a 60 keV monoenergetic x-ray beam of intensity I = 50 × 10−3 W/m2 incident on an area A = 100 cm2. The exposure time is Δt = 0.5 s.

• The wavelength of the radiation is λ = 1.24

E (keV) nm =

1.24

60 nm = 2.07 × 10

−11 _m

• The photon energy (in J) E = hc λ = (6.626 × 10−34)(3.000 × 108) 2.067 × 10−11 = 9.62 × 10 −15 _J • The ﬂux is φ = I E = 50× 10−3 9.619 × 10−15 = 5.20 × 10 12 _photons/m2 -s

• The energy ﬂuence given the exposure time of 0.5 s is

Ψ = I × Δt = (50 × 10−3)(0.5) = 25 × 10−3 J/m2

• The ﬂuence is

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Absorbed dose

The damaging eﬀects of x-rays are due to its ionizing properties, which may lead to harmful genetic changes in cells.

- As the radiation passes through a material, some of its energy is absorbed and ion pairs (electrons and positive ions) are produced. - The absorbed dose (D) is a measure of risk to the patient; it is

deﬁned as the energy absorbed per unit mass of material. The unit is the gray (Gy), which is deﬁned as the absorption of 1 J per kg of material:

1 Gy = 1 J/kg

For example, if a head CT scan delivers a 30 mGy dose, each kg of the tissue absorbs 30 mJ of x-ray energy. If each slice has a mass of 0.25 kg, the absorbed energy is 7.5 mJ.

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Exposure

It is diﬃcult to measure dose directly; instead, we can determine dose by measuring exposure X, which is the amount of electrical charge produced by ionizing electromagnetic radiation per unit mass of air:

X = ΔQ

Δm (C/kg) (13)

The historical unit is the Roentgen (R), deﬁned as

1 R ≡ 2.58 × 10−4 C/kg (14) - Exposure is a useful quantity because ionization can be directly mea-sured. Also, exposure is approximately proportional to dose in soft tissue over the diagnostic x-ray range.

- Exposure is directly proportional to energy ﬂuence, i.e.,

X ∝ Ψ (15)

or

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X-ray Source

X-ray Tube

The usual source of diagnostic x-rays is electron bombardment of a metal target in a vacuum tube.

- A current is passed through the tungsten ﬁlament, which heats up and emits electrons through the process of thermionic emission. - The tube voltage, or anode voltage, accelerates the electrons towards

the anode (the tungsten target). The term kVp is also used to refer to this voltage, with values in the range 15 to 150 kVp.

- The tube current, arising from the ﬂow of electrons from the cathode to the anode, is also referred to as the mA. It is adjustable and ranges from 50mA to 400mA for projection radiography.

- At the target (anode),the kinetic energy of the electrons is converted into x-rays (about 1%) and heat (about 99%). The anode can be tungsten or another high-melting point conductor such as molybde-num.

- The anode rotates at several thousand revolutions per minute to avoid overheating.

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The x-ray beam exhibits a broad range of energies. High-energy electrons striking the atoms in the electrode generate x-rays by various mecha-nisms, resulting in general radiation and characteristic radiation.

General radiation

- General radiation (bremsstrahlung) decreases in ﬂux with increasing x-ray energy. The maximum x-ray energy Emaxdepends on the value

of kVp:

Emax = q × kVp (17)

where q is the electron charge, e.g., for kVp = 100 kV, Emax =

100 keV.

- X-rays with low energies are absorbed within the x-ray tube and its housing, resulting in the internally ﬁltered spectrum.

Characteristic radiation

- Characteristic radiation results in sharp peaks in the x-ray spectrum.

The x-ray energy spectrum can be characterized in terms of an average, or effective, x-ray energy. For example, an x-ray source with a tungsten anode operating at a kVp of 150 kV has an effective x-ray energy of approximately Eeff = 68 keV.

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The intensity I of the x-ray beam is the power incident per unit area (W/m2). It depends on

- the number of photons per unit area per unit time (the photon ﬂux,

φ), which is proportional to the product of tube current and tube

voltage, i.e., φ ∝ (mA)(kVp)

- the energy of the x-rays ¯E, which is proportional to the tube voltage,

i.e., ¯E ∝ (kVp)

Therefore, we have

I = (photon ﬂux) × (x-ray energy) (18)

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It is undesirable for low-energy photons to enter body as they are almost entirely absorbed by body tissues, thus contributing to patient radiation dose but not to image formation. These ﬁltering processes absorb the low-energy photons:

- the tungsten anode

- the housing of the x-ray tube

- added ﬁltering due to metal pieces, usually aluminium, placed out-side the tube.

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Beam restriction is used to avoid exposing parts of the patient that need

not be imaged. This can be done via diaphragms, cones or cylinders, and collimators.

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Factors Aﬀecting X-ray Emission

1. Target (anode) material

- aﬀects the eﬃciency of bremsstrahlung radiation production, with the amount of photons generated increasing with the atomic number Z of the material

- aﬀects the energies of the characteristic x-rays 2. Beam ﬁltration

- modiﬁes the x-ray beam by selectively removing the low-energy photons in the spectrum; this reduces the photon quantity and increases the eﬀective x-ray energy.

3. Tube voltage (kVp)

- a higher tube voltage increases the maximum energy in the bremsstrahlung spectrum and eﬃciency of x-ray production

4. Tube current (mA)

- the photon ﬂux and hence the number of photons generated per unit time is proportional to tube current.

5. Exposure time

- This is the duration of x-ray production.

- Quantity of x-rays (mA-s) ∝ tube current × exposure time

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Eﬀective Energy

For a polyenergetic x-ray beam, the x-ray spectrum, S(E), describes how the ﬂux varies with x-ray energy, E.

- S(E) is the photon ﬂux per unit energy (photons/m2-s-J or photons/m2-s-keV).

- The photon ﬂux Δφ emitted over a small range of photon energies ΔE centered at E is

Δφ = S(E)ΔE (20)

and the corresponding intensity

ΔI = EΔφ = ES(E)ΔE (21)

- The total ﬂux (photons/m2-s) over the entire spectrum is given by

φ =  ∞₀ S(E)dE (22)

and the intensity (W/m2) by

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A polyenergetic x-ray beam with ﬂux equal to φ may be modelled as a monoenergetic source, i.e., the polyenergetic beam and its monoenergetic equivalent have the same intensity.

- For the polyenergetic beam, the intensity is

Ip =  ∞

0 E S(E) dE (24)

- For the equivalent monoenergetic beam, the intensity is

Im = φ × Eeﬀ (25)

where Eeff is the average or effective energy and φ is the beam flux

given by φ =  ∞₀ S(E)dE (26) - Since Ip = Im,  ∞ 0 E S(E) dE =  ∞ 0 S(E)dE × Eeﬀ (27) Eeﬀ =  ∞ 0 ES(E)dE  ∞ 0 S(E)dE (28) 18

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Example

Calculate the eﬀective energy of an x-ray beam with the spectrum given in the ﬁgure.

Beam ﬂux is

φ = S(E)dE (area under S(E) curve)

= 5000k

The equation of line AB is S = 4kE

The equation of line BC is S = −4k₃ E + 400k₃

Beam intensity is given by

I =  ∞₀ ES(E) dE = 25 0 E × 4kE dE + 100 25 E −4k 3 E + 400k 3 dE = 208330k Hence, Eeﬀ = 208330k 5000k = 41.7 keV (29)

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X-ray Detector

- The standard imaging detector is a photographic ﬁlm comprising an emulsion layer coated on both sides of a transparent sheet (the ﬁlm base).

- The emulsion later contains photosensitive silver halide (mixture of silver bromide and silver iodide) granules.

- The ﬁlm has low sensitivity to x-rays, and so is commonly sand-wiched between intensifying screens and enclosed in a metal (alu-minum alloy) cassette.

- These screens contain a phosphor coating that converts the incident x-ray photons to visible light.

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- When exposed to x-rays (A), a photochemical reaction takes place resulting in the formation of an invisible latent image (B) on the ﬁlm.

- The image is made visible (C) by a chemical developing process. - A region of low x-ray attenuation (e.g., air) results in more x-rays

reaching the ﬁlm, and the developed ﬁlm appears dark in that region. - The projected image of bone appears somewhat transparent because

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Film blackening is quantiﬁed by a parameter known as the optical density (OD), deﬁned as

OD = log₁₀ Ii

It (30)

where

Ii is the intensity of the light incident on the developed x-ray ﬁlm, and

It the intensity transmitted through the ﬁlm.

- The darker the ﬁlm, the higher is the value of OD.

- A logarithmic scale is used because the physiological response of the eye to light intensity is itself logarithmic.

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Film characteristics

The relationship between OD and exposure (X) is referred to as the characteristic curve, or the H&D curve (after Hurter and Driﬃeld). Note that

- OD with zero exposure is small (0.13 to 0.18) but not zero. This OD is referred to as the “base + fog” OD, or simply “fog” OD. - The curve ﬂattens out at the toe and shoulder regions, i.e., poor

image contrast in these regions.

- The linear portion is the best region for imaging.

- Range of OD values suitable for viewing is from 0.4 to 2.2 (approx-imately).

- X-ray ﬁlm can be characterized by speed, contrast, and latitude:

Note: Exposure may be taken to be proportional to the energy ﬂuence (intensity× exposure time).

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Film speed

- This refers to the sensitivity of the ﬁlm.

- It is the inverse of the exposure at which OD = 1 + base + fog level. - A fast ﬁlm produces a given OD with a lower exposure than a slow

ﬁlm.

- Produces a grainier image than a slow ﬁlm.

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Film contrast

- Measured by the value of the ﬁlm gamma (Γ), deﬁned as the slope of the linear region of the characteristic curve:

Γ = OD2 − OD1

log X2 − log X1 (31)

- A high value of Γ means that a given difference in exposures for two areas of the film results in a large OD range (i.e., high contrast) in the developed film. (Range of Γ is typically 2.5 to 3.5.)

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Film latitude

- This refers to the ability of an x-ray imaging system to produce acceptable images over a range of exposures.

- Deﬁned as the range of exposure values that delivers OD in the useable range (about 0.4 to 2.2).

- The latitude is also referred to as the dynamic range of the ﬁlm. - Wide latitude ⇒ can image over a greater range of exposure but

with poorer contrast

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Digital X-ray Imaging

The detector is an electronic sensor instead of ﬁlm. Advantages:

- lower radiation dose

- eliminates ﬁlm processing - higher throughput

- ease of archival and transfer

- allows computer processing for enhancement, measurements

Disadvantages:

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Computed radiography

- uses similar equipment to conventional radiography except that the imaging sensor is an imaging plate made of photostimulable phos-phor

- after x-ray exposure, the cassette enclosing the imaging plate is run through a special laser scanner, or CR reader, that reads and digi-tizes the image

- the digital image can then be viewed and enhanced using software

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Digital radiography

- there is no need for a cassette; the ﬂat panel detector directly cap-tures the x-rays and generate a digital image without the need for a separate readout device