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CT Physics
Usman Mahmood, MS, DABR
Lead Diagnostic Medical Physicist
Department of Medical Physics
Memorial Sloan-Kettering Cancer Center

e-mail: [email protected]
1
Text and Reference Books
REFERENCE TEXTS:
Medical Imaging Physics, W.R. Hendee and E.R. Ritenour, Wiley-Liss
Publisher, fourth edition, 2002.

The Essential Physics of Medical Imaging, 2nd Edition. J.T. Bushberg,
J.A. Seibert, E.M. Leidholdt, and J.M. Boone, Lippincott Williams and
Wilkins Publisher, 2002.

Advances in Medical Physics. A. B. Wolbarst, K. L. Mossman, and W. R.
Hendee, Medical Physics Publishing, 2008.

Radiology Review: Radiologic Physics. E.L. Nickoloff, Elsevier/Saunders
Publisher, 2005.

Review of Radiologic Physics, 3rd Edition. W. Huda, Wolters KluwerLippincott Williams & Wilkins Publisher, 2010.

Computed Tomography, 2nd Edition. E. Seeram, Saunders Publishers,
2001.
Mosby – Exam Review for CT

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Some Online Resources

Sprawls Educational Foundation – The Physical Principles of
Medical Imaging
– http://www.sprawls.org/resources/

International Atomic Energy Agency (IAEA) – Radiation
Protection of Patients website
– http://rpop.iaea.org
– CT Tutor.com (have fee associated with them)
**All images are from Stewart Bushong “Radiologic Science for
Technologists”
3
X-ray Fundamentals
Review
Usman Mahmood, MS, DABR
Overview




Electromagnetic Radiation
X-Ray Tubes and X-ray Production
X-Ray Generator
Interaction of Radiation with Matter
Fundamental Principle


CT systems are basically density
measuring devices
An image of an object (i.e. person,
animal, ancient mummy etc.) may be
reconstructed on the basis of the
attenuation that occurs as x-radiation
is transmitted through it.
(Quoted from Mosby review book)
As shown above, a x-ray beam striking a
patient variably interacts with some tissues
of the body. This then produces a
“shadow” of the internal anatomy.
Electromagnetic Radiation

Photons have no mass and no
charge
Have magnetic and electric
fields changing in sinusoidal
fashion
Characteristics:
Travel in straight line
Wavelike
Invisible
Capable of penetrating
through a solid object
–

–
–
–
•
•
At higher energies, they have properties that
are similar to physical particles
Meaning that even though they have no
mass or charge, they are capable of
knocking out electrons (also known as the
ionization process)
–
What is an x-ray and how is it different
than a gamma ray or other EM radiation?
• One of the most energetic forms of light!
• Both gamma and X-rays are part of the EM
spectrum and are indistinguishable.
• However, the primary or only real difference is that
Gamma-rays originate from the nucleus of an atom.
• X-rays originate from outside the nucleus of an
atom.
X-Ray

Ionizing Radiation:
– Is radiation that is able to produce a change (ionization) in matter on the
atomic level. Ionization of an atom refers to removal or addition of
electrons from the atom. There are two types of ionizing radiation:
particulate and electromagnetic.
 X-Ray is a type of electromagnetic radiation

Described as a wave like fluctuation of electric and magnetic fields
– Photons are energy disturbances moving through space at the speed of
light
X-Ray Generators

The x-ray generator provides the
operator control of the radiographic
techniques:
–
–
–
–
Tube voltage (kVp),
Tube current (mA),
Exposure duration
and delivers power to the x-ray tube.
High Voltage Generators
Modify incoming voltage and
current in order to provide the x-ray
tube with the power to provide an xray beam
–

CT Scanners now use High Frequency
Generators (ripple is < 1%).
–
Typically located inside the CT gantry
X-ray Generator




Autotransformer – Is designed to supply a
precise voltage to the filament circuit
kVp = kilo-voltage peak (controls the
energy or quality of x-rays that are
prodcued – overall penetrating ability)
mA – milli-amperage or X-ray tube current
(quantity of radiation or “photon fluence”).
High Voltage Transformer – A “step-up”
transformer. Increases the output voltage
from the auto-transformer to the kVp
necessary for x-ray production.


Bridge Rectifier – Current from a
wall plug is 60 Hz AC (alternating
current).
Converts AC to a direct current
(DC) (means electrons flow in one
direction). Necessary for efficient
and safe operation of x-ray tube.
X-ray Production

X-radiation is created by taking energy
from electrons and converting it into
photons with appropriate energies.

This energy conversion takes place within
the x-ray tube.
X-ray Tube
Glass envelope: maintains a vacuum inside the tube.
Filament: The part of the cathode that emits electrons resulting in a tube
current
Focusing cup: metal shroud surrounding the filament
Target: Region of the anode struck by electrons emitted by the filament
Rotor: Rotating part of the electromagnetic induction motor located
inside the glass envelope
Window: thin section of the glass envelope through which the useful
beam emerges
Tube Glass Envelope
The primary functions of the envelope are –
1.
Ensures a vacuum, which allows for more efficient X-ray production.
i.
2.
If gas/air is present, then electrons flowing from cathod to anode may interact
with the gas/air… hence causing fewer x-rays to be produced, and generally
more heat is generated.
Provide structural support and electrical insulation for the anode and
cathode assemblies

Cathode
Basic Function of Cathode:


The basic function of the cathode
is to expel the electrons from the
electrical circuit and focus them
into a well-defined beam aimed at
the anode. (kept at negative
potential)
Consists of 2 components
2 Filaments – Where the
electrons come from.
–
–
Focusing Cup – helps direct
(“focus”) the x-rays to a
specific spot on the anode.
Cathode
Filament
– Material



Tungsten
High atomic number, High
melting point, Thermal
conductivity
1 – 2 cm coil of wire
– Purpose:

Focusing Cup:
Material
Nickel
Purpose:
Emit a low level negative charge
wherein emitted electrons from the
filament cannot repel from one another,
they are held together in a cloud
Electron emission when heated
to 2200° C
– Aka Thermionic Emission

Dual Focus = Two filaments
housed within one focusing
cup (creating large and small
focal spots (FS)).
Cathode Assembly


Small quantities of tungsten from the filament will vaporize and be
deposited on the floor of the envelope
– Generally at the window
Over time when sufficiently built up:
– Deposit acts as a filter which in turn reduces the efficiency and
intensity of the useful beam
– Compromises the vacuum within the envelope
– Creates a conducting surface which could conduct a current
 Arcing
Anode

The anode is the component in which the xradiation is produced. It is a relatively large
piece of metal that connects to the positive side
of the electrical circuit.

Has 2 functions:
– to convert electronic energy into x-radiation
– to dissipate the heat created in the process

Disk:
– Beveled edge (better heat dissipation and
smaller effective focal spot size)
– “Area” of x-ray production
– Focal (Target) Track
 Area on the surface of the anode disk in
which incoming electrons from the
filament interact
– High speed rotation evenly distributes heat
over the entire track
(+)
Target
(-)

Decelerates the electrons
– Anode: Positive electrode

Properties
– High melting point
– High “Z” material


Tungsten (W): “Z”=74, melts @ 3,370°C
e- always flow from negative to positive
Lead Housing

Attenuates x-rays emitted in directions
other than through the tube window
Housing leakage - <1 mGy/hr @ 1 meter
Anode Assembly
Induction Motor
 2 Parts
– Rotor: Located within the
envelope
 Armature on which the
disk sits
– Stator: Located outside the
envelope
 Series of
electromagnets whose
currents and electrical
fields function to “spin”
the rotor within
X-ray Production


An x-ray tube is an energy converter. It receives electrical energy and converts it
into two other forms: x-radiation and heat.
Main thing to remember:
– Approximately 0.2 % of energy during interactions produces x-ray
 Main production is HEAT
– Heat is problematic in any x-ray based system
 Solutions:
– Tungsten utilized for its thermal conductivity
– Oil is utilized surrounding the tube which helps it cool faster
– Rotation of the anode allows for a greater dissipation of heat over a larger
surface
X-ray Tube Heating


99.5% of all interactions in the x-ray tube
produce heat
0.5 % produce x-rays
– Tungsten Target





90 % - Bremsstrahlung
10 % - Characteristic
Heat units (HU)= kVp x mA x time
Tube Ratings – Heat Curves
Tube Cooling – Rate of Cooling
X-ray Production

Entire area on the focal track where the electron
stream impacts and x-ray photons are produced:
– Actual Focal Spot

Area on the focal track where the x-ray photons
are produced which are only directed out
towards the image receptor:
– Effective Focal Spot
Otherwise known as the Line Focus Principle:
- Focal spot is area of target where x-rays are
emitted
- By angling target (bevel) the “EFFECTIVE”
area of target is smaller than the actual area
of the electron interaction.
Affected by the angle of
the focal spot, generally
between 5 – 20 °
X-Ray Production

Focal Spot is related to detail
– Large Effective Focal Spot = Less detail
– Small Effective Focal Spot = Better detail

Usage of the small focal spot concentrates
heat into a smaller area
– Extended usage could lead to quicker anode
pitting
Anode Heel Effect
Radiation intensity is greater at the
cathode end of the tube then at the
anode end due to the absorbing
properties of the anode…
More pronounced at certain distances
and used in conventional x-ray
The smaller the anode angle, the
larger the heel effect
The difference in intensity across the
useful beam of an x-ray field can
vary by as much as 45%
X-Ray Tube Care

Potential causes for failure:
– Vaporized Tungsten (may lead to arcing)
– Pitted Anode
 High exposures eventually lead to heat creating small areas of melting aka pits on
the focal track
 Leads to vaporized tungsten and arcing
–
Cracked Anode
 Large exposure to “cold” anode can potentially crack the anode when great heat
load causes fast expansion of a cold surface
 WARM UP
– Gassy Tube
 Caused by compromise of the vacuum within the envelope
 Reduces amount of x-ray produced and could cause oxidation and burnout of the
filament
X-ray Production
Summary.. Primary function of X-ray tube –
1. Generate free electrons or an electron cloud that accumulates at the
cathode (free electron accumulation is aks space charge) .

2. Apply high voltage (50 kV to 150 kV supplied by generator) to
accelerate electrons from cathode (negative potential) to anode
(positive potential).
3. Allow for high energy electrons to interact with anode (tungsten
based target) so that x-rays can be produced.
X-ray Production
3. Allow for high energy electrons to interact with anode (tungsten
based target) so that x-rays can be produced.
-
Distance between cathode and anode is about 1 cm.
-
When electrons from the cathode (aka projectile electrons) strike the
atoms of the anode, energy is transferred from the electron to the
atom.
-
The projectile electrons interact with
-
1. Orbital electrons or inner shell electrons
2. Nucleus of atom
99% of the projectile electron energy is
converted to heat. 1% is used for production of
X-rays.
-
Characteristic X-ray

Incident electron knocks out an inner shell
electron ~ ionization
– Incident e- must have energy
(speed ½ mv2)  the binding energy of the
e- being knocked out.

As e- from outer shells fill the inner shell
vacancy – a characteristic x-ray is produced at
an energy equivalent to the difference between
the binding energies of the shells of the vacated
e- and the e- that takes its place

The x-rays produced are at specific energies
characteristic of the binding energies of the
target atom
Bremsstrahlung (braking radiation)

Electron interacts with the nucleus of an atom.
The electron decelerates and changes direction.
Energy of the x-ray
depends on the
amount of energy
the electron looses
during deceleration
KE=½ mv2
Eout
hυ  E in  E out
h
Broad range of
energies produced
– known as
spectrum!
the greater the Z of the target atom the greater the chance of
Bremsstrahlung interaction
X-ray Spectrum

Spectrum refers to range of types and quantity of x-rays

Here, the relative number of x-rays emitted is plotted as a function of energy
of each individual x-ray (known as polychromatic spectrum)

Bremsstrahlung x-rays have a range of energies and form a continuous
emission spectrum

If possible to measure the energy
in each emitted x-ray, would find
that energies range from peak
“electron” energy all the way
down to zero.

Ex. If x-ray tube operated at 100
kVp, can have xrays up to only
100 keV
X-ray Spectrum

Key Points
– Increase in tube current (mA)
from 200 mA to 400 mA means
2 x as many electrons will flow
from the cathode to the anode
(i.e. mAs will be doubled).
Mean 2x as many x-rays are
produced. Figure below.
– As kVp is raised, the x-ray
quantity increases with the
square of the kVp and the
spectrum shifts to the right
towards higher energy (more
penetrating) x-rays. Higher
beam quality.
Filtration

Photon output varies in energy or wavelength
– Lower energy x-rays do not penetrate, therefor do not contribute to final
image.

Why filter?
1. Remove long wavelength (low penetrating) photons which will not
contribute to the quality of the image and only contribute to acquired
dose; Harden the beam
2.
Shape energy distribution across beam in order to produce a more
uniform beam
Filtration

Inherent Filtration
– Materials which are a permanent part of the tube and its housing
 Envelope - Window
 Dilectic oils which surround the tube
– As tube ages, inherent filtration increases as the filament evaporates
 Deposits down onto the window which in turn places it in the path of the
beam

Added Filtration
– Anything added to sufficiently harden the beam
 Al / eq = Aluminum equivalent
X-ray Tube Heating


99.5% of all interactions in the x-ray tube
produce heat
0.5 % produce x-rays
– Tungsten Target





90 % - Bremsstrahlung
10 % - Characteristic
Heat units (HU)= kVp x mA x time
Tube Ratings – Heat Curves
Tube Cooling – Rate of Cooling
Technical Factors

mA
– Milliamperage



s
Amount of current applied to the filament responsible for the
burning off of electrons
Number of electrons crossing tube from cathode to anode
– Seconds


Length of time that the current is applied to the filament
mAs
– Directly proportional to the intensity of the photons
produced

Exposure rate or Number of photons
– Directly proportional to the dose that the patient receives
Technical Factors

kV
– Kilovoltage




Controls quality (and quantity) of the x-ray beam
Selection controls speed and energy levels of the
electrons applied across the x-ray tube
Increasing or Decreasing e- energy results in photons
with either greater or lesser penetrability
Does affect quantity – 15 % rule…
Ie. 80 kV beam will be more penetrating than 70 kV beam…it will also affect
photon quantity as 80 kV beam will have double the photons created…
QUIZ!

Which factors affect the x-ray
spectrum?
– kVp
– mA
– Exposure time
– Filtration
– Target material
QUIZ!

Which factors affect the x-ray
spectrum?
– kVp YES!
– mA NO!
– Exposure time NO!
– Filtration YES!
– Target material YES!
X-ray Beam - Primary vs.
Remnant
Primary vs. Remnant (exit)
The radiation which exits the x-ray
tube makes up the primary beam.
This radiation has not yet
interacted with matter.
•Remnant radiation is radiation which
exits the patient after it has
interacted with the anatomy under
investigation.
3 = primary beam. 4 = secondary
beam.
5 = Scatter radiation. 6
= remnant radiation
Interaction of Radiation and
Matter
Photon Interactions
• 3 major interactions between x-ray and matter
1. Photoelectric Effect
2. Compton Scattering
3. Coherent Scattering*
* Happens at kV levels below diagnostic therefore
does not contribute to imaging in CT
Classical (Rayleigh or elastic) Scattering
•
•
•
•
•
Excitation of the total
complement of atomic
electrons occurs as a result of
interaction with the incident
photon
No ionization takes place
No loss of E
The photon is scattered (reemitted) in a range of different
directions, but close to that of
the incident photon
Relatively infrequent
probability - 5%
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p. 37.
Compton Scattering
•
•
•
Dominant interaction of x-rays with
soft tissue in the diagnostic range
and beyond (approx. 30 keV 30MeV)
Occurs between the photon and a
“free” e- (outer shell e- considered
free when Eg >> binding energy,
Eb of the e- )
Encounter results in ionization of
the atom and probabilistic
distribution of the incident photon
E to that of the scattered photon
and the ejected e A probabilistic
distribution determines the angle
of deflection
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2 nd ed., p. 38.
Compton interaction probability
dependent on electron density
Compton Scattering
•
•
•
Compton interaction probability is dependent on the total
no. of e- in the absorber vol. (e-/cm3 = e-/gm · density)
With the exception of 1H, e-/gm is fairly constant for
organic materials (Z/A = 0.5), thus the probability of
Compton interaction proportional to material density ()
Conservation of energy and momentum yield the
following equations:
•
Eo = Esc + Ee-
•
E0
Esc =
1+
E0
1- cosθ 
2 
m ec
, where mec2 = 511 keV
Compton Scattering
Esc as a function of E0 and angle (q) – Excel spreadsheet
Compton Scattering
•
•
•
•
•
As incident E0  both photon
and e- scattered in more
forward direction
At a given  fraction of E
transferred to the scattered
photon decreases with  E0
For high energy photons most
of the energy is transferred to
the electron
At diagnostic energies most
energy to the scattered photon
Max E to e- at  of 180o; max E
scattered photon is 511 keV at
 of 90o
c.f. Bushberg, et al. The Essential Physics of Medical Imaging,
2nd ed., p. 39.
Photoelectric Effect
•
•
•
Interaction of incident photon with inner shell eAll E transferred to e- (ejected photoelectron) as kinetic energy (Ee)
less the binding energy: Ee = E0 – Eb
Empty shell immediately filled with e- from outer orbitals resulting in
the emission of characteristic x-rays (Eg = differences in Eb of
orbitals), for example, Iodine: EK = 34 keV, EL = 5 keV, EM = 0.6 keV
c.f. Bushberg, et
al. The Essential
Physics of Medical
Imaging, 2nd ed.,
p. 41.
Photoelectric Effect
1. Photoelectric:
Incident photon with an energy level the same as or slightly more
than the binding energy of an inner shell electron interacts
with that electron
Photon gets completely absorbed
Ejects this electron out of its orbit
Electron with a higher energy in an outer shells migrate towards
the nucleus emitting the energy difference between shells to
fill the vacancy
Atom is ionized
Photoelectric Effect
•
Edges become significant factors for higher Z materials
as the Eb are in the diagnostic energy range:
•
•
•
•
•
Contrast agents – barium (Ba, Z=56) and iodine (I, Z=53)
Rare earth materials used for intensifying screens – lanthanum
(La, Z=57) and gadolinium (Gd, Z=64)
Computed radiography (CR) and digital radiography (DR)
acquisition – europium (Eu, Z=63) and cesium (Cs, Z=55)
Increased absorption probabilities improve subject contrast and
quantum detective efficiency
At photon E << 50 keV, the photoelectric effect plays an
important role in imaging soft tissue, amplifying small
differences in tissues of slightly different Z, thus
improving subject contrast (e.g., in mammography)
Dependence on Z and E
• Photoelectric component
–   Z3/E3
• Compton component
–  Z0 logE/E
Mass Attenuation Coefficient
c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1 st ed., p. 26.
Attenuation
scattered
transmitted
absorbed
• Attenuation – reduced intensity
–  is the linear attenuation coefficient; probability of
interaction per unit path length.
– Total attenuation is a due to combination of
scattered(Compton effect) and absorbed
photons(Photoelectric effect)
I = I0 - I