CT Physics CT Physics

Usman Mahmood, MS, DABRUsman Mahmood, MS, DABRLead Diagnostic Medical Physicist Lead Diagnostic Medical Physicist Department of Medical PhysicsDepartment of Medical PhysicsMemorial Sloan-Kettering Cancer CenterMemorial Sloan-Kettering Cancer Center

e-mail: umahmood1@yahoo.come-mail: umahmood1@yahoo.com

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Text and Reference BooksText and Reference BooksREFERENCE TEXTSREFERENCE TEXTS::

Medical Imaging PhysicsMedical Imaging Physics, W.R. Hendee and E.R. Ritenour, Wiley-Liss , W.R. Hendee and E.R. Ritenour, Wiley-Liss Publisher, fourth edition, 2002.Publisher, fourth edition, 2002.

The Essential Physics of Medical ImagingThe Essential Physics of Medical Imaging,, 2nd Edition2nd Edition.. J.T. Bushberg, J.T. Bushberg, J.A. Seibert, E.M. Leidholdt, and J.M. Boone, Lippincott Williams and J.A. Seibert, E.M. Leidholdt, and J.M. Boone, Lippincott Williams and Wilkins Publisher, 2002.Wilkins Publisher, 2002.

Advances in Medical PhysicsAdvances in Medical Physics. A. B. Wolbarst, K. L. Mossman, and W. R. . A. B. Wolbarst, K. L. Mossman, and W. R. Hendee, Medical Physics Publishing, 2008.Hendee, Medical Physics Publishing, 2008.

Radiology Review: Radiologic PhysicsRadiology Review: Radiologic Physics. E.L. Nickoloff, Elsevier/Saunders . E.L. Nickoloff, Elsevier/Saunders Publisher, 2005.Publisher, 2005.

Review of Radiologic PhysicsReview of Radiologic Physics, 3rd Edition, 3rd Edition. W. Huda, Wolters Kluwer-. W. Huda, Wolters Kluwer-Lippincott Williams & Wilkins Publisher, 2010.Lippincott Williams & Wilkins Publisher, 2010.

Computed TomographyComputed Tomography,, 2nd Edition2nd Edition. E. Seeram, Saunders Publishers, . E. Seeram, Saunders Publishers, 2001.2001.

Mosby – Exam Review for CTMosby – Exam Review for CT 22

Some Online ResourcesSome Online Resources Sprawls Educational Foundation – The Physical Principles of Sprawls Educational Foundation – The Physical Principles of

Medical ImagingMedical Imaging

– http://www.sprawls.org/resources/

International Atomic Energy Agency (IAEA) – Radiation International Atomic Energy Agency (IAEA) – Radiation Protection of Patients websiteProtection of Patients website

– http://rpop.iaea.org

– CT Tutor.com (have fee associated with them)CT Tutor.com (have fee associated with them)

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**All images are from Stewart Bushong “Radiologic Science for Technologists”

X-ray Fundamentals X-ray Fundamentals ReviewReview

Usman Mahmood, MS, DABR

OverviewOverview

Electromagnetic RadiationElectromagnetic Radiation X-Ray Tubes and X-ray ProductionX-Ray Tubes and X-ray Production X-Ray GeneratorX-Ray Generator Interaction of Radiation with Interaction of Radiation with

MatterMatter

Fundamental PrincipleFundamental Principle

CT systems are basically density CT systems are basically density measuring devicesmeasuring devices

An image of an object (i.e. person, An image of an object (i.e. person, animal, ancient mummy etc.) may be animal, ancient mummy etc.) may be reconstructed on the basis of the reconstructed on the basis of the attenuation that occurs as x-radiation attenuation that occurs as x-radiation is transmitted through it. is transmitted through it.

(Quoted from Mosby review book)(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 RadiationElectromagnetic Radiation

Photons have no mass and no Photons have no mass and no chargecharge

– Have magnetic and electric Have magnetic and electric fields changing in sinusoidal fields changing in sinusoidal fashionfashion

Characteristics:Characteristics:– Travel in straight lineTravel in straight line– WavelikeWavelike– InvisibleInvisible– Capable of penetrating Capable of penetrating

through a solid objectthrough 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 What is an x-ray and how is it different than a gamma ray or other EM than a gamma ray or other EM radiation?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-RayX-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 GeneratorsX-Ray Generators The x-ray generator provides The x-ray generator provides

the operator control of the the operator control of the radiographic techniques:radiographic techniques:

– Tube voltage (kVp), Tube voltage (kVp), – Tube current (mA), Tube current (mA), – Exposure durationExposure duration– and delivers power to the x-ray and delivers power to the x-ray

tube.tube.

High Voltage GeneratorsHigh Voltage Generators– Modify incoming voltage and Modify incoming voltage and

current in order to provide the x-ray current in order to provide the x-ray tube with the power to provide an tube with the power to provide an x-ray beamx-ray beam

CT Scanners now use High Frequency CT Scanners now use High Frequency Generators (ripple is < 1%). Generators (ripple is < 1%).

– Typically located inside the CT gantryTypically located inside the CT gantry

X-ray GeneratorX-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-rayX-ray Production 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 X-ray Tube

Glass envelope:Glass envelope: maintains a vacuum inside the tube. maintains a vacuum inside the tube.

Filament:Filament: The part of the cathode that emits electrons resulting The part of the cathode that emits electrons resulting in a tube currentin a tube current

Focusing cup:Focusing cup: metal shroud surrounding the filament metal shroud surrounding the filament

Target:Target: Region of the anode struck by electrons emitted by the Region of the anode struck by electrons emitted by the filamentfilament

Rotor:Rotor: Rotating part of the electromagnetic induction motor Rotating part of the electromagnetic induction motor located inside the glass envelopelocated inside the glass envelope

Window:Window: thin section of the glass envelope through which the thin section of the glass envelope through which the useful beam emergesuseful beam emerges

Tube Glass EnvelopeThe primary functions of the envelope are –

1.Ensures a vacuum, which allows for more efficient X-ray production.i. 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 .

2.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.

CathodeCathode

FilamentFilament– Material Material

TungstenTungsten High atomic number, High High atomic number, High

melting point, Thermal melting point, Thermal conductivityconductivity

1 – 2 cm coil of wire1 – 2 cm coil of wire

– Purpose:Purpose: Electron emission when heated Electron emission when heated

to 2200° Cto 2200° C– Aka Thermionic EmissionAka Thermionic Emission

Dual Focus = Two filaments Dual Focus = Two filaments housed within one focusing housed within one focusing cup (creating large and small cup (creating large and small focal spots (FS)). focal spots (FS)).

Focusing Cup:Material

NickelPurpose:

Emit a low level negative charge wherein emitted electrons from the filament cannot repel from one another, they are held together in a cloud

Cathode AssemblyCathode Assembly

Small quantities of tungsten from the filament will vaporize Small quantities of tungsten from the filament will vaporize and be deposited on the floor of the envelopeand be deposited on the floor of the envelope– Generally at the window Generally at the window

Over time when sufficiently built up:Over time when sufficiently built up:– Deposit acts as a filter which in turn reduces the Deposit acts as a filter which in turn reduces the

efficiency and intensity of the useful beamefficiency and intensity of the useful beam– Compromises the vacuum within the envelope Compromises the vacuum within the envelope – Creates a conducting surface which could conduct a Creates a conducting surface which could conduct a

currentcurrent ArcingArcing

Anode  The anode is the component in which the x-

radiation 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

TargetTarget

Decelerates the electronsDecelerates the electrons– Anode: Positive electrodeAnode: Positive electrode

PropertiesProperties– High melting pointHigh melting point– High “Z” materialHigh “Z” material

Tungsten (W): “Z”=74, melts @ 3,370Tungsten (W): “Z”=74, melts @ 3,370°C°C ee- - always flow from negative to positive always flow from negative to positive

(-)

(+)

Lead HousingLead Housing

Attenuates x-rays emitted in Attenuates x-rays emitted in directions other than through the directions other than through the tube windowtube window

Housing leakage - <1 mGy/hr @ 1 Housing leakage - <1 mGy/hr @ 1 metermeter

Anode AssemblyAnode Assembly

Induction MotorInduction Motor 2 Parts2 Parts

– Rotor: Located within Rotor: Located within the envelopethe envelope

Armature on which Armature on which the disk sitsthe disk sits

– Stator: Located outside Stator: Located outside the envelope the envelope

Series of Series of electromagnets electromagnets whose currents and whose currents and electrical fields electrical fields function to “spin” function to “spin” the rotor withinthe rotor within

X-ray ProductionX-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:Main thing to remember:– Approximately 0.2 % of energy during interactions produces x-rayApproximately 0.2 % of energy during interactions produces x-ray

Main production is Main production is HEATHEAT

– Heat is problematic in any x-ray based systemHeat is problematic in any x-ray based system Solutions:Solutions:

– Tungsten utilized for its thermal conductivityTungsten utilized for its thermal conductivity

– Oil is utilized surrounding the tube which helps it cool fasterOil is utilized surrounding the tube which helps it cool faster

– Rotation of the anode allows for a greater dissipation of heat over a larger Rotation of the anode allows for a greater dissipation of heat over a larger surfacesurface

X-ray Tube HeatingX-ray Tube Heating

99.5% of all interactions in the x-ray 99.5% of all interactions in the x-ray tube produce heattube produce heat

0.5 % produce x-rays0.5 % produce x-rays– Tungsten TargetTungsten Target

90 % - Bremsstrahlung90 % - Bremsstrahlung 10 % - Characteristic10 % - Characteristic

Heat units (HU)= kVp x mA x timeHeat units (HU)= kVp x mA x time Tube Ratings – Heat Curves Tube Ratings – Heat Curves Tube Cooling – Rate of CoolingTube Cooling – Rate of Cooling

X-ray ProductionX-ray Production Entire area on the focal track where the electron Entire area on the focal track where the electron

stream impacts and x-ray photons are produced:stream impacts and x-ray photons are produced:

– Actual Focal SpotActual Focal Spot

Area on the focal track where the x-ray photons Area on the focal track where the x-ray photons are produced which are only directed out are produced which are only directed out towards the image receptor:towards the image receptor:

– Effective Focal SpotEffective Focal Spot

Otherwise known as the Line Focus Principle:Otherwise known as the Line Focus Principle:

- Focal spot is area of target where x-rays are Focal spot is area of target where x-rays are emittedemitted

- By angling target (bevel) the By angling target (bevel) the “EFFECTIVE” area of target is smaller than “EFFECTIVE” area of target is smaller than the actual area of the electron interaction.the actual area of the electron interaction.

Affected by the angle of the focal spot, generally between 5 – 20 °

X-Ray ProductionX-Ray Production

Focal Spot is related to detailFocal Spot is related to detail– Large Effective Focal Spot = Less detailLarge Effective Focal Spot = Less detail– Small Effective Focal Spot = Better detailSmall Effective Focal Spot = Better detail

Usage of the small focal spot concentrates Usage of the small focal spot concentrates heat into a smaller areaheat into a smaller area– Extended usage could lead to quicker anode Extended usage could lead to quicker anode

pittingpitting

Anode Heel EffectAnode Heel EffectRadiation intensity is greater at the Radiation intensity is greater at the

cathode end of the tube then at the cathode end of the tube then at the anode end due to the absorbing anode end due to the absorbing properties of the anode…properties of the anode…

More pronounced at certain distances More pronounced at certain distances and used in conventional x-rayand used in conventional x-ray

The smaller the anode angle, the The smaller the anode angle, the larger the heel effectlarger the heel effect

The difference in intensity across the The difference in intensity across the useful beam of an x-ray field can useful beam of an x-ray field can vary by as much as 45%vary by as much as 45%

X-Ray Tube CareX-Ray Tube Care Potential causes for failure:Potential causes for failure:

– Vaporized Tungsten (may lead to arcing)Vaporized Tungsten (may lead to arcing)

– Pitted AnodePitted Anode High exposures eventually lead to heat creating small areas of melting aka pits on High exposures eventually lead to heat creating small areas of melting aka pits on

the focal trackthe focal track Leads to vaporized tungsten and arcingLeads to vaporized tungsten and arcing

– Cracked AnodeCracked Anode Large exposure to “cold” anode can potentially crack the anode when great heat Large exposure to “cold” anode can potentially crack the anode when great heat

load causes fast expansion of a cold surfaceload causes fast expansion of a cold surface WARM UPWARM UP

– Gassy TubeGassy Tube Caused by compromise of the vacuum within the envelopeCaused by compromise of the vacuum within the envelope Reduces amount of x-ray produced and could cause oxidation and burnout of the Reduces amount of x-ray produced and could cause oxidation and burnout of the

filamentfilament

X-ray ProductionX-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 ProductionX-ray Production3. 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 99% of the projectile electron energy is

converted to heat. 1% is used for production of converted to heat. 1% is used for production of

X-rays. X-rays.

Characteristic X-rayCharacteristic X-ray

Incident electron knocks out an inner shell Incident electron knocks out an inner shell electron ~ electron ~ ionizationionization– Incident Incident ee-- must have energy must have energy

(speed ½ mv(speed ½ mv22) ) the binding energy of the the binding energy of the ee-- being knocked out. being knocked out.

As As ee- - from outer shells fill the inner shell from outer shells fill the inner shell vacancy – a vacancy – a characteristic x-raycharacteristic x-ray is produced at is produced at an energy equivalent to the difference between an energy equivalent to the difference between the binding energies of the shells of the vacated the binding energies of the shells of the vacated ee-- and the and the ee-- that takes its place that takes its place

The x-rays produced are at specific energies The x-rays produced are at specific energies characteristic of the binding energies of the characteristic of the binding energies of the target atomtarget atom

Bremsstrahlung -Bremsstrahlung -(braking radiation)(braking radiation) Electron interacts with the nucleus of an atom.Electron interacts with the nucleus of an atom.

The electron decelerates and changes direction.The electron decelerates and changes direction.

outin EEhυ Energy of the x-Energy of the x-ray depends on ray depends on the amount of the amount of energy the energy the electron looses electron looses during during decelerationdeceleration

KE=KE=½½ mv mv22

Eout

Broad range of energies produced – known as spectrum!

the greater the Z of the target atom the greater the chance of Bremsstrahlung interaction

h

X-ray SpectrumX-ray Spectrum Spectrum refers to range of types and quantity of x-raysSpectrum 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 Here, the relative number of x-rays emitted is plotted as a function of energy of each individual x-ray (known as polychromatic spectrum)of each individual x-ray (known as polychromatic spectrum)

Bremsstrahlung x-rays have a range of energies and form a continuous Bremsstrahlung x-rays have a range of energies and form a continuous emission spectrumemission spectrum

If possible to measure the energy If possible to measure the energy in each emitted x-ray, would find in each emitted x-ray, would find that energies range from peak that energies range from peak ““electron” electron” energy all the way energy all the way down to zero. down to zero.

Ex. If x-ray tube operated at 100 Ex. If x-ray tube operated at 100 kVp, can have xrays up to only kVp, can have xrays up to only 100 keV100 keV

X-ray SpectrumX-ray Spectrum Key Points Key Points

– Increase in tube current (mA) Increase in tube current (mA) from 200 mA to 400 mA means from 200 mA to 400 mA means 2 x as many electrons will flow 2 x as many electrons will flow from the cathode to the anode from the cathode to the anode (i.e. mAs will be doubled). (i.e. mAs will be doubled). Mean 2x as many x-rays are Mean 2x as many x-rays are produced. Figure below. produced. Figure below.

– As kVp is raised, the x-ray As kVp is raised, the x-ray quantity increases with the quantity increases with the square of the kVp and the square of the kVp and the spectrum shifts to the right spectrum shifts to the right towards higher energy (more towards higher energy (more penetrating) x-rays. Higher penetrating) x-rays. Higher beam quality. beam quality.

FiltrationFiltration

Photon output varies in energy or wavelengthPhoton output varies in energy or wavelength

– Lower energy x-rays do not penetrate, therefor do not contribute to Lower energy x-rays do not penetrate, therefor do not contribute to final image. final image.

Why filter?Why filter?

1.1. Remove long wavelength (low penetrating) photons which will not Remove long wavelength (low penetrating) photons which will not contribute to the quality of the image and only contribute to acquired contribute to the quality of the image and only contribute to acquired dose; Harden the beamdose; Harden the beam

2.2. Shape energy distribution across beam in order to produce a more Shape energy distribution across beam in order to produce a more uniform beamuniform beam

FiltrationFiltration 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 HeatingX-ray Tube Heating

99.5% of all interactions in the x-ray 99.5% of all interactions in the x-ray tube produce heattube produce heat

0.5 % produce x-rays0.5 % produce x-rays– Tungsten TargetTungsten Target

90 % - Bremsstrahlung90 % - Bremsstrahlung 10 % - Characteristic10 % - Characteristic

Heat units (HU)= kVp x mA x timeHeat units (HU)= kVp x mA x time Tube Ratings – Heat Curves Tube Ratings – Heat Curves Tube Cooling – Rate of CoolingTube Cooling – Rate of Cooling

Technical FactorsTechnical Factors

mAmA– Milliamperage Milliamperage

Amount of current applied to the filament responsible for Amount of current applied to the filament responsible for the burning off of electronsthe burning off of electrons

Number of electrons crossing tube from cathode to anodeNumber of electrons crossing tube from cathode to anode ss

– SecondsSeconds Length of time that the current is applied to the filamentLength of time that the current is applied to the filament

mAsmAs– Directly proportional to the intensity of the photons Directly proportional to the intensity of the photons

producedproduced Exposure rate or Number of photonsExposure rate or Number of photons

– Directly proportional to the dose that the patient Directly proportional to the dose that the patient receivesreceives

Technical FactorsTechnical Factors

kVkV– KilovoltageKilovoltage

Controls quality (and quantity) of the x-ray beamControls quality (and quantity) of the x-ray beam Selection controls speed and energy levels of Selection controls speed and energy levels of

the electrons applied across the x-ray tubethe electrons applied across the x-ray tube Increasing or Decreasing e- energy results in Increasing or Decreasing e- energy results in

photons with either greater or lesser photons with either greater or lesser penetrabilitypenetrability

Does affect quantity – 15 % rule…Does affect quantity – 15 % rule…

Ie. 80 kV beam will be more penetrating than 70 kV beam…it will 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 also affect photon quantity as 80 kV beam will have double the photons created…photons created…

QUIZ!QUIZ!

Which factors affect the x-ray Which factors affect the x-ray spectrum?spectrum?– kVpkVp– mAmA– Exposure timeExposure time– FiltrationFiltration– Target materialTarget material

QUIZ!QUIZ!

Which factors affect the x-ray Which factors affect the x-ray spectrum?spectrum?– kVp YES!kVp YES!– mA NO!mA NO!– Exposure time NO!Exposure time NO!– Filtration YES!Filtration YES!– Target material YES!Target material YES!

X-ray Beam - Primary vs. X-ray Beam - Primary vs. RemnantRemnant

Primary vs. Remnant (exit)Primary vs. Remnant (exit)

The radiation which exits the x-The radiation which exits the x-ray tube makes up the ray tube makes up the primary beam. This primary beam. This radiation has not yet radiation has not yet interacted with matter.interacted with matter.

••Remnant radiationRemnant radiation is radiation is radiation which exits the patient after it which exits the patient after it has interacted with the has interacted with the anatomy under investigation.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 matter1. Photoelectric Effect2. Compton Scattering3. Coherent Scattering*

* Happens at kV levels below diagnostic therefore does not contribute to imaging in CT

Classical (Rayleigh or elastic) ScatteringClassical (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 (re-

emitted) 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, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p. 37. ed., p. 37.

Compton ScatteringCompton 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 E >> 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, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p. 38. ed., p. 38.

Compton interaction probability dependent on electron density

Compton ScatteringCompton Scattering

• Compton interaction probability is dependent on the total Compton interaction probability is dependent on the total no. of eno. of e-- in the absorber vol. (e in the absorber vol. (e--/cm/cm33 = e = e--/gm · density) /gm · density)

• With the exception of With the exception of 11H, eH, e--/gm is fairly constant for /gm is fairly constant for organic materials (Z/A = 0.5), thus the probability of organic materials (Z/A = 0.5), thus the probability of Compton interaction proportional to material density (Compton interaction proportional to material density ())

• Conservation of energy and momentum yield the Conservation of energy and momentum yield the following equations: following equations:

• EEoo = E = Escsc + E + Eee--

• , where m, where meecc22 = 511 keV = 511 keV

0

sc0

2e

EE =

E1+ 1- cosθ

m c

Compton ScatteringCompton Scattering

Esc as a function of E0 and angle () – Excel spreadsheet

Compton ScatteringCompton 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, c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 22ndnd ed., p. 39. ed., p. 39.

Photoelectric EffectPhotoelectric Effect

• Interaction of incident photon with inner shell e-

• All 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 (E = differences in Eb of orbitals), for example, Iodine: EK = 34 keV, EL = 5 keV, EM = 0.6 keV

c.f. Bushberg, et c.f. Bushberg, et al. The Essential al. The Essential Physics of Medical Physics of Medical Imaging, 2Imaging, 2ndnd ed., ed., p. 41.p. 41.

Photoelectric EffectPhotoelectric 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 absorbedEjects this electron out of its orbitElectron 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 EffectPhotoelectric 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 CoefficientMass Attenuation Coefficient

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1 stst ed., p. 26. ed., p. 26.

Attenuation

• 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)

scattered

transmitted

absorbed

I = I0 - I