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Physics of RadiographySource: Medical Imaging Signals and Systems

By Jerry Prince and Jonathan Links

Projection x-ray basics (before physics)

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Projection x-ray basics (before physics)

X-ray physics: WE MAP THE ATTENUATION OF X-RAYS BY THE BODYWhat causes the attenuation?

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radiography

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What is “ionizing” radiation?Ans: Radiation that carries enough energy to ionize an atom (high

energy EM radiation)For our purposes, EM radiation with energy > 13.6eV, the energy

necessary to ionize a Hydrogen atom.

What does “ionization” mean?Ans: the ejection of an electron from an atom,

creating a free electron and an ion

Is it harmful to humans?Ans: yes, when not controlled

Ionizing radiation has sufficient energy to produce ionization events and breakmolecular bonds. If this energy is deposited in the intercellular fluid, toxiccompounds may be formed that can be detrimental to cell survival (damage byindirect action). A photon could also directly impact cellular DNA, causing strandbreakage (damage by direct action).

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Atomic Structure

Quantum mechanical picture of the atom from the 1920’sarose from the Bohr model of the hydrogen atom, 1913

Atomic number, Z = number of protons in the nucleus, defines the element= number of electrons

Mass number, A = number of nucleons (protons + neutrons)Nuclide = any unique combination of protons and neutrons which form a nucleus

Certain combinations of nucleons are stable, and others aren’t.Unstable nuclides are radionuclides, and their atoms are radioactive - Ch. 7,8,9Produce particulate radiation and gamma rays – both other forms of “ionizing”

Atomic Structure

Electrons are organized into orbits or shells.Max number of e- per shell is 2n2, where n is the shell number:

Binding energy: is the energy required to remove an electron from an atom,molecule, or ion, and also the energy released when an electron joins an atom,molecule, or ion. The binding energy of a single proton or neutron in a nucleus isabout a million times greater than that of a single electron in an atom.-Usually specified in electron volts (eV)-Depends on the element and the shell. Electron binding energy decreases w/increasing shell number.

Examples: Hydrogen, 13.6eV Lead, 1keV Tungsten, 4keV

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Ionization

IFradiation transfers energy to an orbiting electron > the electron’s binding energyTHENElectron is ejected from the atom.

This process is called ionization. It yields

-ion-electron

Radiation with energy > 13.6eV is considered ionizingAll other radiations are considered non-ionizing

ion pair

Excitation: If some energy is transferred to a bound electron, but less than thebinding energy, the electron is raised to a higher energy state (more outer orbit),but not ejected.

“Characteristic Radiation”: filling the “hole”

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Forms of ionizing radiation

Particulate ElectromagneticAny sub-atomic particle can beconsidered ionizing radiation if itpossesses enough kinetic energy toionize an atom.

Electric wave and magnetic wavetraveling together at right angles to oneanother

No rest massNo chargeParticle or Wave behavior

When photon energy>13.6eV, ionizing

Forms of ionizing radiation - notes

-X-rays and gamma rays are not distinguished by their frequency (or photon energy)-Instead, by origin:

-X-rays are created in the electron cloud-Gamma rays are created in the nuclei, which are undergoing reorganization dueto radioactive decay=> gamma rays are associated with radioactivity and x-rays are not

-Gamma rays tend to have higher energies than x-rays, BUT huge overlap in rays usedin medical imaging-Once produced, x-rays and gamma rays behave the same in terms of propagationand interaction with matter

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Properties of ionizing radiation

We care about effects/actions of ionizing radiation for two reasons:

1. Imaging capabilities/effects2. Biological consequences

Ionizing Interactions

Particulate(incident “energetic electron” interactions)

Electromagnetic(incident photon interactions)

*most common withenergies used inimaging

Incident e- collides, isredirected, untilkinetic energyexhausted

(infrared radiation isgenerated ininteractions;Sometimes deltaray)

*produces x-rays

characteristicradiation

bremsstrahlungradiation

*primary sourceof x-rays froman x-ray tube

Photoelectriceffect

ComptonScatter

PairProduction

Collisionaltransfer

Radiativetransfer

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Ionizing Interactions

Particulate(incident “energetic electron” interactions)

PairProduction

Photon>1.02MeVMed Img <500keV

Collisionaltransfer

Radiativetransfer

Electromagnetic(incident photon interactions)

*limits resolutionEinc=ħν, incident photon

interacts with valence(outer-shell) electron

Ee-=ħν- ħν’

*provides contrast

Einc=ħν, incident photon interacts with coulomb fieldof nucleas => K-shell (inner) interaction

Einc absorbed totally, e- ejected, Ee-=ħν-EB,

Transitions from higher orbits =>

Characteristic radiation =>Sometimes Auger electron _ 0 2'

1 (1 cos ) /( )comp phtE

m c

Photoelectric effect ComptonScatter

Probability of EM interactions(P-E event or Compton scatter)

• P-E events involve interaction with nucleus =>

1. more nucleus positive charge => more likely

2. more incident photon energy => less likely (more penetration)

• Sharp increase when Einc rises above bindingenergy of K-shell, L-shell electrons, then decrease

4

3Prob[photoelectric event] effZ

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Probability of EM interactions(P-E event or Compton scatter)

• Compton scatter involves loosely bound e-s(outer shell) =>

1. electron density = ED = electrons/kilogram

higher ED=> more likely scatter

2. Einc higher => less likely (but very gradualdecrease and very complicated relationship)

Attenuation

• Attenuation: the process describing the loss ofstrength of a beam of electromagnetic radiation.

• Tissue dependent attenuation = primary contrastmechanism in radiography

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Attenuation: X-ray Beam Strength

Photon fluence

Photon fluence rate

INTENSITY

Attenuation: X-ray Beam Strength(practical)

• Actual photon burst (beam) is polyenergetic -> plot of N(number photons) vs. E (energy) is a line spectrum.

• Line density (# photons per unit energy) is constant persource

• S(E) – x-ray spectrum, function of E, line density

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Attenuation: Linear Attenuation Coefficient(monoenergetic)

• N photon burst, N’ < N detected (P-E effectand Compton scatter in slab) = “attenuation”

• n “lost” photons,where n α N and Δx

Attenuation: Linear Attenuation Coefficient(monoenergetic)

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Attenuation: Linear Attenuation Coefficient

(monoenergetic)

What thickness of a givenmaterial will attenuate half ofthe incident photons?

• X-rays exhibit less attenuation at higher frequencies => musttreat LAC, μ , as a function of E…… i.e. μ(E)

Attenuation: Linear Attenuation Coefficient

(polyenergetic)

• Therefore, instead of

**** the energy dependence of μ ,while useful in helping to understand thebasic imaging properties, is intractable from a mathematical standpoint.The concept of effective energy (treating polyenergetic as monoenergetic)is more useful ****

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Attenuation: Broad Beam Case• X-ray beam is (for example) 7 times wider (7N photons)• Slab removed, detects N photons• Slab in place, photons within line-of-sight might be scattered or

absorbed…. But photons out of line-of-sight might get scattered towardsdetector = “BEAM SOFTENING”

• Detector collimation combats this => narrow beam assumption(for imaging point-of-view. Have to keep broad beam for dose since nocollimation on human “detectors”)

Radiation Dosimetry• “Dose”: concerned with what EM radiation does as

opposed to what it is. As EM radiation passesthrough a material, it deposits energy in it through P-E effect and Compton Scattering.

• Recall def’n: ionizing radiation is capable of ionizinghydrogen atom

• “exposure” = X = number of ion pairs produced in aspecific volume of air by electromagnetic radiation.

– SI: [C/kg]

– Standard: roentgen [R], 1C/kg = 3876R

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• “Dose”: As EM radiation passes through amaterial, it deposits energy in it through P-Eeffect and Compton Scattering

– Unit of absorbed dose: rad [D], rem,100rems=1Sievert

1 rad = absorption of 100ergs per gram of material

*note: rad is an energy-deposition concentration

• 1 R of exposure yields one D of absorbed dosein soft tissue

Radiation Dosimetry

Dosimetry: measures

• kerma [K] is amount of energy per unit massimparted directly to the electrons – related todose

• Linear energy transfer (LET) – measure of energytransferred by radiation to the material throughwhich it is passing per unit length

• Specific ionization (SI) – number of ion pairsformed per unit length

• LET and SI are related by W – the average amountof energy required to form one ion pair (acharacteristic of the material)

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Dosimetry

• In soft tissue, 1R exposure => 1rad dose, or10mSv

• In air, b/c of def’ns of R and rad, relationshipb/t exposure and dose is

1R = 0.87rad

• To compute dose to material other than air,use f-factor:

D=fX

where

0.87 material

air

f

μ is linear attenuation coefficientρ is mass density of material (or air)(μ/ ρ) is mass attenuation coefficient

Dosimetry

• “dose equivalent”, H, accounts for the fact thatsome types of ionizing radiation are “worse” thanothers:

H=DQ , where Q is quality factor

Examples:

Q (x-rays, gamma rays, electrons, beta particles) ≈ 1

Q (neutrons, protons) ≈ 10

Q (alpha particles) ≈ 20

For medical imaging, Q ≈ 1 and H=D with units [rems]

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Dosimetry• Effective dose: that which would have been received if

the whole body had been irradiated uniformly. Allowsfor risk assessment between tissues and radiations:

• Typical:– Annual effective dose: 300mrems (3mSv), 81% from

natural exposure. Rest is primarily from medical imaging.

– Chest x-ray: 10mrem

– Flouroscopic study: 3rem

• Main risk: cancer production (radiogeniccarcinogenesis)

Information Accountability:

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• Description/characteristics of electromagneticradiation, and in particular ionizing radiation

• See problems 4.5a, 4.6

• Understanding of attenuation

• See problem 4.8a

• (very general) understanding of dosimetry

Information Accountability: