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Physics of Radiography

Ho Kyung Kimhokyung@pusan.ac.kr

Pusan National University

Medical Physics

• Ionizing radiation

– Capable of ejecting electrons from atoms

• X-ray

• Gamma-ray

• Particulate radiation

• Radiographic imaging

– Transmission vs. emission imaging

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• Transmission imaging

– Making use of the transmission of ionizing radiation thru the body

– X-ray tube + imaging detector

– e.g., projection radiography & computed tomography (CT)

– Various tissues & organs attenuate the intensity of the x-ray beam as it passes thru the body

– The attenuation characteristics are determined by the effective atomic number Z & density of the tissues or organs

• Depicting structures within the body; hence anatomical imaging

– CT shows much higher “contrast” than the projection radiography because of the lack of superposition of out-of-plane tissues

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Ionization

• The ejection of an electron from an atom, creating a free electron & an ion

• Atomic structure

– Atom = nucleus + electrons

– Nucleus (consisting of “nucleons”) = protons + neutrons

– Atomic number, Z

= # of protons & defining the element

• Representing # of orbiting electrons

– Mass number, A

= # of nucleons (= protons + neutrons)

– Nuclide

• Referring to any unique combination of protons & neutrons which forms a nucleus

• Denoted by 𝑍𝐴𝑋 or 𝑋 − 𝐴 (e.g., 6

12𝐶 or 𝐶 − 12)

– Radionuclides

• Unstable nuclides & their atoms are radioactive

• Statistically likely to undergo radioactive decay causing a rearrangement of the nucleus, which in turn gives off energy & results in a more stable nucleus

• e.g., 614𝐶 → 7

14𝑁 + −1𝛽

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– Electron orbits or shells• K, L, M, …

• Max. number of electrons = 2𝑛2, where 𝑛 = the shell number

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• Electron binding energy

– E[atom] > E[nucleus] + E[electrons] energy difference binding energy

– BE as 𝑛

– BE of e– in H = 13.6 eV

– BE of e–‘s in Hg = 7.8 eV

• Average binding energy

– Avg. BE for air = ~34 eV

– Avg. BE for Pb = ~1 keV

– Avg. BE for W = ~4 keV

• Ionization & excitation

– Ionization ion + electrons (ion pairs)

– Excitation

• Transferring some energy to a bound electron but less than the electron’s binding energy

e– is raised to a higher energy state (e.g., a more outer orbit) but is

– Characteristic radiation

• Produced when “holes” or vacancies of e–‘s made due to ionization or excitation are filled w/ e–‘s from higher shells

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Forms of Ionizing Radiation

• Ionizing radiation: particulate vs. electromagnetic

• Particulate radiation

– Subatomic particles (proton, neutron & electron) w/ an enough kinetic energy to ionize an atom

– From Einstein’s theory of relativity

• 𝑚 =𝑚0

1− 𝑣2 𝑐2& 𝐸 = 𝑚𝑐2

– The K.E. of a particle

• 𝐾𝐸 = 𝐸 − 𝐸0 = 𝑚𝑐2 −𝑚0𝑐2

𝐾𝐸 =1

2𝑚𝑣2, 𝑣 ≪ 𝑐

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• Electromagnetic radiation

– Radio waves, microwaves, infrared light, visible light, ultraviolet light, x rays, rays

– No rest mass, no charge

– Acting like either a particle or wave

– Photons: “packets” of energy

• 𝐸 = ℎν

– ℎ = 6.626 10-34 Js = Plank’s constant

– 𝜈 = frequency (𝜆 = 𝑐 𝜈)

– 𝑐 = 3.0 108 m/s = the speed of light

– X rays from the electron cloud of atoms & gamma rays from the nuclei of atoms

• The same behavior in their propagation properties & interaction w/ matter

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Nature and Properties of Ionizing Radiation

• Particulate & EM ionizing radiations interact w/ the materials:

– Imparting energy to the material

– Losing energy from & redirecting their own radiation

– Generating new types of particles & radaition

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Imaging Dose

Particulate

BremsstrahlungCharacteristic radiationPositron annihilationRange

Linear energy transferSpecific ionization

Electromagnetic

AttenuationPhotoelectric effectCompton scatterCharacteristic radiationPolyenergetic

Air kermaDoseDose equivalentEffective dosef-factor

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Primary energetic electron interaction

• Electron & positron

– Only particles of direct consequences to the formation of medical images

– Positrons: discussed in nuclear medicine (PET)

• Electron interactions

– Electrons continue many (collisional & radiative) interactions successively until the incident e–‘s KE is exhausted

– Collisional energy transfer

• Transferring a typically “small” fraction of the e–‘s KE to another e–w/ which it collides

• Deexcitation process of the affected atom produces heat thru infrared light generation

• Occasionally, transferring a “large” amount of energy to a struck e– creating a new energetic e–‘s delta ray

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– Radiative energy transfer

• Producing x rays: characteristic vs. bremsstrahlung x rays

• Characteristic radiation

– Loss of energy in EM photons as e– fills the vacancy in the shell

– Energy of characteristic radiation = the difference in e– BE’s btwn two shells

– Discrete (monoenergetic) spectrum

• Bremsstrahlung radiation

– Caused by the interaction of an energetic e– w/ the nucleus of an atom

– Loss of energy in EM photon as e– decelerates (“braking radiation”)

– Intensity ~ E0 of e– & Z of the target

– Primary source of x rays from an x-ray tube

– Continuous (polyenergetic) spectrum

– Max. energy when the rare direct collisions btwn energetic e–’s & nuclei

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Primary EM radiation interactions

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• Pair production (PP)

– Occurring when E 1.02 MeV

– Negligible in medical imaging because of the typ. photon energies of 25–500 keV

• Photoelectric effect (PE)

– Interactions w/ (tightly-bound) electrons

– Complete energy absorption by an atom

– Ejecting a photoelectron & leaving a vacancy

• 𝐸𝑒− = ℎ𝜈 − 𝐸𝐵

– Filled the vacancy by electron transition, producing “characteristic” radiation

• Transfer of the characteristic radiation E to an outer-orbit electron Auger electron

– Energetic photoelectrons & Auger e–’s further interacts w/ matter (collisional/radiative), contributing to the detrimental biological effects of ionizing EM

– “Primary mechanism providing contrast btwn different types of tissues”

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• Compton scattering (CS)

– Interactions w/ (loosely-bound or free) electrons

– Ejecting a valence (outer-shell) e–, yielding a new energetic e– Compton electron

• 𝐸𝑒− = ℎ𝜈 − ℎ𝜈′

– Loss of the incident photon E & change in direction Compton photon

• ℎ𝜈′ =ℎ𝜈

1+ℎ𝜈

𝑚0𝑐2(1−cos 𝜃)

– Energy of Compton (or scattered) photons ~ -1

Max. E loss of primary photons when backscatter

– “Primary mechanism limiting the resolution of x-ray images”

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Probability of EM interactions

• Important for

– Differential attenuation in imaging

– Blocking or shielding from the source of ionizing EM radiation

• Photoelectric effect

– Occurring w/ the coulomb field of the nucleus of an atom (more likely more protons)

– Prob[PE] ∝𝑍𝑒𝑓𝑓4

(ℎ𝜈)3

• For high-Z materials: 𝑍𝑒𝑓𝑓4 → 𝑍𝑒𝑓𝑓

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• Increasing “abruptly” when the energy rises above BE of L- or K-shell electrons

contrast agent

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• Compton scattering

– Occurring w/ very loosely bound (or “free”) electrons in the outer shells

– Dependent upon # of e–’s per kilogram of material (electron density, ED)

• ED =𝑁𝐴𝑍

𝑊𝑚[e–’s/g or e–’s/kg]

– 𝑁𝐴 = Avogadro’s number (atoms/mole)

– 𝑍 = e–’s/atom

– 𝑊𝑚 = the molecular weight of the atom (grams/mole)

• ED for various biological materials is nearly the same as 3 1026 e–’s/kg

Prob. of CS is nearly independent of (actual or effective) Z

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Material Density (kg/m3) Zeff ED (e–’s/kg)

HydrogenCarbon

AirWaterMuscle

FatBone

0.08992250.0000

1.29301000.00001040.0000916.0000

1650.0000

1.06.07.87.57.66.5

12.3

5.97 1026

3.01 1026

3.01 1026

3.34 1026

3.31 1026

3.34 1026

3.19 1026

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– Energy dependence

• Klein-Nishina formula: the prob. of CS generally decreases w/ increasing ℎ𝜈

• Prob. of CS is reasonably constant in diagnostic imaging

• Prob[CS] ∝ ED

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Photon energy (keV)% of Compton

interactions% of deposited E due to Compton interactions

1015203040506080

100150

3.211.826.458.377.988.090.097.098.499.5

0.10.41.36.8

19.337.255.078.889.697.4

Attenuation of EM Radiation

• Attenuation

– Process describing the loss of strength of a beam of EM radiation

– Tissue-dependent attenuation (primarily) creating “contrast” in radiography

• Measures of x-ray beam strength

To characterize the inherent noise in the system;

To adjust the dynamic range of the detection system;

To estimate the (adverse) biological effects of ionizing radiation;

– Photon fluence Φ =𝑁

𝐴[#/mm2]

– Photon fluence rate 𝜙 =𝑁

𝐴Δ𝑡[#/mm2s]

– Energy fluence Ψ =𝑁ℎ𝜈

𝐴[keV/mm2] assuming monoenergetic photons

– Energy fluence rate 𝜓 =𝑁ℎ𝜈

𝐴Δ𝑡[keV/mm2s] assuming monoenergetic photons

• Also known as intensity of an x-ray beam 𝐼 = 𝐸𝜙 where 𝐸 = ℎ𝜈

– For polyenergetic photons or spectrum 𝑆(𝐸)

• 𝜙 = 0∞𝑆 𝐸′ d𝐸′ & 𝐼 = 0

∞𝐸′𝑆 𝐸′ d𝐸′

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Narrow beam, monoenergetic photons

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– Narrow beam geometry

• Photon beam is no wider than the detector

– Ignoring statistical effects & problems of detector efficiency

– 𝑛 photons are “lost” due to the attenuation

• Some photons are absorbed w/i the slab by the PE

• Other photons are deflected from the detector by CS

• 𝑛 = 𝜇𝑁∆𝑥

– 𝜇 a constant of proportionality linear attenuation coefficient

– 𝜇 = 𝑛 𝑁

∆𝑥the fraction of photons that are lost per unit length

• Consider a beam of N monoenergetic photons incident on a thin slab of homogeneous material

• Change in # of photons upon interaction w/ the slab:

– ∆𝑁 = 𝑁′ −𝑁 = −𝑛 = −𝜇𝑁∆𝑥

» 𝑁′ the counted photons in the detector

–d𝑁

𝑁= −𝜇d𝑥 𝑁 = 𝑁0𝑒

−𝜇𝑥 fundamental photon attenuation law

𝑁0 the number of photons at 𝑥 = 0

𝐼 = 𝐼0𝑒−𝜇𝑥 in terms of the intensity

𝐼0 the intensity of the incident beam

– Half-value layer (HVL):

• a thickness of a given material that the incident photons will attenuate half

•𝑁

𝑁0=

1

2= 𝑒−𝜇HVL HVL =

ln 2

𝜇=

0.693

𝜇

• Suppose the slab is not homogeneous: 𝜇 → 𝜇(𝑥)

–d𝑁

𝑁= −𝜇(𝑥)d𝑥 𝑁 = 𝑁0𝑒

− 0𝑥𝜇 𝑥′ d𝑥′

𝐼 = 𝐼0𝑒− 0

𝑥𝜇 𝑥′ d𝑥′

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Narrow beam, polyenergetic photons

• Replace 𝜇 by 𝜇(𝐸)!!!

– For an incident x-ray beam having spectrum 𝑆0(𝐸);

• 𝑆 𝐸 = 𝑆0(𝐸)𝑒−𝜇(𝐸)𝑥

– In addition, for a heterogeneous slab;

• 𝑆(𝑥; 𝐸) = 𝑆0(𝐸)𝑒− 0

𝑥𝜇 𝑥′;𝐸 d𝑥′

– For the overall intensity of the beam;

• 𝐼 = 0∞𝑆0 𝐸′ 𝐸′𝑒−𝜇 𝐸′ ∆𝑥d𝐸′

• 𝐼(𝑥) = 0∞𝑆0 𝐸′ 𝐸′𝑒− 0

𝑥𝜇 𝑥′;𝐸′ d𝑥′d𝐸′

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Broad beam case

• Broad beam geometry

– An additional possibility that photons from outside the detector’s line-of-sight geometry might get scattered toward the detector by Compton interactions

– More photons are generally detected than predicted by a monoenergetic, narrow beam analysis

– Even for the monoenergetci photon incidence, no longer monoenergetic in detected photons due to the CS which reduces photon energy beam softening

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• In practice, detector collimation makes the “narrow beam geometry” assumption possible

– Narrow-beam geometry for imaging (due to collimation)

– Broad-beam geometry for dose (due to no collimation)

Radiation Dosimetry

• Exposure 𝑋

– # of ion pairs produced in a specific volume of air by EM radiation

• C/kg of air in SI unit

• R (roentgen) in classic unit

• 1 R = 2.58 10-4 C/kg

• 1 C/kg = 3876 R

• Ionization chamber

– Measuring the current produced btwn two plates held at a fixed potential due to radiation producing ions in the air btwn the two plates

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• Dose 𝐷 & kerma 𝐾

– Absorbed dose

• rad 1 rad = 100 ergs/g in classic unit

» Note: 1 eV = 1.6 10-12 ergs = 1.6 10-19 J

• gray (Gy) 1 Gy = 1 J/kg = 100 rads in SI unit

• In soft tissue, 1 R of exposure 1 rad of absorbed dose

– Kerma

• The amount of energy per unit mass imparted directly to the electrons in a given material

• Measured in unit of “Gy”

• Essentially equivalent to “dose” at diagnostic x-ray energies

• Air kerma 𝐾𝑎𝑖𝑟– Used in air for calibration purposes

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• Linear energy transfer (LET)

– A measure of the energy transferred by radiation to the material through which it is passing per unit length

– Higher LET radiation producing greater adverse biological consequences

– Specific ionization (SI)

• # of ion pairs formed per unit length

– W-value

• Average amount of energy required to form one ion pair

• The f-factor

– A relationship between exposure in air & dose in air: 1 R = 0.87 rad

– To compute the dose to a material other than air;

• 𝐷 = 𝑓𝑋

– 𝑓 = 0.87( 𝜇 𝜌)𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙

( 𝜇 𝜌)𝑎𝑖𝑟

– 𝜇 𝜌 = the mass attenuation coefficient

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• Dose equivalent

– To consider the fact that different types of radiation can actually have different effects on the body even when delivering the same dose

– 𝐻 = 𝐷𝑄

• 𝑄 quality factor

a property of the types of radiation used

𝑄 ≈ 1 for x rays, gamma rays, electrons & beta particles

𝑄 ≈ 10 for neutrons & protons

𝑄 ≈ 20 for alpha particles

• 𝐻 in rems (rem) for 𝐷 in rads in classic units

• 𝐻 in siverts (Sv) for 𝐷 in grays in SI units

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• Effective dose

– For the purpose of relating “dose” of ionizing radiation to “risk”

– Comparing risks for different radiations & different target tissues

– An extension of the “dose equivalent” as the “dose equivalent” which would have been received if the whole body had been irradiated uniformly

– The sum of dose equivalents to different organs or body tissues weighted in a such fashion as to provide a value proportional to radiation-induced somatic & genetic risk even when the body is not uniformly irradiated

• 𝐷𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 = 𝑜𝑟𝑔𝑎𝑛𝑠 𝐻𝑗𝑤𝑗

– 𝐻𝑗 dose equivalent for organ j

– 𝑤𝑗 weighting factor for organ j

– 𝑜𝑟𝑔𝑎𝑛𝑠𝑤𝑗 = 1

– Average annual effective dose ~300 mrems

– Typical chest x-ray 10 mrems

– Fluoroscopy several rem

– Radiogenic carcinogenesis: cancer production

– Note that the physicians & patient together should make the decision that the medical benefits of the imaging procedure outweigh any potential risks

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