physics of radiography - pusanbml.pusan.ac.kr/resources/lecture/medphys/4_physicsradiography.… ·...

HK Kim

Revision: September 2013

DM223764/MedicalPhysics/PhysicsRadiography.doc Available at http://bml.pusan.ac.kr

Physics of Radiography

Ionization

Forms of Ionizing Radiation

Nature and Properties of Ionizing Radiation

Attenuation of Electromagnetic Radiation

Radiation Dosimetry

ionizing radiation: capable of ejecting electrons from atoms

- x-ray

- gamma ray

- particulate radiation

What is the difference between x-ray and gamma ray?

radiographic imaging

- transmission vs. emission imaging

transmission imaging

- making use of the transmission of ionizing radiation through the body

- x-ray tube + detector

- e.g., projection radiography and computed tomography (CT)

various tissues and organs attenuate the intensity of the beam as it passes through the body

the attenuation characteristics are determined by

the effective atomic number & density of the tissues or organs

depicting structures within the body; hence anatomical imaging

- CT shows much higher contrast than projection radiography

because of the lack of superposition of out-of-plane tissues

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HK Kim




HK Kim



Ionization

; the ejection of an electron from an atom, creating a free electron and an ion

ionizing radiation

- radiation carrying enough energy to ionize an atom

- capable of ejecting electrons from atoms

Atomic structure

atom = nucleus + electrons

nucleus (consisting of nucleons) = protons + neutrons

atomic number Z

= the number of protons and defining the element

- also representing the number of orbiting electrons

mass number A

= the number of nucleons

nuclide

- referring to any unique combination of protons and neutrons which forms a nucleus

- denoted by XA

Z or X-A (e.g., C126 or C-12)

radionuclides

- unstable nuclides and their atoms are radioactive

- statistically likely to undergo radioactive decay causing a rearrangement of the nucleus,

which in turn gives off energy and results in a more stable nucleus

- e.g., 1147

146 NC


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electron orbits or shells

- K, L, M, …

- a maximum number of electrons = 2n2, where n = the shell number

Electron binding energy

E[atom] < E[nucleus] + E[electrons] energy difference electron binding energy

- BE as n

- BE of the electron in H = 13.6 eV

- BE of electrons in the O-shell of Hg = 7.8 eV

average binding energy

- average BE for air = ~ 34 eV

- average BE for Pb = ~ 1 keV

- average BE for W = ~ 4 keV


HK Kim



Ionization and excitation

ionization ion + electrons (ion pairs)

ionizing radiation

- radiation with E 13.6 eV

- in medical imaging, 25–500 keV

excitation

- transferring some energy to a bound electron but less then the electron's binding energy

the electron is raised to a higher energy state (e.g., a more outer orbit) but is not ejected

characteristic radiation

- produced when "holes" or vacancies of electrons made due to ionization or excitation

are filled with electrons from higher shells


HK Kim



Forms of Ionizing Radiation

ionizing radiation: particulate vs. electromagnetic

Particulate radiation

subatomic particles (proton, neutron, & electron) with an enough kinetic energy to ionize an atom

From Einstein's theory of relativity,

22

0

/1 cv

mm

& 2mcE

The kinetic energy of a particle is

20

20KE cmmcEE

2

2

1KE mv , v << c

Electromagnetic radiation

radio waves, microwaves, infrared light, visible light, ultraviolet light, x rays, gamma rays

no rest mass, no charge

acting like either a particle or a wave

photons: "packets" of energy

hE

where h = 6.626 10-34 Js = Plank's constant

= frequency ( = c/)

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

x rays from the electron cloud of atoms and gamma rays from the nuclei of atoms

- the same behavior in their propagation properties and interaction with matter


HK Kim



Nature and Properties of Ionizing Radiation

Particulate and electromagnetic ionizing radiations interact with the materials:

- imparting energy to the material

- losing energy from and redirecting their own radiation

- generating new types of particles and radiation

radiation concepts

Imaging Dose

Particulate Bremsstrahlung

Characteristic radiation

Positron annihilation

Range

Linear energy transfer

Specific ionization

Electromagnetic Attenuation

Photoelectric effect

Compton scatter

Characteristic radiation

Polyenergetic

Air kerma

Dose

Dose equivalent

Effective dose

f-factor


HK Kim



Primary energetic electron interactions

electrons and positrons

- the only particles of direct consequences to the formation of medical images

- positrons: discussed in nuclear medicine (PET)

electron interactions: collisional energy transfer vs. radiative energy transfer

Electrons continue many (collisional and radiative) interactions successively

until the incident e–'s KE is exhausted

collisional transfer

- transferring a typically small fraction of the e–'s KE to another e– with which it collides

- deexcitation process of the affected atom produces heat through infrared light generation

- occasionally, transferring a large amount of energy to a struck e–,

creating a new energetic e– delta ray

radiative transfer

- producing x rays: characteristic vs. bremsstrahlung x rays

i) characteristic radiation

loss of energy in EM photon as e– fills the vacancy in the shell

the energy of characteristic radiation = the difference in e– BE's between two shells

discrete spectrum (monoenergetic)

ii) bremsstrahlung radiation

caused by the interaction of an energetic e– with the nucleus of an atom

loss of energy in EM photon as e– decelerates ("braking radiation")

intensity ~ E0 of e– and Z of the target

primary source of x rays from an x-ray tube

continuous spectrum (polyenergetic)

maximum energy when the rare direct collisions between energetic e–'s and nuclei


HK Kim



Primary electromagnetic radiation interactions

photoelectric effect (PE), Compton scattering (CS), pair production (PP)

pair production

- occurs when E 1.02 MeV

- typical photon energies in medical imaging range from 25–500 keV; hence negligible


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photoelectric effect

- interactions with (tightly-bound) electrons

- complete energy absorption by an atom

- ejecting a photoelectron and leaving a vacancy

BeEhE

- filled the vacancy by electron transition, producing characteristic radiation

the transfer of the characteristic radiation energy to an outer-orbit electron Auger electron

- energetic photoelectrons & Auger electrons further interacts with matter (collisional/radiative),

contributing to the detrimental biological effects of ionizing EM

- "primary mechanism providing contrast between different types of tissues"

Compton scattering

- interactions with (loosely-bound or free) electrons

- ejecting a valence (outer-shell) electron, yielding a new energetic electron Compton electron

' hhEe

- loss of the incident photon energy and change in direction Compton photon

)cos1(1

'

20

cm

h

hh

- the energy of Compton (or scattered) photons ~ (the scattering angle)-1

max E loss of primary photons when backscatter

- "primary mechanism limiting the resolution of x-ray images"

probability of EM interactions

- important for differential attenuation in imaging

blocking or shielding from the source of ionizing EM radiation

photoelectric effect

occurring with the coulomb field of the nucleus of an atom (more likely more protons)

3

4

)(event] electricProb[photo

h

Zeff

for high Z materials, 4effZ

3effZ

increasing abruptly when the energy rises above BE of L- or K-shell electrons

contrast agent


HK Kim



Compton scattering

occurring with very loosely bound (or "free") electrons in the outer shells

dependent upon the number of electrons per kilogram of material (electron density ED)

m

A

W

ZNED (electrons/g or electrons/kg)

where NA = Avogadro's number (atoms/mole)

Z = electrons/atom

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

ED for various biological materials is nearly the same as 3 1026 electrons/kg

the probability of CS is nearly independent of (actual or effective) Z

Material Density

(kg/m3) Zeff

Electron density

(electrons/kg)

Hydrogen

Carbon

Air

Water

Muscle

Fat

Bone

0.0899

2250.0000

1.2930

1000.0000

1040.0000

916.0000

1650.0000

1.0

6.0

7.8

7.5

7.6

6.5

12.3

5.97 1026

3.01 1026

3.01 1026

3.34 1026

3.31 1026

3.34 1026

3.19 1026

Energy dependence

Klein-Nishina formula: the prob of CS generally decreases with increasing hv

the probability of CS is reasonably constant in diagnostic imaging

Therefore, EDevent]on Prob[Compt

- Photoelectric vs. Compton interactions in water

Photon Energy (keV) % of Compton interactions % of deposited E due to

Compton interactions

10

15

20

30

40

50

60

80

100

150

3.2

11.8

26.4

58.3

77.9

88.0

90.0

97.0

98.4

99.5

0.1

0.4

1.3

6.8

19.3

37.2

55.0

78.8

89.6

97.4


HK Kim



Attenuation of Electromagnetic Radiation

attenuation

- the process describing the loss of strength of a beam of electromagnetic 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 A

N [#/mm2]

photon fluence rate tA

N

[#/mm2s]

energy fluence A

Nh [keV/mm2] assuming monoenergetic photons

energy fluence rate tA

Nh

[keV/mm2s] assuming monoenergetic photons

- also known as intensity of an x-ray beam EI where E = h

For polyenergetic photons, or spectrum S(E)

0

'd)'( EES &

0

'd)'(' EESEI


HK Kim



Narrow beam, monoenergetic photons

Consider a beam of N monoenergetic photons incident upon a thin slab of homogeneous material.

narrow beam geometry

- the photon beam is no wider than the detector

ignoring statistical effects and problems of detector efficiency

n photons are "lost" due to the attenuation

- some photons are absorbed within the slab by the photoelectric effect

- other photons are deflected away from the detector by Compton events

xNn

where a constant of proportionality linear attenuation coefficient

x

Nn

/ the fraction of photons that are lost per unit length

Change in # of photons upon interaction with the slab:

xNnNNN '

where N' the counted photons in the detector

xN

Nd

d xeNN 0 fundamental photon attenuation law

where N0 the number of photons at x = 0

xeII 0 in terms of the intensity

where I0 the intensity of the incident beam


HK Kim



half-value layer (HVL): a thickness of a given material that the incident photons will attenuate half

HVL

0 2

1 eN

N

693.02lnHVL

Suppose the slab is not homogeneous; (x)

xxN

Nd)(

d

x

dxxNN0

0 ')'(exp

x

dxxII0

0 ')'(exp

What is the average distance that a photon travels in a material?

Narrow beam, polyenergetic photons

Replace by (E)!!!

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

xEeESES )(0 )()(

In addition, for a heterogeneous slab,

x

dxExESExS0

0 ');'(exp)();(

For the overall intensity of the beam,

0

0 'd)'(exp')'( ExEEESI

0 00 'd')';'(exp')'()( EdxExEESxI

x


HK Kim



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 monoenergetic photon incidence, no longer monoenergetic in detected photons

due to the Compton scattering which reduces photon energy

beam softening

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)


HK Kim



Radiation Dosimetry

Exposure X

the number 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 between two plates held at a fixed potential

due to radiation producing ions in the air between the two plates

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 kirma Kair

used in air for calibration purposes

Linear energy transfer (LET)

a measure of the E transferred by radiation to the mat'l through which it is passing per unit length

higher LET radiation producing greater adverse biological consequences

specific ionization (SI)

- the number of ion pairs formed per unit length

W-value

- the average amount of energy required to form one ion pair


HK Kim



The f-factor

a relationship between exposure in air and dose in air: 1 R = 0.87 rad

to compute the dose to a material other than air;

fXD

where air

materialf)/(

)/(87.0

/ = the mass attenuation coefficient

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;

Define the concept of dose equivalent;

DQH

where Q quality factor

a property of the type of radiation used

Q 1 for x rays, gamma rays, electrons and beta particles

Q 10 for neutrons and protons

Q 20 for alpha particles

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

H in sieverts (Sv) for D in grays in SI units


HK Kim



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;

effective dose

- 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 and genetic risk

even when the body is not uniformly irradiated

organs

jjeffective wHD

where Hj dose equivalent for organ j

wj weighting factor for organ j

1organs

jw

average annual effective dose ~ 300 mrems

typical chest x-ray 10 mrem

fluoroscopy several rem

radiogenic carcinogenesis: cancer production

Note that the physician & patient together should make the decision that the medical benefits of the

imaging procedure outweigh any potential risks.


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