02a MI MEBiom Xrays
02a MI MEBiom Xrays
02a MI MEBiom Xrays
X ray imaging
Patrícia Figueiredo
IST 2013-2014
Overview
• Production of X rays
• Interaction of electrons with matter
• X ray spectrum
• X ray tube
X rays are produced through the acceleration of an electron beam from a cathode
where they are emitted towards an anode where they interact with a target.
Heating through
passage of
electric current Thermionic
emission of Acceleration of
electrons free electrons X ray emission
towards the anode through
interaction of
free electrons
with the target
Interactions of electrons with matter
Atomic excitation:
Ionization:
Joule effect:
Heating!
Interactions of electrons with matter
Bremsstrahlung
Efficiency of
Bremsstrahlung
radiation:
η ∝ kVpZ
Relative nb photons
Maximum energy
Emax ∝ kVp
Photon energy
[keV]
Interactions of electrons with matter
e-
Ee=Einc-E0 Eo
X
e-
E1
Einc E1-E0
Eo
e-
E2 X
e-
Eo E2-E0
Ei = ΔEi
Atomic level transitions: discrete enery levels
Interactions of electrons with matter
Eo
X
E=20-2.6=17.4 eV E=69-11=58 eV e-
E1
E1-E0
E2 X
e-
Bremsstrahlung
Emax ∝ kVp
Maximum energy
[keV]
X ray tube
Range
D
θ
f
F
-Tube current: mA
~50 – 400 mA in radiography, ~1000 mA em CT, <50 mA in fluoroscopy
I ∝ (kVp)2 I ∝ mA
Emax ∝ kVp Emax unchanged
Epeak shifted to higher energies Epeak unchanged
Nb characteristic lines ↑ Nb characteristic lines unchanged
X ray tube
e-
E0
E1<<E0 Valence shell θ
E0 An electron is ejected
E2<<E0
E1<E0
Coherent (Rayleigh): elastic diffusion
Pair production: annihilation Secondary radiation
e-
E0
E0 Incident radiation is θ
γanhilation converted in thermal
e+ vibration of the electrons E1<E0
• there is no ionization
• Scattered angle increases
Interaction of X rays with matter
Distribuição de Compton:
E X ,inc
E X , scat =
1 + E X ,inc mc 2 (1 − cosθ )
EX,inc [keV]
θ 25 50 100 150
EX,scat [keV]
30° 24.8 49.4 97.5 144.4
60° 24.4 47.4 91.2 131.0
90° 23.8 41.9 72.1 94.6
X ray attenuation
e- e-
E1<<E0
E0 E0
E2 <<E0
θ
E1 <E0
•Incident X rays are absorbed and energy of •Incident X rays are scattered and energy of
secondary X rays is insufficient to reach detector scattered X rays is sufficient to reach detector
⇒ X rays reaching the detector are: ⇒X rays reaching the detector are:
primary radiation, with preserved energy secondary radiation with modified
and direction. energy and direction.
•Depends on atomic number Z •Does not depend on atomic number Z
⇒ provides contrast betwen materials ⇒ does not provide contrast betwen
materials
X ray attenuation
I0 I0exp{-µlΔx} ΔI = −I 0σ Nv Δx ⇒ I(x ) = I 0e −σ Nv x = I 0e − µl x
Operation region of
X-rays used in
medical diagnosis
X ray attenuation
I x = I 0e − µ x
µ = µ photoelectric + µCompton + µcoherent
Energy dependence:
The optimum X ray energy is
~ 30 keV (kVp ~ 80-100 kV)
In water where the photoelectric effect
dominates.
X ray attenuation If the X-rays have to pass
through a large amount of
tissue, such as in abdominal
imaging, then beam
Energy dependence: hardening reduces image
contrast by increasing the
Low Energy proportion of Compton-
Beam hardening:
Δx [mm] scattered X-rays due to the
lower energy X
higher effective energy of the
rays suffer more X-ray beam.
attenuation, hence
the mean energy of
the X-ray beam
increases as it goes
through the tissues.
High Energy
- Affects HVL
- Artifacts in CT
X ray attenuation
1
6
7
8
11
12
15
16
19
20
X ray attenuation
m = 3.8
PE effect dominates
(Zeff dependence)
good
contrast
Compton effect dominates
(ρN0 dependence)
bad
contrast
X ray attenuation
K-edge
better
contrast
X-ray tube
materials
Dosimetry
Dosimetric measures:
Exposition X: [1 R = 3.33 × 10-10 C/cm3 = 2.58 × 10-4 C/Kg ]
Dose D: [1 Gy = 1 J/Kg ou 1 rad = 100 erg/g ]
Factor f: f=D/X
Equivalent dose: H E = ∑ ωi Di QF [Sv ou rem]
i
+7T
1
CT dose index: CTDI = ∫ Dz dz
T − 7T
Overview
X ray production:
X ray tube / source
X ray transmission:
X ray attenuation
X ray detection:
X ray detectors
Instrumentation
1
CNR ∝
I
1 + scatt
I primary
Collimator
• restricts the FOV to the desired value ~10 – 30 cm
• ↑ CNR,
• ↓ dose
collimator (Pb)
Even with a collimator, scattered radiation can represent 50 – 90% of the detected radiation…
Instrumentation
I inc
scatt
1+
Pb I inc
primary
Δ (CNR) =
h I scatt I trans
inc
scatt
1+ inc trans
I primary I primary
t d
Bucky factor:
Exposure with grid
F=
Exposure without grid
intensifying
screen
Conventional radiography:
Optical density
linear
d region
latitude
Log exposure
OD 2 − OD1
γ=
log E 2 − log E1
Instrumentation
Computed radiography:
-Instead of a photographic emulsion, a cassette housing a plate of photostimulable phosphor is used.
-Instead of film exposure, a laser scanner is used to read the cassette.
Exposure to radiation ⇒
phosphor excitation ⇒
oxidation of Eu2+
X ray detectors: X rays → must be converted into radiation accessible to human vision
Digital radiography:
δ P
θ
f δ d0 d1
S0
S1
Image characteristics
S1
S0
~75 µm
f (S1 − S0 ) S0
P= ⇒f =P
S0 S1 − S0
Image characteristics
Spatial resolution:
-Quantum mottle: statistical variance of the distribution of X rays from the source
µ N e −µ
Poisson distribution: p( N ) =
N!
Contrast agents
K-edge
Iodinated contrast agents are
used to enhance contrast:
Fluorescent image intensifier (CsI:Na) → optimize SNR (in face of low energy)
Radiography techniques
Mammography: imaging soft tissue with high resolution and CNR