Biomedical Imaging I
-
Upload
evangeline-joseph -
Category
Documents
-
view
38 -
download
0
description
Transcript of Biomedical Imaging I
BMI I FS05 – Class 1 “X-Ray Physics” Slide 1
Biomedical Imaging IBiomedical Imaging I
Class 1 – X-Ray Imaging I: Background and Physics
9/14/05
BMI I FS05 – Class 1 “X-Ray Physics” Slide 2
BackgroundBackground
BMI I FS05 – Class 1 “X-Ray Physics” Slide 3
IntroductionIntroduction
Aim of medical imaging:
Creating images of internal structures (and functions) in a living (human) organism
Preferably non (or minimally) destructive / noninvasive
Diagnostic implications
Achieved by using the capability of various forms of energy to penetrate and interact with matter.
Historic starting point:
W. K. Röntgen’s discovery of the X rays experimenting with a cathode ray tube and fluorescent screen/photographic film (1895, 1901 first Nobel award in physics).
BMI I FS05 – Class 1 “X-Ray Physics” Slide 4
Discovery of x-raysDiscovery of x-rays
X-ray history on the web:
http://www.xray.hmc.psu.edu/rci/centennial.html
Physical Institute, University of Würzburg, Germany.
Wilhelm Konrad Wilhelm Konrad RRööntgen (1845-1923)ntgen (1845-1923)
(photographed in 1896)(photographed in 1896)
BMI I FS05 – Class 1 “X-Ray Physics” Slide 5
Discovery of x-raysDiscovery of x-rays
Cover of Original Publication: "A New Kind of Rays"
Wilhelm Konrad Wilhelm Konrad RRööntgen (1845-1923)ntgen (1845-1923)
(photographed in 1896)(photographed in 1896)
BMI I FS05 – Class 1 “X-Ray Physics” Slide 6
First x-ray imagesFirst x-ray images
Radiograph of the hand of Albert von Kolliker, made at the conclusion of Roentgen's lecture and demonstration at the Würzburg Physical-Medical Society on 23 January 1896.
The famous radiograph made by Roentgen on 22 December 1895, and sent to physicist Franz Exner in Vienna. This is traditionally known as "the first X-ray picture" and "the radiograph of Mrs. Roentgen's hand. "
BMI I FS05 – Class 1 “X-Ray Physics” Slide 7
Early x-ray setupEarly x-ray setup
BMI I FS05 – Class 1 “X-Ray Physics” Slide 8
X-rays in clinical useX-rays in clinical use
Dr. Edwin Frost (1866-1935) is credited with making the first diagnostic radiograph in the U.S. at Dartmouth on 3 February 1896.
BMI I FS05 – Class 1 “X-Ray Physics” Slide 9
X-rays in clinical useX-rays in clinical use
E. Haschek and 0. Lindenthal produce first contrast-enhanced radiograph of veins in hand (Vienna, January 1896).
BMI I FS05 – Class 1 “X-Ray Physics” Slide 10
X-ray dangersX-ray dangers
Mihran Kassabian (1870-1910) meticulously noted and photographed his hands during progressive necroses and serial amputations.
BMI I FS05 – Class 1 “X-Ray Physics” Slide 11
X-ray publicationsX-ray publications
In May of 1897, Heber Robarts, M.D., of St. Louis, launched the American X-ray Journal.
BMI I FS05 – Class 1 “X-Ray Physics” Slide 12
X-ray imaging principleX-ray imaging principle
X-ray imaging background, foundations:
(History)
X-rays
Atomic structure
Important x-ray-matter interactions
X-ray instrumentation / applications:
Generation of x-ray
Detection of x-ray
Specific applications
BMI I FS05 – Class 1 “X-Ray Physics” Slide 13
Physical foundationsPhysical foundations
BMI I FS05 – Class 1 “X-Ray Physics” Slide 14
Atom and electronic transitionsAtom and electronic transitions
Electrons (-) are organized in shells around nucleus (+)
Higher shell (greater shell radius) = higher electronic energy
Electronic transitions between shells require or release energy
+
-
--
n = 1
n = 2
n = 3
E = h = E3 - E2
E = h = E2 - E1
Absorption
Emission
Excitation
Relaxation
BMI I FS05 – Class 1 “X-Ray Physics” Slide 15
Complex AtomsComplex Atoms
Number of protons Z: Atomic number (determines element)
Number of neutrons N: Neutron number
Number of protons + neutrons Am = Z + N: Mass numberNa
22
11
-
-
-
-
--
- -
--
-+
+
+
+ ++
+ +
+
K-shell (n=1, strongly bound)
L-shell (n=2)
M-shell (n=3, weakly bound)
...
Valence electron
BMI I FS05 – Class 1 “X-Ray Physics” Slide 16
Energy schemeEnergy scheme
Binding energy (BE): energy binding electron to atom
Ionization energy IK,L,… BE: amount of energy needed to remove electron from atom
BE counted in negative units of electron volts (eV)
At infinity, BE 0. Continuum
Zero
K
L
M
N
E
Binding energy for 53I: -33.2 keV (K), -4.3 keV (L), -0.6 keV (M)
BE for valence electrons: ~ -10 eV (H: -13.6 eV)
BMI I FS05 – Class 1 “X-Ray Physics” Slide 17
Wave vs. particle interpretationWave vs. particle interpretation
X-ray as electromagnetic wave:
Frequency = 1/T [s-1 = Hz]
Wavelength [m]
Propagation at speed of light c = inverse relationship of and
X-ray as particle (photon):
Stream of weightless, neutral particles moving at speed of light
Each photon carries energy:
Radiation intensity I [W/cm2]:
2 2
number of photons photon energyPower W Energy J
Area cm Time Area cm Time Areapn E h
h
n
AEp h hc/
BMI I FS05 – Class 1 “X-Ray Physics” Slide 18
Electromagnetic spectrumElectromagnetic spectrum
BMI I FS05 – Class 1 “X-Ray Physics” Slide 19
X-rays characteristicsX-rays characteristics
EM radiation at wavelengths 0.1 – 100 keV (10 – 0.01 nm)
Diagnostic Range ~1-100 keV
Ionization energy for valence electrons < ~10 eV X-rays is ionizing radiation (harmful)
BMI I FS05 – Class 1 “X-Ray Physics” Slide 20
Energy unitsEnergy units
SI unit: 1 Joule [J] = 1 Nm = 1 kg m2 s-2
Electron volt [eV]: The potential energy of one elementary charge gained/lost (e = 1.610-19 C) when crossing a potential difference of 1V:
1 eV = 1.610-19 C 1 V = 1.610-19 [A s V] = 1.610-19 J
100 keV = 105 1.610-19 J = 1.610-14 J = 16 fJ (… per photon)
+
-
1V
BMI I FS05 – Class 1 “X-Ray Physics” Slide 21
X-Ray Interaction with MatterX-Ray Interaction with Matter
BMI I FS05 – Class 1 “X-Ray Physics” Slide 22
Interaction Processes Interaction Processes
Absorption: photon is destroyed and its entire energy is transferred to the target
Scattering: photon is deflected and might or might not transfer portion of its energy to the target (inelastic & elastic scattering, respectively)
Each interaction removes photon from beam path, thereby decreasing the beam intensity
target detector
beam path
BMI I FS05 – Class 1 “X-Ray Physics” Slide 23
X-Rays in a Homogeneous TargetX-Rays in a Homogeneous Target
Consider the relative change in intensity dI across small distance dx:
dI is proportional to: – I dx
t n linear attenuation coefficient
dIdI I dx I
dx
x
dx
I0 Id
Target
I I - dI
l0
BMI I FS05 – Class 1 “X-Ray Physics” Slide 24
Exponential Law of AbsorptionExponential Law of Absorption
Integration over entire target length:
The exponential law of absorption:
0 0
00
0
ln ln ln
dI l
I
dd
ld
dIdx
I
II I l l
I
Ie
I
0xI x I e
BMI I FS05 – Class 1 “X-Ray Physics” Slide 25
Linear attenuation coefficientLinear attenuation coefficient
Linear attenuation coefficient [cm-1] depends on photon energy and material absorption spectra
Half value layer HVL = the thickness after which intensity is reduced to half of the initial value:
Mass-attenuation coefficient / [cm2/g] independent of physical state of material
HVL0 HVL 0.52
ln 2 HVL
ln 2 0.693HVL
xII x e
BMI I FS05 – Class 1 “X-Ray Physics” Slide 26
Physical interaction processesPhysical interaction processes
Relevant interaction processes and their individual coefficients:
Photoelectric absorption
Compton scattering
linear absorption coefficient is the sum of individual absorption and scattering coefficients
= pecs
Coefficients = pecs are proportional to the interaction probabilities
(also: “cross-section” [ and, respectively]) of each process.
Questions:
• What are the mechanisms for the different interaction processes?
• What do they depend on?
BMI I FS05 – Class 1 “X-Ray Physics” Slide 27
Photoelectric absorptionPhotoelectric absorption
The photon knocks an electron out of one of the inner shells of a target atom. The electron is excited into the continuum; the photon is destroyed in the process.
Possible for a given shell only if photon energy Ep exceeds ionizing energy for the shell:
Kinetic energy of electron Ke according to energy conservation:
-
--
-
--- -
--
-
Ep = h
Ke
KLM
Continuum0
IK
IL
IM
IN
E
Ep IK, L, M,...
Ke= Ep IK, L, M,...
BMI I FS05 – Class 1 “X-Ray Physics” Slide 28
Photoelectric absorptionPhotoelectric absorption
Photoelectric absorption process is most likely – i.e. the cross section is largest – for Ep IK, L, M,... (resonance)
Photoelectric absorption cross section decreases strongly with photon energy ( Ep
-3) as photon energy increases relative to IK, L, M,...
Photoelectric absorption cross section increases strongly with Z (~ Z3) because I Z
Photoelectric absorption in K shell usually dominates
Photoelectric absorption depends on:
Z – The atomic number of the element
E – The radiation (photon) energy
3
3p
Z
E
BMI I FS05 – Class 1 “X-Ray Physics” Slide 29
Compton scatteringCompton scattering
The x-ray photon interacts with one of the weakly bound electrons of the atom. This electron can be considered free because Ex-ray 1-100 keV >> Ee,b few eV.
Inelastic scattering process:
x
y
px
y
'p
e
2;
1 (1 cos ) 511p p p
p p ee
E E EE E E
m c
keV
BMI I FS05 – Class 1 “X-Ray Physics” Slide 30
Compton cross-section Compton cross-section
Compton scattering cross-section decreases with photon energy
Compton scattering cross-section increases with electron density e[electrons/cm3]
Weak dependence (increase) on Z
Compton scattering depends on:
E – The radiation (photon) energy
– The electron density
1eE
BMI I FS05 – Class 1 “X-Ray Physics” Slide 31
Compton scattering angular distributionCompton scattering angular distribution
Likelihood of a photon to be scattered into a certain direction depends on photon energy Ep:
Low Ep high “backscatter” probability (~180)
High Ep high “forward scatter” probability (peaked distribution,~ 0)
incidentphotons
180
0
BMI I FS05 – Class 1 “X-Ray Physics” Slide 32
Cross section examples ICross section examples I
PE: Photoelectric absorption
S: Compton scatter
PR: Pair production (for E > 2MeV, not
relevant for medical imaging)
BMI I FS05 – Class 1 “X-Ray Physics” Slide 33
Cross section examples IICross section examples II
/[
cm2 /
g]
Z = 6 Z = 53 Z = 82
Legend:
: Photoelectric absorption: Compton scatter: Pair production
Not discussed in detail in lecture:
r: Raleigh scattertr: Triplett productiontr: mass energy transfer coeff.tr: photoelectric energy transfer coeff.en: mass energy absorption coeff.
BMI I FS05 – Class 1 “X-Ray Physics” Slide 34
Attenuation coefficient dependenciesAttenuation coefficient dependencies
Legend:
: photoelectric cross-sect. @ Z = 6(C): photoelectric cross-sect. @ Z = 64 (Gd): Compton cross-sect. @ Z = 6(C): Compton cross-sect. @ Z = 64 (Gd) : photoelectric cross-sect. @ 20 keV: photoelectric cross-sect. @ 60 keV: Compton cross-sect. @ 20 keV: Compton cross-sect. @ 60 keV
Z3/4
BMI I FS05 – Class 1 “X-Ray Physics” Slide 35
Contribution of interactionsContribution of interactions
Z (tissue) < 10E (diagnostic x-ray) < 10…100 keV
BMI I FS05 – Class 1 “X-Ray Physics” Slide 36
X-ray contrastX-ray contrast
Soft tissue components: Z < 10
Bone: 20Ca
Air filled spaces
I
x
BMI I FS05 – Class 1 “X-Ray Physics” Slide 37
X-ray contrast examplesX-ray contrast examples