X-ray and CT Flashcards
For X-rays:
* Wave lengths:
* Energy range:
* Diagnostic X-ray energy range
- Wave lengths: ca. 1 nm to smaller than 1 pm
- Energy range: ca. 1 keV to several MeV
- No hard wavelength/energy boundaries
- Diagnostic X-ray energy range 20 – 150 keV
How can X-rays be generated?
X-ray tube: static target
X-ray tube: rotating anode
Synchrotron facilites
Inverse-Compton sources (MuCLS: Munich Compact Light Source)
Liquid metal jet sources
rotating anode adv-disadv
Extemely inefficient process (ca. 1 % X-rays), high heat load
* Rotating anode for higher power & better heat distribution
* Rotating anode tubes higher heat capacity due to improved material cooling
X-ray generation – two effects
- Bremsstrahlung:
Negative acceleration of an electron in the
Coulomb field of the atom nucleus. - Characteristic emission of X-rays:
Electron transitions in the inner shells lead to
the emission of characteristic X-ray energies.
How can the X-ray spectrum be changed?
- Changing acceleration voltage: shape plus intensity
- Effect of changes of current: merely intensity
*different filtration
*dfferent application (eg. CT or mammography)
How do X-rays interact with matter?
-photoelectric absorption
-Rayleigh (elastic) scattering(wo/ loss of energy)
-compton (inelastic) scattering(w/ loss of energy)
-pair production
photoelectric effect info
- Albert Einstein discovered (nobel prize 1921)
- The incoming photon is absorbed completely by one of the
electrons, which is ejected from its shell - This effect is strongly depending on the X-ray energy and the
atomic number (≈ Z^4/E^3) - At lower X-ray energies and high atomic numbers this effect is the
dominant effect in X-ray imaging
Compton scattering info
- A.H. Compton discovered (nobel prize 1927)
- Inelastic scattering
- Fraction of the energy of a photon is transferred to the kinetic energy of a free electron
- Scattered photon with lower energy
- Proportional to the atomic number and only slightly dependent on
energy (≈ Z/E0.2)
attenuation coefficient µ depends on
material type and energy of incoming photon
Lambert-Beer’s law
-exponential loss of intensity I0
-transmission of X-rays through a material decays exponentially
I = I0*exp(- µz)
How can X-rays be detected?
-film detectors (silver bromide-still used in industry)
-Photo-stimulated illumination
-charge coupled devices (CCDs) (Photo diode as in digital cameras
* Coupled with scintillators for X-rays
* Needs relatively large optics)
-scintillators
materials: gadolinium oxysulfide (Gadox), caesium iodine (CsI)
– flat-panel detectors (directly coupled to photodiode array)
Which parameters are relevant for X-ray detection?
- Physical pixel size -> spatial resolution
- Point spread function (PSF) -> spatial resolution
- Efficiency (quantum efficiency), spectral response & read out time
- Noise defined by dark current ->readout noise
- Artifacts like pixel defects, afterglow, long dead time
Novel detector technique
– photon-counting detectors
* Fast readout
* No readout noise (dose reduction)
* Small pixel sizes: in CT 225 x 225 µm²
* Spectral separation
* Homogeneous signal response
Limitations of photon-counting detectors
- Pile-up
- K-edge fluorescence
- Charge sharing
- High flux
- High energy tail (limits spectral separation)
technical components of a modern CT
- Patient table
- Gantry
X-ray tube/generator
Filters
Collimator
Detector - Computer
X-ray tube related components
- Bow tie filter for homogeneous intensity
- Collimator( field of view for dose reduction)
- Additional filters (filtering of low energy photons for dose reduction)
How does tomographic reconstruction work?
- Line integral at each detector position
- Several projection from different angles
- Reconstruction
General reconstruction approaches:
Analytical reconstruction:
* Brute force
* Simple backprojection
* Fourier based methods:
- Fourier-slice theorem
- Filtered backprojection (FBP)
Iterative reconstruction:
* Hybrid model iterative reconstruction
- Iterative filtering
* Model-based iterative reconstruction
- Algebraic reconstruction method (ART)
- Statistical iterative reconstruction (SIR)
Fourier slice theorem
1D Fourier transform of line integral equals cut through 2D Fourier transform
of object under same angle
Fourier based methods – 2D approach
- First idea:
1. Take 1D Fourier transform of projections from Fourier slice theorem
2. Sample 2D frequency space f(u,v)
3. Multiply with 2D filter kernel (𝜔, 𝜃)
4. Take 2D inverse Fourier transform
Works in theory, but:
* Prone to distortions
* High spatial resolution high dose & slow
Filtered backprojection (FBP)
- Limitation to 1D Fourier transform
- Include backprojection
- Essential steps in filtered backprojection (FBP)
1. Fast Fourier transform of line integral p
2. Multiplication with filter function k
3. Inverse Fast Fourier transform
4. Backprojection over all angles
How many projections are needed?
- Nyquist sampling criterion has to be fulfilled:
number of projections = 𝝅 /2 times sample width (=detector width)
Beam geometry
Parallel beam
* 180 degrees
* Simple reconstruction algorithm
Fan beam
* 180 degrees plus fan angle
* Managable reconstruction algorithm
Cone beam
* Approximation
* FDK algorithm
Iterative reconstruction
Hybrid techniques
* Iterative filtration on projections or reconstructed images
Model-based (projection and backprojection)
* Algebraic reconstruction technique (ART)
* Statistical iterative reconstruction (SIR)
Currently combination of iterative reconstruction with deep learning
* Sparse sampling for further dose saving
Iterative CT reconstruction – biggest impact
Dose reduction
How is CT data represented?
CT number – Hounsfield units
CT number relates attenuation coefficient µ(x,y,z) to water
How can we define image quality and dose ?
- Contrast, noise, dose, & spatial resolution
Major clinical scan parameters defining image quality
- Tube rotation time
- Tube current and exposure time
- Tube voltage (80 – 150 kVp)
- Slice thickness & increment
- Reconstruction kernel / algorithm
- Patient size-dependent techniques
double tube current
double number of photons and thus dose
Tube voltage change
- Defines contrast
- Change spectrum shape and
intensity - Increase tube voltage from 120 kV
to 140 kV ->double number of photons and dose / non-linear increase
Reduce slice thickness to half
half the number of photons
dose needs to be doubled for same image quality
What is dual-energy CT?
- Attenuation coefficient energy dependent
- Energy dependency can be used for material/tissue differentiation
Photon-counting CT
Advantages:
* high spatial resolution (250 x 250 µm²)
* always on
* standardized output
* multimaterial decomposition with K-edges
CT Artifacts
- Scattering
- Ring artifacts (Hot/dead/miscalibrated detector pixel)
- Motion artifact
- Reconstruction artifacts
- Metal artifacts(implants, correction by posrprocessing algorithms)
- Beam hardening(X-ray spectrum changes with transition of object)
- Undersampling & missing projections
