Basic CT Physics 4

Cutting Edge Technology made Simple

Basic CT Physics


Basic CT Physics

•Conventional X-Rays– Single projection image superimposed tissues

•Computerized Tomography – Axial image obtained from hundreds

of projections

Std. Resolution: 500 - 1200 projections

High Resolution: 900 - 2400 projections

– Tissue superposition only within one slice thickness


Basic CT Physics

•Measured physical entity: tissue density

•Information provided: organ structure

•CT density unit: 1 Hounsfield Unit (HU) = 0.1% density of

water Air (zero density) = -1000 HU; Water = 0 HU

•Precision & validity of CT densities:– Relative only; CT uses a polychromatic X-ray beam – CT densities are voltage, object size & real density

dependent– Precise density measurements in CT require dedicated calibrations


CT Spectrum of densities

HU


Fan & Cone Beam Angles


2D Fan Beam Rebinning


CT Image Reconstruction

•2D Fan Beam Image Reconstruction (1970 – 2001) – Filtered back-projection into a 2D

matrix (Pixels) assuming parallel X-ray beams & ignoring the Cone Angle

• COBRA (COne Beam Reconstruction

Algorithm) (>2001)– Filtered back-projection into a 3D

matrix (Voxels)– Each Voxel reconstructed individually.– Only views passing through each

individual voxel during the acquisition process are back-projected into it


Computer Simulation(16 x 1.5mm)

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4 mm from mid -plane

8 mm from mid -plane

Cone Beam ReconFan Beam Recon

COCOnene B Beameam RReconstructioneconstruction AAlgorithm - lgorithm - COBRACOBRA


2D back-projection 3D back-projection2D back-projection 3D back-projection



64 channel

1.4 pitch

128 channel

simulation

1.4 pitch

2D Fan Beam

Philips 3D COBRA



CT - Image Quality

•Purpose of CT: Image guided radiographic diagnosis

•Image Quality determines diagnostic capability•Image Quality parameters:

– Low Contrast Resolution: The ability to discriminate between tissues of similar densities. Image noise plays a limiting role – High Contrast Spatial Resolution: The smallest (high contrast) object which can be recognized in

an image. Spatial resolution is determined by the basic scanner

design

– Temporal Resolution: The smallest time difference to observe two events


Low Contrast Resolution


Factors Determining Low Contrast Resolution•Detection System: type, design & efficiency

•X-ray beam filtration: optimal design for beam hardness

•Scan Voltage: lower voltage provides improved low contrast resolution

•Signal-to-Noise Ratio: – Proportional to Dose (mAs)

– Improved when post-collimation is available, protecting the detectors from scattered

radiation


Mx8000: Low Contrast Resolution Scan

Phantom details Axial Scan

0.3%

1% Contrast or 10 HU

0.5%


High Contrast Spatial Resolution

•It is recommended to measure spatial resolution in terms of spatial frequencies [lp/cm]

•The relation between spatial coordinates [mm] and spatial

frequencies [lp/cm] is:

Object [mm] = 10 / (2*[lp/cm])

For example: a cutoff spatial frequency of 20 lp/cm corresponds to a spatial resolution of 0.25 mm


Factors Determining Spatial Resolution

•Design Parameters:– Detector aperture width (Aeff) at isocenter– Focal spot size (s)– Sampling density (< Aeff/2)

•Reconstruction Algorithm:– Filter Modulation Transfer Function

•Display Parameters:– Pixel size: p = FOV/(Matrix * Zoom)– Good Imaging Practice: p < image spatial

resolution


Spatial Resolution: Sampling Rate

•Nyquist Theorem “Aliasing” artifacts suppression in the image of an object which has a maximum frequency N (Nyquist frequency), requires a sampling frequency of AT LEAST 2xN

•Nyquist frequency of a CT scannerN = 1 / Aeff

•Conclusion: Successful suppression of “aliasing” artifacts requires a sampling rate of AT LEAST 2/Aeff, or

Two Samples per Effective Detector Aperture WidthTwo Samples per Effective Detector Aperture Width


Spatial Resolution in 3rd Generation

Scanners“Aliasing” Suppression: Quarter Detector Offset between

center of rotation and

central detector line providing

2 “interleaved” [0o & 180o ] samples

per effective detector aperture, displaced by one-half detector

width


3rd Generation Scanners: Quarter Detector Offset

“Aliasing” Artifacts Suppression: 2 samples per detector width


Commercial High Contrast Spatial Resolution Phantom (up to 20 lp/cm)

20 lp/cm

18 lp/cm


Proprietary High Contrast Resolution Phantom (15 cm f & up to 25 lp/cm)


Mx8000 – Spatial Resolution

23lp/cm @ 3% MTF 24 lp/cm @ 2% MTF


CT - Image Quality Low Contrast versus High Contrast Resolution

Rule of thumb: Increase in Spatial Resolution Decrease in Low Contrast Resolution

Smooth Filter Sharp Filter


Nominal Slice Width

• The Nominal Slice Width is The Nominal Slice Width is the the convolution of the detectorconvolution of the detector aperture in the Z-axis and the aperture in the Z-axis and the focalfocal spot in the Z-axisspot in the Z-axis

• The result depends on the The result depends on the realreal respective distributions:respective distributions:

– The detector can be very The detector can be very well represented by a uniform well represented by a uniform distributiondistribution– The Focal Spot distribution The Focal Spot distribution

is more complex since it is in is more complex since it is in between a gaussian and a between a gaussian and a uniform distributionuniform distribution


Mathematical Convolution

Convolution of Gaussian Distributions

Gaussian

w/ STD

Gaussian

w/ STD

Gaussian

w/ STD

= 2 + 2

=

a - b

a + b

a

a b

Convolution of Uniform Distributions


DFSTM X-Ray Tube Design

Dynamic deflection of Dynamic Focal Spot Design

cathode electron beam,back and forth, creating2 focal spot positionson the same anodetrack and at a fixeddistance between them,so that the distance between two samplesat the isocenter is exactlyone-half detector width


DFSTM X-Ray Tube Design

DFS Tube Conventional Tube

Dynamic Focal Spot

X-ray Tube Design

Doubles

Ray Density and thus

Doubles

Spatial Resolution with the same number of detectors


Scan with Dynamic Focal Spot feature

Without With


Without With

Scan with Dynamic Focal Spot feature


Patient Dose Path


CT Artefacts

The problem How it looks like

Unconsistent data (partial volume) Streaks

Polychromatic X-ray beam Bands

Sampling (Nyqusit theorem) Aliasing

Cone Beam Hyper/hypo dense streaks at density gradients

High density tissues/objects Blooming (apparent size)


Streaks, Polychromatic & Cone Beam Streaks, Polychromatic & Cone Beam artefacts…artefacts…


Blooming Artefact: density

White

Dark

WwWc

Apparent size


Wc

1

Reduce apparent size: increase window center

Wc

2

Blooming Artefact: density


UncompromizedSpiral Scanning


Spiral (Helical) Scanning

Continuous data acquisition during gantry rotation and patient table displacement at constant speed


Spiral Scanning Benefits

• Volumetric Volumetric data acquisitiondata acquisition

• SingleSingle breath-holdbreath-hold acquisitionacquisition – No lesion misregistration No lesion misregistration – 94% of patients can hold their94% of patients can hold their breath forbreath for 30 sec30 sec

• Good control of delayGood control of delay between injection and scan:between injection and scan:– Study performed within a desired blood phaseStudy performed within a desired blood phase– Multi-phase studies can be performed with back-to-back Multi-phase studies can be performed with back-to-back

spiral acquisitionsspiral acquisitions

• Efficient use of contrast materialEfficient use of contrast material


Common Compromises in Single-Slice CT

Image QualityImage Quality OROR Organ CoverageOrgan Coverage

Pitch Pitch 1 1 Pitch Pitch 1 1


The Solution: Multi-Slice CT


Multi-Slice CT: No Need to Compromise

Pitch Pitch Q1 Q1 Pitch Pitch Q1 Q1

Image QualityImage Quality ANDAND Organ CoverageOrgan Coverage


Multi-Slice RSVP Advantages


Multi-Slice RSVP Advantages


Multi-Slice Resolution Advantage Quad-Slice Dual-Slice Single-Slice

4x2.5mm; 2.5cm/sec 2x5.0mm; 2.5cm/sec 10mm; 2.5cm/sec72 cm coverage; 28 sec; 120kV / 130 mAs


72 cm coverage 36 cm coverage 18 cm coverage 3.2 mm Eff. ST; 28 sec; 120kV / 130mAs

Multi-Slice Volume Advantage Quad-Slice Dual-Slice Single-Slice


Spiral Scanning: Basic Concepts

Pitch (P)

Table displacement during one full (3600) gantry rotation

Beam collimation

Example: Pitch 1:1 (P=1) means that the table advances by exactly one beam collimation during one full gantry rotation


Coverage (V)

V = (n x P / RT) x NST x T = SAR x NST x T where: n x P / RT = Slice Acquisition Rate (SAR) [slices / sec] n slices acquired during one gantry rotation of RT sec @ pitch P NST = Nominal Slice Thickness; C = n x NST = Collimation T = Acquisition Time; P = Pitch (when applicable)




Image

Reconstruction

• The bed position of the image and the reconstruction increment

are at user’s choice, within the acquired volume

• The actual raw data for an image reconstruction, at a given position, is obtained by interpolating data points from successive

gantry rotations


Spiral Scanning: Image Reconstruction

Documents

Basic CT Physics 4