Computed Tomography (CT)

Image Reconstruction Techniques

  • voxel = volume element
  • μ (linear attenuation coefficient) determined by composition, thickness and quality of beam
  • profiles = views = projections
  • matrix inversion = intensities in different directions used to infer voxel values through simultaneous equations, but large number of equations with big matrices means it is prohibitively slow
  • Fourier analysis =1D FT of each profile added in frequency domain to obtain 2D FT, the final image obtained by taking inverse FT
  • iterative methods = intuitive guesses made to each pixel values, with multiple adjustments when compared to true ray sums, fast and reduced number of artefacts, but difficult to obtain FDA approval due to statistical approach

Filtered Back Projection

  • simple back projection = back projection of 1st profile (P1) adds total value to each pixel; with each additional profile adding more values; final image obtained after subtraction of an offset and renormalisation
  • increased projections improves quality
  • spoking = star artefact = blurring = from high density objects adding values to adjacent pixel in each projection; ie from convoluting it with point spread function dependence on 1/r (r = distance); due to finite number of projections (infinite projections will produce true circular shapes)
  • filtered back projection = profiles first convoluted/filtered to counterbalance sudden density changes with a convolution filter = kernel = reconstruction algorithm (eg reducing density adjacent to sharp borders); usually performed in frequency domain with iFT before back-projection process
  • before FT, profile is corrected for detector offset, gain, non-linearity, scatter and beam hardening
  • filters can be selected to enhance soft tissue or bone detail
  • ramp/Lak filter increases A linearly with spatial frequency compensating for 1/r spoking provided there is no noise
  • smoothing/Shepp-Logan filter with ramp also compensates with reduced A in high frequency noise
  • Hamming filter has more pronounced high freq roll-off with better high f noise suppression
  • bone filters – less high freq roll-off to accentuate high f image at expense of noise for high contrast resolution
  • soft-tissue filters – large high freq roll-off for low contrast resolution
Tissue HU
air -1000
lung -300
fat -30
water 0
white matter 30
grey matter 40
muscle 50
trabecular bone 300-500
cortical bone 600-3000

post processing can be performed with a different filter after the scan

Image Display

after linear attenuation coefficients calculated for each pixel, number normalised to water as reference (0); Hounsfield unit = CT-number = H = ; are beam quality hence machine dependent

window level (usually central CT-number) and window width of range of CT-numbers selected by user for display

Scanning Geometry

1st Generation Translate-Rotate

pencil beam and single detector on a gantry 1st translate with 160 samples to produce the single profile before rotation of 1°

takes 5min for a single slice

head usually clamped and surrounded by water bag to help overcome afterglow in scintillator and reduce signal dynamic range

2nd Generation Translate-Rotate

small fan beam with up to 30 detectors and less translations and rotations (30°) required, scan times 5-90s

3rd Generation Rotate-Rotate

  • large fan beam with hundreds of detector elements (along an arc centred on the focus) so a whole projection is obtained at once
  • hundreds of profiles obtained through one rotation, with XRT pulsed or continuous
  • scans <1s
  • bow tie = beam flattening filters chosen to suit body or head to partially overcome variations in signal strength and change in beam quality at edges of beam
  • variations in XR output with time normalised with reference detectors at extremes of array
  • individual detector elements need to be calibrated prior to any study to minimise ring artefacts from unequal detector element efficiency
  • pre-detector anti-scatter collimation between adjacent detector elements
  • off-setting centre of rotation removes the doubling of profiles during one 360°
  • jumping/flying focus XRT – switching betw foci that are spaced ½ a detector element on the anode, effectively doubling number of detectors, also removing the doubling of profiles

4th Generation Rotate-Fixed

  • ring of fixed detectors, with only a small fraction used at any given time
  • similar scan times to 3rd generation
  • poor geometry as XRT must be closer to pt than detectors thus increasing magnification/focal spot blurring
  • post patient collimation between detector elements cannot be used
  • rotate-nutate scanners use nutating geometry with XRT external to ring and out of detector plane

Helical/Spiral/Volumetric Scanning (VCT) = 6th Generation

  • continuous XRT motion combined with continuous advance of patient cradle (1-10mm/s)
  • pitch = ratio of couch advance in one rotation to slice thickness, usually 1-2
  • SSP (slice sensitivity profile) = effective slice width is higher than nominal as profile must be convoluted with triangular profile; increased with higher pitch; reduced with z-interpolation techniques
  • z-interpolation – helical data interpolated into series of planar images data sets
  • interleaved reconstruction enables additional overlapping images and additional images along the z-axis
  • reduces scan time allows for single breath-hold scanning and sagittal/coronal/3D reconstruction feasible with minimal loss of spatial resolution
  • arbitrary positions and spacing/increments of reconstructed slices can be made retrospectively
  • XRT must be able to dissipate heat during longer scanning times and off a constantly moving gantry
  • large amounts of data must be taken of the moving gantry wirelessly or stored until the gantry movement stops
  • advantages: reduced dose if pitch >1, shorter exam time, multiplanar reconstruction
  • disadvantages: ease of larger volumes than necessary, possible inappropriate pitch (high>insufficient quality), lower z-axis resolution, inherent artefact

Volume/Multi-Slice/Multi-Detector CT (MDCT)

  • detector array with length along z-axis with faster volume acquisition (0.5s/cycle) making ECG-gated cardiac and coronary artery calcification scoring possible
  • large number of thin slices improves z-axis resolution
  • XRT loading less severe
  • z-interpolation algorithms are more complicated
  • increased dose with over-beaming required (penumbra region cannot be used as need even slice irradiation; whereas single slice scanning can have the beam narrower than the detectors)
  • cone beam CT – beam collimated to large rectangular cone with full 3D image of patient obtained in a single rotation, but large amounts of scatter

Electron Beam CT

  • XRT is a large circular arc of 210° with electron beam (600mA; electron gun 3m from scan plane) steering around the target (2m W) below the patient, collimated to small fan of 30° and 2cm width
  • harder beam (130kVp 10.5mmAl)
  • fixed 210° array of CdWO4 elements
  • images obtained in 50ms with high resolution in 100ms
  • 4 focal tracks and 2 detector arrays (one 432 elements and second 864 for high res) enables 8 slices of 8mm width possible without moving patient
  • enables cine CT

CT Components

X-Ray tube

  • must be capable of quick dissipation of enormous heat loads, enhanced through oil/chilled water heat exchangers and liquid metal bearings
  • W/Rh anode track layer brazed or evaporated onto graphite body (constituting bulk of anode mass) increases track loading and improves heat storage:mass ratio
  • mechanical gantry moves XR tube ± detector
  • beam collimated to pencil beam or large fan with thickness defined by pre-patient collimation; hence scatter reduced
  • heavy filtration to minimise beam hardening (~5.5mm Al at 120-140kVp)
  • proposed use of synchrotron (particle accelerator) to produce monoenergetic XRs
  • Detectors
  • post patient collimators minimise out-of-slice scatter
  • original NaI:Tl scintillator-PMT bulky and suffered afterglow (newer detectors minimal afterglow)
  • pressurised (30atm) Xe gas detectors have small dimensions, excellent scatter rejection, reliable, in ion chamber mode have current directly proportional to intensity of detected XR flux
  • solid state detectors from ceramic (yttrium-gadolinium oxides or Gd2O2S) or crystal CdWO4 coupled to photodiode are easily manufactured, small, high QDE
  • detector pitch = centre to centre spacing of detectors
  • detector aperture = width of active element of one detector
  • crosstalk between detectors reduced with high detector efficiency

Computer System

  • manages gantry rotation, patient table positioning and advance, XR initiation and termination
  • central computer controls several microcomputers and large array processor (which performs bulk of arithmetic)

Tube Current Modulation (CT Equivalent of AEC)

  • longitudinal (betw slices), circular (within rotation) or temporal (eg heart studies) dose modulation adapts mA to attenuation of patient
  • can be based on scout views, attenuation measured at the same tube angle from the previous slice, and/or from detectors at edge of array in the direction of gantry movement

Image Quality

Spatial Resolution

  • focal spot size (~1mm) the main limiting factor of resolution, length may define minimum slice thickness; magnification ~1.4-2.0 and surface magnification increases up to 2.7 with patient size
  • detector aperture/element sizes
  • sampling frequency from detector spacing and number of projections (circumferential/angular resolution), also reducing aliasing
  • high contrast limited by detector aperture, sampling frequency, kernel, pixel size, motion and focal spot
  • scan and image field size impacts on pixels size
  • reconstruction filter, with bone or edge enhancement algorithm enhancing resolution at expense of noise
  • display monitors
  • patient motion
  • resolution measured by MTF or FWHM of LSF


  • statistical fluctuation in CT-numbers predominantly due to quantum mottle
  • measured by measuring standard deviation in ROI (region of interest)
  • low contrast resolution (~0.5% contrast, ~10mm) determined by detector efficiency, number of profiles, object size and composition (attenuation of beam), slice width, mAs and beam quality, kernel (smoothing kernel reduces noise, edge kernel increases noise)


  • beam hardening = cupping – reduction of CT numbers in centre (lucent streaks between dense bones), reduced with heavy filtered beam (5-8mm Al)
  • aliasing – high freq manifest as low freq, alternate black/white streaking at edges of sharp bones/metal implants from inadequate ray sampling; reduced with quarter detector offsets or flying focal spot; max freq limited by focal spot size and detector aperture
  • partial volume effect – more than one density contributes to voxel, may appear as streak if object distant from centre of rotation; reduced with thin slices and small pixels
  • non-uniformity of CT-numbers – important when quantitative measurements taken
  • non-linearity of CT-numbers – H vs μ not linear, related to beam hardening
  • detector faults = ring artefact – when detector element fails completely or not calibrated on regular basis, most serious in centre of fan; usually correction applied for missing data
  • algorithm limitation – eg with edge enhancement H will vary in damped sine wave from bone interface
  • detector over ranging – when pixel values outside maximum of 3070 (eg metal, dental fillings), shown as black or white
  • motion – blurring of tissue boundaries or streaking, reduced if using just half of data set (ie only 180°)
  • streak artefact – from hi dense object, partial volume effects, motion, inadequate sampling or photon starvation (eg arms in FOV of shoulder imaging)
  • miscellaneous XRT induced artefacts – off-focal radiation. XRT arcing, anode wobble
  • spiral CT artefacts – noise and spatial resolution deteriorate with distance from rotation axis; from changing anatomy and z-interpolation, worse with higher pitch; windmill artefact:
    • cone artefact –eg crescent bands along skull-brain interface
    • rod artefact – from rod shaped object angled wrt scan plane causing distorted ellipse

Quality Control

  • CT number accuracy – check water value is 0; depends on voltage, filtration, object thickness
  • CT number uniformity – HU across pixels in homogenous object should be the same; tested at same time as noise by measuring mean and of 4 peripheral ROIs and 1 central ROI; central ROI mean should be similar to peripheral
  • CT number linearity – contrast scale – measured HU vs known μ in a sample, and should be linear; dependent on energy (tested at different kVp), phantom size and composition
  • check of noise, spatial resolution, slice thickness, dose, positioning of couch

CT Safety

  • CTDI (mGy)= CT dose index = estimated dose within slice in a head or body Perspex phantom
  • DLP (mGycm) = dose-length product (used in NZ) = CTDI x T x N; T = slice thickness, N = N of slices
  • low contrast requirements – hence mAs, which is proportional to dose
  • higher kVp increases dose due to AEC/complex feedback mechanism and complex relationship between kVp, dose and contrast which is currently being researched
  • reduced dose with spiral if pitch>1, also reduces retakes
  • skin dose (5-50mGy, higher with heads due to skull backscatter) 3x midline
  • if edge of scan <10-15cm from testes, lead purse shield will afford protection
  • as a general rule, each reduction in kVp by 20 halves DLP. However reducing kVp also reduces dynamic range, ie reduces the grey-scale giving the image a more black and white appearance. mAs is directly proportional to DLP. Reducing kVp closer to the k-edge of iodine increases vessel contrast with CTA (hence able to reduce contrast dose).

Scan/Digital Projection Radiography (SPR/DPR)

  • SPR = DPR = scout view = scanogram – fan beam not rotated and patient couch is moved in small steps
  • detector signals digitised to produce image, but not processed to much extent
  • ~2% of total CT study dose


  • real-time CT = continuous CT = CT fluoroscopy (CTF in biopsy related applications)
  • cine CT using spiral CT with fast continuous rotation and high speed array processor capable of few fps
  • originally for chest and head biopsies in regions where USS guidance not possible
  • compared to other forms of biopsy, overlapping structures are removed, images displayed in real-time, fine needle control possible, 30-50% reduction in procedure time, increased confidence with very small/poorly accessible lesions
  • current is 30-50mA (cf 4mA in fluoroscopy), additional beam filtration may be introduced automatically to reduce exposure by 50%
  • fine z-axis resolution required for improved localisation; lesion shifting and pull-back phenomenon can be used to confirm localisation
  • processing speed increased by restricting reconstruction to circular area, not applying beam hardening or other artefact corrections, modified kernels, reconstructing to smaller matrix (256 x 256), partial/incremental reconstruction technique (each new image contains data from previous)
  • after a 360°rotation, each next N° reconstructs the image from the most recent 360°, where N 30°/45°/60° with 12/8/6 frames/sec


  • doses to hands measured using TLD disks and rings, reduced using needle holders
  • protective goggles, Pb aprons, gloves, drape over patient (2cm caudal to slice plane), using distal side of gantry (shielding from electronic racks in gantry) and extra shielding to gantry
  • skin doses 2-10mGy/s with exposure times up to 200s; technologist required to monitor time and technique factors and to inform operation when 2Gy threshold reached