Computed Tomography. Principles of Medical Imaging. Contents. Prof. Dr. Philippe Cattin. MIAC, University of Basel. Sep 26th/Oct 3rd, 2016

Transcription

1 Computed Tomography Principles of Medical Imaging Prof. Dr. Philippe Cattin MIAC, University of Basel Contents Abstract 1 Computed Tomography Basics Introduction Computed Tomography Hounsfield's CT Prototype EMI-Scanner Detectors Important Terminology 2 Single Slice CT First Generation CT Scanner Design Second Generation CT Scanner Design Third Generation CT Scanner Design Fourth Generation CT Scanner Design Spiral Scanning CT Spiral Scanning CT (2) Spiral Scanning CT (3) Drawback of these Designs 3 Multi-Detector Row CT Multi-Detector Row CT Detector Design Detector Design (2) Detector Design (3) Detector Design (4) Detector Design (5) Detector Design (6) Contents Principles of Dual Medical Source Imaging CT 27 1 of :34 2 of :34

2 Open Dual Source CT Advantage of the DSCT 4 Electron Beam Tomography Electron Beam Computed Tomography Electron Beam Computed Tomography (2) Dosage Comparison: EBCT vs. CT 5 Image Reconstruction 5.1 Introduction Image Reconstruction Image Reconstruction (2) 5.2 Radon Transform Radon Transform Parallel Projection The Radon Transform The Discrete Radon Transform Radon Transform Examples Radon Transform Examples (2) 5.3 Fourier Slice Theorem Fourier Slice Theorem Fourier Slice Theorem (2) Reconstruction with the Fourier Slice Theorem Reconstruction with the Fourier Slice Theorem (2) 5.4 Filtered Backprojection Principle of Filtered Back-Projection Numerical Back-Projection Example Example Reconstructions Example Reconstructions (2) 5.5 Helical Reconstruction Principles of Medical Helical Imaging Reconstruction Linear Interpolation 180 Linear Interpolation 5.6 Hounsfield Unit Hounsfield Unit 6 Automatic Exposure Control Automatic Exposure Control Automatic Exposure Control (2) 7 Artefacts Artefacts Partial Volume Effect High Density Artefacts Gating in Cardio CT CT and Medical Image Analysis 8 X-Ray Dosage Summary X-Ray Dosage Summary of :34 4 of :34

3 Abstract (2) Computed Tomography Basics Introduction (4) One of the major disadvantages associated with conventional planar radiography is its inability to produce sectional information. The images produced on film represent the total attenuation of the X-ray beam as it passes through the patient. Depth information is completely lost! Two general classes of tomography exist that solve this problem: Linear tomography, which produces longitudinal sections Computed axial tomography, which produces sectional or axial slices 5 of :34 6 of :34

4 Computed Tomography Basics Computed Tomography Basics Computed Tomography (5) Hounsfield's CT Prototype (6) Computed Tomography (CT) [ /wiki/computed_axial_tomography] originally known as Computed Axial Tomography (CAT) or Body Section Röntgenography is a medical imaging modality used to generate 3D images of the internals of an object from a large series of 2D X-ray images taken around a single axis of rotation. Fig 3.1: CT Apparatus The original 1971 prototype took parallel readings through angles, each apart, with each scan taking a little over five minutes. The images from these scans took hours to be processed by algebraic reconstruction techniques on a large computer. Godfrey Newbold Hounsfield [ /wiki/godfrey_newbold_hounsfield] conceived the CT scanner idea in 1967 and publicly announced it in Allan McLeod Cormack [ /wiki/allan_mcleod_cormack] independently invented a similar process and they shared the Nobel price in Fig 3.2: Hounsfield's original CT prototype Fig 3.3: Principle of the prototype It is claimed that the CT scanner was the greatest legacy of the Beatles; the massive profits from their record sales enabled EMI to fund scientific research 7 of :34 8 of :34

5 Computed Tomography Basics Computed Tomography Basics EMI-Scanner (7) Detectors (8) The EMI-Scanner was the first production X-ray CT machine. It was limited to scan two adjacent slices of the brain, but acquired the image data in about. The computation time was about per picture. The scanner required the use of a water-filled Perspex tank with a pre-shaped rubber head-cap at the front. The water-tank was used to reduce the dynamic range of the radiation reaching the detectors (scanning outside the head vs. through the skull). The images were relatively low resolution, being composed of a matrix of only. The CT scanner was a huge success: by machines were installed across the world. Fig 3.4: EMI brain scanner with a Data General Nova minicomputer. The first scanner was installed at Atkinson Morley's Hospital, Wimbledon, England in 1971 Scintillator [ Detectors Low maximum count rate leads to longer scan times or more image noise Xenon Gas Detectors Pressurised Xe gas capable of higher count rates, but low detection efficiency Modern Ceramic Scintillators [ Coupled with photodiodes these detectors offer the best performance 9 of :34 10 of :34

6 Important Terminology In-plane resolution: acquisition resolution in the -plane Out-of-plane, through-plane resolution: slice distance in axis Anisotropic scan: the resolution in the axis is generally less than in the axis Isotropic scan: the voxel dimensions are equal in the, and axis Computed Tomography Basics (9) Fig 3.5: Coordinate system generally used Single Slice CT First Generation CT Scanner Design The generation of CT scanner used the translate-rotate geometry. The EMI scanner, for instance, used a pencil X-ray beam and a single detector. During translation of the gantry, the X-ray beam was sampled 160 times. After a rotation of a new profile was acquired. This procedure was repeated for 180 different angles and took roughly. (11) To minimise patient movement the head was usually clamped. Fig 3.6: First generation CT principle 11 of :34 12 of :34

7 Single Slice CT Single Slice CT Second Generation CT Scanner Design (12) Third Generation CT Scanner Design (13) The generation scanner tried to reduce the excessive scan times by using a small fan beam with multiple detectors (up to 30 in some designs). Scan times of between were possible with this design. The introduction of multiple detectors was an important development. The generation brought down scan times even further by using the rotaterotate geometry. As the large fan beam encompasses the patient completely the translatory motion of the previous designs can be avoided. The X-ray tube and the detector array rotate as one about the patient. Fig 3.8: Third generation CT principle Fig 3.7: Second generation CT principle The number of detector elements is typically in the hundreds. To avoid excessive variations in signal strength various manufacturers use a bow-tie shaped filter to suit the body or head shape. 13 of :34 14 of :34

8 Single Slice CT Single Slice CT Fourth Generation CT Scanner Design The generation CT uses a rotate-fixed ring geometry where the ring of detectors completely surrounds the patient. As the X-ray tube must be closer to the patient than the detectors it has a poor radiographic geometry, i.e. large geometric magnification. Scan times as low as with interscan delays of can be achieved with this type of geometry. Using many thousand detector elements a in-plane resolution of can be obtained. (14) Fig 3.9: Fourth generation CT principle Spiral Scanning CT Advances in slip-ring technology have enabled the X-ray tube to rotate continuously in the same direction which overcomes problems of interscan delays. If the continuous motion of the gantry is combined with a continuous advance of the patient table along the longitudinal axis we have a spiral/helical scanner. The spiral scanning technology brought about a significant reduction in scan times. The gained speed came at a price of increased complexity for reconstructing the helical data. (15) Fig 3.10: Illustration of helical scanning Fig 3.11: Nice 3D rendering of helical CT 15 of :34 16 of :34

9 Single Slice CT Single Slice CT Spiral Scanning CT (2) (16) Spiral Scanning CT (3) (17) The X-ray source is collimated to a fan beam rotating around the patient. The X-ray tube and the detectors are fixed together as a single rotating unit. Post patient collimation defines the slice sensitivity profile. Fig. 3.12: Basic design of a single slice CT used in a spiral CT In the context of helical scanning a parameter called Pitch is defined as the Ratio of the distance that the patient couch moves in one rotation to the collimation thickness (number of slices slice thickness) (3.1) In other words, for a couch advance of and a nominal collimation width of, the pitch is 1. Pitch values are typically in the range of 1 to 2 depending on the required spatial resolution in the direction of the couch motion. Its a coverage indicator, in other words. Fig 3.13: Pitch 17 of :34 18 of :34

10 Drawback of these Designs Single Slice CT (18) Ideally, volume data are of high isotropic spatial resolution, have minimal motion artefacts, and optimally utilise the contrast agent bolus. To reduce motion artefacts CT examinations need to be completed within a certain time frame, e.g. on breath hold, for the heart. If, however, a large scan range such as the entire thorax has to be covered a thick collimation (large inter slice distance) must be used, leading to anisotropic voxel sizes (whilst the in-plane resolution only depends on the system geometry). Multi-Detector Row CT Multi-Detector Row CT Strategies to achieve a better longitudinal resolution and faster scans include the simultaneous acquisition of multiple slices at a time, thus termed Multi-Detector Row CT or Multi-Slice CT (MSCT). Interestingly, the very first commercial CT systems (EMI-Scanner and Siemens Siretom) were already two-slice systems. Only the introduction of the helical scanning principle allowed to fully leverage the advantages of multi-detector row CT. Fig 3.14: Multi-slice CT (20) Fig 3.15: SOMATOM Sensation 16 Gantry (Siemens) 19 of :34 20 of :34

11 Multi-Detector Row CT Multi-Detector Row CT Detector Design (21) Detector Design (2) (22) The figure shows, how different slice widths can be achieved by prepatient collimation for a single slice detector. The principle can be easily extended to slices if the sensor is separated midway along the axis. Fig 3.16: Prepatient collimation of the X-ray beam to obtain different slice thicknesses with a single detector row CT. Fig 3.17: Collimation of the X-ray beam to obtain different slice thicknesses with a two detector row CT. For detectors a more elaborate detector design is required. 21 of :34 22 of :34

12 Multi-Detector Row CT Multi-Detector Row CT Detector Design (3) (23) Detector Design (4) (24) The various manufacturers introduced different detector designs in order to allow utmost flexibility in selecting slice widths. All designs combine several detector rows electronically to a smaller number of slices according to the selected slice width. The total coverage of this detector design is (measured in the isocenter). Fig 3.18: Fixed array detector, 16 rows, 4 slices A more efficient approach (needs less detector channels) uses the adaptive array design. This design allows the following collimated slice widths: two slices at, four at, four at, two at, and two at. Fig 3.19: Adaptive array detector, 8 rows, 4 slices With prepatient collimation the following slice widths can be realised:,,, and. 23 of :34 24 of :34

13 Multi-Detector Row CT Multi-Detector Row CT Detector Design (5) (25) Detector Design (6) (26) Sixteen-slice CT systems usually have adaptive array detectors similar to the one depicted in Fig It uses 24 detector rows with a total coverage of at the isocenter. 32, 40, and 64 slice systems are now available. By properly combining the detector rows, either 12 or 16 slices with or can be acquired simultaneously. Fig 3.20: Adaptive array detector, 24 rows, 16 slices (Siemens) Fig 3.21: Toshiba detector mock-ups 25 of :34 26 of :34

14 Multi-Detector Row CT Multi-Detector Row CT Dual Source CT (27) Open Dual Source CT (28) A different approach to acquire more slices in parallel was followed by Siemens with their Dual Source CT [ (SOMATOM Definition). Fig 3.22: Dual Source CT (Siemens SOMATOM Definition) Fig 3.23: Comparison of LAD & Cx in diastole and systole 27 of :34 28 of :34

15 Multi-Detector Row CT Advantage of the DSCT (29) The scan is in cardiac-mode virtually independent of the heart rate no -blocker needed If the two X-Ray tubes are operated with two different tube voltages (other spectra) tissue types can be better differentiated Fig 3.24: Movie of the an open rotating dual source CT Fig 3.25: HU values for different tissue types (theoretical simulation) 29 of :34 30 of :34

16 Electron Beam Tomography Electron Beam Computed Tomography Electron beam computed tomography (EBCT or EBT) [ /wiki/electron_beam_tomography] is a specific form of CT scanner in which the X-Ray tube is not mechanically spun in order to rotate the source of X-Ray photons. This different design was explicitly developed to better image heart structures which never stop moving. As in conventional CT technology, the X-ray source still rotates around the circle in space containing an object to be imaged tomographically, but the X-Ray tube is much larger than the imaging circle and the electron beam current within the vacuum tube is swept electronically, in a circular path and focused on a stationary tungsten anode target ring. (31) Fig 3.26: Patent illustration showing a cutaway view of an electron beam CT system. Components are 22. electron gun, 23. electron beam, 27. beam bending coil, target rings, 14. detector array. The electron beam is reflected by the target rings through the patient, to the detector on the opposite end of the scan tube. 31 of :34 32 of :34

17 Electron Beam Tomography Electron Beam Tomography Electron Beam Computed Tomography (2) (32) Dosage Comparison: EBCT vs. CT (33) Design Advantages The most advanced commercial EBCT can perform image sweeps in as little as compared to of the mechanically swept X-Ray tube designs. Design Disadvantages Larger footprint and smaller scanning volume More than twice as expensive Higher demands on room shielding from electro-magnetical interferences Sensitive to small vibrations Fig 3.27: GE espeed 300 Fig 3.28: Imatron C150 As a general rule, the electron beam CT delivers only about of the radiation [ /radiationdosage.htm] than a conventional CT scanner would. The primary explanation being that the EBCT is a fast shuttered camera that only turns on the beam as needed to acquire the image. Conventional CT scanners have their X-ray emitter always on (often modulated) during the acquisition. 33 of :34 34 of :34

18 Image Reconstruction Introduction Image Reconstruction (36) Image Reconstruction (2) Introduction (37) Already in 1917 Johann Radon [ published a paper with the mathematical theory, the Radon transform [ useful to reconstruct a 2D image from multiple projections such as in CT systems. Hounsfield used, for the first CT scanner, an iterative technique to exactly solve the Radon transform. Its disadvantages are that it is slow and that all data must be collected before reconstruction can begin. From the scanning process we have a set of image projections. Given these projections we want to determine the X-ray attenuation coefficients of the original image as accurate as possible. Todays CT systems mainly use variants of the filtered back-projection approach that is computationally more efficient. Fig 3.29: Image projections Fig 3.30: A small section of the final matrix showing individual attenuation values combined as a ray-sum 35 of :34 36 of :34

19 Radon Transform Radon Transform A straight line in Cartesian coordinates can be either described by its slope-intercept form (3.2) (39) Parallel Projection Radon Transform (40) An arbitrary point in the projection is given by the raysum along the line (3.4) in the continuous space the raysum is then given by (3.5) or by its normal representation see Fig (3.3) Fig. 3.31: Different line representations where is the impulse function. (3.6) with. The integrand is zero unless the argument in the delta function is zero. This is valid for all points on the line. Fig. 3.32: Projection geometry 37 of :34 38 of :34

20 Radon Transform Radon Transform The Radon Transform We can generalise this equation to arbitrary lines (41) The Discrete Radon Transform (42) (3.7) In the discrete case the integrals in the Radon transform are replaced by sums This projection is called Radon transform. Often used notations for the Radon transform of are (3.8) (3.9) The Radon transform forms the corner stone of reconstruction from projections used e.g. in Computed Tomography, PET, SPECT. 39 of :34 40 of :34

21 Radon Transform Radon Transform Radon Transform Examples (43) The figure below shows an example image with its Radon transform. The interpretation of the sinogram is still quite easy. Radon Transform Examples (2) The figure below shows an example phantom with its Radon transform. The interpretation of the sinogram is not possible anymore, although the phantom's structure is quite simple. (44) Fig. 3.36: Sinogram of the phantom with projections over Fig. 3.33: Double box image Fig. 3.34: Sinogram of the double box image with projections over Fig. 3.35: Shepp-Logan phantom 41 of :34 42 of :34

22 Fourier Slice Theorem Fourier Slice Theorem Fourier Slice Theorem (2) (47) Fourier Slice Theorem (46) In the following slide we will relate the Fourier transform of 1-D projection with the 2-D Fourier transform of the scanned object. Without loss of generality, we take the projection line to be the -axis in the derivation below. Given is the image and its projection onto the -axis where (3.10) The Fourier transform of is Fig. 3.37: Graphical representation of the Fourier slice theorem The Fourier slice theorem states that, the 1-dimensional Fourier transform of a projection corresponds to the slice (line) - at the same angle - in the 2-dimensional Fourier transform of the object (3.11) the slice at is then (3.12) which is the Fourier transform of. 43 of :34 44 of :34

23 Fourier Slice Theorem Fourier Slice Theorem Reconstruction with the Fourier Slice Theorem (48) Reconstruction with the Fourier Slice Theorem (2) (49) In principle we could reconstruct the image by filling up the Fourier space with the Fourier transforms of the individual projections and then calculate the inverse Fourier transform. This approach is, however, computationally very expensive. If we just sum the spectra of the individual projection beams, the spectral density for low frequencies would be too high as the beams are closer to each other for small radii lower frequencies too strong. We therefore must correct the spectrum with a suitable weighting factor. As the density of the projection beam goes with (Frequency) the spectra must be multiplied with ramp filter. Fig. 3.39: Spectral density must be corrected to get suitable results Fig. 3.38: Image reconstructing using the Fourier slice theorem Each projection direction thus has to be multiplied with a suitable weighting function. As will be seen in the next section, this can also be performed as a convolution with the inverse Fourier transform of in the spatial domain filtered back-projection. 45 of :34 46 of :34

24 Filtered Backprojection Numerical Back-Projection Example Filtered Backprojection (52) Principle of Filtered Back-Projection (51) (1) The measured projections are smeared back, i.e. combined as a ray-sum, across the output matrix. (2) As the back-projected image is heavily blurred and shows star artefacts it has to be filtered with a highpass yielding the final reconstructed image. Fig 3.40: Filtered back-projection principle 47 of :34 48 of :34

25 Filtered Backprojection Filtered Backprojection Example Reconstructions (53) Example Reconstructions (2) (54) Back-projection without filtering using 2, 4, 8, 16, and 32 projections. Strong artefacts can be seen and the images are heavily blurred. Back-projection with highpass filtering using the same 2, 4, 8, 16, and 32 projections. Strong artefacts can be seen and the images are heavily blurred. Fig 3.41: Back-projection without filter Fig 3.42: Back-projection with filter 49 of :34 50 of :34

26 Helical Reconstruction Helical Reconstruction (56) 360 Linear Interpolation Helical Reconstruction (57) Idea: Use attenuation data from points apart on the helix for interpolation We would like to use the same filtered back-projection method as before: Choose the interpolation position along the z-axis Only one projection is from the reconstruction position, others are from different z-positions Fig 3.43: Problem of the helical reconstruction Fig 3.44: Interpolation Interpolation makes the effective image width broader. Introduces artefacts when the structures change along the z-axis. 51 of :34 52 of :34

27 180 Linear Interpolation Helical Reconstruction Idea: Use attenuation data from complementary projections in addition to points apart on the helix (58) Hounsfield Unit Hounsfield Unit (60) Fig 3.45: Complementary projections Fig 3.46: Interpolation Slice profile is narrower, as the z-axis distances are shorter than in interpolation. The tissue absorption coefficient depends on the tube voltage. To make them comparable, the absorption coefficients have to be related to that of water a the same tube voltage. This way a number [Hounsfield unit = Hu] insensitive to tube voltage can be obtained: (3.13) In practice CT values are produced from for air, for water, and between for bone. Fig 3.47: Common CT numbers 53 of :34 54 of :34

28 Automatic Exposure Control Automatic Exposure Control (62) To minimise radiation exposure and optimise radiation efficiency automatic exposure control (AEC) methods have been integrated into todays CT systems. Several different fields to control the tube current (ma) are explored: Relative patient attenuation Depending on the patients body weight (diameter) tube current has to be adjusted. Rotational attenuation As the total X-ray attenuation is smaller in the AP-direction than in the LR-direction, tube current can be dynamically adapted. z-axis attenuation Tube current is automatically adapted to the patient geometry reducing the radiation exposure. In this example the 6 year old boy was irradiated with on average instead of in the standard protocol. Heart cycle gating For heart and aorta scans heart-gating to synchronise the acquisition with the pulse is required. Tube power is generally reduced to in uninteresting parts of the heart cycle. 55 of :34 56 of :34

29 Automatic Exposure Control Automatic Exposure Control (2) (63) Allows the scanner to be controlled by setting a required image quality level Can avoid over- and under-exposure of patients and thus minimises rescans 57 of :34 58 of :34

30 Artefacts Artefacts (65) Several inherent CT artefacts have an important influence on the applied Medical Image Analysis Methods and generally need to be accounted for: Partial Volume Effect High density artefacts Gating in Cardio CT Partial Volume Effect The partial volume effect, common to most medical imaging modalities, poses an important problem for many medical image analysis methods. The sampling of the imaging volume renders it difficult/impossible to exactly locate the boundary of an object. Artefacts (66) The Good News: CT data is geometrically very accurate. If MR/US data is to be registered with CT, then CT should be used as the reference! If not taken special care of, a simple shift of the object can drastically change the result, e.g. area measurement in Fig 3.48(c)+(d). The measured area of (d) is higher than the area of (c). Fig 3.48: (a) Original object, (b) object sampled on a discrete grid, (c) thresholded object, (d) thresholded shifted object 59 of :34 60 of :34

31 Artefacts Artefacts High Density Artefacts (67) Gating in Cardio CT (68) High density streak artefacts or Windmill artefacts result from the finite width of the detector rows, which require interpolation. The artefacts appear close to high contrast gradients. For many acquisitions of the heart and arterial system ECG gating is used. To reduce exposure, the AEC reduces the tube current to during systole (when no images are captured). Proper gating, however, depends on a regular sine rhythm not present in all diseased patients. Fig 3.49: High density artefact example Fig 3.51: Image of good quality with decent SNR Fig 3.52: Gating failed, image was acquired with of the dose very noisy image Fig 3.50: Windmill effect 61 of :34 62 of :34

32 Artefacts segmentation CT and Medical Image Analysis (69) Medical image analysis is an indispensable tool in CT. Without the aid of advanced image analysis methods, radiologists would need substantially more time to find interesting location in the CT datasets. Fig 3.53: Plaque detection aid Fig 3.54: Automatic Sep 26th/Oct dissection 3rd, of :34 64 of :34

33 X-Ray Dosage Summary X-Ray Dosage Summary (71) Examination X-Ray Dosage [msv] CT Dosage [msv] Ratio Skull Thorax Abdomen Spine Extremities The average X-ray exposition in central Europe is approximately 65 of :34