X-ray Computed Tomography: Principle and Recent Advancements

Transcription

1 X-ray Computed Tomography: Principle and Recent Advancements Jiang Hsieh, Ph.D. GE Medical Systems, Milwaukee, WI Jiang Hsieh SPIE MI 2003 Course Note 1

2 Principle and Recent Advancements in X-ray Computed Tomography Basics of Computed Tomography Image Artifacts and Corrections Recent Advancement in CT Technology Recent Advancement in CT Applications Jiang Hsieh SPIE MI 2003 Course Note 2

3 The First Attempt In 1921, Bocage conducted the first experiment of tomography. x-ray source x-ray source B B A focal plane A focal plane A1 B1 A1+A2 B1 B2 film Jiang Hsieh SPIE MI 2003 Course Note 3

4 Computed Tomography In 1967, Godfrey N. Housfield at the Central Research Laboratories of EMI conducted a CT experiment. Jiang Hsieh SPIE MI 2003 Course Note 4

5 First Clinical Scanner The first clinical scanner was installed in Atkinson-Morley Hospital in September photo courtesy of Mr. N. Keat at the ImPACT group Jiang Hsieh SPIE MI 2003 Course Note 5

6 The Modern CT Scanner In the last 30+ years, CT technology has undergone tremendous development. Jiang Hsieh SPIE MI 2003 Course Note 6

7 Utility of CT Application of CT is not limited to humans. Jiang Hsieh SPIE MI 2003 Course Note 7

8 Acquisition Speedup Scan time/slice for consecutive volume coverage has reduced by a factor of 15,000 over the last 30+ years. This is a reduction of factor 1.36/year. Data acquisition speed doubles every 2.2 years! scan time per slice (s) year Jiang Hsieh SPIE MI 2003 Course Note 8

9 1 st translation x-ray tube 91 st translation 1 o increment detector 1 st translation x-ray tube 6 o increment 16 th translation detector x-ray tube detector x-ray tube detector 3RD GENERATION 4TH GENERATION 1ST GENERATION 2ND GENERATION Jiang Hsieh SPIE MI 2003 Course Note 9

10 Electron Beam Scanner Electron Beam scanner was built between 1980 and 1984 for cardiac applications. electron gun section of vacuum drift tube and magnetic focus and deflection coils x-ray fan beam detector scan field electron beam Jiang Hsieh SPIE MI 2003 Course Note 10

11 Sampling Geometries The sampling geometry of CT scanners can be described the following three configurations. We will limit our discussion to the parallel sampling geometry. detector detector detector source source source parallel beam fan beam cone beam Jiang Hsieh SPIE MI 2003 Course Note 11

12 X-ray Generation X-ray photons are produced when a substance is bombarded by highspeed electrons. high-speed electron high-speed electron 0.04 Bremsstrahlung ejected K electron M L K K characteristic radiation bremsstrahlung normalized output x-ray energy (kev) Jiang Hsieh SPIE MI 2003 Course Note 12

13 X-ray Tube Early vintage of x-ray tube is built with glass envelope and the newer designs employ metal frames. cathode rotor assembly target Jiang Hsieh SPIE MI 2003 Course Note 13

14 X-ray Detector Most CT scanners employ either Xenon gas detectors or solid-state detectors. x-ray photon x-ray photon + + reflective material x-ray photons e Xe Xe Xe Xe + Xe + Xe e light photons scintillating material e Xe + Xe Xe Xenon photodiodes Solid-state Jiang Hsieh SPIE MI 2003 Course Note 14

15 CT Data Measurement Under ideal conditions, x-ray intensity observes exponential decay law. I o I = I o e µ x I o x I = I o e x e µ x µ 1 2 e ( µ n ) x = Ioe 1 µ 2 µ µ 2 µ 3 µ 4 µ n µ 1 µ( I x ) dx o e µ x n P I = ln = µ ( x ) dx I o Jiang Hsieh SPIE MI 2003 Course Note 15

16 Ideal Projections The measured data are not line integrals of attenuation coefficients. beam hardening scattered radiation detector and data acquisition non-linearity off-focal radiation patient motion others The measured data has to be calibrated prior to the tomographic reconstruction to obtain artifact-free images. Jiang Hsieh SPIE MI 2003 Course Note 16

17 Trajectory of a Point For parallel geometry, the loci of a point (r,φ) in the rotating coordinate system is x' = r cos ( φ β ) projection y object x β φ β x x sinogram Jiang Hsieh SPIE MI 2003 Course Note 17

18 Sinogram A plot of projection over 2π view angle forms a sinogram. object cross-section sinogram Jiang Hsieh SPIE MI 2003 Course Note 18

19 Jiang Hsieh SPIE MI 2003 Course Note 19 X-ray Computed Tomography: Principle and Recent Advancements Image Reconstruction Image reconstruction can be treated as a pure algebraic problem by solving a set of simultaneous equations µ 1 µ 2 µ 3 µ 4 = + = + = + = µ µ µ µ µ µ µ µ = = = = µ µ µ µ 4 equations 4 unknowns 5 4

20 Image Reconstruction Independence conditions have to be satisfied for valid solution. 1 2 µ 1 µ 2 µ 3 µ µ 1 µ 3 µ 1 µ µ µ µ µ = = = = equations 3 independent Infinite number of possible solutions Jiang Hsieh SPIE MI 2003 Course Note 20

21 Image Reconstruction In most commercial CT scanners, reconstruction algorithm is based on the Fourier Slice Theorem (central slice theorem). The theorem is based on the one-to-one correspondence between a two dimensional function and its Fourier transform. FT IFT f ( x, y) F( u, v) = f ( x, y) e i2π ( ux+ vy) dxdy Jiang Hsieh SPIE MI 2003 Course Note 21

22 6000 i πux ( P( u) = f ( x, y) e 2 dxdy P( u) p x) = f ( x, y) dy i2πux = f ( x, y) e dxdy PROJECTION FFT 900 = v=0 2D FFT f ( x, y) F( u, v) = f ( x, y) e i2π ( ux+ vy) dxdy Jiang Hsieh SPIE MI 2003 Course Note 22

23 Implementation Issues Due to sampling pattern, direct implementation of the Fourier slice theorem is difficult. Cartesian grid sample location Jiang Hsieh SPIE MI 2003 Course Note 23

24 Filtered Backprojection For parallel geometry, a projection sample can be uniquely specified by the projection angle, θ, and the distance, t. y θ t x Jiang Hsieh SPIE MI 2003 Course Note 24

25 Filtered Backprojection The filtered backprojection formula can be derived as follows. Any image function, f(x,y) can be recovered from its Fourier transform, F(u,v), by the inverse Fourier transform: f ( x, y) = F ( u, v) e j 2π ( ux + vy ) dudv Jiang Hsieh SPIE MI 2003 Course Note 25

26 Filtered Backprojection Express the equation in a polar coordinate system (w,q) and make use of the symmetry, F(ω,θ+π)=F(-ω, θ): f = π j 2πω t F ( ω, θ ) ω e 0 ( x, y) dωdθ Make use of the Fourier slice theorem: f = π j 2πω t P θ ( u ) ω e 0 ( x, y ) dω dθ Jiang Hsieh SPIE MI 2003 Course Note 26

27 Implementation The filter kernel as specified does not exist. k( t) = ω e ω j2 πω t d The filter needs to be band-limited: K(ω) k( t) = W W ω e j2πωt dω -w w ω Jiang Hsieh SPIE MI 2003 Course Note 27

28 Filtered Backprojection Filtered backprojection uses weighting function to approximate ideal condition. weighting function ideal frequency data from one projection actual frequency data from one projection weighting function for approximation Jiang Hsieh SPIE MI 2003 Course Note 28

29 Filter Characteristics The filter emphasizes high frequency contents of the projection over the low frequency contents. It acts as an edge enhancement intensity intensity channels channels Jiang Hsieh SPIE MI 2003 Course Note 29

30 Filtering Let us consider an example of reconstructing a phantom object of two rods. Object Original Sinogram Filtered Sinogram Jiang Hsieh SPIE MI 2003 Course Note 30

31 Backprojection Backprojection is performed by painting the intensity of the entire ray path with the filtered sample. filtered projection Jiang Hsieh SPIE MI 2003 Course Note

32 Backprojection 0 o -30 o 0 o -60 o 0 o -90 o 0 o -120 o 0 o -150 o 0 o -180 o Jiang Hsieh SPIE MI 2003 Course Note 32

33 Filtered Backprojection The filtered backprojection process can be described by the following flow chart. pre-processed processed data filter the data backprojection convolve the data with the ramp filter to achieve de-blurring sum up the contribution of the filtered projection over all view angle, for pixel in the image. Jiang Hsieh SPIE MI 2003 Course Note 33

34 Equiangular Fan Beam Reconstruction When detector cells with identical size is arranged along an arc concentric to the x-ray focus, equiangular sampling is formed. Each ray in a fan beam can be specified by β and γ. Reconstruction formula can be derived by specifying each sample in (γ, β) coordinate with a (t, θ) coordinate. y β γ x fan beam geometry Jiang Hsieh SPIE MI 2003 Course Note 34

35 Jiang Hsieh SPIE MI 2003 Course Note 35 X-ray Computed Tomography: Principle and Recent Advancements Equiangular Fan Beam Reconstruction The projection is first multiplied by the cosine of the detector angle. In the backprojection process, the filtered sample is scaled by the distance to the source. = π γ γ γ γ γ γ β γ β cos ) ' ( ), ( ), ( m m d D h p d L y x f

36 Fan Beam Reconstruction Alternatively, the fan beam data can be converted to a set of parallel samples. Parallel reconstruction algorithms can be used for image formation. projection angle, β β=β 0 γ parallel samples detector angle, γ Jiang Hsieh SPIE MI 2003 Course Note 36

37 Definition of CT Number One of the key advantages of CT over conventional x-ray is its low-contrast differentiability (a fraction of a percent). Attenuation coefficient of soft-tissue is similar to that of water. CT images are typically represented by a remapped scale of the linear attenuation coefficients of the object, called CT number. CT µ µ _ Number = water 1000 µ water Jiang Hsieh SPIE MI 2003 Course Note 37

38 Display Window Width and Level Most display devices has either 8-bit of dynamic range (256 gray levels). The reconstructed images are typically 16-bit (well over 30,000 distinct values). original CT number W W >3000 W L 256 remapped intensity Display window width and level is used to map a small range of the intensities to the display device Jiang Hsieh SPIE MI 2003 Course Note 38

39 Display Window Width and Level For the same reconstructed image, its appearance varies significantly over the selection of display window and level. WW=2700 HU WW=100 HU, WL=20 HU Jiang Hsieh SPIE MI 2003 Course Note 39

40 Image Reformation With the introduction of helical and multi-slice CT, there is an explosion on the number of images available for each exam. Advanced image display techniques provide opportunities to reduce the amount of information and provides better visualization of the data. These display techniques include MPR, shaded surface display, MIP, and volume rendering. Jiang Hsieh SPIE MI 2003 Course Note 40

41 MPR Multi-planar reformation produces coronal, sagittal, or oblique plane images from a stack of axial images. right superior posterior stack of CT images anterior coronal plane left axial plane sagittal plane Jiang Hsieh SPIE MI 2003 Course Note 41

42 right MPR coronal plane coronal plane left Jiang Hsieh SPIE MI 2003 Course Note 42

43 right superior MPR curved plane left MPR planes does not need to be flat. This feature is useful for vascular or bone structure display. curved plane Jiang Hsieh SPIE MI 2003 Course Note 43

44 Maximum Intensity Projection (MIP) The projection intensity equals the maximum pixel intensity along the ray path. hypothetical screen mathematical rays observer 3D volume data Jiang Hsieh SPIE MI 2003 Course Note 44

45 Maximum Intensity Projection (MIP) MIP offers improved contrast and visibility for vascular structures. Jiang Hsieh SPIE MI 2003 Course Note 45

46 Volume Rendering The projection intensity equals weighted sum of pixel intensities based on opacity function. hypothetical screen 1 mathematical rays opacity 3D volume data observer 0 pixel intensity (HU) Jiang Hsieh SPIE MI 2003 Course Note 46

47 Volume Rendering Volume rendering provides improved visualization of structural relationship. Jiang Hsieh SPIE MI 2003 Course Note 47

48 Shaded Surface Display The projection intensity equals the reflected light intensity off the object surface. hypothetical screen light source observer 3D volume data mathematical rays Jiang Hsieh SPIE MI 2003 Course Note 48

49 Shaded surface display provides geometric information about the surface of the object. Shaded Surface Display Jiang Hsieh SPIE MI 2003 Course Note 49

50 Key Performance Parameters There are many important performance parameters for x-ray computed tomography. The most important parameters are: CT number accuracy Spatial resolution Low contrast detect-ability Temporal resolution Noise Dose Jiang Hsieh SPIE MI 2003 Course Note 50

51 CT Number Accuracy By definition, CT number of water is zero and air is In addition, the CT number has to be homogeneous over the entire FOV. Jiang Hsieh SPIE MI 2003 Course Note 51

52 Spatial Resolution The MTF was originally defined as the Fourier transform of the PSF of the system. Two dimensional Fourier transform is performed on the reconstructed thin wire and the magnitude of the function represent the MTF MTF frequency (LP/cm) Jiang Hsieh SPIE MI 2003 Course Note 52

53 Impact of Reconstruction Kernel By modifying the cutoff frequency and the window function of the reconstruction kernel, spatial resolution of the image can be changed. Standard Bone Jiang Hsieh SPIE MI 2003 Course Note 53

54 Why z-resolution is important? In many clinical practice today, radiologists are viewing images in 3D instead of 2D. Images are reformatted, volume rendered, or MIP. Iso-tropic spatial resolution is crucial. Multi-slice CT allow clinicians not to be forced to trade off SSP vs. coverage. Jiang Hsieh SPIE MI 2003 Course Note 54

55 Spatial Resolution in Z AAPM resolution insert was scanned so that resolution pattern is along z. Reformatted image is used to examine the spatial resolution in z 1.75 mm 1.5 mm 1.25 mm 1.0 mm 0.75 mm 0.6 mm 0.5 mm 0.4 mm z 16x0.625mm using conjugate sampling 16x0.75mm using row sampling 16x1.25mm using conjugate sampling Jiang Hsieh SPIE MI 2003 Course Note 55

56 Low-Contrast Resolution Visibility of an object depends on the size of the object and its contrast to background. contrast to background disc size Jiang Hsieh SPIE MI 2003 Course Note 56

57 Low-Contrast Resolution Visibility of an object also depends on the noise level of the image. contrast to background noise level Jiang Hsieh SPIE MI 2003 Course Note 57

58 Measurement of Dose For the step-and-shoot mode, all radiation dose is confined to a thin section, T. X-ray dose is also delivered to regions outside the primary beam due to beam divergence, scattered radiation, and beam penumbra. relative dose T distance (cm) Jiang Hsieh SPIE MI 2003 Course Note 58

59 Measurement of Dose To account for the contribution of the tails with multiple scans, multiple-scanaveraged-dose (MSAD) is defined: MSAD = 1 I I I / 2 / 2 D N, I ( z) dz relative dose MSAD T distance (cm) Jiang Hsieh SPIE MI 2003 Course Note 59

60 Factors That Impact Dose Scan Mode full scan half scan Beam Quality Flat filter (Al, Cu, etc.) Bowtie filter Scan Technique X-ray tube current and voltage Scan time Beam umbra to penumbra ratio Tube current modulation Jiang Hsieh SPIE MI 2003 Course Note 60

61 Image Artifacts Image artifacts can be defined as any discrepancy between the reconstructed value and the true attenuation. We limit our discussion to the ones that are clinically significant. In a typical CT, nearly 10 6 independent measurements are used to form an image. Therefore, CT is more sensitive to artifacts. Jiang Hsieh SPIE MI 2003 Course Note 61

62 Artifact Appearance -streaking artifact When a few channels in a few projections deviates significantly from the true signal, streaking artifact appears. error signal reconstructed image filtered projection Jiang Hsieh SPIE MI 2003 Course Note 62

63 Artifact Appearance -ring artifact When a single channel deviates from true signal for an extended projection angle, a ring artifact is formed. backprojecting of an error channel reconstructed image Jiang Hsieh SPIE MI 2003 Course Note 63

64 Artifact Appearance -shading artifact When a group of adjacent signals deviate gradually from true signal for several projections, shading artifacts are formed. error channels reconstructed image Jiang Hsieh SPIE MI 2003 Course Note 64

65 Outline SYSTEM LEVEL ARTIFACT aliasing, partial volume, scatter, noise streaks X-RAY TUBE INDUCED ARTIFACT off-focal radiation, tube arcing, rotor wobble DETECTOR RELATED ARTIFACT offset/nonlinearity/radiation damage, primary speed afterglow PATIENT INDUCED ARTIFACT motion, beam hardening, metal, truncated projection Jiang Hsieh SPIE MI 2003 Course Note 65

66 Aliasing Artifact Shannon theory states that the sampling rate needs to be twice the highest frequency contents in the signal. Fourier transform δ δ 1/δ 1/δ distance frequency Jiang Hsieh SPIE MI 2003 Course Note 66

67 Aliasing Artifact For a third generation CT scanner, this condition could not be easily met. Aliasing artifacts will result. x-ray tube detector reconstructed image of a wire Jiang Hsieh SPIE MI 2003 Course Note 67

68 4 th Generation Scanner To overcome aliasing artifact, the concept of 4th generation scanner was developed. x-ray tube detector Jiang Hsieh SPIE MI 2003 Course Note 68

69 Detector Quarter Offset Sampling density can be increased by detector quarter offset. angle=β angle=β 1/4 detector angle=β+π Jiang Hsieh SPIE MI 2003 Course Note 69

70 Detector Quarter Offset The same concept can be applied to fan beam. 180 o rotation iso-center 1/4 detector detector original quarter offset Jiang Hsieh SPIE MI 2003 Course Note 70

71 Focal Spot Wobble (flying focal spot) Double sampling can be obtained by deflecting x-ray focal spot. x-ray focal spot x-ray focal spot detector detector Jiang Hsieh SPIE MI 2003 Course Note 71

72 Image Quality Comparison Computer simulation was performed to compare the image performance. original quarter offset focal spot wobble Jiang Hsieh SPIE MI 2003 Course Note 72

73 View Aliasing Similar to projection aliasing, the view sampling has to satisfy conditions to ensure aliasing-free image. For parallel beam: Nmin = 2πRν M maximum resolvable spatial frequency For fan beam: N min = 4πRν M ψ 1 sin 2 maximum fan angle sampling pattern of iso-ray Jiang Hsieh SPIE MI 2003 Course Note 73

74 View Aliasing Artifact View aliasing can be observed when view number is reduced. 984 views 704 views Jiang Hsieh SPIE MI 2003 Course Note 74

75 Partial Volume When the object scanned is smaller than the slice thickness, partial volume can result. Partial volume error is in general projection angle dependent. z partially intruded object x-ray source iso-center detector x-ray beam at angle β+π x-ray beam at angle β Jiang Hsieh SPIE MI 2003 Course Note 75

76 Partial Volume The most effective method of combating partial volume artifact is to use thin slices. 7mm aperture 1mm aperture Jiang Hsieh SPIE MI 2003 Course Note 76

77 Scatter A significant portion of the x-ray photon exiting from the object is scattered photon. Scattered photons generally deviate from their original path. Post patient collimator can be used effectively to reject the scatter. A small portion of the scattered radiation can reach the detector. scattered photons collimator scintillator object input x-ray photons primary photons photodiode Jiang Hsieh SPIE MI 2003 Course Note 77

78 Impact of Scatter Scattered radiation creates a low frequency bias to the true projection signal. The low frequency bias produces shading artifact. true projection original intensity scatter signal distance with scatter Jiang Hsieh SPIE MI 2003 Course Note 78

79 Photon Starvation At low signal level, the noise in the projection is no longer dominated by the x-ray photon. Convolution filtering operation will further amplify the noise and streak artifacts will result. example of a patient scan Jiang Hsieh SPIE MI 2003 Course Note 79

80 Artifact Reduction Correction algorithm can be derived that adaptively filters out the noise for the channels with low photon counts. original image adaptively filtered image Jiang Hsieh SPIE MI 2003 Course Note 80

81 X-ray Tube Cathode Focal track (region of off- Focal radiation Focal spot Target (anode) Jiang Hsieh SPIE MI 2003 Course Note 81

82 Off-focal Radiation -compensation Off-focal radiation can be minimized by placing a collimator near the x-ray focal spot. collimator off-focal x-ray focal spot x-ray from focal spot x-ray Detected off-focal radiation Jiang Hsieh SPIE MI 2003 Course Note 82

83 Off-focal Radiation -algorithmic correction Off-focal radiation effect can also be corrected by algorithmic correction. image without correction image with correction Jiang Hsieh SPIE MI 2003 Course Note 83

84 Tube Rotor Wobble X-ray tube target rotates at as high as 10,000 RPM. In conjunction with high temperature, significant wear and tear occurs to the tube assembly. with rotor wobble without rotor wobble Jiang Hsieh SPIE MI 2003 Course Note 84

85 Primary Speed and Afterglow The output signal of most solid state detector does not reach zero right after the termination of x-rays. The primary speed (fastest decay) is mainly determined by the nature of the activator. The afterglow (slower decay) is related in general to the impurities (traps) in the material. The detector primary speed and afterglow can be improved by doping the detector with rare-earth materials. Jiang Hsieh SPIE MI 2003 Course Note 85

86 Impact of Slow Decay potential loss of spatial resolution possible production of image artifact. 1.0s scan 0.5s scan Jiang Hsieh SPIE MI 2003 Course Note 86

87 Experimental Result No loss of resolution or image artifact can be observed: 1.0s scan 0.5s scan Jiang Hsieh SPIE MI 2003 Course Note 87

88 MTF Measurement Quantitative analysis on spatial resolution 1.2 MTF s 4.0s frequency (LP/cm) 0.5s 4.0s 4.0s 0.5s 50% MTF (LP/cm) % MTF (LP/cm) Jiang Hsieh SPIE MI 2003 Course Note 88

89 Noise Comparison Standard deviation measured on water phantom: 25 standard deviation distance to iso (mm) 0.5s 4.0s Jiang Hsieh SPIE MI 2003 Course Note 89

90 Impact of Afterglow Non-uniform afterglow can cause rings and shading in the image. Afterglow can also be corrected with software. original with correction Jiang Hsieh SPIE MI 2003 Course Note 90

91 Patient Motion Patient motion causes inconsistency in the projection data set. Patient motion can cause steaks and shading artifacts. motion artifact example of a patient scan Jiang Hsieh SPIE MI 2003 Course Note 91

92 Patient Motion Correction The most inconsistency occurs between the start and end of a scan. Patient motion effect can be reduced by suppressing the contribution of the projections in the worst regions. 2π N t end of scan t start of the scan projection view regions of most motion 0 detector channel Jiang Hsieh SPIE MI 2003 Course Note 92

93 Patient Motion Correction By weighting the projections prior to the reconstruction, patient motion artifacts can be significantly reduced. The weighting function needs to be continuous and differentiable. without correction with correction Jiang Hsieh SPIE MI 2003 Course Note 93

94 Beam Hardening The attenuation characteristics, µ(e), are dependent on the input x- ray energy. For all commercially available CT scanners, the x-ray generated by x-ray tube, T(E), is poly-energetic. µ ( se, ) ds I = T( E) e de The measured projection does not represent the line integral of µ. µ(e) energy, E x-ray flux, T(E) energy, E Jiang Hsieh SPIE MI 2003 Course Note 94

95 Water Beam Hardening If not properly compensated for, cupping artifact will result. ideal -ln ln(i/i o ) actual path length no correction Jiang Hsieh SPIE MI 2003 Course Note 95

96 Water Beam Hardening Water beam hardening can be corrected with polynomial expansion of the projections. N n p' = α corrected ideal n= 1 n p -ln ln(i/i o ) actual path length no correction with correction Jiang Hsieh SPIE MI 2003 Course Note 96

97 Bone Beam Hardening The attenuation characteristics of bone is significantly different from that of soft tissue. bone -ln ln(i/i o ) water path length WATER BH CORRECTED Jiang Hsieh SPIE MI 2003 Course Note 97

98 Bone Beam Hardening Software correction schemes can be used to reduce the bone induced artifacts. threshold forward projection sinogram of bones scale/ subtraction error image filtered backprojection error projection polynomial mapping Jiang Hsieh SPIE MI 2003 Course Note 98

99 Bone Beam Hardening Software correction schemes can be used to reduce the bone induced artifacts. ORIGINAL CORRECTED Jiang Hsieh SPIE MI 2003 Course Note 99

100 Note CT is inherently prone to image artifacts. Artifacts can be the results of malfunction of any component in the system, data acquisition protocols, inherent physics limitations, or the scanned object. We discussed only the causes and corrections of artifacts that are in the public domain. Jiang Hsieh SPIE MI 2003 Course Note 100

101 Helical Scanning In helical scanning, the patient is translated at a constant speed while the gantry rotates. Helical pitch: h = q d distance gantry travel in one rotation collimator aperture q Jiang Hsieh SPIE MI 2003 Course Note 101

102 Helical Scanning Advantage Larger volume coverage due to zero inter-scan delay. Reconstruction at arbitrary locations due to uniform sampling pattern in z. Better 3D image quality Improved contrast due to object centering Improved tube utilization Slice thickness modifiable with reconstruction algorithm Jiang Hsieh SPIE MI 2003 Course Note 102

103 Clinical Examples Jiang Hsieh SPIE MI 2003 Course Note 103

104 Helical Scanning Disadvantage Inherent projection inconsistency Jiang Hsieh SPIE MI 2003 Course Note 104

105 Helical Scanning The helical data collection is inherently inconsistent. If proper correction is not rendered, image artifact will result. reconstructed helical scan without correction Jiang Hsieh SPIE MI 2003 Course Note 105

106 Helical Reconstruction The plane of reconstruction is typically at the mid-point between the start and end planes. Interpolation is performed to estimate a set of projections at the plane of reconstruction. data sampling helix start of data set plane end of data set plane plane of reconstruction Jiang Hsieh SPIE MI 2003 Course Note 106

107 Helical Reconstruction -360 o interpolation Samples at the plane of reconstruction is estimated using two projections that are 360 o apart. p' ( γ, β ) = wp( γ, β ) + (1 w) p( γ, β + 2π ) where x q w = q q x data sampling helix p(γ,β) p (γ,β) p(γ,β+2π) Jiang Hsieh SPIE MI 2003 Course Note 107

108 Helical Reconstruction -180 o interpolation In fan beam, each ray path is sampled by two conjugate samples that are related by: γ ' = γ β ' = β + π 2γ For helical scan, these two samples are taken at different z location because of the table motion. Jiang Hsieh SPIE MI 2003 Course Note 108

109 Helical Reconstruction -180 o interpolation Linear interpolation is used to estimate the projection samples at the plane of reconstruction. Because the samples are taken at different view angles, the weights are γ and β dependent. plane of reconstruction wp( γ, β) + (1 w) p( γ, β + π 2γ ) p n (-γ,β+π 2γ) p k (γ,β) z-axis Jiang Hsieh SPIE MI 2003 Course Note 109

110 Interpolation Verses Weighting The backprojection process is essentially a summation operation. The interpolation first weights the samples and sums up the weighted samples. If we weight the samples prior to the filtering operation, the summation process will be performed automatically by the backprojection process. Jiang Hsieh SPIE MI 2003 Course Note 110

111 Artifact Suppression Helical reconstruction algorithm effectively suppresses helical artifacts. without helical correction with helical correction Jiang Hsieh SPIE MI 2003 Course Note 111

112 Algorithm Comparision -slice sensitivity profile Because 180 o based interpolation interpolate two points that are located closer than the 360 o based interpolation, 180 o based has a better slice sensitivity profile. 360 o interpolation uses 4π projection data and has better noise property. 180 degree interpolation 360 degree interpolation Jiang Hsieh SPIE MI 2003 Course Note 112

113 Helical Reconstruction -projection weighting Interpolation can be performed by weighting the projections prior to the filtered backprojection. The backprojection step sums up contribution from different views. pre-processed processed data multiply data by weights filter the data backprojection Jiang Hsieh SPIE MI 2003 Course Note 113

114 Artifact Property In single slice CT, image artifacts increase monotonically with the helical pitch. p=0 p=1 p=1.5 p=2 Jiang Hsieh SPIE MI 2003 Course Note 114

115 Surface Rendering Artifact 3D graphics techniques often enhances the artifacts that are not visible in 2D images. 3D image (helical scan, 5mm collimator at 1mm spacing) 3D image (axial scan, rotating start angle, 5mm collimator at 1mm spacing) Jiang Hsieh SPIE MI 2003 Course Note 115

116 Artifact Suppression The artifact can be reduced by modifying the weighting function in the reconstruction process. 3D SSD image original (threshold=10%) 3D SSD image (threshold=10%) with new reconstruction Jiang Hsieh SPIE MI 2003 Course Note 116

117 Noise In-homogeneity The noise ratio is a function of the starting angle of the scan as well as the spatial location HI HE Jiang Hsieh SPIE MI 2003 Course Note 117

118 MIP Artifacts Dark and bright bands will result in MIP or volume rendered images if not properly corrected. 48 POLY PHANTOM PATIENT Jiang Hsieh SPIE MI 2003 Course Note 118

119 Artifact Reduction Based on the noise analysis, adaptive filtering schemes can be derived to combat the artifact. ORIGINAL FILTERED ORIGINAL FILTERED Jiang Hsieh SPIE MI 2003 Course Note 119

120 Multi-slice CT Multi-slice CT contains multiple detector rows. For each gantry rotation, multiple slices of projections are acquired. Similar to the single slice configuration, the scan can be taken in either the step-and-shoot mode or helical mode. Unlike the single slice, the slice thickness is defined by detector aperture. x-ray source detector Jiang Hsieh SPIE MI 2003 Course Note 120

121 Advantages of Multi-slice Helical Large coverage and faster scan speed Better contrast utilization Less patient motion artifacts Near-isotropic spatial resolution 8-slice data acquisition Jiang Hsieh SPIE MI 2003 Course Note 121

122 Advantages of Multi-slice Helical Large coverage and faster scan speed Better contrast utilization Less patient motion artifacts Isotropic spatial resolution Jiang Hsieh SPIE MI 2003 Course Note 122

123 Detector Configuration matrix array adaptive array 4x1.25mm 4x1mm 4x2.5mm 4x2.5mm 4x3.75mm 4x5mm 4x5mm Jiang Hsieh SPIE MI 2003 Course Note 123

124 Detector Configuration mixed array To provide sub-mm slice thickness, the center 8 detector cells are further sub-divided into two 16x0.625mm cells. Similar to the 4 or 8 slice configuration, neighboring cells can be 16x1.25mm grouped to form a single cell. Jiang Hsieh SPIE MI 2003 Course Note 124

125 Multi-slice Helical When acquiring data in a helical mode, the N (4 or higher) detector rows form N interweaving helixes. Because multiple detector rows are used in the data acquisition, the acquisition speed is typically higher. Similar to the single slice helical, the projection data are inherently inconsistent. Jiang Hsieh SPIE MI 2003 Course Note 125

126 Major Challenges Two major challenges of multislice helical reconstruction are helical interpolation and cone beam. Cone beam challenge is due to the fact that the projections collected from multi-detector rows are not parallel to each other. For all multi-slice scanner on the market, the cone angle is about 1 o. z single-slice multi-slice Jiang Hsieh SPIE MI 2003 Course Note

127 Reconstruction Algorithm Impact Helical reconstruction requires interpolation of the acquired projections to a consistent set of projections. Either row-to-row or conjugate interpolation can be used. plane of reconstruction projection angle detector location in z Jiang Hsieh SPIE MI 2003 Course Note 127

128 Reconstruction Algorithm Impact Projection samples from conjugate samples are used to interpolate projections at the plane of reconstruction. In general, row-to-row interpolation produces roughly 30% thicker FWHM than the conjugate interpolation. projection angle β+π β plane of reconstruction detector location in z Jiang Hsieh SPIE MI 2003 Course Note 128

129 Cone Beam Artifact center slice z edge slice multi-slice Jiang Hsieh SPIE MI 2003 Course Note

130 Cone Beam Algorithm (1) FDK-based algorithm is one of the popular cone beam reconstruction algorithms. FDK-based algorithm uses projection weighting combined with 3D backprojection that follows the actual cone beam sampling geometry. z multi-slice Jiang Hsieh SPIE MI 2003 Course Note

131 Example FDK algorithm can be combined with different weighting functions to optimize its performance in different performance parameters. simple FDK-based Jiang Hsieh SPIE MI 2003 Course Note 131

132 For high pitch multi-slice helical scan, the interpolated sample and the plane of reconstruction overlaps only at the iso-center. To overcome the discrepancy, tilted planes are defined as the plane of reconstruction. interpolated sample Cone Beam Algorithm (2) plane of reconstruction z helical path tilted plane conventional POR Jiang Hsieh SPIE MI 2003 Course Note 132

133 Example When the SAME weighting function is used, reconstructions with the tilted plane produces better image quality than the conventional reconstruction plane with 2D backprojection. conventional plane tilted plane Jiang Hsieh SPIE MI 2003 Course Note 133

134 Cone Beam Algorithm (3) In helical mode, each ray path is sampled multiple times by different detector rows. Samples from different detector rows can be treated differently. The final result is the convolution of several weighting functions. z multi-slice Jiang Hsieh SPIE MI 2003 Course Note

135 Example acquired with 16x0.625mm at 26:1 helical pitch and reconstructed with Standard kernel ww=400, wl=-50 Jiang Hsieh SPIE MI 2003 Course Note 135

136 Single vs. Quad axial axial single 1.5:1 pitch single 2:1 pitch quad 3:1 pitch quad 6:1 pitch Jiang Hsieh SPIE MI 2003 Course Note 136

137 Slice Thickness Change with Algorithms Slice thickness can be selected by modifying the reconstruction process. By low-pass filtering in the z- direction, the slice sensitivity profile can be broadened to any desired shape and thickness. From an image artifact point of view, images generated with the thinner slice aperture is better. Filtering z Jiang Hsieh SPIE MI 2003 Course Note 137

138 Example Z filtering can be applied in either the projection domain or the image domain. In general, z-smoothing provides artifact suppression capability. 16x0.625mm detector aperture at 1.75:1 helical pitch FWHM=0.625mm FWHM=2.5mm Jiang Hsieh SPIE MI 2003 Course Note 138

139 Thick Scan vs. Thick Reconstruction It is always better to scan with thin slice and reconstruct to thicker slice than scan with thicker slice from artifact point of view. 2.5mm reconstructed from 8x2.5mm at 1.675:1 helical pitch 2.5mm reconstructed from 16x0.625mm at 1.75:1 helical pitch Jiang Hsieh SPIE MI 2003 Course Note 139

140 Recent Advancement in CT Applications Cardiac Fluoroscopy Perfusion Screening Jiang Hsieh SPIE MI 2003 Course Note 140

141 Cardiac CT Two key factors contribute to the recent advancement of cardiac application: faster scan speed (0.5s or faster) introduction of multi-slice CT Two type of cardiac application: calcification screening coronary artery imaging One of the key performance parameters for cardiac CT is the reduction or elimination of motion artifacts. Jiang Hsieh SPIE MI 2003 Course Note 141

142 Single-Cycle Gated Cardiac Scans Projection data used in the reconstruction is selected based on the EKG signal to minimize motion artifacts. acquisition interval for image No. 1 acquisition interval for image No. 2 acquisition interval for image No. 3 acquisition interval for image No magnitude time (sec) Jiang Hsieh SPIE MI 2003 Course Note 142

143 Selection of Helical Pitch Improper selection of helical pitch results in either overlapped coverage or gaps in the coverage. detector row 1, 2, 3, 4 detector row 1, 2, 3, 4 detector row 1, 2, 3, 4 overlapped region cycle 1 gap time time cycle 2 time coverage cycle 3 detector location (z) detector location (z) detector location (z) Jiang Hsieh SPIE MI 2003 Course Note 143

144 Half Scan Reconstruction For relatively slow heart rate, single sector reconstruction produces satisfactory results. Jiang Hsieh SPIE MI 2003 Course Note 144

145 Selection of Helical Pitch Volume rendering technique is also used for image display. Jiang Hsieh SPIE MI 2003 Course Note 145

146 Image Artifacts-Motion Cardiac motion artifacts can result due to non-optimal gating. Jiang Hsieh SPIE MI 2003 Course Note 146

147 Image Artifacts-High Density Objects Metal or high-density objects, such as pacemaker leads, can produce severe image artifacts. Jiang Hsieh SPIE MI 2003 Course Note 147

148 Image Artifacts-Phase Mis-registration Inconsistency in the gating can produce artifacts in reformatted images. Jiang Hsieh SPIE MI 2003 Course Note 148

149 Multi-cycle Gated Cardiac Scans Projection data used in the reconstruction is selected based on the EKG signal to minimize motion artifacts. acquisition interval for one image total acquisition interval for one image magnitude time (sec) Jiang Hsieh SPIE MI 2003 Course Note 149

150 Performance Comparison Motion artifacts can be further reduced by utilization of multicycle gating. single-cycle gating four-cycle gating Jiang Hsieh SPIE MI 2003 Course Note 150

151 CT Fluoroscopy Device table-side monitor floatable table hand-held control Jiang Hsieh SPIE MI 2003 Course Note 152

152 Volumetric Display With the introduction of multi-slice scanner, volumetric display of fluoroscopy images become feasible. Jiang Hsieh SPIE MI 2003 Course Note 153

153 Image Reconstruction CT fluoroscopy requires images to be reconstructed and display in real time to provide timely feedback to the operator. State-of-the-art reconstruction with conventional algorithm takes 0.5s/image. Specialized reconstruction algorithms have to be utilized to obtain significantly improvement in reconstruction speed. Jiang Hsieh SPIE MI 2003 Course Note 154

154 Rapid Image Reconstruction One of the key performance parameters is the image reconstruction speed. S r, n S u, n+1 S u, n+2 S u, n+3 S u, n+4 S u, n+5 S u, n+6 S d, n+8 S u, n+7 S r, n S d, n+1 S r, n+8 S d, n+9 + image n image n+1 Jiang Hsieh SPIE MI 2003 Course Note 155

155 Jiang Hsieh SPIE MI 2003 Course Note 156 X-ray Computed Tomography: Principle and Recent Advancements Rapid Image Reconstruction An example of a weighting function: < < = , , 0, 2 3 ) ( β π β π β β β π β β β π π β β β β β β β β β w The production of image I n+1 from image I n is described: 9, 8, 1,, = n d n r n d n r n n S S S S I I S r,n and S d,n is the sub-images produced by the ascending and descending weighting functions.

156 CT Perfusion Blood flow provide oxygen and nutrients to the brain. Basic brain functions are interrupted at different blood flow levels. CBV vascular structure MTT CBF venous outlet arterial inlet Jiang Hsieh SPIE MI 2003 Course Note 157

157 Perfusion Human brains has intricate self-regulating system. Measurement of cerebral blood flow (CBF) alone is inadequate to assess the viability of brain tissue. Cerebral blood volume is the total volume of blood in the large conductance vessels, arteries, arterioles, capillaries, venules, and sinuses. Mean transit time (MTT) is defined as the average time for the blood to travel from the arterial inlet to the venous outlet. CBV = CBF MTT The algorithms to measure CBV, CBF, and MTT can be classified into two classes: direct-measurement based and deconvolution based. Jiang Hsieh SPIE MI 2003 Course Note 158

158 Direct Measurement Methods flow x arterial concentration F Ca(t) mass concentration Q(t) These methods are based on Fick principle. Based on the conservation of contrast medium, the rate of accumulation of contrast medium in an organ is the difference between the influx rate and the efflux rate of the contrast. flow x venous concentration F Cv(t) Jiang Hsieh SPIE MI 2003 Course Note 159

159 Fick Principle (direct-measurement based) For an arterial contrast medium of concentration C a (t) and CBF of F, the rate of contrast influx into a volume is C a (t)f. Due to the conservation of contrast medium, the rate of contrast accumulation, q(t), is the derivative of the total amount of contrast in the volume, Q(t): dq( t) q( t) = = F a v t dt Q( t) [ C ( t) C ( )] t t = F C a ( t) dt C 0 0 v ( t) dt C a (t) and Q(t) are the time density curve (TDC) measured at artery and the entire volume. Jiang Hsieh SPIE MI 2003 Course Note 160

160 Fick Principle (direct-measurement based) If we ignore the venous outflow (C v (t)=0), the blood flow can be approximated by: F = Q( t) C a ( t) To reduce the underestimation of blood flow due to the no venous flow assumption, we need to either reduce total contrast volume or increase injection rate. Reduction of contrast volume leads to poor signal-to-noise ratio of the time-density curve. Increase injection rate raises patient safety concerns. Jiang Hsieh SPIE MI 2003 Course Note 161

161 De-convolution Method De-convolution methods treat the organ perfusion as a linear system. δ(t): contrast medium of unit volume injected over extremely short time system impulse response (residual function) h(t) g(t): contrast medium injected clinically system response h(t)*g(t) Jiang Hsieh SPIE MI 2003 Course Note 162

162 Impulse Residual Function The residual function, h(t), represents the tissue TDC to an arterial bolus of contrast of unity volume over an extremely short period of time. The area under the impulse residual function represents the mean-transit time: 1 h(t) MTT = 0tdh 1 h fraction of the contrast with transit time, t 0 t, t+ t t Jiang Hsieh SPIE MI 2003 Course Note 163

163 Linear System Approach Impulse residual function cannot be measured directly in clinical practice. Based on the linear system theory, we have: Q( t) = C ( t) F h( t) = C ( t) g( t) a a Q(t) and C a (t) are the measured TDC of the volume and artery. g(t) can be solved by de-convolution. F is the height of the plateau of g(t). Area under g(t) represents CBV (product of MTT and CBF). Jiang Hsieh SPIE MI 2003 Course Note 164

164 Example of Brain Perfusion Jiang Hsieh SPIE MI 2003 Course Note 165

165 Example of Body Perfusion Jiang Hsieh SPIE MI 2003 Course Note 166

166 Screening With the recent technology development, examination of the whole body by CT can be completed in a single breath-hold. CT can be a useful tool for screening applications. The key to the screening application is the reduction of x-ray dose encountered in a CT exam. Because of the large amount of images involved, computed assistant detection (CAD) becomes a necessity. Jiang Hsieh SPIE MI 2003 Course Note 167

167 Impact of Reconstruction Kernel The shape and size of the lung nodule can vary significantly with the selection of different reconstruction kernel. Standard Bone Lung Jiang Hsieh SPIE MI 2003 Course Note 168

168 Impact of Reconstruction Kernel All images were acquired with axial mode at 0.63mm at 0.63mm spacing and reconstructed with 20cm FOV. Kernel Standard Lung Bone Acquisition axial 0.63mm/0.63mm axial 0.63mm/0.63mm axial 0.63mm/0.63mm Volume (mm 3 ) Jiang Hsieh SPIE MI 2003 Course Note 169

169 Impact of Data Acquisition The size and shape of the nodule also vary significantly with the selection of data acquisition. Different slice thickness and data acquisition modes were used. All reconstructed with Standard algorithm at 20cm FOV. mode axial axial axial axial helical helical thickness/spacing 0.63mm/0.63mm 1.25mm/1.25mm 2.5mm/2.5mm 5mm/5mm 4x1.25HS/0.63mm 4x2.5HS/0.63mm volume (mm 3 ) Jiang Hsieh SPIE MI 2003 Course Note 170

170 Impact of Data Acquisition axial 0.63mm at 0.63mm spacing axial 1.25mm at 1.25mm spacing axial 2.50mm at 2.50mm spacing axial 5.00mm at 5.00mm spacing helical 4x1.25mm HS 0.63mm spacing helical 4x2.50mm HS 0.63mm spacing Jiang Hsieh SPIE MI 2003 Course Note 171

171 Future Technology Volumetric CT (VCT) Advantages of VCT include the improved temporal resolution and multi-modes operation. Jiang Hsieh SPIE MI 2003 Course Note 172

172 Future Technology Super-high Spatial Resolution Current CT scanners are capable of providing spatial resolution of 20-30LP/cm with 1mm detector size. Using new detector technology, the detector cell size can be reduced to 50µm to 200µm. Jiang Hsieh SPIE MI 2003 Course Note 173

173 VCT for Dental Application Clinical CT Today VCT 140µm Resolution Jiang Hsieh SPIE MI 2003 Course Note 174

174 Resolution Challenges in Animal Imaging Size does matter... Mouse Volume CT Image VCT Provides resolution required for small animal imaging Jiang Hsieh SPIE MI 2003 Course Note 175

175 Summary We outline the principles and key performance parameters of x-ray computed tomography. We present causes and corrections of various image artifacts. New artifacts are likely to be produced with the introduction of new technologies. Jiang Hsieh SPIE MI 2003 Course Note 176

176 Summary X-ray computed tomography is experiencing tremendous technology advancement in recent years. These technology advancements have inspired more advanced clinical applications. The advancement of x-ray CT is only the beginning. The technology and applications of CT will likely be significantly different than what we see today. Jiang Hsieh SPIE MI 2003 Course Note 177

177 REFERENCES J. Hsieh, Computed Tomography: principles, design, artifacts, and recent advances, SPIE Press, Categorical Courses in Diagnostic Radiology Physics: CT and US Cross-sectional Imaging, ed. L. W. Goldman and J. B. Fowlkes, RSNA, Oakbrook, IL, A. Kak and M. Slaney, Principles of Computed Tomographic Imaging, IEEE Press, Jiang Hsieh SPIE MI 2003 Course Note