1. Principle of Computed tomography
嘉義長庚放射科　　廖書柏

2. Introduction
In 1950，Allan M. Cormack develop the theoretical and mathematical methods used to reconstruct CT images.
In 1972 Godfrey N. Hounsfield and colleagues of EMI Central Research Laboratories built the first CAT scan machine, taking Cormack's theoretical calculation into a real application.
For their independent efforts, Cormack and Hounsfield shared the Nobel Prize in medicine and physiology in 1979.
早在1950年代，Allan M. Cormack開始探討各種CT的原理；但直到1960年代末期，英國EMI公司的實驗中心才根據Cormack原理，嘗試建立一套CT設備。Godfrey Hounsfield是整個實驗計畫的主持人，1971年他所領導的工作小組在tkin-son Morley’s Hospital建立了第一套CT系統，並於1972年春正式發表頭部的CT影像。由於掃瞄範圍的限制，早期CT僅用於頭部斷層檢查
Cormark與Hounsfeild因在CT發展上的傑出貢獻，分享1979年之諾貝爾醫學獎。

3. What is CT scanner? A X-ray device capable of cross-section imaging
-creates images of “slice” through patient

4. Advantages of CT scanning
Ability of differentiate overlying structure
Excellent contrast
-overlying structure don’t decrease contrast
-digital images, so variable window settings

5. X-ray Source and detectors
-rotating anode disk
-small focus spot (down to 0.6 mm)
-polychromatic beam
Detectors
-xenon
-solid-state:
NaI(Tl)、CsI scintillaton crystals、 ceramic materials containing rare-earth oxides、BGO and CdWO4

6. xenon
xenon
Pressured xenon gas
ionization
Electrical signal

7. Solid-state Solid state Ceramic or crystal scintillatior
Photon capture
Light
Photo-diode
Electrical signal

8. Collimators Pre-patient collimator- control slice thickness
Pre-detector collimator-reduce scattered radiation

9. History of CT

10. Variations in scanner design based on :
X-ray tube and detector movement
Detector arrangement
Rotating mechanism

11. First-generation ~1972 single X-ray tube and one detector element
Pencil beam
about 5 minutes per slice from 180 degrees rotation.
Translate-rotate movement

12. EMI CT1000

13. Second-generation ~1975
Single X-ray tube and multiple detector elements
Narrow fan beam(~10。)
About one minute per slice
Translate-rotate movement

14. Third-generation ~1975 Single X-ray tube, rotating movement
Multiple detectors in curvilinear design, rotating movement
Fan beam(~30。)
Several seconds per slice
在第三代CT中，X光源處於某一角度曝光時，所有偵測器所獲得的資訊，被視同是在該角度下，整個剖面所有路徑的資訊
Rotate-rotate movement

15. Fourth-generation ~1976 Single X-ray tube, rotating movement
Fixed ring as many as 8000 detectors inside of gantry
1-s scan time
Avoiding ring artifact problem of 3rd generation scanner
第四代CT每次曝光時，各偵測器所獲得的信息，分別只是不同角度之某一路徑的信息，必須等到X光源旋轉某段扇形弧度後，集合各旋轉位置下，X光源對某特定偵測器的曝光資訊，才算完成某一角度各路徑資訊的收集，
Rotate-stationary movement

16. Fifth-generation ~1984
four semicircular tungsten target rings spanning 210 degrees about the patient
Multiple detectors of two banks, fixed inside of the gantry
no mechanical movement
By using four target rings and two detector banks, eight slices of the patient may be imaged without moving patient.
Because of the speed with which the electron beam may be steered magnetically, a scan may be accomplished in as little as 50 ms and repeated after a delay of 9 ms to yield up to 17 images per second.

17. EBCT( electron beam CT)
A sub-second scanner, called “Imatron”

18. Each sweep of a target ring requires 50 ms and 8 ms delay to reset the beam. eight parallel slices (scanned two per sweep) requires approximately 224 milliseconds to complete

19. Sixth-generation ~1989
Helical /spiral CT was introduced in 1989, based on Generation Three
Single X-ray tube and single-row detector
Never-stop and one-direction rotating X-ray tube, detectors
Capability to achieve one second image acquisition, or even sub-second
Slip ring replaced with the x-ray tube voltage cables enable continual tube rotation.

20. Slip ring technology in 1985
Slip ring allow continuous gantry rotation

21. Conventional mechanism

22. Seventh-generation ~1998
Single X-ray tube ,Multiple-row detector, rotating movement
Allow simultaneous acquisition of multiple slice in a single rotation
Half-second rotation(0.5 s)
Sub-second scanner

23. The Basic CT Term Image matrix Linear attenuation coefficient
CT numbers

24. Image matrix
Every CT slice is subdivided into a matrix of up to 1024X1024 volume element (voxel)
The viewed image is then reconstructed as a corresponding matrix of picture element (pixel)
Each pixel is assigned a numerical value (CT number), which is the average of all the attenuation values contained within the corresponding voxel.

25. Voxel size= pixel size X slice thickness
The diameter of image reconstruction is called the field of view (FOV).
Pixel size=FOV/matrix size

26. Linear Attenuation Coefficient (μ)
Basic property of matter
Depends on x-ray energy and atomic number (Z) of materials.
Attenuation coefficient reflects the degree to which x-ray intensity is reduced by a material x I0 I
I = I0 e-μx

27. I = I0 e-(μ1x1+μ2x2) I = I0 e-Σμixi x1 x2 x3 x1 xn I0 I I0 I n i=1
                                                                                       
i=1
μ(x, y) is the linear attenuation coefficient for the material in the slice

28. CT numbers
The precise CT number of any given pixel is calculated from the X-ray attenuation coefficient of the tissue contained in the voxel.
CT number ranged from -1000~3095(12 bit) k
When k=1000, the CT numbers
are Hounsfield units

29. Tissue μ(cm-1) Bone 0.528 Blood 0.208 Gray matter 0.212 White matter
0.213
CSF
0.207
Water
0.206
Fat
0.185
Air
0.0004
CT numbers normalized in this manner provide a range of several CT numbers for 1% change in attenuation coefficient.
除了骨骼之外，生理組織大部份由水組成，衰減係數稍大於水，但差異極微；為了有效區分各種不同生理組織，必須使用相對值觀念拉大組織間衰減係數的差異，以便利影像的重建；這種以相對值表現各生理組織對X光的吸收差別，就是所謂的生理組織CT值
Linear attenuation coefficient of various body tissues for 60 keV x-ray

30. The hounsfield scale of CT numbers

31. Image reconstruction

32. Image reconstruction
The image is reconstructed from projections by a process called Filtered Backprojection .
"Filtered" refers to use digital algorithms called convolution to improve image quality or change certain image quality characteristics, such as detail and noise
"Backprojection" is the actual process used to produce or "reconstruct" the image. 

33. The filtered backprojection process involves the following steps:
generating a sinogram from a set of N projections
filtering the data to compensate for blurring
Backprojecting the data .

34. Projection and sinogram
Ray: the X-ray read by every one detector within a short time interval.
Projection: all rays sum in a direction
Sinogram: all projections y 
P(t) t p  x
μ(x,y) t
Sinogram
X-rays

35. P(t) =

36. Filter
a de-blurring function is combined (convolved) with the projection data to remove most of the blurring before the data are backprojected.
A high-frequency filter reduces noise and makes the image appear “smoother.”
A low-frequency filter enhances edges and makes the image “shaper.”
A low-frequency filter may be referred to as a “high-pass” filter because it suppresses low frequencies and allows high frequencies to pass.

37. Backprojection
Projection data (in Sinogram)  1D-FT  filled in k-space  central slice projection theorem  2D-inverse FT  CT images
中央切面投影理論
(Central Slice Projection Theorem, CSPT)：
If a 1D Fourier Transform is performed on a projection of an object of some angle, the result will be identical to one line on 2D Fourier Transform of that object and at that angle.

38. Central Slice Projection Theoremky y
P(t) t
F[P(t)]  x  kx
μ(x,y)
F(kx,ky)
CSPT can relate the Fourier transform of the projection to one line in the 2D K space formed by the 2D Fourier transform of μ(x,y)

39. ky y x v u
F-1[F(kx,ky)]
u(x,y)
F(kx,ky) kx
Inverse 2D-FT

40. object
1D-FT
image
Inverse 2D-FT

41. Backprojection

42. Filtered backprojection
Filtered backprojection removes the star-like blurring seen in simple backprojection.

43. Filtered backprojection

44. Image display

45. Image manipulation
Image manipulation belongs to the domain of digital image processing.

46. Window width and level
The window width covers CT numbers of all the tissue of interest that is displayed as shades of gray, ranging from black to white. Thus width controls the contrast in the displayed image. 
The level control adjust the center of the window and identifies the type of tissue to be imaged.
Window level 的設定是將我們所想要看的tissue放在影像灰階的中間，經由改變window的寬度來改變其對比

47. Reducing window width increases the displayed image contrast among the tissues

48. WL= 40 WW= 350
WL= WW=1500

49. Spiral CT technology

50. Pitch
Pitch is defined as the patient couch movement per rotation divided by the slice thickness.
Pitch= couch movement per rotation
beam collimation
Couch movement
Slice thickness
pitch
5 mm/rot
5 mm
5/5=1
10 mm/rot
5 mm
10/5=2

52. effects of increasing pitch
Faster scan time for a specific volume body.
Dose is reduced because radiation is less concentrated
Image resolution might be reduced
when the pitch is increased,
table appears to move faster along the patient's body

53. Reconstruction interval/increment
The RI determines the degree of sectional overlap to improve image quality.
As RI decreases, image quality increases” but with trade-offs of increase image processing time, data storage requirements, and physician time for image review”

54. Slice thickness=5 mm RI=2
Slice thickness=5 mm RI=2.5 mm overlaping 50% RI=2 mm overlaping (5-2)/5=60%

55. Image quality

56. Spatial resolution in CT
focal spot size
detector dimensions
Slice thickness
Pixel size
Pitch
artifact
Pixel size= FOV/matrix size

57. Image Artifact in CT

58. Image Artifact
Artifacts are any discrepancy between the CT numbers represented in the image and the expected CT numbers
Common artifacts
Beam hardening
Partial volume effect
bad detector(3th scanner)
Metal
Patient motion

59. Beam hardening effect
Linear attenuation coefficients vary with photon energy.
After passing through a given thickness of tissue , lower-energy x-rays are attenuated to a greater extent than high-energy x-rays are.
artifacts such as a reduced attenuation toward the center of tissue (cupping) and streaks that connect tissues with strong attenuation.

60. polychromatic spectrums

61. Cupping Artifact

62. Means for suppressing beam hardening effect
pre-filtering X-rays
avoiding high X-ray absorbing regions if possible
applying appropriate algorithms

63. Partial volume effect
Partial volume artifacts are the result of a variety of different tissue types being contained within a single voxel
Measured attenuation coefficient are averaged by all components
use thinner slice to reduce

64. bad detector(3th scanner)
Each detector views a separate ring of an anatomy.
any single detector or a bank of detectors malfunctions will produce ring artifact

65. Metal artifact
Metal materials can cause the streaking artifacts due to block parts of projection data
ex: Dental fillings
Prosthetic devices
Surgical clip
Remove the metal material as possible to reduce the artifact

66. Patient motion
Voluntary and involuntary motion can cause streaking artifacts in the reconstructed image.
Reduce motion:
-Shorter scan time
-Immobilization and
positioning aid

67. Effect of reducing projections24 96 12
the number of views (projections)

68. Effect of reducing rays
200 25 50
The numbers of the data point (rays) per projection

69. Thanks for your attention~