2 IntroductionIn 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 structureExcellent 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 beamDetectors-xenon-solid-state:NaI(Tl)、CsI scintillaton crystals、 ceramic materials containing rare-earth oxides、BGO and CdWO4
6 xenonxenonPressured xenon gasionizationElectrical signal
7 Solid-state Solid state Ceramic or crystal scintillatior Photon captureLightPhoto-diodeElectrical signal
13 Second-generation ~1975Single X-ray tube and multiple detector elementsNarrow fan beam(~10。)About one minute per sliceTranslate-rotate movement
14 Third-generation ~1975 Single X-ray tube, rotating movement Multiple detectors in curvilinear design, rotating movementFan 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 gantry1-s scan timeAvoiding 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 ~1984four semicircular tungsten target rings spanning 210 degrees about the patientMultiple detectors of two banks, fixed inside of the gantryno mechanical movementBy 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 ~1989Helical /spiral CT was introduced in 1989, based on Generation ThreeSingle X-ray tube and single-row detectorNever-stop and one-direction rotating X-ray tube, detectorsCapability to achieve one second image acquisition, or even sub-secondSlip 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
22 Seventh-generation ~1998Single X-ray tube ,Multiple-row detector, rotating movementAllow simultaneous acquisition of multiple slice in a single rotationHalf-second rotation(0.5 s)Sub-second scanner
23 The Basic CT Term Image matrix Linear attenuation coefficient CT numbers
24 Image matrixEvery 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 matterDepends on x-ray energy and atomic number (Z) of materials.Attenuation coefficient reflects the degree to which x-ray intensity is reduced by a materialxI0II = 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=1μ(x, y) is the linear attenuation coefficient for the material in the slice
28 CT numbersThe 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)kWhen k=1000, the CT numbersare Hounsfield units
29 Tissue μ(cm-1) Bone 0.528 Blood 0.208 Gray matter 0.212 White matter 0.213CSF0.207Water0.206Fat0.185Air0.0004CT 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
32 Image reconstructionThe 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 projectionsfiltering the data to compensate for blurringBackprojecting 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 directionSinogram: all projectionsyP(t)tpxμ(x,y)tSinogramX-rays
36 Filtera 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 BackprojectionProjection 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 Theorem kyyP(t)tF[P(t)]xkxμ(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)
45 Image manipulationImage manipulation belongs to the domain of digital image processing.
46 Window width and levelThe 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
50 PitchPitch is defined as the patient couch movement per rotation divided by the slice thickness.Pitch= couch movement per rotationbeam collimationCouch movementSlice thicknesspitch5 mm/rot5 mm5/5=110 mm/rot5 mm10/5=2
52 effects of increasing pitch Faster scan time for a specific volume body.Dose is reduced because radiation is less concentratedImage resolution might be reducedwhen 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%
58 Image ArtifactArtifacts are any discrepancy between the CT numbers represented in the image and the expected CT numbersCommon artifactsBeam hardeningPartial volume effectbad detector(3th scanner)MetalPatient motion
59 Beam hardening effectLinear 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.
62 Means for suppressing beam hardening effect pre-filtering X-raysavoiding high X-ray absorbing regions if possibleapplying appropriate algorithms
63 Partial volume effectPartial volume artifacts are the result of a variety of different tissue types being contained within a single voxelMeasured attenuation coefficient are averaged by all componentsuse 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 artifactMetal materials can cause the streaking artifacts due to block parts of projection dataex: Dental fillingsProsthetic devicesSurgical clipRemove the metal material as possible to reduce the artifact
66 Patient motionVoluntary and involuntary motion can cause streaking artifacts in the reconstructed image.Reduce motion:-Shorter scan time-Immobilization andpositioning aid
67 Effect of reducing projections 249612the number of views (projections)
68 Effect of reducing rays 2002550The numbers of the data point (rays) per projection