Presentation on theme: "Principle of Computed tomography 嘉義長庚放射科 廖書柏. Introduction In 1950 ， Allan M. Cormack develop the theoretical and mathematical methods used to reconstruct."— Presentation transcript:
Principle of Computed tomography 嘉義長庚放射科 廖書柏
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.
What is CT scanner? A X-ray device capable of cross-section imaging -creates images of “slice” through patient
Advantages of CT scanning Ability of differentiate overlying structure Excellent contrast -overlying structure don’t decrease contrast -digital images, so variable window settings
X-ray Source and detectors Source -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 CdWO 4
xenon Pressured xenon gas ionization Electrical signal
Solid-state Ceramic or crystal scintillatior Photon capture Photo-diode Electrical signal Solid state Light
Variations in scanner design based on : X-ray tube and detector movement Detector arrangement Rotating mechanism
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
Second-generation ~1975 Single X-ray tube and multiple detector elements Narrow fan beam(~10 。 ) About one minute per slice Translate-rotate movement
Third-generation ~1975 Single X-ray tube, rotating movement Multiple detectors in curvilinear design, rotating movement Fan beam(~30 。 ) Several seconds per slice Rotate-rotate movement
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 Rotate-stationary movement
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.
EBCT( electron beam CT) A sub-second scanner, called “ Imatron ”
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
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.
Slip ring technology in 1985 Slip ring allow continuous gantry rotation
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
The Basic CT Term Image matrix Linear attenuation coefficient CT numbers
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.
Pixel size=FOV/matrix size The diameter of image reconstruction is called the field of view (FOV). Voxel size= pixel size X slice thickness
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 I0I0 x I I = I 0 e -μx
x1x1 x2x2 x3x3 I0I0 I I = I 0 e -(μ 1 x 1 + μ 2 x 2 ) x1x1 xnxn I = I 0 e - Σ μ i x i i=1 n I0I0 I μ(x, y) is the linear attenuation coefficient for the material in the slice
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
CT numbers normalized in this manner provide a range of several CT numbers for 1% change in attenuation coefficient. Tissueμ(cm -1 ) Bone0.528 Blood0.208 Gray matter0.212 White matter0.213 CSF0.207 Water0.206 Fat0.185 Air Linear attenuation coefficient of various body tissues for 60 keV x-ray
The hounsfield scale of CT numbers
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.
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.
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 P( t) μ(x,y) t y x X-rays Sinogram t
P( t) =
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.
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. 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.
Central Slice Projection Theorem ky kx F(kx,ky) P( t) t y x F[P( t)] μ(x,y) 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)
ky y x v u F -1 [F(kx,ky)] u (x,y)F(kx,ky) Inverse 2D-FT kx
object 1D-FT Inverse 2D-FT image
Filtered backprojection Filtered backprojection removes the star-like blurring seen in simple backprojection.
Image manipulation Image manipulation belongs to the domain of digital image processing.
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.
Reducing window width increases the displayed image contrast among the tissues
WL= 40 WW= 350WL= -600 WW=1500
Spiral CT technology
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
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
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”
Slice thickness=5 mm RI=2.5 mm overlaping 50% RI=2 mm overlaping (5- 2)/5=60%
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
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.
Means for suppressing beam hardening effect pre-filtering X-rays avoiding high X-ray absorbing regions if possible applying appropriate algorithms
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
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
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
Patient motion Voluntary and involuntary motion can cause streaking artifacts in the reconstructed image. Reduce motion: -Shorter scan time -Immobilization and positioning aid
Effect of reducing projections the number of views (projections)
Effect of reducing rays The numbers of the data point (rays) per projection