CT scanning. By Mikael Jensen & Jens E. Wilhjelm Risø National laboratory Ørsted DTU. (Ver /9/07) by M. Jensen and J. E.

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1 1 Overview CT scanning By Mikael Jensen & Jens E. Wilhjelm Risø National laboratory Ørsted DTU (Ver /9/07) by M. Jensen and J. E. Wilhjelm) As it can be imagined, planar X-ray imaging has an inherent limitation in resolving overlying structures as everything seen in the images are the result of a projection. It is, however, possible to resolve the 3D distribution of X-ray attenuation from a set of projections. This is actually what we do mentally when we access the 3D structure of an object, for example the head of a person, by walking around the object and looking at it from all different angles. The CT scan is exactly such a reconstruction of the 3D distribution based on a large set of X-ray projections obtained at many angles covering a complete circle around the patient. CT is an abbreviation of computed tomography. In Anglo-American literature one also occasionally finds the abbreviation CAT denoting computed axial tomography. Tomography by itself means the rendering of slices: naturally the 3D information cannot easily be displayed 3 dimensionally on a screen, instead it is most often displayed as a series of axial slices. The CT scanner was developed in the early 1970ies by Geoffrey Hounsfield and and his colleague Alan Cormack in England (actually working for EMI on funds stemming from music record sales). For this they were awarded the Nobel Prize in Medicine in The basic three components of a CT scanner are still the same as in planar X-ray imaging: An X-ray tube, an object (patient) and a detection system. In the earliest scanners the output of the X-ray tube was collimated to a narrow, pencil-like beam and detected by a single detector. X-ray tube and detector were translated in unison (see Figure 1) across the object making a linear scan. After each scan, Figure 1 Early CT scanner geometry 1/8

2 Rotating X-ray tube Rotating X-ray tube Patient Patient Static ring of detectors Rotating arc of detectors Active detectors Figure 2 Geometry of gantry in CT scanner. Left: The third generation is of type rotate-rotate, where both X-ray tube and detectors rotate. Right: The fourth generation is of type rotate-fixed, where only the X-ray tube rotate. The x-ray tube emits a fan-shaped beam. typically lasting 10 seconds, the entire setup was rotated a few degrees, the scan repeated, and so forth. From a set of such 256 scans the final image (a single slice) would be reconstructed by overnight computing. This reconstruction - which derives an image from a large set of projections - will be considered in Subsection 2.3. Modern scanners are now essentially of two types: the rotate-rotate system and the rotate-fixed system. These are illustrated in Figure 2. Both systems use narrow fan-shaped beams collimated to spread across the full width of the patient. In the rotate-rotate system as many as 700 detectors may be placed in an arc centered at the focal spot of the X-ray tube. The tube is run continuously as both it and the detectors revolve around the patient. The fast electronics of the detectors take as many as thousand readings per detector for a total of readings in one second. In the rotatefixed system as many as 2000 fixed detectors form a circle completely around the patient. The X-ray tube is rotating concentrically within the detector ring. The detectors are normally focused at the centre of the ring. Acquiring the detector responses every one third of a degree produces more than readings per second. 1.1 Hounsfield value Using mathematical algorithms (as will be shown latere in Subsection 2.3), the computer can calculate the linear attenuation coefficient for each point (pixel) in the object and assign an attenuation value to it. Normally, this attenuation is not depicted as attenuation coefficients, instead radiology uses a special unit, now called Hounsfield unit (HU). The corresponding Hounsfield value is defined as follows: HV = 1000 (μ m -μ w )/ μ w (1) where μ m is the (average) linear attenuation coefficient within the voxel it represents and μ w is the linear attenuation coefficient for water at the same spectrum of photon energies. The Hounsfield unit is dimensionless. From the above definition, one should think, that the Houndsfield values are very well-defined. This is not so, as can be seen from Figure 3, which represent data from two different teaching books. There can be a number of reasons for these differences: Different spectra of emitted energy (the center frequency (or energy) of the spectrum, the shape of the spectrum). 2/8

3 (a) (b) Figure 3 Hounsfield values according to different text books: (a) is from [2] while (b) is from [3]. As can be seen, the values does not fully agree. Different definitions of what a given tissue type actually represents. Tissue types seldomly consist of just one component (e.g. muscular tissue can contain various amount of lipid, but still be described as muscular tissue ). 1.2 Single slice versus multi-slice system Originally the CT scanner only acquired one slice at a time, making extended axial field of view a time consuming process. Today the scanners, whether of the third or fourth generation, acquire many slices (16 to 256) at a time using an X-ray tube with an extended axial beam and multiple stacked detector chains. Rotation time is now down to fractions of a seconds making acquisition of of multi-slice 3/8

4 representation of the heart, almost motion arrested. If the patient is continuously slid through the gantry ring during the rotation, a so-called spiral CT scan is acquired. Proper reconstruction can thus yield large series of closely lying slices over extended parts of the body, in principle from head to foot. 2 System details 2.1 CT scanner X-ray tube Proper reconstruction of the CT scans is only possible if a very large number of photons are available for the detectors. If the acquired projections are not statistically well-determined, the reading from a detector will be noisy and the reconstruction algorithm will propagate this noise, leading to unacceptable high noise in the final image. Thus, normally, the CT scan is done with a high output from the CT tube corresponding to large kilovolts and milliampere settings. As the scan are normally extended for many slices and many revolutions, the final dose can be as high as 50 to 100 millisievert (see definition of Sievert in nuclear medicine chapter of this book). As the number of CT scans has been increasing with the wide spread installation of potent multi-slice and/or spiral scanners, the total collective radiation dose from CT scans to the entire medical irradiation constitutes a major part The high current and voltage and the extended exposure time, deposits very large amounts of primary electron beam energy in the anode of the X-ray tube. Special tubes have been developed for these X-ray scanners, with large, fast rotating anodes of high melting point materials. Special problems are related to the technology of bringing electricity of high voltage forward to the X-ray tube, rotating at an orbital diameter of more than one meter with the speed of more than two revolutions per minute. The rapid revolution of X-ray tube and perhaps detector chain also puts a large mechanical strain on the entire X-ray gantry, which must be of extraordinary sturdy construction. 2.2 Detector chain technology Today, at least three types of detectors are used. These detectors can be classified according to the type of material stopping the X-rays: Gas (Xenon) I0 I0 I0 μ11 μ12 Ir1 = I0 exp(-μ11dx -μ12dx) I0 μ21 μ22 Ir2= I0 exp(-μ21dx -μ22dx) Ic2 = I0 exp(-μ12dx -μ22dx) Ic1 = I0 exp(-μ11dx -μ21dx) Figure 4 For a medium assumed to consist of four different types of materials, four measurements will allow enough information to obtain four equations with four unknowns. 4/8

5 Scintillator (transforms the X-ray energy into visible light, detected by a photo diode) Solid state semiconductor The gas detectors are less efficient than the other two types of detectors, but by using high pressure, and extended radial dimensions efficiencies as high as 40 % can be achieved. These deep detectors has the important property of being most sensitive to radially incoming X-rays thus providing inherence protection against too much scattered radiation. With the other two detectors, which are more like surface detectors, the scattered radiation cannot be separated, and must be removed by the mathematical reconstruction algorithm. This is possible, because the scattered radiation has little spatial structure, and can thus be detected and subtracted as a uniform blanket in the image matrix. With many detectors in each chain and many slices the total data sampling rate of a modern CT scanner is extremely high. At present, it is exactly this data sampling rate which limits the performance of state-of-the-art CT scanner technology. 2.3 Reconstruction The reconstruction of the slices from a large number of different projections forms an algebraic problem. This can be seen by considering a CT image with two by two pixels. If the object is irradiated with X-rays from two perpendicular directions, the detectors will measure the four values indicated in Figure 4. The four attenuation values of the CT image can now be found by solving four equations of four unknowns. The corresponding equations are: ln(i 0 /I r1 ) dx 1 = μ 11 + μ 12 (2) ln(i 0 /I r2 ) dx 1 = μ 21 + μ 22 (3) ln(i 0 /I c1 ) dx 1 = μ 11 + μ 21 (4) ln(i 0 /I c2 ) dx 1 = μ 12 + μ 22 (5) Note that the basic physics does not require sampling of projections for more than 180, as the measurement is basically a transmission measurement covering the entire depth forwards to backwards of For all projections, the measured values are added to all contributing pixels Figure 5 Back projection. Each attenuation value is put back into the cells of the image that are located at the line of sight. The same values are put into each cell. 5/8

6 Figure 6 Evolution of backprojection. The first five images are derived from filtered projections, whille the last is derived from raw projections. the object. However, because of system stability, artifact suppression and noise reduction, scans are normally acquired based on 360 acquisitions. However beautiful the algebraic reconstruction looks the practical application is difficult due to the larger number of equations and unknowns. Reconstructing a single slice represented by a 512 by 512 matrix corresponds to the diagonalization of such a matrix, which is no simple task. Some algorithms, however, obtain this goal by iterative measures: first making a guess of the distribution of attenuation values, subtracting the corresponding projections from the actual projections measured and then iteratively minimizing this error difference. 2.4 Filtered backprojection Because it is computationally more effective, the most used algorithm is the so-called filtered backprojection. Consider an image matrix whit pure zeros. Backprojection by itself simply fills the attenuation values of individual projections into each cell of the matrix along the line of sight. The values filled in, are added to those already in the image matrix. This is sought illustrated in Figure 5. When the backprojection is performed on a large number of projections, the final image begins to emerge, 6/8

7 Window width LL UL Greyscale value Window centerline Houndsfield units Figure 7 Windowing. Only HU between -300 and 600 are visualized in the gray scale bar. LL = lower level. UL = upper level (drawing not fully to scale). as seen in Figure 6. However, the image is blurred: a single point object with high attenuation (e.g. a thin tube of water in air) will by this reconstruction be depicted as a 1/r distribution. By filtering the measured projections before backprojection, this blurring can be reduced. The filtering is actually a convolution of the individual projection with a suitable spatial filter, amplifying high spatial frequencies and damping low spatial frequencies. The final reconstruction algorithm is often called LSFB, an abbreviation for linear superposition of filtered backprojections. The exact choice of filter function should be matched with the scanner characteristics, field of view and object of interest. There is no need to reconstruct with filters using higher spatial frequencies than the inherent limits given by the finite detector size in the detection chain. The reconstructed image represents the attenuation coefficients. These are re-calculated to Hounsfield units, and this image is displayed as gray values on the screen. However, the range of Hounsfields units (or attenuation) can be very large, and if only soft tissue is to be visualized, only a small window of values are displayed, as illustrated in Figure 7. Because of the large dymaic range of the CT scanner, it is often better from the beginning of the reconstruction to limit the interest area of the image values to a suitable range. For this reason reconstruction is often formed in brain window, lung window or bone window. 3 Example of clinical CT image Finally, a comparison between an anatomical photograph and a CT image from exactly the same plane is included in Figure 8. The data is from the Visible Human Project. From the CT image, it is very clear which types of tissue, that is best distinguished in the CT image. 4 Acknowledgements Student Jonas Henriksen is greatfully acknowledged for the help with the tables for Hounsfield values. 7/8

8 Figure 8 An anatomical photograph and corresponding CT image at a horizontal scan plane of the head. Data from: [1] 5 References [1] The visible human project: [2] Willi A. Kalender, "Computed Tomography", 2005, 2nd edition, Publicis Corporate Publishing, Erlangen. [3] Erich Krestel, "Imaging Systems for Medical Diagnostics", 1990, Siemens Aktiengesellschaft, Berlin and Munich. 8/8

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