Computed Tomography January 2002 KTH A.K.

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1 CT A.K. Computed Tomography January KTH 1

2 Introduction X-ray was discovered (accidentally) by a German physicist, Wilhelm Konrad Röntgen in A few years later, in 191, Röntgen was awarded the first Nobel Prize in physics for his discovery. Since than, it has been the most important and most widely used tool in clinical medicine. The technique of traditional X-ray imaging of to-day does not differ much from Röntgen s. An object is irradiated by photons from an X-ray source and the transmitted photons are registered on a photographic plate. Since X-ray attenuation in tissue is proportional to electron density, the X-ray intensity that traversed a region of lower density (i.e. muscle) will be grater than that which has traversed a region of higher density (i.e. bone). In other words the gray level of the image is inversely proportional to the attenuation of the tissue in the ray path. This most commonly used clinical method has however, some serious drawbacks. The - dimensional image will be a complex superposition of all the structures of the 3- dimensional body. The depth information is lost. Furthermore, the size on the image of an object is dependent on its distance to the X-ray source resulting in a distorted scaling factor of the picture. In addition, as it will be explained in the next section, the contrast of the image suffers from limited dynamic range of the attenuation coefficients that exists in the human body. All these obstacles found its solution in Computed Tomography, CT. During the last decade the use of CT, increased dramatically as a diagnostic tool in hospitals. The idea of Computed Tomography is not new. The mathematical basis for this approach has been developed by the Austrian mathematician Johan Radon in Much later, in early 196 s, Allan Cormack from the Tufts University published a work on the CT as a new approach for imaging and the first scanner was built by Godfrey N. Hounsfield at EMI in England in 197. Cormack and Hounsfield were awarded the Nobel Prize in Physiology and Medicine in To demonstrate the principles of CT, a simple set-up for educational purposes have been designed and constructed. With this the understanding of the principles of CT, the data acquisition and the image reconstruction is possible. Absorption of low energy gamma radiation in matter As a result of the interactions the low energy (< 1 MeV) photons either Compton scattered with some loss of energy or completely absorbed in a photoelectric interaction. This means that if a well-collimated beam of photons is considered, photons will disappear from the beam as a result of interactions. Only those photons that have not undergone any interactions at all remain in the beam, which means that a beam of photons is not degraded in energy as a result of passing through matter, just attenuated in intensity (number of photons per unit time and unit area). The probability of photon attenuation can be expressed per thickness of attenuator, the Beer equation I(x) = I o e -µx (1), where the linear attenuation coefficient µ has units of 1/length, for instance cm -1. In other words equation (1) above says that the linear attenuation coefficient µ is the fractional change in intensity of the incident beam per unit thickness of the attenuating material. The linear attenuation coefficient is a function of both the energy of the photons and the elemental composition of the attenuating material. This is a fact that medical imaging with photons relies on.

3 The linear attenuation coefficient is dependent on the density of the absorbing material this dependency can be overcome by normalizing the linear attenuation coefficient for density. This normalized term is called the mass attenuation coefficient µ m, thus µ m [cm /g] = µ [cm -1 ] / ρ [ g/cm 3 ] The mass attenuation coefficient as function of photon energy can be found in the literature. A useful reference is where coefficients for elemental material as well as compounds are shown. The medical imaging using photons is based on the differences of attenuation coefficients. these can be large like a bone surrounded by soft tissue or air filled cavities in the body. However, when soft objects in the human body is investigated the small difference in the attenuation coefficient will give little intensity contrasts and the object will thus be invisible. The reason is the limited contrast for films ( ~ %) in traditional X-ray imaging. One way to overcome this is the use of contrast media with high attenuation coefficient. For instance barium compounds can be injected into the blood system of the patient. The atomic number of barium is 56 compared to the main constituents of the soft tissue: for hydrogen is 1, for oxygen is 8 and for carbon is 6. An other way to detect the soft anatomy of the human body is by using the CT technique. CT is able to present images from structures with extremely small differences in linear attenuation coefficient, i.e. observing a tumor surrounded by soft tissue. Intensity differences smaller than.1 % can be visualized. The principles of computed tomography, CT In computed tomography a planar slice of the body is examined by measuring the attenuation of a narrow beam of X-rays for different positions and directions. This, a simple scanning system for transaxial tomography is the oldest type of CT s and is used in the present set-up. A pencil beam of photons passes through the object and is detected on the far side. The source -detector assembly is scanned sideways to generate one projection, a set of attenuation data for one angle.. This is repeated for many viewing angles to obtain the required set of projection data. Figure1 The principles of the first CT scanner 3

4 The mathematics of CT x y F φ (x ) x f(x,y) B A φ x Figure. The coordinate systems in CT. The function F φ (x ) is the Radon transform of f(x,y) for the angle φ. Two different coordinate systems have to be defined, one that is fixed in the object being X-rayed (x,y) and another that rotates with the source and detector (x,y ), see figure above describing a general two-dimensional distribution f(x,y). For CT imaging, the two-dimensional distribution to be measured is that of the linear attenuation coefficient µ(x,y). For a certain angle, φ, the source of X-rays and the detector are translated along the x axis and the parallel projection F φ (x ) is built up point by point. Each data point in a parallel projection is a measure of the attenuation of X-ray beams of a specific energy along a straight line AB. The linear absorption coefficient, µ, is a function of the y coordinate along AB and each infinitesimal element dy gives a contribution to the total attenuation of the X-ray beam. The transmitted intensity measured is the sum of all those infinitesimal contributions and hence a line integral along AB. If the following assumptions are made: (i) the X-ray beam is a narrow pencil beam (ii) the radiation is monoenergetic (iii) none of the scattered radiation hits the detector then the transmitted X-ray intensity along a specific line AB is given by the expression µ ( x, y) dy' AB Iφ ( x' ) = Iφ ( x' ) e (), where AB is a straight line parallel to the y axis located at the distance x from the origin and φ is the angle between the (x,y) and (x,y ) frames. From this expression the projection of the object measured at an angle φ and distance x is defined as F ( ') ln( ( ') / φ x = I φ x I φ ( x' )) = µ ( x, y) δ ( x cosφ + y sinφ x' ) dxdy (3) 4

5 These are the line integrals that make up the projection sets. Since the equation of the straight line AB is x = xcosφ + ysinφ, the Dirac delta function indicates that the integration is carried out only along the line AB. This relation is the Radon transform. To calculate the image this relation must be inverted using the inverse Radon transform, so that µ(x,y) is recovered from the projection set F φ (x ). This operation is called image reconstruction and from equation (3) it is obvious that this is not a trivial task with a general solution. Image reconstruction The simplest way of image reconstruction is the back-projection method and its principles are shown in figs. 3 and 4. The recorded data for a given angle is an array of attenuation values. These are back-projected evenly for each angle when the image is reconstructed. Figure 3. Recording of attenuation data Photon source Detector Absorption values and backprojection of data: 4 The quality of the reconstructed image is improved with increasing number of projections. Figure 4. Backprojection of data from three directions: 6 A star-shaped pattern around each object will occur by using the simple back-projection method. However, by applying appropriate filters this artefact can be surpressed. Therefor the most commonly applied method is the so-called filtered back-projection algorithm. It relies on the Fourier slice theorem, which in effect states that it is possible to 5

6 reconstruct an object from a set of projections provided that projection data set contains enough information. By enough information is meant that the projections must be taken for a large number of angles over a complete half revolution (18 ). This method involves Fourier transformation of the data set with respect to spatial co-ordinates (x and φ). Statistical fluctuations are of course more or less always present in any data set. After Fourier transformation of a data set these fluctuations will appear as high-frequency noise in the spatial frequency domain. One drawback of this method is that such high-frequency components are amplified unproportionally. To reduce the effect of this amplification different filters are applied. Such a filter is a mathematical function that the data is multiplied by in the process of transformation. Commonly used filters are for instance Ramachandran- Lakshminarayanan, Shepp-Logan, Hamming, Hann and Butterworth. The KTH-CT set-up A 1 mci 41 Am low energy gamma-rays source is used to simplify the operation. This replaces the X-ray tube of the traditional CT and at the same time emits photons with discrete energies. In the table below the emitted photons and their relative energies are summarized. Energy (kev) Intensity (%) CharacteristicX-rays Gamma decay The radioactive source is placed in a heavy metal (tungsten alloy: 8% W and % Cu) cylinder with wall thickness of 5 mm. The absorption of the housing reduces the radiation for the highest energy gamma-rays by a factor of. (calculate!). A 3 mm diameter hole collimates the beam on the object to be examined. The remotely controlled electronic shutter closes the source with a 4 mm thick heavy metal absorber. Never look into the beam! A new type of solid state detector, a CdZnTe (CZT) is used. Since CZT is made of material having high atomic numbers, it has a high intrinsic efficiency: The detector will register all photons up to approx. 75 kev energy that enter its front-face. The size of the detector is 3 x 3 mm and its thickness is mm. The detector is mounted in a vacuum cryostat and cooled below C o by a Peltier element. A 5 µm thick beryllium window in front of the detector allows also very low energy photons to penetrate. The beryllium window is extremely brittle. Do not allow any object come in contact with the window. Also, do not touch the window because the oil from the fingers will cause it oxidize. The window can not be repaired. If the window shatters the detector assembly must be replaced, 5 USD. The maximum volume of the CT study object is cylinder-shaped with 9 cm diameter and cm length. The CZT detector and the source are mounted 11 cm apart co-linearly on a common arm and perpendicular to the cylinder axis surrounding the object. The object can be rotated and moved horizontally along the axis of the cylinder, the z-axis. The detector-source arm can be moved perpendicular to the cylinder axis, the r-direction. All three movements are controlled with the help of stepper motors and with programs written in LabVIEW. 6

7 a i r φ d e h f g b z c Figure 5. A schematic view of the CT demonstrator In the figure 5 above a, b, and c are the three different stepper motors. When motor a is running, the screw f rotates and the source-detector arm i moves in the vertical direction. When motor b is running, the examined object h rotates about its centre axis. When motor c is running, the screw g rotates and the object holder is translated in the horizontal direction. d is the CZT detector and e is a holder for the cylindrical steel tube that contains the 41 Am source. The vertical co-ordinate is denoted r, the horizontal co-ordinate z and the angle of the object is φ. A picture of the CT demonstrator is shown in fig. 6 with a test object, a phantom consisting of three rods of different material and dimensions. Figure 6. The set-up with the three-rod phantom 7

8 The data acquisition The charge from the CZT detector is proportional to the energy of the absorbed photon. This signal is converted to a pulse with an amplitude proportional to the charge and amplified for further analysis. In order to identify the different components of the energy spectrum of the radioactive 41 Am source, the signals are sorted according to their amplitude by a Multi Channel Analyzer, MCA. The set-up and the photon spectrum of 41 Am is shown in fig 7. PC with MCA card Detector Preamp. Amp. ADC < 1 kev 17.8 kev Figure 7. Energy spectrum of 41 Am recorded by the CZT detector 59.5 kev To study the behavior of an CT image for different photon energies gates can be applied in the above spectrum. The gates are selected by letting the analog signals pass a window discriminator, a Singel Channel Analyzer, SCA, that selects an amplitude range, an energy region. Only those signals will be accepted that fulfills the condition of the SCA, see fig 8. Detector Preamp. Amp. SCA IN Gate PC with MCA card Figure 8. The 59.5 kev gated energy spectrum of 41 Am. 8

9 Several energy-gates can be applied to the detector signal and data from up to nine different energies can be recorded simultaneously. The signals selected by the different SCA energy-windows are counted by scalers in the data acquisition system. The computer programs of the set-up controls also the collection time for each detector position as well as the movement of the detector and the object. The block diagram of the control of data acquisition and movements are shown in figure 9. Stepper motor control boards SCA 1 SCA From amplifier, detector COM COM 1 Scaler Scaler Vertical direction Angle and horisontal direction Figure 9. The movement control and data acquisition system of the CT demonstrator Data collection the sinogram The raw data of a slice of the examined object (i.e. the three-rod-phantom), the registered counts in the energy region selected, are recorded sequentially for different y positions by moving the source-detector arm vertically. In this way the different absorption values are collected for a given φ angle. The measurement is repeated for several angles between o and 18 o. The different steps of the collection of the absorption data of the three-rod phantom is shown in fig 1. For each selected energy, the data set acquired thus consists of an array of transmitted photon intensity values stored together with the position values of the stepper motors. Such an array can be plotted as a two-dimensional pseudo-color plot, a sinogram, where the vertical and horizontal axes indicate radial and angular co-ordinates (r and φ) and the intensity in each position is represented by the color value. Fig. 11 shows the sinogram of the three-rod phantom present in the photo of Fig. 6. 9

10 CdZnTe detector Collimated γ ray source φ o r φ o φ φ o r φ φ = o φ=18 o +r r -r φ 18 Figure 1. The different steps of the collection of absorption data for the three-rod phantom and the corresponding sinogram. 1

11 +45 mm r -45 mm φ 18 r Figure 11. Sinogram of the three-rod phantom, acquired at 59.5 kev. The three curves represent the different solid rods. The two thickest rods are made of the same material (plastic), while the thinnest rod is made of a material that absorbs much more (steel) Image reconstruction in practice The basic idea of CT imaging is to convert the gamma absorption data, the sinogram, to a picture. The picture of the examined object is constructed of the photon absorption values for each point, µ(x,y), of the examined plane across the object. This means that one has to perform an inverse Radon transformation which is the mathematical tool of the reconstruction, as described in the previous subsections, c.f. equation (3). In practice the sinograms that are collected with the KTH-CT system are transformed by commercially available programs implemented in the Image Processing Toolbox of MATLAB ver.6. The spatial resolution of the CT image is dependent on the number of parallel beam projections and the number of data points in each projection. A larger data set means a more detailed description of the depicted object and hence more and smaller pixels, i.e. better spatial resolution. As described above, the detector is exposed to the photon beam from the 41 Am source. To improve the spatial resolution the sensitive area of the 3x3 mm detector must be narrowed. Therefore a steel collimator with a circular opening of 1.5 mm diameter is mounted in front of the detector window on the expense of detector efficiency. The data acquisition program lets the user select different values of the distance between consecutive data points in the vertical direction, r, and the spacing between different projection angles, φ. Without the collimator in front of the detector, the highest spatial resolution achievable is when r = 3 mm and φ = 3.6. On the other hand, with the 1.5 mm collimator on, it is possible to increase the spatial resolution to r = 1 mm and φ = 1.8. By doing this for improving the resolution, the number of collected data points in a 9x9 mm field of view are increased from 9mm mm 3.6 = 31 5 = 155 9mm 18 to + 1 = 91 1 = 91 1mm 1.8 At the same time the count rate of the detector is decreased by a factor 5.1 since the collimator is limiting the detector area from 3 x 3 = 9 mm to (.75) x π =1.77 mm. This means for obtaining the same statistical accuracy for each point the time of the data acquisition must increase by a factor of 5.1. This factor and the increased number of data points (5.9 times) 11

12 will prolong the data acquisition by a factor of 3!Due to the limited time avaible in the laboratory exercise the area of the detector can not be decreased by the collimator. Thus, the 3x3 mm detector behind the red plastic protective cover (do not remove!) is exposed to radiation. A comparison between different choices of spatial resolution is displayed in Fig. 1. φ = 9, r = 1 mm φ = 1.8, r = 1 mm mm mm 66 datapoints 1 datapoints Figure 1 (a) and (b). CT images of the three rod phantom at 59.5 kev for two different choices of spatial resolution. In Fig. (a) r = 3 mm and φ = 9, which corresponds to a total of 66 pixels, while in Fig. (b) r = 1 mm and φ = 1.8, giving 1 pixels in total. The dimension of the field of view is 95x95 mm in both (a) and (b). To make CT imaging more realistic, two other objects, two Barbie dolls, can be imaged. They have the right size, are made of a plastic material that has suitable absorption in the considered energy range, and are light and rigid enough to be mounted in the CT set-up, Fig. 13. To demonstrate the imaging capacity in terms of contrast and spatial resolution, a reference object, a solid steel sphere of 3 mm diameter, is attached to the front side of the doll. Figure 13. Photo of Ken mounted in the CT set-up. 1

13 To observe the influence of photon energy on the contrast level of the image, reconstructions are made from data acquired for different energies. Such a comparison is illustrated in Figs. 16 and 17. The image shows a cross-section of Ken, the male doll, in the middle of the chest, where the solid steel sphere is attached. Sinogram (1x1 = 1 4 pixels) CT image Radial distance (mm) o Angle 18 o Figure 14. The sinogram and the corresponding image across the chest of Ken recorded at 17.8 kev photon energy. The dark spot on the CT image is a 3mm steel sphere on the chest of the doll. Sinogram (1x1 = 1 4 pixels) CT image Radial distance (mm) mm Angle 18 o mm Figure 15. The sinogram and the corresponding image across the chest of Ken recorded at 59.5 kev photon energy. 13

14 During the process of image reconstruction, mathematical artifacts, visible as distortions, are introduced into the resulting image. This is an unavoidable consequence of the reconstruction algorithm used and different algorithms offer different possibilities of dealing with these artifacts. In the 'Filtered Back Projection' algorithm implemented in the MATLAB Toolbox used in this set-up, different so-called filtering functions (see previous subsection on the mathematics of CT) can be applied during reconstruction. The user can choose between five different filtering functions (Ram-Lak, Shepp-Logan, cosine, Hamming and Hann) and three different types of interpolation (nearest neighbour, linear and spline). There is also a possibility to disregard all spatial frequencies above a certain threshold set by the user. In Fig. 16, image reconstructions for 17.8 kev photon energy, based on the same data as presented in Fig. 14, are shown for two different filtering options. (a) (b) Fig. 16 (a) and (b). Two different image reconstructions of a cross section of Ken based on the same data set, recorded at 17.8 kev. In Fig. (a) a poor choice of filtering options has been used, while in Fig. (b) the filtering parameters have been optimized. The acquisition time in each data point is two seconds and the spatial resolution is r = 1 mm and φ = 1.8, which makes 1 pixels in total. The dimension of the field of view is 95x95 mm in both (a) and (b). In both reconstructions spline interpolation has been applied. In Fig. (a) the filter applied was Ram-Lak with all spatial frequencies included, while in Fig. (b) the Hamming filter with a frequency threshold value of 6% was used. 14

15 What to do 1. The KTH-CT is controlled by a PC via a control unit. The LabVIEW program Motor Control.vi is the master-program of the KTH-CT system. Using this program window the three movements with the stepper motors and the data acquisition with scalers can be controlled. This program window also allow the access of the CT- Acquisition and Multi Slice Scan programs.. The beam is blocked by an electromagnetic shutter. Do not put your fingers or any other part of your body in front of the source! Never look into the beam! 3. Connect the MCA to the amplifier of the CZT detector. Do not remove the red protective plastic cover from the detector! 4. Identify the gamma ray spectrum of 41 Am. 5. Put gates with SCA s on different peaks (like 17.8 and 59.5 kev) by gating the MCA with the appropriate SCA output. Use the MCA in the coincidence mode. 6. Connect the SCA to the scaler inputs of KTH-CT control unit. 7. Check the count-rate without any absorber for the different energy channels using the scalers controlled by the Motor Control.vi. 8. Go to the CT-Acquisition mode for collecting a data for a slice of the three-rod phantom. Optimize the steps r, φ and the data acquisition for each point time so that an image can be collected in approx. one hour. Save the data in the directory: c:\ct, filename: xyz.dat 9. Reconstruct the image by using MATLAB, try different filters. 1. Now it is time for Barbie or Ken! Find the approx. position of the 3 mm steel sphere under their cloths. Put appropriate scan limits and run the Multi Slice Scan program to find out the exact position. 11. Go to the slice of interest, set parameters and run CT-Acquisition for collecting data for a slice image of the doll. Use one to two hours collection time. You can use this time for study the CT literature and writing the report. There is also time for coffee! Store the data as above. 1. Reconstruct the image by using MATLAB, try different filters. Information about the available filters, interpolation options and frequency limitations are described in the manual of the Image Processing Toolbox accessible from MATLAB. 15

16 Questions: 1. The three major interaction modes of photons with matter are. The probability of the three interaction processes are depending on the energy of the incoming photons. The three dominating energy regions are 3. The amplitude of the attenuation coefficient exhibits drastic changes (edges) in the low energy region. These edges depend on the absorbing material. Explain! 4. In traditional X-ray examination the detection limit (i.e. the measurable intensity change) is %. Is it possible to observe a 1 mm diam. bone in a human surrounded by soft tissue using kev or 5 kev photons? For attenuation coefficients use NIST: 5. The KTH CT setup uses a 1 mci 41 Am source. The diameter of the source is 7. mm and collimated by a 3 mm diam. aperture. Estimate the count-rate of the 59.5 kev photons (without any absorber). The 3 x 3 mm CZT detector is placed behind a mm diam. collimator 11 cm from the source. 6. Estimate the count-rate if a 1mm thick plastic absorber is placed in front of the detector. 7. Estimate the shielding effect of the 5 mm thick tungsten alloy (8 % W and % Cu) housing for 59.5keV photons. 8. Who is the patient on the front page of this document and what are his symptoms? Who are the persons around him? 16

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