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Suplernentary reading: Introduction to Physics in Modern Medicine, Susan Arnador Kane, 2003 Taylor & 41 5-29963-2. Chapter: X-ray vision: diagnostic x-rays and CT s c a n s --

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Generation and properties of X-RAYS

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In the x-ray tube, electrbns are emitted by a hot filament cathode and are focused onto restricted area of the anode that is typically made of tungsten or a tungsten alloy. X-ray photons are emitted when the electrons penetrate the anode surface. Tungsteri is used as the anode material because of its high melting point and high atomic number. Accelerating electrons through high voltage and allowing them to strike a tungsten target produce X-rays. When the high-speed electron approaches a metal atom, it is strongly repelled and decelerated by the electron cloud of the atom, thereby loosing kinetic energy. Most of this energy goes into raising the temperature of the metal target, but about 1% of it is given off in the f o m of x-rays - the electromagnetic radiation. Because different electrons may be decelerated at different rates, x-ray can be produced with a high spread of wavelength.

Usually me long-wave part Of the spedrurn is eliminated by tillers made of copper or alurriniurn

X-ray spectra for two different voltages U, a n d U2 s u c h t h a t U2>U1. For voltage uzt h e characteristic spectrum of

Wavelength determining h e radiation hardness

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Distribution of energy in the continuous x-ray spectrum. -

The shortest wave is produced when all of the electron kinetic energy is changed to energy of X-ray photon: E =h

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The electron kinetic energy Ek is equal to the work performed by an electric field existing between cath-

ode and anode (metal target) of an X-ray tube: Ek= eU Thus:

The wavelengths of X-rays range from about 0.01 to 10 nm

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X-ray prcduction: X-my are produced b y accelerating electrons through high DC voltage ;?;,CEO tc ZOC,OCO vci:s) and allowing them to strike a metal target.

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where: Z - atomic number U - DC voltage /A - anode current i~tensity C - lamp constant

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The energy of electromagnetic radiation absorbed in bones, fat tissue, muscle of incident photons. As you can notice, a occur for small and for very big energies of

of Computed Tomography - EM1 Limited in Middllesex - G.N. Hounsfield) The basic principle of CT is that the internal structure of an object can be reconstnrcted from multiple projections of the object. The projections can be obtained by passing an x-ray through the object at different directions and different positions and measuring the transmitted radiation (i.e. intensity or number of photons). Numbers at the sides of the rectangles represents attenuated radiation by the number of blocks in each row. The horizontal sums called ,ray projections" are shown on the right; the vertical ray sums are shown below the object. The ray projections are formed by scanning a thin cross section of the body (a slice) with a narrow X-ray fan-like beam and measuring the transmitted radiation with a sensitive radiation detector (Fig.1). The detector itself does not form an image. It merely adds up the energy of all the transmitied photons ihat pass i h i ~ i i g h: h ~iirabiated siiiple j3.g. zleizefii of a patient body). The intensity of electromagneiic X-ray radiation that passes through a sample of a material of thickness d is attenuated and the attenuation is described by the Lambert-Beer law:

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DATAACCLlMLlLATlON Four generations of data-gathering techniques have been distinguished. The division or differentiation is based upon the X-ray tube and detector configuration I . First generation -translate-rotate, one detector. ections are collected by translation motion and rotational motion. A rigid scanner gantry the relative position of x-ray tube and detector and ensures their proper alignment (Fig. 2). The X-ray beam is exactly collimated to the exact size of the detector. The gantry moves through two different types of motion, one Iinear and one the other rotary. The linear motion is repeated over and over 160 times. Between each of these 160 linear movements, the gantry rotates l o . Thus the total rotatory motion encompasses a 180" semicircle. The axis of rotation passes through the center of the patient's body. In Fig.6 the linear motion are called "scans". Three of the 180 possible linear mtions are shown: 4 5 , 90- and

Fig.2 The first generation scanner - translate-rotate, single detector. The possible total number of transmission measurements (that is the detector readings) by this type of CT machine is equal to: linear.mov&

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A major objective of all later configurations was to shorten the scanning time. The increased speed was accomplished by abandon~ngthe single detector and pencil-like beam by a an-shaped beam and multiple detectors.

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The physical makeup and movements of a typical second-generation scanner is shown in Fig.3. --.,--nn+ nf + n uI he rllvvr;lllr;llL ,hL n ruJ tu [ha2nd , r,l e t ~-,.r t n rxrrav -. .- I i.-q hnth linear and rotary, just like a first generation scanner but the beam is narrow fan-shaped. 1

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In computed tomography a cross~sectionallayer of the body is divided into many tiny blocks (Fig.6).The individual blocks are called voxels (volume elements). Then, each block is assigned a number proportional to the degree that it attenuate x-ray beam. To quantitate the attenuation the linear attenuation coefficient p is used. Value of p depends on: composition of the doxel (bone, bone mara) row, soft tissue fatty tissue), and the quality of X-ray beam that is on energy b) of incident photons (E=h vj because the value of the linear attenuation coefficient depends on energy of photons.

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The tissue section represented in the computer matrix.

Evaluation of linear attenuation p of a voxel ~f two blocks of tissue with different linear attenuation coefficients pl and are placed in the path of the beam (Fig.7) the Lambert law equation has two unknowns and takes the following form: The values of both variables cannot be found without additional information. At least one additional equation is required. Additjonal equation can be obtained by examining the blocks from different direction. In the fig.8 there are four blocks that is potentially four unknown coefficients of attenuation p ~f,i , and B. To find out values of the four unknowns one needs four independent equations. These equations have the following form:

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Fig 8 Exactly the same principle applies to computed tomography, but he number of unknowns is much larger. For instance in the first EM1 scanner (first geceration scanner) the matrix in the computer contained of 80~80=6400 separate picture elements. Each transmission measurement recorded the compcsite of 80 separate linear cceffibut it has exactly the same fcrmat: cients. In this case the equation is longer

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ALGORITHMS FOR IMAGE RECONSTRUCT1ON The objective of all methods of image reconstruction is to produce an accurate cross-section display of the Iin-

ear attenuation coefficients of each element in the image matrix. The body cross-section must be represented by numbers to be displayed on the monitor screen -fig. 9 and 10 present how the numerical representation can be created. Fig. 10a

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Back projection method of image reconstruction (summation method) The block shown in Fig.11 is scanned from both the left size and from the top by a moving X-ray beam, to produce the so-called image profiles The image profiles look like steps. The height of the steps is proportional to the amount (intensity) of radiation that passed through the block. At the center have passed most radiation, so this is the highest step in the image profile The steps are next assigned to a gray scale density, which is proportional to the height of the steps. These densities are arranged in rows and are called rays. When the rays from two projections are superimposed or ,,back-projected they produce an approximate not very exact reproduction of original object. In practice many more projections are added to improve the image quality.

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CT NUMSERS A computer program that processes data collected during scanning procedure converts values of the linear attenuation coeffcients p of each matrix element to a new numbers d i e d "CT" numbers (CTN). The calculation allows the computer to present the information as a picture with a large gray scale. Hcw is the CT number determined? The computer program calculat€s a relati~nshipbetween the actual value of pv of a vcxe! and the the following way:

C T N = K PY - P L V Pw where:

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To honor Hounsfield, CT numbers based on magnlfrcat~onconstant equal to 1000 are expressed In Hounsfreld Units (Hu) (compare fig 12) ?

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IMAGE DISPLAY Typically display unit is a monitor of resolution 512x512 (or more) picture elements (pixels). Typically 256 shades of gray are available. How to represent 2000 Hu (from -1000 H to + I 000 H) with 256 shades of gray? 2000 One could simply assigned 8 CT numbers to the same shade of gray= 8 and display the entire range of in256 formation In a compressed scale This IS however rarely done Usually an average CT number characteristic for a tissue being examined is chosen Such a CT number might be -200 for lungs. The computer may then be instructed to assign one shade of gray to each of the 128 CT numbers below and each of the 128 CT numbers above the baseline equal to -200 In this case CT numbers would take the values from -328 H to -72 H The center CT number is called the "w~ndowlevel' and the range of CT numbers above and below the w~ndowlevel is called the "wmdow widfh" Of course, it is posslble to set the window level at any des~redCT number and set the w~ndow w~dthto any width desired by the operator (Fig 13) Vzlues of window level and window wrdth may varj widely depending on the type of exam~natrcnand pathology In prsctlce multiple window leveis and multlple w~ndowwldths may be exarn~nedIn an effort to extract rnaxlmurn Infomailcn from each exarnilnatron jr

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