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1. PRINCIPLE AND BASIC PHYSICS OF COMPUTED TOMOGRAPHY

3. PRINCIPLE OF COMPUTED TOMOGRAPHY The internal structure of an object can be reconstructed from multiple projections of the object. Mathematical principles of CT were first developed in 1917 by Radon Proved that an image of an unknown object could be produced if one had an infinite number of projections through the object

4. Basically, a narrow beam of X ray scans across a patient in synchrony with a radiation detector on the opposite side of the patient. The sufficient no. of transmission measurements are taken at different orientation of X ray source & detectors, the distribution of attenuation coefficients within the layer may be determined. By assigning different levels to different attenuation coefficients, an image can be reconstructed with aid of com. that represent various structures with diff attenuation properties.

13. Since CT images are related to x-ray radiation, attenuation is followed by Lambert's law of absorption. In the simplest case, the linear absorption coefficient can be expressed by where I is the intensity of the transmitted x-ray beam after passing through thickness x, I 0 is the intensity of the incident beam, and  is the linear absorption coefficient. When x-rays penetrate a nonhomogeneous material, the general expression for absorption should be where,  (s) is the linear absorption coefficient at each point on the x-ray path. Rearranging Equation B yields CT THEORY

14. Each square in the image matrix was called a pixel , And it represent a tiny elongated block of tissue Called a voxel . The size of pixel was determined by the computer Program and not by the dimensions of x-ray beam.

18. IMAGE RECONSTRUCTION Since composition and thickness of voxel along with quality Of beam determine the degree of attenuation. So for a single block of homogeneous tissue and monochromatic beam of x–ray N = N 0 e -µx Since e is natural log N 0 is initial photon N is transmitted photon X is the thickness of slab In computed tomography, a cross sectional layer of the body is divided into tiny blocks

19. Similarly if N no. of block is there then the equation becomes N = N 0 e -(µ1+µ2+µ3…………………µn)x Since to solve this problem we must have transmission reading Taken from at least to different direction . Since the more is projection and lines more is equation formed As for example orignal EMI scanner 28,800 reading Fan beam scanner can took 1 lak to2 lak. Readings .

21. ALGORITHMS FOR IMAGE RECONSTRUCTION An algorithm is a mathematical method for solving a problem. Thousand of equation must be solved to determine the linear Attenuation coefficient of all pixel in the image matrix. The three mathematical method of image recontstruction Will be described are:- 1.Back projection 2.Iterative methods 3.Analytical methods

22. BACK PROJECTION 1.Also called summation method 2.Is the oldest means of image reconstruction 3.its principle demonstrates When a ray from two projection is superimosed, or back projected They produce a crude repoduction of orignal object. ITERATIVE METHOD It start with assumption that all point in matrix have same value And it was compared with measured value and make correction until Values come with in acceptable range.

23. ITERATIVE METHOD It start with assumption that all point in matrix have same valueAnd it was compared with measured value and make correction until Values come with in acceptable range. It contain three correction factor 1. SIMULTANEOUS RECONSTRUCTION 2. RAY BY BY CORRECTION 3. POINT BY POINT CORRECTION

24. ANALYTICAL METHOD Today commenly used Two popular method used in that method are:- 1. 2-D FOURIER ANALYSIS 2.FILTERED BACK PROJECTION

25. 2-D FOURIER ANALYSIS In it any function of time or space can be represented by the sum of various frequencies and amplitude of sine and cosine waves. For example the actual projected image of orignal object is more rounded Than those shown which would be slowly simplyfy and corrected by Fourier transformation.

26. FILTERED BACK PROJECTION Same as back projection except that the image is filtered , or Modified to exactly counterbalance the effect of sudden density Changes,which cause blurring(star like pattern) in simple back projection The density of projected ray is adjusted to cmpensate The star effect.

28. IMAGE MATRIX :- The CT Scan format consists of many cells ,each assigned a no. and displayed as an optical density or brightness level on the video monitor CT NUMBER It is defined as a relative comparision of x-ray attenuation of each voxel of tissue with an equal vol of water. CT no= k(  -  )  To honour Hounsfield CT no. base on magnification constant of 1000 are also called HU (Hounsfield unit)

32. Hounsfield Values Water Air Fat Fluid Soft tissue Calcification Bone 0 HU -1000 HU -20 to - 200 HU 0 to 15 HU 20-60 HU 150-200 HU 1000 HU

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