PRINCIPLE AND BASIC PHYSICS OF COMPUTED TOMOGRAPHY
INTRODUCTION <ul><li>COMPUTED TOMOGRAPHY is well accepted imaging modality for evaluation of the entire body. </li></ul><ul><li>The images are obtained directly in the axial plane </li></ul><ul><li>of varying tissue thickness with the help of a </li></ul><ul><li>computer. </li></ul><ul><li>Some pathology can be seen in sagittal or coronal </li></ul><ul><li>plane by reconstruction of the images by computer. </li></ul><ul><li>CT has undergone several evolutions & now the </li></ul><ul><li>days multi-detectors CT scanners have been </li></ul><ul><li>evolved which have application in the clinical field. </li></ul>
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
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.
Basic principles (cont.) <ul><li>Plain film imaging reduces the 3D patient anatomy to a 2D projection image </li></ul><ul><li>Density at a given point on an image represents the x-ray attenuation properties within the patient along a line between the x-ray focal spot and the point on the detector corresponding to the point on the image </li></ul>
Basic principles (cont.) <ul><li>With a conventional radiograph, information with respect to the dimension parallel to the x-ray beam is lost </li></ul><ul><li>Limitation can be overcome, to some degree, by acquiring two images at an angle of 90 degrees to one another </li></ul><ul><li>For objects that can be identified in both images, the two films provide location information </li></ul>
CT Scan Methodology <ul><li>X-ray tube and detectors rotate around the patient, with the axis of rotation running from the patient’s head to toe </li></ul><ul><li>Detectors measure the average linear attenuation coefficient, µ, between the tube and detectors </li></ul><ul><li>Attenuation coefficient reflects the degree to which the X-ray intensity is reduced by the material it passes through </li></ul><ul><li>2D measurement are taken in a helical manner all around the patient </li></ul><ul><li>Attenuation data is summed up from thousands of angles used in a process called reconstruction </li></ul><ul><li>Contrast dye is sometimes used to make the internal organs more visible in the image </li></ul>
Methodology continued…. <ul><li>Radiation detection system is composed of detection elements, such as scintillating crystals and photodiodes </li></ul><ul><li>Data acquisition system measures the radiation data transmitted through the object and digitizes it so the computer system can read it </li></ul><ul><li>Computer reconstructs the image from raw scan data then a picture is created by a cathode ray tube </li></ul><ul><li>Computer allows the technologist to shade, rotate, correlate and measure the organs in the image </li></ul><ul><li>Bone appears white; gases and liquids are black; tissues are gray </li></ul><ul><li>Measurements taken in Hounsfield units (Hu), calibrated universally with air at -1000 Hu and water at 0 Hu (other typical values include fat ~-50 Hu, muscle ~40 Hu, and bone ~1000 Hu) </li></ul><ul><li>The same study data can show bone structure or soft tissue detail, simply by altering the window and leveling (ie, which Hu range will the 0-255 greyscale values will correspond to) </li></ul>
Tomographic images <ul><li>The tomographic image is a picture of a slab of the patient’s anatomy </li></ul><ul><li>The 2D CT image corresponds to a 3D section of the patient </li></ul><ul><li>CT slice thickness is very thin (1 to 10 mm) and is approximately uniform </li></ul><ul><li>The 2D array of pixels in the CT image corresponds to an equal number of 3D voxels (volume elements) in the patient </li></ul><ul><li>Each pixel on the CT image displays the average x-ray attenuation properties of the tissue in the corrsponding voxel </li></ul>
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
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.
Tomographic acquisition <ul><li>Single transmission measurement through the patient made by a single detector at a given moment in time is called a ray </li></ul><ul><li>A series of rays that pass through the patient at the same orientation is called a projection or view </li></ul><ul><li>Two projection geometries have been used in CT imaging: </li></ul><ul><ul><li>Parallel beam geometry with all rays in a projection parallel to one another </li></ul></ul><ul><ul><li>Fan beam geometry , in which the rays at a given projection angle diverge </li></ul></ul>
Acquisition (cont.) <ul><li>Purpose of CT scanner hardware is to acquire a large number of transmission measurements through the patient at different positions </li></ul><ul><li>Single CT image may involve approximately 800 rays taken at 1,000 different projection angles </li></ul><ul><li>Before the acquisition of the next slice, the table that the patient lies on is moved slightly in the cranial-caudal direction (the “z-axis” of the scanner) </li></ul>
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
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 .
CORRECTION FACTOR INCORPORATED INTO CT PROGRAMME <ul><li>Hetrochromatic beam </li></ul><ul><li>Weighting factor </li></ul>Since hetrochromatic radiation passes through an absorber Filtration increases its mean energy . And secondly weighting factor to compensate the difference Between the size and shape of the scanning beam and the picture Matrix.
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
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.
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
ANALYTICAL METHOD Today commenly used Two popular method used in that method are:- 1. 2-D FOURIER ANALYSIS 2.FILTERED BACK PROJECTION
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.
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.
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)
<ul><li>Windowing is a system where the CT no. range of </li></ul><ul><li>interest is spread cover the full grey scale available on </li></ul><ul><li>the display system </li></ul><ul><li>WINDOW WIDTH –Means total range of CT no. </li></ul><ul><li>values selected for gray scale interpretation. </li></ul><ul><li>It corresponds to contrast of the image. </li></ul><ul><li>WINDOW LEVEL – represents the CT no. selected for </li></ul><ul><li>the centre of the range of the no. displayed on the </li></ul><ul><li>image. It corresponds to brightness of image . </li></ul>
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