principle and basic physics of computed tomography
TRANSCRIPT
PRINCIPLE AND BASIC PHYSICS OF COMPUTED TOMOGRAPHY
INTRODUCTIONINTRODUCTION
COMPUTED TOMOGRAPHYCOMPUTED TOMOGRAPHY is well accepted is well accepted imaging modality for evaluation of the entire body.imaging modality for evaluation of the entire body.• The images are obtained directly in the axial planeThe images are obtained directly in the axial plane of varying tissue thickness with the help of aof varying tissue thickness with the help of a computer.computer.
•Some pathology can be seen in sagittal or coronalSome pathology can be seen in sagittal or coronal plane by reconstruction of the images by computer.plane by reconstruction of the images by computer.
•CT has undergone several evolutions & now theCT has undergone several evolutions & now the days multi-detectors CT scanners have beendays multi-detectors CT scanners have been evolved which have application in the clinical field.evolved which have application in the clinical field.
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 Basically, a narrow beam of X ray scans across a patient in synchrony scans across a patient in synchrony with a radiation detector on the with a radiation detector on the opposite side of the patient.opposite side of the patient. The sufficient no. of transmission The sufficient no. of transmission measurements are taken at different measurements are taken at different orientation of X ray source & orientation of X ray source & detectors, the distribution of detectors, the distribution of attenuation coefficients within the layer attenuation coefficients within the layer may be determined.may be determined.
By assigning different levels to By assigning different levels to different attenuation coefficients, an different attenuation coefficients, an image can be reconstructed with aid of image can be reconstructed with aid of com. that represent various com. that represent various structures with diff attenuation structures with diff attenuation properties.properties.
Basic principles (cont.)
• Plain film imaging reduces the 3D patient anatomy to a 2D projection image
• 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
Basic principles (cont.)
• With a conventional radiograph, information with respect to the dimension parallel to the x-ray beam is lost
• Limitation can be overcome, to some degree, by acquiring two images at an angle of 90 degrees to one another
• For objects that can be identified in both images, the two films provide location information
•X-ray tube and detectors rotate around the patient, with the axis of rotation running from the patient’s head to toe
•Detectors measure the average linear attenuation coefficient, µ, between the tube and detectors
•Attenuation coefficient reflects the degree to which the X-ray intensity is reduced by the material it passes through
•2D measurement are taken in a helical manner all around the patient
•Attenuation data is summed up from thousands of angles used in a process called reconstruction
•Contrast dye is sometimes used to make the internal organs more visible in the image
CT Scan Methodology
Radiation detection system is composed of detection elements, such as scintillating crystals and photodiodes
•Data acquisition system measures the radiation data transmitted through the object and digitizes it so the computer system can read it
•Computer reconstructs the image from raw scan data then a picture is created by a cathode ray tube
•Computer allows the technologist to shade, rotate, correlate and measure the organs in the image
•Bone appears white; gases and liquids are black; tissues are gray
•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)
•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)
Methodology continued….
Tomographic images
• The tomographic image is a picture of a slab of the patient’s anatomy
• The 2D CT image corresponds to a 3D section of the patient
• CT slice thickness is very thin (1 to 10 mm) and is approximately uniform
• The 2D array of pixels in the CT image corresponds to an equal number of 3D voxels (volume elements) in the patient
• Each pixel on the CT image displays the average x-ray attenuation properties of the tissue in the corrsponding voxel
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, I0 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 tissueCalled a voxel.
The size of pixel was determined by the computer Program and not by the dimensions of x-ray beam.
Tomographic acquisition
• Single transmission measurement through the patient made by a single detector at a given moment in time is called a ray
• A series of rays that pass through the patient at the same orientation is called a projection or view
• Two projection geometries have been used in CT imaging:– Parallel beam geometry with all rays in a
projection parallel to one another– Fan beam geometry, in which the rays at a given
projection angle diverge
Acquisition (cont.)
• Purpose of CT scanner hardware is to acquire a large number of transmission measurements through the patient at different positions
• Single CT image may involve approximately 800 rays taken at 1,000 different projection angles
• 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)
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 = N0e-µx
Since e is natural logN0 is initial photon
N is transmitted photonX is the thickness of slab
In computed tomography, a cross sectional layer of the body is divided In computed tomography, a cross sectional layer of the body is divided into tiny blocksinto tiny blocks
Similarly if N no. of block is there then the equation becomes
N = N0e-(µ1+µ2+µ3…………………µn)x
Since to solve this problem we must have transmission readingTaken from at least to different direction .Since the more is projection and lines more is equation formedAs for example orignal EMI scanner 28,800 readingFan beam scanner can took 1 lak to2 lak. Readings.
CORRECTION FACTOR INCORPORATED INTO CT PROGRAMME
1. Hetrochromatic beam2. Weighting factor
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 recontstructionWill be described are:-1.Back projection2.Iterative methods3.Analytical methods
BACK PROJECTION
1.Also called summation method2.Is the oldest means of image reconstruction3.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 valueAnd 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 RECONSTRUCTION2. RAY BY BY CORRECTION3. 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 densityChanges,which cause blurring(star like pattern) in simple back projection
The density of projected ray is adjusted to cmpensateThe star effect.
IMAGE MATRIXIMAGE MATRIX:-:-
The CT Scan format consists of many cells ,each The CT Scan format consists of many cells ,each assigned a no. and displayed as an optical density or assigned a no. and displayed as an optical density or brightness level on the video monitorbrightness level on the video monitor
CT NUMBERCT NUMBER
It is defined as a relative It is defined as a relative comparision of x-ray attenuation comparision of x-ray attenuation of each voxel of tissue with an of each voxel of tissue with an equal vol of water.equal vol of water.CT no=CT no=k(k( - - ) ) To honour Hounsfield CT no. To honour Hounsfield CT no. base on magnification constant base on magnification constant of 1000 are also called HU of 1000 are also called HU (Hounsfield unit)(Hounsfield unit)
WindowingWindowing is a system where the CT no. range is a system where the CT no. range ofof
interest is spread cover the full grey scale interest is spread cover the full grey scale available onavailable on
the display system the display system
WINDOW WIDTHWINDOW WIDTH –Means total range of CT no. –Means total range of CT no.
values selected for gray scale interpretation. values selected for gray scale interpretation.
It corresponds to contrast of the image.It corresponds to contrast of the image.
WINDOW LEVELWINDOW LEVEL– represents the CT no. selected – represents the CT no. selected forfor
the centre of the range of the no. displayed on the centre of the range of the no. displayed on thethe
image. It corresponds to brightness of image .image. It corresponds to brightness of image .
Hounsfield ValuesHounsfield Values
WaterWater
AirAir
FatFat
FluidFluid
Soft tissueSoft tissue
CalcificationCalcification
BoneBone
0 HU0 HU
-1000 HU-1000 HU
-20 to - 200 -20 to - 200 HUHU
0 to 15 HU0 to 15 HU
20-60 HU20-60 HU
150-200 HU150-200 HU
1000 HU1000 HU
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