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PRINCIPLE AND BASIC PHYSICS OF
COMPUTED TOMOGRAPHY
INTRODUCTION
COMPUTED TOMOGRAPHY is well accepted
imaging modality for evaluation of the entire body.
• The images are obtained directly in the axial plane
of varying tissue thickness with the help of a
computer.
•Some pathology can be seen in sagittal or coronal
plane by reconstruction of the images by computer.
•CT has undergone several evolutions & now the
days multi-detectors CT scanners have been
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
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.)
• 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 xray 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
CT Scan Methodology
•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
Methodology continued….
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)
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 xray attenuation properties of the tissue in the
corrsponding voxel
CT THEORY
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 m is the linear
absorption coefficient. When x-rays penetrate a nonhomogeneous material,
the general expression for absorption should be
where, m (s) is the linear absorption coefficient at each point on the x-ray
path. Rearranging Equation B yields
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
• 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
In computed tomography, a cross sectional layer of the body is divided
into tiny blocks
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 log
N0 is initial photon
N is transmitted photon
X is the thickness of slab
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 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
1. Hetrochromatic beam
2. 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 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(m - m)
m
To honour Hounsfield CT no.
base on magnification constant
of 1000 are also called HU
(Hounsfield unit)
Windowing is a system where the CT no. range of
interest is spread cover the full grey scale available on
the display system
WINDOW WIDTH –Means total range of CT no.
values selected for gray scale interpretation.
It corresponds to contrast of the image.
WINDOW LEVEL– represents the CT no. selected for
the centre of the range of the no. displayed on the
image. It corresponds to brightness of image .
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