RAD 264 – Computed Tomography Physics,
Instrumentation, and Imaging
Module F
Required reading for this module is Chapters 8 of your text. Seeram,
Computed Tomography 2nd edition, Saunders/Elsevier.
Module F continues the study of CT physical parameters. So far the basis of
attenuation has been defined as it relates to CT. Remember attenuation is based
on the Lambert-Beer Law, an exponential relationship that explains what
happens to x-ray photons as they travel through matter, which, for our purposes,
is human anatomy. Radiologic technologists are quite aware of the density
differences in body tissues, therefore have the basic knowledge required to
understand explained in a prior module in this course and in your previous
radiation physics course, body tissues have different densities.
As discussed previously, the CT image is made up of many cells (pixels). These
pixels represent segments of the anatomy scanned, and each contains numerical
information on the density values of the anatomy. Pixels are two-dimensional
representations of the anatomy scanned. The addition of slice thickness turns the
pixels into voxels or volume elements representative of the corresponding tissue
volume. The numerical information derived from each pixel/voxel, is expressed
in the form of a CT number or Hounsfield unit. The CT numbers or Hounsfield
units are used by the CT computer in image reconstruction. The specific CT
number or Hounsfield unit of each pixel is directly related to the x-ray
attenuation coefficient of the tissue contained within the volume, representing
the pixel.
X-rays are attenuated exponentially as defined in the Lambert-Beer Law. X-rays
then, have a defined range within body tissues. Remember that they are reduced
by a certain percent for each incremental tissue thickness through which they
travel. The degree of attenuation is based upon the average energy of the photons
(kVp), as well as the effective atomic (Z) number and the atomic density
(atoms/volume) of the absorber. This is expressed by the attenuation coefficient,
and can be determined using the following equation:
CT number = k x Φ0 - Φw / Φw
Φo = the x-ray attenuation coefficient of the pixel
Φw = the x-ray attenuation coefficient of water
k = a constant that determines the scale factor for the range of CT
numbers
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The attenuation of water is always 0 and is used as the anchor on the CT number
(Hounsfield) scale. Below is a representation of the CT number scale. Note the
relationship of tissue densities (CT numbers) on the left to the shades of gray on the
right.
Figure 4-16 taken from Seeram, Computed Tomography Physical Principles, Clinical Applications, and Quality
Control, 2nd edition, Copyright © 2001, 1994 by Saunders
The above scale provides only a range of CT numbers for some tissues and their relationship
to shades of gray.
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The information below may be more beneficial to an understanding of the CT
numbers/Hounsfield units assigned to various body tissues.
Water
Cerebrospinal fluid
Tumors
Blood (fresh)
Blood (coagulated)
Brain (white matter)
Brain (gray matter)
Muscle/aorta
0
+ 15
+5 - 35
+35-60
+55 - 75
+36 – 46
+20 – 40
+35 – 50
Soft tissue
+40 – 70
(liver, spleen, kidney, pancreas, etc. )
Bone (average)
Petrous bone
Air
Lung tissue
Fat
+100 – 1000
+3000
-1000
-150 – 400
-100
The process of “windowing” in CT defines the shades of gray of interest.
The “window- level” determines the center of the gray scale and is generally set at
the “average tissue density” of the structures within the anatomy being scanned.
The “window-width” is normally set to include other structures or pathology that
may also be located in the scan plane. Most tissues, as seen in the information
above, fall into a narrow range of CT numbers. Consequently most CT windows
are rather narrow. The exceptions are when bone or air is being imaged.
Note that those structures or tissues that have densities greater than water are
assigned CT numbers/Hounsfield units in the positive portion of the scale (above
that of water), and will appear increasingly lighter (whiter) on the resultant
image as their densities increase. Those less dense than water will be assigned
values that are in the negative aspects of the scale and will appear decreasingly
darker as their densities decrease related to the density of water. Remember that
the elements of the image matrix (pixels and subsequently voxels) allow
association of a specific structure, within the object being imaged, with a specific
pixel or group of pixels.
The object (anatomy) must be sampled to differentiate structures and to assign
shades of gray (CT numbers/Hounsfield units) to each of the pixels. Sampling
determines the degree of attenuation of the x-ray photons in each pixel of the
image matrix. Sampling must be performed at a minimum of at least twice the
spatial frequency of the object scanned, as defined by the Nyquist Theorem.
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The Nyquist Theorem relates to inherent spatial frequencies. Sampling consists
of two components; Angular and Ray.
1. Angular Sampling is determined by the distance between each view obtained
during the scan.
2. Ray Sampling is determined by the angle between each pair of rays within a
view.
In order to understand either angular or ray sampling, the terms rays and views must be
explained.
Rays and Views
rd
In 3 generation CT scanners, each ray of the fan-beam falls on a single
detector.
Each set of rays constitutes a view (with the tube in a single position.
th
In 4 generation scanners, a view is a set of rays that strike a single
detector as the tube rotates around the gantry.
The value of each ray is directly proportional to the transmitted photon
measured by each of the detectors and characterized by a CT number.
The data measured in each view is called “raw” or “scan” data.
The detectors receive the attenuated x-ray photons, but in order to be detected, an
attenuated photon must;
1. be captured by the detector chamber
2. “collide” with an atom of detector material
3. as the result of the “collision”, produce an electromechanical conversion
suitable for measurement
4. be able to be amplified and transmitted
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There are two types of CT detectors in use today; gas and solid-state.
Gas detectors:
contain Xenon and therefore sometimes referred to as Xenon detectors
have inherent post-patient collimation
are approximately 1 mm wide
have air-tight chambers
contain widely dispersed Xenon atoms
are pressurized 30 times normal atmospheric pressure to compress the gas
(Xenon atoms)
are most sensitive (actually only sensitive) to x-ray photons entering along
axis of the detector chamber
upon detection of x-ray photons (collision between photon and detector
material), generate electrical impulses
the impulse is amplified and sent on to the ADC (analog-to digital converter)
for sampling and conversion from analog to digital form (digitization)
the digital signals are then sent to the array processor for image
reconstruction
are NOT suitable for use in 4th generation CT scanners because of the need
for these types of detectors to be in total alignment with the radiographic
th
tube. (detector arrays in 4 generation CT scanners may “nutate”, causing
the non-detection of x-ray photons)
Solid-state detectors:
are composed of numerous types of crystals
may be referred to as “scintillation” detectors because they,
emit light in response to the detection of x-ray photons
convert the light into electrical signals using a photodiode
Continue……
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amplify the signals and transmit them to the ADC for sampling and digitization and
transmission of the signals to the array processor
are sensitive to incoming attenuated photons from various angles
rd
th
are suitable for use in both 3 and 4 generation CT scanners
Whether the CT system uses gas or scintillation detectors, an integer (CT
number/Hounsfield unit) is assigned to each amplified electrical signal in the form of
a positive or negative whole number.
The value of the assigned integer is determined by the strength of the signal
emanating from a patient’s body (as determined by the pixel density).
The stronger the signal the greater the value of the assigned integer.
The signals reaching the analog-to-digital converter (ADC) are in analog form. The
ADC performs the task mentioned above before transmitting the signals on to the
array processor.
The array processor is a special purpose logical processing unit, used to perform
rapid image reconstruction. In some systems, the array processor may constitute a
second computer.
In CT, the array processor primarily functions to reconstruct projected attenuated
raw data into anatomically accurate CT images. It solves all of the complex
mathematical problems in CT, including routine CT image reconstruction,
retrospective reconstructions, and post-processing techniques.
Reconstructive algorithms are applied in the array processor.
In conventional CT (step and shoot or slice-by-slice acquisition), the most common
and simplest form of reconstruction algorithm used is filtered-back-projection,
although several different algorithms have been used, including simple-backprojection and convolution. Considered an analytical reconstruction algorithm,
filtered-back-projection is also called the convolution method.
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In this method, convolution method, the following steps are incorporated:
1. projection profiles are obtained via the ADC
2. the logarithm of the data is obtained
3. logarithm values are multiplied by a digital or convolution filter, called a
kernel, generating a set of filtered profiles
4. the filtered profiles are then back-projected
5. the filtered profiles are then added causing the negative and positive
components to be cancelled, leading to the generation of blur-free CT
images
Convolution filters can only be applied to raw data (also called scan data). Raw data
result from the CT scan process and has not been processed into image data. This is
the data that can be stored and retrieved as needed for use in retrospective
reconstructions. Once the raw data has been through reconstruction (reconstruction
algorithm applied and image generated, it becomes image data or reconstructed
data. This data can be used in post-processing techniques (reformations), such as 3D
reformations, maximum intensity projections (MPRs), volume rendering (VR), etc.
In spiral CT, because the data is acquired in volume rather than slice-by-slice
fashion, filtered-back-projection cannot be used alone to generate images. Filteredback-projection with linear interpolation is used as the reconstruction algorithm in
single-detector-row spiral and depending on the CT system manufacturer.
Interpolation is defined as a mathematical technique used to determine the value of a
function from known values on either side of it. It is a mathematical estimation
technique. Linear interpolation is the simplest form of interpolation. The equation
used by the CT computer for linear interpolation is:
Y3 = Y1 + (x3-x1)(Y2-Y1)(x2-x1)
Filtered-back-projection using interlaced sampling, longitudinal interpolation by zaxis filtering, or fan-beam reconstruction is used in multi-detector-row CT scanning.
To assure that the anatomy scanned is accurately represented on the final CT image,
reconstruction filters are used. As a secondary function, these filters are responsible
for enhancing the spatial or contrast resolution of the final image depending on the
anatomy scanned. Spatial resolution is the degree of blurring in an image. This is
regarded as “the measure of the ability of a CT scanner to discriminate objects of
varying densities located close together, against a uniform background”.
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Imaging objects with excellent spatial resolution is dependent upon the chosen slice
thickness or section collimation, the selection of which depends on whether
conventional or spiral scan operational mode is selected. In CT, the spatial resolution
is represented by the Point Spread Function (PSF), Line Spread Function (LSF), and
the Modulation Transfer Function (MTF). These functions will be discussed in a later
module. Spatial resolution is affected by geometric factors and the reconstruction
algorithm. The geometric factors concerned are:
focal spot size
detector response curve
slice thickness
focal distance
isocenter (center of rotation of the gantry)
detector and sampling distance
Reconstruction algorithms and filters influence resolution by their ability to enhance
or smooth borders and edges.
Contrast resolution, also called low-contrast resolution or tissue resolution, is the
ability of the CT scanner to demonstrate small changes in tissue contrast. The ability
of the scanner to image objects 1-2 mm in size that may vary only slightly from that
of the environment in which they are located. Factors that affect low-contrast
resolution are:
1. photon flux
2. slice thickness
3. patient size
4. detector sensitivity
5. reconstruction algorithm
6. image display
7. image recording
8. quantum noise
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The CT technologist controls both the scanning and reconstruction processes by
selecting certain parameters either manually or by selecting pre-determined
procedural protocols. These parameters include:
scan field of view (SFOV)
reconstructed field of view (RFOV) (DFOV)
window settings
matrix size
slice thickness
radiographic tube output
scan time and rotational arch
focal spot size
This module has provides significant information based on the physical interaction
of radiation with matter (radiation physics). This information was used to explain
how radiation physics is applicable to the CT process.
In addition, some parameters regarding the CT instrumentation were also presented,
along with parameters related to the imaging process in CT.
Module G will provide information on the scan factors, geometric factors, and
contrast resolution factors introduced in this module.
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