5.1 CT: image formation and reconstruction Flashcards
CT is abbreviation of? what kind of images does it produce?
- computed tomography
- tomography = obtaining images in 3D
what advantage do 3D images have over 2D images?
- in 2D images, structures overlap (ex: ribs overlap with heart & lungs in a chest x-ray)
- in 3D images, we can avoid this overlap
what is CT?
a volumetric imaging modality based on X-ray absorption
why does it mean for CT to be “volumetric”?
takes volume into consideration during measurement (3D)
in practice, what do CT images measure?
the absorption of X-rays into structures
how does CT compare to X-ray imaging?
- CT vastly exceeds X-ray imaging in soft tissue contrast
- however, CT spatial resolution is significantly lower than that of plain X-ray imaging
why does CT have better soft tissue contrast?
CT has great sensitivity to contrast, providing excellent visualization of soft tissue
CT exceeds X-ray imaging in _____, while X-ray imaging exceeds CT in _____
- soft tissue contrast
- having higher spatial resolution
what was special about CT when first invented?
it was the first imaging modality where the computer was essential in image reconstruction
describe the progress that was made with CT
- in early days, data acquisition was fairly slow, taking ≈ 4min for each rotation, while nowadays it takes ≈ 0.4sec
what is an advantage and disadvantage to modern clinical CT scanners?
- very fast and can now produce 2D cross-sectional images in less than a second
- expensive, high cost per CT scan
do CTs or normal X-rays cause higher patient radiation dose? explain
- CT results in higher patient radiation dose compared to normal X-rays
- this is because energies used in acquisition of images in CTs are in the high range of diagnostic X-rays
what is an issue that we face in standard X-ray projection image, but not in a CT scan?
- in a projection image, the exact location of an area of interest cannot be determined (we cannot tell if this area is in front of behind another, so the 2 overlap in the image)
- this means we cannot obtain any info regarding the depth of the organ/structure, and cannot localize the structure in a 2D image
how is this issue with X-ray projection images resolved?
radiologists often take 2 perpendicular projections :
(1) lateral
(2) AP (anterior–posterior)
why do CT scans not share this same issue?
because we obtain 3D images in CTs (an image that gives us info in 3 directions)
what is data acquisition?
the collection of X-ray transmission measurements through the patient
what does data acquisition require?
an X-ray source which is collimated into the shape of a fan or cone
what is one possible geometry for CT scanner source and detectors?
- both the source and arc-shaped detector array rotate in tandem
- recording projections through a single plane within the body for many different angles
explain the 3D image acquisition process in this geometry
- the position of the X-ray tube and detector is fixed, and rotates together
- the detector faces the X-ray
- we have only 1 X-ray tube, but we have multiple detectors
- the rotation creates images from different angles
- we combine these 2D images & reconstruct them into one 3D image
describe how a CT works
- CT is a procedure that creates cross-sectional images with the help of computer processing
- special digital x-ray detectors are located directly opposite the x-ray source
- as the x-ray passes through the patient, they are immediately picked up by the detectors and transmitted to a computer
compare conventional X-rays to CT scans
- conventional x-ray uses a fixed tube that sends x-rays in only one direction
- CT scanner uses a motorized x-ray source that shoots narrow beams of x-rays as it rotates around the patient
what is an advantage that CT images have over conventional x-ray images?
CT images are more detailed and can reveal bones, soft tissue, organs
what are the ways image slices can be displayed?
- displayed individually in 2D form
- stacked together to generate a 3D image that can reveal abnormal structures or help the physician plan & monitor treatments
what happens to photons when an X-ray beam passes through an object, what does this result in?
- some of the photons are absorbed or scattered
- this results in the reduction of X-ray transmission (attenuation)
what is X-ray attenuation?
- attenuation is the reduction of the intensity of an x-ray beam as it traverses matter
- the reduction may be caused by absorption or by deflection (scatter) of photons from the beam
what does attenuation (the reduction of x-ray transmission) depend on?
- the atomic number of the crossed tissues
- density of the crossed tissues
- the energy of the photons
give an example of how attenuation of x-rays depends on the atomic number or composition of tissues
the bone has a high atomic number, so x-rays are highly absorbed due to that
explain how x-ray attenuation depends on the energy of the photons
- low energy photons are absorbed into the structures
- higher energy photons can exit the patient body & reach the detector for the formation of an image
- therefore, low-energy photons are more easily attenuated than those with higher energy during X-ray scans
- increasing photon energy generally decreases the probability of interactions (attenuation) and, therefore, increases penetration
where are partially attenuated x-rays collected after passing through an objected?
by x-ray detectors on the opposite side
what then happens to x-rays that are detected from the receptor?
- they are then converted from x-ray photons to electrical signals
- these signals are then converted into digital data
- after which the attenuation value is calculated
what is the filtered back projection method?
a mathematical technique to convert x-ray projections into cross-sectional images
why do we use the filtered back projection method?
to obtain attenuation value for each pixel of the digital image
what do the detectors measure in the filtered back projection method?
the forward projection (the shaded areas)
in the forward projection, what do the shaded regions and the white regions represent each?
- the shaded region represents the x-ray absorber (absorption of x-rays)
- the white regions represent no absorption of x-rays
describe the filtered back projection method
(1) first we measure the number of absorbing regions in both directions (vertical & horizontal)
(2) we then add the contribution for each region
(3) we translate these numbers into different shades of grey
in the reconstructed image, how do the regions with high absorption and regions with low absorption appear each?
- regions with high absorption appear white
- regions with low absorption appear black
- (inverse of the forward projection)
what do we obtain for each projection?
- for each projection we obtain a 2D image
- we then reconstruct these slices into a 3D image
what is the aim of CT?
- to obtain a spatially resolved map of absorption coefficients in one slice of the patient’s body
- if such map is sampled at a finite resolution, it provides an image
describe the mathematical foundations behind image reconstruction
- μ1, μ2, μ3, μ4 are linear coefficients, each represents structures of different materials
S1 = μ1 + μ2 ,
S2 = μ3 + μ4 ,
S3 = μ2 + μ4 ,
S4 = μ1 + μ3 - we can obtain 4 different projections and determine the overall attenuation (attenuated beams I1, I2, I3, I4)
- since each projection follows Lambert Beer’s law, we obtain a linear equation system that we can solve for μ1, μ2, μ3, μ4
- Beer’s law: we can find the intensity (I) of the x-ray beam based on the thickness & linear coefficient of each material
- Law formula: I1 = I0exp^(-μ1d-μ2d) ,
I2 = I0exp^(-μ4d-μ5d) , etc - this simple equation system can only one solved when one of the absorption coefficients is known
why do we use computers during CT when it comes to image formation?
- an arbitrary object, composed of n-by-n different materials requires n^2 independent equations
- however in CT, we obtain data from MANY angles (many projections)
- to solve this more projections are taken at different angles
- this requires a lot of time to do the calculations, so using a computer helps solve these equations very quickly
what steps does the reconstruction of images to 3D form from the x-ray measurements involve?
- measurements
- pre-processing
- raw data
- filtering
- filtered data
- interpolation
- back-projection
- axial source images
what is another image reconstruction method that does not involve filtering the projection data before the back projection known as?
convolution
(or convolution-back projection procedure)
what is convolution?
- a mathematical operation that combines two functions to produce a third
- you drag the projections back through the image and sum them to obtain an approximation of the original image
what advantage does using convolution back-projection method have over not using using convolution?
using convolution back-projection method, we produce images of higher quality (compared to images obtained without convolution)
the selected ‘field of view’ is divided into small image elements, known as?
pixels
what is a voxel?
- voxel = volume pixel
- the pixels that make up each cross-sectional image represent a small volume of tissue, called a voxel
- in other words, the 3D representation of a pixel
what is the function of a voxel?
- a voxel is used for volume element, as it takes into consideration volume
- represents a quantity of 3-D data just as a pixel represents a point or a cluster of points in 2-D data
- used in scientific and medical applications that process 3-D images
what is the relationship between pixel size and image resolution?
the smaller the pixel, the higher the resolution (as more information is given about the structure)
what does the density value of each pixel depend on?
SOS
the composition of the tissue it represents
how is the density value of each pixel expressed?
SOS
in Hounsfield units (HU)
CT scanners represent x-ray absorption using a quantity called the _____, which we measure in _____
- the CT number
- Hounsfield units (HU)
how are the Hounsfield units calculated? what is the reference for HU?
SOS!!!
the Hounsfield units are calculated from the attenuation measurements relative to the ATTENUATION OF WATER
what do Hounsfield units range from?
-1024 to +3071
since water is the reference, structures before water on the HU scale have _____ densities, and structures past water have _____ densities
lower, higher
what is the HU of each of the following:
(1) air
(2) lung
(3) fat
(4) water
(5) CSF (any simple fluid)
(6) blood / soft tissue
(7) muscle
(8) adrenal tumor
(9) white matter
(10) grey matter
(11) liver
(12) bone
SOS!!!
(1) -1000
(2) -500 (mainly have air)
(3) -100 to -50
(4) 0
(5) +15 (range: -10 to 20)
(6) +30 to +45
(7) +10 to +40
(8) less than +10
(9) +20 to +30
(10) +37 to +45
(11) +40 to +60
(12) +700 to +3000 (>1000)
why is the Hounsfield scale very important for physicians?
it is very important for physicians as they can decide from the HU if a structure is a cyst, soft tissue, or a cancer
