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Medical Imaging notes for exam
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Exam questions Medical Imaging- per categoryCT:
1. Which properties of X-rays can you change (amount of rays + energy of photons)?
Two parameters can be set when we use an X-ray source: First the number of emitted photons is set. This
is determined by current of cathode and the duration the current is on. Typical values are 30 to 100 mAs.
The second parameter is the energy of the emitted photons. This determined by the voltage U between
anode and cathode. Typical values for U are 50-150 kV resulting in X-rays with energy from 50-150 keV.
2. How are x-rays produced? What are the different components used (don't remember the exact question but
the point was that you had to explain the filter, the collimator grid and where they were placed and why
they're needed.) + what is beam hardening
X-rays are produced in an Rontgen tube, through a process called X-ray generation. The key components
involved in the production of X-rays are:
• Cathode: The cathode is a negative electrode inside the X-ray tube. It typically consists of a
tungsten filament. When an electric current is passed through the filament, it heats up, releasing
electrons through a process known as thermionic emission.
• Anode: The anode is a positive electrode, usually made of tungsten as well. It is positioned
opposite the cathode. The high-speed electrons emitted by the cathode are focused and accelerated
towards the anode.
• X-ray Tube: The X-ray tube is a vacuum tube that contains both the cathode and anode. The
vacuum is maintained to prevent the electrons from colliding with air molecules, ensuring a more
efficient production of X-rays.
• Production of X-rays: When the high-speed electrons from the cathode strike the tungsten target
of the anode, two main processes contribute to the generation of X-rays:
o Bremsstrahlung Radiation: This is the most common mechanism of X-ray production. In
this process, the high-speed electrons are deflected by the positively charged nucleus of
the tungsten atoms, leading to the emission of X-rays. The term "bremsstrahlung" is
German for "braking radiation."
o Characteristic Radiation: When an incoming electron knocks an inner-shell electron out
of its orbit, an electron from a higher energy shell may fall down to fill the vacancy. This
transition results in the emission of X-rays with characteristic energies.
The combination of bremsstrahlung and characteristic radiation produces a spectrum of X-rays with
various energies. To optimize imaging, a filter is often used to selectively absorb lower-energy X-rays,
and a collimator helps shape and limit the X-ray beam.
Overall, the controlled interaction between electrons and the tungsten target in the X-ray tube leads to
the emission of X-rays that can be directed toward the patient for medical imaging or other
applications.
§ Cathode: The cathode is a negative electrode that produces a focused electron beam. It usually
consists of a tungsten filament heated to produce a cloud of electrons.
, § Anode: The anode is a positive electrode typically made of tungsten. When the high-speed
electrons from the cathode strike the anode, X-rays are produced through the process of
bremsstrahlung radiation and characteristic radiation.
§ Collimator: The collimator is a device that shapes and limits the X-ray beam. It is positioned near
the tube and includes lead shutters or a lead-lined tube that can be adjusted to control the size and
shape of the X-ray field. This helps in focusing the X-rays on the area of interest and reduces
unnecessary radiation exposure to surrounding tissues.
§ Filter: X-ray beams often include unwanted low-energy (soft) X-rays that contribute to patient
dose without contributing useful diagnostic information. Filters, typically made of aluminum, are
used to selectively absorb these low-energy X-rays, resulting in a "harder" beam that is more
penetrating and provides better image quality.
§ Collimator Grid: The collimator grid is another component that helps improve image quality. It
consists of lead strips arranged in a grid pattern and is positioned between the patient and the X-
ray detector. The grid absorbs scattered radiation, which can degrade image contrast, and allows
only the primary (non-scattered) X-rays to reach the detector.
Beam Hardening:
Beam hardening is a phenomenon that occurs when X-rays pass through a material, and lower-energy
X-rays are preferentially absorbed, leaving a higher average energy for the remaining X-rays. This can
result in a "harder" X-ray beam. It is particularly relevant in computed tomography (CT) imaging,
where X-rays pass through different tissues with varying thicknesses. Beam hardening can affect the
accuracy and quality of the CT image, and correction techniques are often employed to minimize its
impact.
3. Explain principle of CT, reconstruction, 3rd generation
The third generation (used in most systems nowadays) uses a wide fan beam covering the complete object
(illustrated in 1.20). There are about 500-700 detectors (ionization chambers or scintillation detectors). No
more translation is needed and the scan time is reduced to seconds. This results in a reduced dose and
limits the number of motion artefacts. Due to the increase in computer power (and dedicated hardware)
the reconstruction time is in the order of seconds. These systems make use of a pulsed source to reduce
the heat production.
CT reconstruction involves mathematical algorithms that combine the acquired data from multiple angles
to create detailed images. The process includes the following steps:
• Filtered Back Projection: Historically, CT images were reconstructed using a technique called
filtered back projection. This method involves back projecting the attenuated data from each
detector to create a two-dimensional image. While it is effective, it can result in some artifacts.
The Radon transform is a mathematical operation used in computed tomography to obtain detailed
images of the human body. When we project a two-dimensional object along a projection angle θ,
we are essentially integrating the density distribution of this object along a line.
The Radon transform integrates information along different lines of sight, thus acquiring a series
of projections. These projections are then used to reconstruct a three-dimensional image of the
object inside the body. The projections of a single slice are often stored in a format called a
sinogram, which graphically represents how various projection lines interact with the body's
structures. This sinogram can later be used for the reconstruction of the final image.
• Iterative Reconstruction: Modern CT scanners often use iterative reconstruction algorithms.
Instead of a single-pass approach, iterative reconstruction involves multiple iterations to refine the
image. This method can reduce noise and improve image quality.
,3rd Generation CT:
In the context of CT scanners, generations refer to the design of the scanner's hardware, particularly the
arrangement of the X-ray tube and detectors. In 3rd generation CT scanners:
• Single Rotation Source and Detector Array: 3rd generation CT scanners have a single X-ray tube
and a detector array fixed opposite each other. The X-ray tube and detectors rotate around the
patient to acquire data.
• Helical Scanning: 3rd generation CT scanners are often capable of helical or spiral scanning,
where the patient table moves continuously through the rotating X-ray beam. This allows for faster
image acquisition and improved patient throughput. It is needed an interpolation to obtain the
projections of the slices. It can be done with a single row of detectors or multiple rows. Two
parameters are important in this kind of scanning:
§ Table feed: axial distance which table shifts during the rotation (360°)
!"#$% '%%(
§
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»1/2. Higher pitch is used to reduce dose, artifacts and to have a shorter scan
time.
• High-Resolution Imaging: With advancements in technology, 3rd generation CT scanners
typically offer high-resolution imaging, allowing for detailed visualization of small structures
within the body.
In summary, the principles of CT involve using X-rays, detectors, and computer algorithms to create
detailed cross-sectional images of the body. Reconstruction methods have evolved from filtered back
projection to iterative techniques. 3rd generation CT scanners have a specific design with a single rotating
source and detector array, enabling helical scanning and high-resolution imaging.
Reconstruction:
§ Forward Projection and Sinogram: The forward projection involves calculating the line integral of
an object represented by f(x,y) along various projection angles θ. This process results in a
sinogram, a graphical representation of the object's projections at different angles. In the sinogram,
the projection of a central point forms a straight line, while off-center points create sinusoidal
patterns.
§ Back projection: From the sinogram, back projection is employed to reconstruct an image. This
operation distributes the sinogram values over corresponding rays in image space. However, back
projection alone is not perfect, particularly when dealing with a point source, as it results in a
blurred image due to uncertainties in the location along the projection line.
§ Impulse Response and Convolution: The impulse response of back projection is expressed as
/
ℎ𝑏(𝑟) = 0 . This implies that the reconstructed image obtained from back projection is the
convolution of the original image with this impulse response. The convolution process introduces
a certain level of blurring.
§ Inverse Radon Transform: to address the limitations of back projection, the text emphasizes the
importance of the inverse Radon transform in reconstructing images from measured transmission
data. The inverse Radon transform enhances the accuracy of image reconstruction compared to
back projection alone.
In summary, while back projection provides a basic method for image reconstruction, its limitations
necessitate the incorporation of the inverse Radon transform for more accurate results.
The text further explores a 2D Fourier-based reconstruction technique to address blurring effects in back
projected images. This method involves transforming the image to the Fourier domain and implementing
specific operations, including the use of the Central Section Theorem.
, § Convolution Back projection: An alternative to Filtered Back projection (FBP) is introduced,
known as Convolution Back projection. This method replaces initial steps with a convolution
involving the inverse Fourier transform of the ramp filter. The convolution introduces negatives
in the projections to counteract blurring during back projection, like the FBP algorithm.
§ Properties of FBP: FBP is acknowledged for its speed but assumes exact projection data and many
angles. The text notes that iterative reconstruction methods offer more flexibility in handling
corrections and non-exact projections.
§ Transforming CT Data into Projection Data: The discussion shifts to X-ray transmission
tomography, where the goal is to reconstruct the spatial distribution of the attenuation coefficient
μ(x,y,z) from measured X-ray attenuation. The relationship between measured intensity ( I) and
the attenuation coefficient is described through a logarithmic equation.
§ Challenges in Real-world Imaging Systems: Deviations from the idealized line integral model in
CT are addressed, considering factors like the limited number of projections, spatial resolution,
measurement errors, deviations from mathematical models, and patient movements during data
acquisition.
In conclusion, Convolution Back projection is presented as an alternative to FBP, offering a similar
outcome in image reconstruction. The properties of FBP, its speed, and assumptions are discussed, along
with challenges encountered in real-world CT imaging systems.
4. Give components of 3rd generation CT, which acquisition methods are used? How do you go from
measurements to final image in HU?
Third-generation CT scanners typically consist of the following key components:
§ X-ray Tube: This component generates X-rays that pass through the patient's body during
scanning. The X-ray tube is a crucial element in determining the quality and intensity of the
X-ray beam.
§ Detector Array: The detector array is positioned on the opposite side of the patient from the
X-ray tube. It captures the X-rays that pass through the body, converting them into electrical
signals. Modern CT scanners use a large array of detectors to improve spatial resolution.
§ Gantry: The gantry is the rotating frame that houses the X-ray tube and detector array. It
allows for the rotation of these components around the patient, acquiring data from different
angles.
§ Patient Table: The patient table is movable, allowing precise positioning of the patient during
the scan. It ensures that the area of interest is aligned with the X-ray beam.
§ Data Acquisition System (DAS): The DAS collects and processes the electrical signals from
the detector array. It plays a critical role in converting raw data into meaningful information
for image reconstruction.
§ Image Reconstruction System: The image reconstruction system processes the acquired data
to generate cross-sectional images of the body. It utilizes mathematical algorithms, such as
filtered back projection or iterative reconstruction, to produce the final images.
Acquisition Methods: In third-generation CT scanners, data is typically acquired using the axial or helical
scanning method:
§ Axial Scanning: In axial scanning, the X-ray tube and detector array remain stationary while
the patient table moves incrementally. Data is acquired at each table position, resulting in a
series of axial slices. It’s not so common.
§ Helical Scanning: Helical scanning involves continuous rotation of the gantry as the patient
table moves through the scanner. This spiral or helical motion enables the acquisition of
volumetric data, providing more efficient and faster scanning compared to axial methods.
From Measurements to Final Image in Hounsfield Units (HU): The process of converting raw
measurements into Hounsfield Units (HU) involves several steps:
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