# Computed Tomography

## Computed Tomography Basics

#### Basic Imaging Process

1. The X-ray tube emits an X-ray beam at a given gantry angle.
2. The beam passes through the patient and is intercepted by an imaging detector element.
3. The detector element emits a scintillation photon which is detected by a photon detector and converted into an electronic signal.
4. The electronic signal of each element at each gantry position is assembled in a computer and a sinogram is generated.
5. The sinogram is converted into a CT image using either filtered back projection or iterative reconstruction.

#### Important Terms

Ray: A single transmission measurement made by a detector element at a given gantry position.

Projection: The sum of all rays at a given gantry angle is referred to as a projection.

Sinogram: A sinogram is a map of projections as a function of gantry orientation.

#### What CT Scans Measure

##### Hounsfield Units

CT images are essentially maps of the linear attenuation coefficient (μ) of each voxel. The linear attenuation coefficient is measured in units of Hounsfield Units sometimes also called CT numbers:

Hounsfield units, also called CT numbers, are measures of linear attenuation coefficient relative to water.

#### Linear Attenuation Coefficient

Linear attenuation coefficient, μ, is the percentage of a beam attenuated per unit path length. For kilovoltage energy beams passing through tissue, linear attenuation coefficient is dominated by the Compton interaction:

• I0 is the initial intensity of the beam
• Ix is the intensity of the beam after passing through x distance of material
• x is the length of material traversed

Since the Compton interaction is proportional to Z/A, linear attenuation coefficient is approximately proportional to physical density for human body tissues. This is because the Z/A for most elements common to organic materials is 0.5. Hydrogen is an exception to this with a Z/A of 1.

### Scanner Hardware

#### External Components

Gantry

The gantry is the main structure of the scanner.

Bore

The patient transits through the bore during a scan. Typical bore sizes are between 70cm and 85cm in diameter.

Setup Lasers

Setup lasers projected from the bore are used to center the patient in the bore prior to a scan.

Couch

The patient rests on the couch or table which is able to raise or lower and travel into and out of the bore during a scan.

Control Panel

The control panel is used to position the couch, activate the lasers and perform other necessary tasks prior to a scan.

Components of a modern CT scanner.

#### Internal components

##### X-ray Source

The X-ray source consists of a heated filament electron gun which accelerates electrons toward a positively charged anode. The anode, also known as the target, generates kilovoltage (kV) photons via the Bremsstrahlung interaction.

Typical source features

• Tungsten alloy target
• Oil circulated to improve heat dissipation
• Focal spot size: 0.6-1.2mm
• Smaller means less penumbra (sharper images) but also greater local head buildup.
• Operating voltage: 80 - 140kVp
• Beam filtration: 5-10 mmAl
##### Detector Array

Detector arrays consist of multiple rows of scintillation type detectors. Scintillation signal is read out by photodiodes and converted to a digital signal for processing.

The array rotates opposite of the X-ray source on the gantry and collects data along multiple channels simultaneously.

Typical detector array features

• Scintillation type Gd2O2S  detectors
• Modern scanners can collect at least 64 slices simultaneously
• Some scanners collect up to 320 or more slices per rotation!
Internal components of modern CT scanner.
##### Bow Tie (Beam Shaping) Filter

The Bow Tie filter attenuates the lateral portions of the beam which would pass through less tissue during imaging. This reduces patient dose while yielding more uniform fluence pattern at the detector.

Bowtie filters reduce patient dose and normalize fluence at the CT dector array

### Image Acquisition Parameters

#### Energy and Current

##### Peak Potential (kVp)

Beam energy is typically referred to as peak potential or kVp (kilovoltage peak). Higher kVp increases the beam's ability to penetrate tissue resulting in a lower dose for the same exposure but at the expense of soft tissue contrast.

Effects of increasing kVp

• Decreased patient dose
• Decreased soft tissue contrast
##### Beam Current (mA)

Photon fluence is directly proportional to beam current. Increasing mA will not impact CT number or contrast but will increase patient dose and signal.

Typical values: 100-600mA

Effects of increasing mA

• Increased patient dose
• No impact on contrast
• Reduced image noise

#### Automatic Exposure Control (AEC)

Automatic exposure controls modulate either kVp or mA in an attempt to normalize the detector fluence. This yields a roughly uniform signal-to-noise ratio in the image while minimizing patient dose.

##### mA Modulation

mA modulation changes the X-ray tube current as the tube rotates to account for variable thickness of the body. That is, it may reduce mA in the head and neck but increase the current at the level of the clavicle. mA modulation typically requires a scout image to assess the appropriate beam current at each position.

##### kVp Modulation

kVp modulation is not regularly used in radiation therapy because the non-uniform changes to CT number make attenuation corrections in treatment planning difficult.

Illustration of mA modulation used to reduce patient dose while maintaining consistent SNR.

#### Spatial Resolution

##### Image Grid

Image grids refer to the number of voxels in each slice. Typical modern scanners produce 512 by 512 voxels per slice although older 256 by 256 scanners may still be encountered. Increased image grid size increases spatial resolution.

##### Field-of-View (FOV)

Since image grid doesn't change, changing the FOV impacts the amount of tissue encompassed in a single voxel. The typical nominal FOV is 50cm in diameter meaning that, for a 512 by 512 image grid, each voxel encompasses approximately 1mm2 of tissue. If the field of view is reduced to 25cm, each voxel would contain approximately 0.5mm2 of tissue.

##### Slice Thickness

Slice thickness is the axial width of each image. Reducing slice thickness improves axial spatial resolution and reduces volume averaging. Typical values range from 0.6-5mm per slice.

#### Acquisition Mode: Axial vs. Helical Scans

Axial Scan

The gantry rotates and collects imaging data while the patient is stationary. This is an image > step forward > image type acquisition.

Axial scan images with stationary couch.

Helical Scan

The couch moves continuously forward during imaging. This approach, not in use until generation six scanners, improved the speed of image acquisition.

Helical CT acquisition the couch moves continuously during imaging.

#### Pitch

Pitch is the ratio of table motion per revolution to beam width. Pitches greater than 1 indicate a gap in the helix of the scan but do not cause missed slices. Typical pitch values range from 0.5 to about 1.5.

Effects of increasing pitch

• Decreased scan time
• Decreased patient dose
• Decreased image resolution
• Increased image noise

### Factors Impacting Image Noise

Noise in CT images (σ) is inversely proportional to the square root of the number of photons reaching the imager.

Noise may be approximated by the expression:

• Patient attenuation (B)
• Voxel size (V)
• mAs settings (mAs)

Key Point: To reduce image noise by 50%, the number of photons recorded per voxel must by quadrupled!

#### Contrast Agents

Most CT contrast agents take advantage of a k-edge to increase photon attenuation. The k-edge is the binding energy of the inner (k-shell) electron orbital of an atom. There is a sudden increase in the attenuation coefficient for photons of energies just above the k-edge of an atom. This increase in attenuation may be thought of as a resonance phenomenon and occurs because of the photoelectric interaction.

#### Iodine

Iodine is the most commonly used CT contrast agent for vascular studies. Iodine contrast is administered intravenously. The k-edge of iodine is 33.2keV.

#### Barium

Barium is a common CT contrast agent used in gastrointestinal studies. The k-edge of barium is 37.4keV.

The k-edge absorption of iodine and barium is used to provide contrast in CT studies.
Abdominal CT with iodine contrast (right) is able to detect lesion that is undetectable without contrast (left).

### Reconstruction Algorithms

#### Filtered Back Projection

Back projection takes the data gathered at a given gantry angle (a projection) and projects it backward across the slice. All projections of a given slice are back-projected together resulting in a crude reconstruction of the original image. Back projection alone results in significant blurring, referred to as 1/r blurring, which degrade image quality.

Back projection reconstruction improves with greater number of projections.
1/r blur results from back projection process.
Application of a convolution kernel can be used to reduce characteristic blurring.
##### Filters and Kernels

The characteristic 1/r blurring of a back projected image can be overcome by applying a filter or kernel using a mathematical operation known as Convolution. Convolution allows the combination of a projection image with a filter/kernel resulting in an image free of characteristic blurring.

Many different kernels are available for purposes such as improving soft tissue contrast, increasing the sharpness of images, and artifact reduction.

Reconstruction Kernels impact spatial resolution, contrast, and noise.
Illustration of a ramp filter in the frequency and spatial domains.
##### Ramp Filter

The ramp filter is commonly employed to eliminate 1/r blurring. Ramp filters are applied to k-space (frequency domain) data and act by suppressing low spatial frequencies. This filter also has the negative effect of increasing image noise which is largely contained in the unsuppressed high frequency portion of k-space.

#### Iterative Reconstruction

Iterative reconstruction begins with a seed image, which is either model based (e.g. a general brain image) or based on a filtered back projection. The computer then determines what projections would have been measured is the seed image was the true image. Based on the differences between the calculated projections and the measured projections, the computer generates a new seed image. This process is repeated until arriving at a final image.

##### Iterative Reconstruction Process
1. Initial seed image is generated
• Initial seed may be a stock image, a random guess or a filtered back projection image.
2. Computer determines what projections would have been measured if the seed image was the true image.
3. The difference between the calculated projections and the measured projections is computed and used to determine a new seed image.
4. This process is repeated until the difference between calculated and measured projections is below a given threshold.
Iterative reconstruction process.

• Higher signal-to-noise ratio than back projection with the same patient dose.
• Very high-quality reconstructions can be generated.

• Seed image may bias final image.
• I.e. Local minima of projection agreement metric may be sub-optimal.
• Possible false details consistent with seed image but smaller than the scanner can truly resolve.

## CT Dosimetry

### CT Dose in the United States

Use of computed tomography is increasing and with this increase has come a growing awareness of the population risks involved. As of 2015 as many as 80 million CTs were taken in the U.S. alone. Between 1980 and 2006, CT dose per capita rose 566% from 0.53mSv to 3.0mSv. While the risk of radiation induced cancer is low on an individual level (about 5% per Sv for adults and about 15% per Sv for children) this level of radiation exposure is likely responsible for a significant number of cancer inductions across the U.S. One study (external link) has estimated that CT alone is responsible for as much as 1.5% to 2% of U.S. cancers at the 2007 use level.

#### Factors Impacting CT Dose

• kVp (Dose ∝ kVp2)
• mAs (Dose ∝ mAs)
• Pitch (Dose ∝ 1/pitch)
• Beam quality
• Patient size and anatomy
• Filtration (bow tie filter shape and material)
• Source to detector distance
• Use of automatic exposure control (AEC)

### Measuring CT Dose

#### CT Dose Phantoms

Two 150mm long PMMA phantoms are used to measure Computed Tomography Dose Index (CTDI). Both have ion chamber drillings along the center and edges for measurement of CTDIw.

• Adult body phantom: 32 cm diameter

#### Computed Tomography Dose Index (CTDI)

CTDI is defined as the integral of the dose profile along the z-axis of a phantom divided by the nominal beam width.

• N is the number of slices in a scan
• T is the slice width
##### CTDI100

CTDI100 is defined as the cumulative dose at the center of a 100mm axial scan.

• is the ion chamber calibration factor (typically ~1.0)
• f is the exposure-to-dose conversion factor (f = 0.87 cGy/R)
• R is the  chamber reading
##### CTDIW

CTDIw is a weighted average of CTDI100 values measured at the center of the phantom and at the edge of the phantom. The Concept of CTDIw was created to give a better sense of integral dose throughout the phantom. Because of attenuation, CTDI may vary by a factor of 2 or more between measurements made at the surface and those made at the center of the phantom.

Typical CTDIw values

• ~3cGy for body phantom

##### CTDIVol

CTDIvol normalizes dose from a helical scan with an arbitrary pitch to a pitch of 1 or axial scan. For an axial scan, CTDIvol = CTDIw.

• I is the table motion per rotation. Unit: mm/rotation

#### Dose Length Product (DLP)

Practical methods of CTDI measurement integrate dose of 100mm but in a typical scan, much more of the patient will be exposed than 100mm. DLP accounts for differences in scan length.

##### Effective Dose

Effective dose is used to estimate the radiation risk from various radiological exams. Effective dose incorporates a weighting factor k which signifies risk to an organ relative to whole body exposure.

Limitation of Effective Dose

The value of is dependent upon age but specifies risk to a "standard human" not any individual patient.  Further, acrylic cylindrical phantoms are standard for measurement of CTDI. This geometry and difference in material composition means that effective dose is computed on dose data which is fundamentally unrepresentative of a human dose distribution.

Source: AAPM report No. 96

Under 1 year old1 year old5 years old10 years oldAdult
Neck0.0170.0120.0110.00790.0059
Chest0.0390.0260.0180.0130.014
Abdomen & Pelvis0.0490.0300.0200.0150.015
Trunk0.0440.0280.0190.0140.015

#### Size Specific Dose Estimate

SSDE attempts to make CT dose estimates more applicable to individual patients by applying a conversion factor, fsize, to CTDIvol. The conversion factor, fsize, is found via a lookup table in TG-204 (external link) and is based on the concept of effective diameter (equation below). Effective diameter may also be estimated based on patient age using additional tables with TG-204 (external link). With this modification, SSDE is believed to be accurate to +/-20%.

One interesting aspect of SSDE is that it is found to be only weakly dependent on kVp. Within the range of 80-140kVp, SSDE varies by less than +/-5%.

Key Point: On a per-patient basis, our knowledge of dose is limited to only about +/-20% using SSDE.

Key Point: SSDE should not be used with k-factors to determine effective dose.

## CT Artifacts

The term Artifact refers to any systematic discrepancy between the CT numbers in the reconstructed image and the true attenuation coefficients of the object. CT artifacts are generally divided into three categories: Physics-Based Artifacts, Patient-Based Artifacts, and Scanner-Based Artifacts.

Physics-Based Artifacts: Artifacts which arise from the physical processes involved in image acquisition. Examples include beam hardening artifact, partial volume artifact,  projection/view aliasing, photon starvation artifact and cone beam artifact.

Patient-Based Artifacts: Artifacts caused by factors related to the patient during the scan. Examples include motion artifact and metal artifact.

Scanner-Based Artifacts: Artifacts resulting from imperfections in the scanner’s function. Examples include ring artifact and wobble artifact.

### Physics Based Artifacts

#### Beam Hardening

The X-ray beam is composed of a spectrum of energies. As the beam passes through an object, the beam hardens (i.e. becomes more high energy dominant). This results in two effects: cupping and streaking, both of which are physics-based artifacts.

• Cupping: CT numbers obtained in the center of the object are lower than at the periphery.
• Streaking Artifact:  Appearance of dark bands or streaks between dense objects in the image.
Left: Image with cupping artifact. Right: Image without cupping.
Streaking artifact caused by beam hardening.

#### Photon Starvation (Noise)

Photon starvation is a physics-based artifact that results from an insufficient number of photons reaching the detector. As a result, statistical variation in photon count becomes a dominant source of contrast in the image. This results in an image with streaks along high attenuation beam paths such as those intersecting metal objects or those passing through significant volumes of bone.

Photon starvation may be resolved by increasing mAs or through the use of iterative reconstruction techniques.

Photon starvation in lateral projections through the clavicle.

### Scanner Based Artifacts

#### Partial Volume Artifact

Partial volume artifact is the averaging of CT number over the volume of the voxel. For example, a voxel which samples a bone (CT number = 800HU) and lung (CT number = -800) would display a CT number of 0 which is representative of water. Because voxel size impacts volume averaging, its effect may be reduced by decreasing field-of-view and by decreasing slice thickness.

Partial volume artifact (circled in yellow) decreases with decreased voxel size.

#### Projection/View Aliasing (Undersampling)

Projection aliasing results from the use of too few projections in image reconstruction resulting in aliasing of high frequency objects. The artifact appears as regular streaks projecting from hard, high-contrast edges within the image. This artifact is typically resolved in software by increasing the imager sampling frequency.

#### Ring Artifact

When one of the detectors is out of calibration in a rotating detector scanner, the detector will induce a systematic error at its position for each projection. Upon reconstruction, this results in a ring being superimposed on the image. Ring artifact can typically be repaired by recalibration of the detector array or by turning off the faulty detect element.

#### Cone Beam Artifact

As the number of slices acquired per rotation increases, the beam becomes cone-shaped rather than fan shaped. Beam divergence of this wide cone can cause under sampling (collecting data at too few angles) for objects which are far from the central axis of the scanner. This fundamental undersampling is the cause of cone beam artifact which appears as irregular deformation of the object. Cone beam artifact can be reduced by decreasing pitch or otherwise increasing sampling.

Be aware, several online resources list this problem as similar to volume averaging as a result of a larger volume being collected near the periphery of the detector array. This interpretation is incorrect as can be seen by noting: 1) all detector elements are commonly the same size; and 2) beam divergence means that, although path length is greater, the cross-sectional area sampled is actually smaller for objects sampled with the edge row of the detector. Further, this explanation is not supported by Bushberg et al. (Bushberg, J. T., Seibert, J. A., Leidholt, E. M., & Boone, J. M. (2012). The essential physics of medical imaging. Philadelphia, PA: Wolters Kluwer / Lippincott Williams & Wilkins.)

### Patient Based Artifacts

#### Metal Artifact

The presence of metal in the field of view is beyond the normal range of densities handled by the scanner. This results in severe streaking artifacts projecting from the metal. Additionally, metal can saturate the scanner resulting in a display CT number equal to the scanner's maximum (often +1024). This may result in lead (z=82) being mapped to the same CT number as high-density bone (zeff = 13.8) despite being significantly more attenuating.

Metal artifact can be reduced by increasing kVp with megavoltage CTs (MVCT) yielding a significant reduction in artifact. Additionally, several commercial reconstruction algorithms are available for metal artifact reduction.

Metal artifact resulting from metal vertebral pin.
Motion artifact causes streaks across image.

#### Motion Artifact

Patient motion during a scan can result in misregistration of the ray data. This usually appears as directional shading or streaking in the reconstructed image. Motion artifact may be reduced by improved patient immobilization, patient coaching or increased scan speed.

## CT History

### Important Dates

1917: Johann Radon develops a mathematical theory to reconstruct an image from transmission measurements.

1963: Allan Cormack creates the first CT scanner. This scanner used an X-ray pencil beam and two NaI detectors.

1972: Godfrey Hounsfield (working with EMI, Ltd.) creates the first commercial CT scanner. The system, known as the EMI scanner was only able to image the patient's head. Interestingly, the EMI scanner was developed completely independent of Cormack's prior work.

1979: The Nobel prize in medicine goes to Hounsfield and Cormack for work in computed tomography.

1980’s: Helical CT scan mode was first introduced.

1990’s: Multi-detector array CT was developed, reducing scan time.

2000’s: Cone-beam and dual energy CT were introduced.

### Scanner Generations

#### First Generation

First generation scanners laterally translated both the X-ray tube and imaging detector at discrete gantry angles to create images.

Characteristics

• Used kilovoltage pencil beam and single detector.
• Acquisition required laterally translating both X-ray tube and detector.
• Scans required 5+ minutes per slice.

First Generation CT Scanner
Second Generation CT Scanner

#### Second Generation

Second generation scanners incorporated broad fan beams and detector arrays but retained the "translate while imaging, rotate, repeat" acquisition.

Characteristics

• Used broad kilovoltage fan beam and an array of detectors to accelerate acquisition.
• Detector array had between 3 and 60 elements (discrete detectors).
• Reduced imaging time to 15-20 seconds per slice (an over 93% reduction in scan time).
• Increased data acquisition rate strained limited computing power during image reconstruction.

#### Third Generation

Third generation scanners were the first to acquire projection data while the gantry rotated. This innovation eliminated the need to translate the X-ray tube and detector array, further reducing acquisition time. Early third generation designs were limited in how far they could rotate without rewinding cables by reversing direction. This limitation was overcome in the 1980s with the incorporation of a slip ring.

Characteristics

• First to collect data during gantry rotation.
• Later designs incorporated a slip ring.
• Reduced imaging time to 15-20 seconds per scan.
• Significantly faster than the 15-20 seconds per slice scans of a second generation scanner.
• Axial scans only.
• Helical acquisition is characteristic of generation six scanners.
• Limitations
• A single faulty detector element can lead to a ring artifact.
Third Generation CT Scanner

Ring artifact caused by faulty detector element

Slip rings used to facilitate continuous rotation

#### Fourth Generation

Fourth generation scanners feature a full 360-degree array of detectors meaning only the X-ray tube rotates. This effectively removed the ring artifacts of third generation scanners but was very expensive.

Characteristics

• 360 degree detector and spinning X-ray tube.
• Expensive
• Resolved ring artifact issue of third generation but introduced wobble artifact.
• Wobble artifact is caused by slight misalignment between center of detector array and center of X-ray tube rotation.
Fourth Generation CT Scanner
Uniform phantom with wobble artifact.
Fifth generation CT scanner

#### Fifth Generation

Fifth generation removed traditional spinning X-ray tubes entirely. Rather, an electron gun would accelerate  an electron beam through a set of steering "deflection coils." The deflection coils direct the electron beam into a large circumferential target located along the gantry. During acquisition the electron beam is directed around the target allowing for circumferential acquisition without any moving parts. This design is very expensive but allows for acquisition speeds greatly exceeding what is possible with a physically rotating X-ray tube.

Characteristics

• Replaced X-ray tube with deflected electron tube and circumferential target.
• Magnetic steering of electron beam allows acquisition.
• Extremely fast acquisition thanks to no moving parts.
• Very high cost.

### Sixth Generation

Sixth generation CT scanners essentially returned to the hardware of a third generation scanner (rotating fan beam X-ray tube and detector array) but with the addition of a helical acquisition mode. This reduced costs relative to the fourth and fifth generation scanners while increasing acquisition speed above what was possible with a third generation scanner.

Characteristics

• Introduced helical acquisition mode.
• Uses third generation hardware
• Rotating fan beam and detector array mounted on slip ring gantry.
Helical acquisition is characteristic of a sixth generation CT scanner.
Seventh generation scanners incorporated large "cone beam" sources.

#### Seventh Generation

Seventh generation CT scanners incorporates a larger cone beam X-ray source and detector array. In cone beam acquisition, multiple rows of detectors are arranged together, allowing the system to collect multiple rows of data in a single rotation.

Characteristics

• Introduced cone beam acquisition.
• Several slices can be measured in a single gantry rotation.
• Modern CT scanners are usually seventh generation scanners.

## Knowledge Test

1. What energy photon is most attenuated by Barium contrast?

Question 1 of 3

2. A given material has a linear attenuation coefficient 1.5 times that of water for a given photon spectrum. How many Hounsfield units would it represent?

Question 2 of 3

3. What is depicted in the below image?

Question 3 of 3