### FRCR Physics Notes

#### FRCR physics notes contents

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# CT image quality

The image quality is mainly determined by 3 factors:

• Resolution
• Noise
• Contrast

## Resolution

Resolution is the measure of how far apart two objects must be before they can be seen as separate details in the image. For two objects to be seen as separate the detectors must be able to identify a gap between them.

Resolution is measured in line pairs per centimeter (lp/cm) i.e. the number of line pairs that can be imaged as separate structures within one centimeter.

There are two types of resolution in CT scanning:

• Transaxial resolution (7 lp/cm)
• Axially across the patient
• Z-sensitivity (0.5 – 10 mm)
• Along the length of the patient in the z-direction

### Transaxial resolution

The minimum transaxial resolution is determined by the actual detector size, however it is often quoted as the “effective detector width” at the isocenter of the scanner (centre of the bore of the scanner). The “effective detector width” and the actual detector size are slightly different due to the divergence of the beam. The smaller the “effective detector width” the higher the resolution.

The transaxial resolution is affected by scanner (hardware) factors or scan and reconstruction parameters.

#### Scanner factors

##### 1. Focal spot
• Size
• Smaller focal spots give higher resolution, but the max mA is limited to prevent damage to the anode.
• There are usually two available focal spot sizes on CT scanners, for example:
• Fine = 0.7 mm
• Properties
• Flying focal spot: the position of the focal spot is rapidly altered in the transaxial plane and/or the Z-axis. Each focal spot position increases the number of projections sampled and improves spatial resolution. For example, if the position of the focal spot moves in the X-Y plane, then the in-plane resolution increases.
• Focus-detector distance (FDD)
• Focus-isocentre distance (FID)
##### 2. Detector size

Smaller detectors give higher resolution but more detectors within an area also means more partitions (dead space) and a reduced overall detection efficiency.

##### 3. Detector design properties

Quarter ray detector offset: the centre of the detector array is offset from the centre of rotation by one quarter the width of an individual detector. As the gantry rotates to 180° the centre of the detector array is now offset by half the width of a detector giving an interleaved sampling of the patient.

#### Scan parameters

##### 1. Number of projections
• Larger number of projections gives finer resolution (up to a point).
##### 2. Reconstruction filter
• Higher resolution or “sharp” kernels (e.g. bone reconstruction) have better spatial resolution than soft kernels (e.g. soft tissue reconstruction).
• However, higher resolution kernels do not average out high spatial frequency signals and therefore produce more noise.
##### 3. Pixel size
• The pixel size (d) in mm is give by the equation:
d = FOV/n
where:
FOV = field of view (mm)
n = image matrix size
• The highest spatial frequency that can be obtained (fmax) is called the Nyquist limit and is given by:

fmax = 1/2d

• From this equation you can see that the higher the pixel size, the lower the maximum spatial frequency.
• To improve spatial frequency we can:
• Reduce the field of view (smaller FOV = smaller pixel size as seen in the first equation). We can do this retrospectively by a targeted reconstruction of the original data into a small field of view.
• Increase the matrix size (larger n = small pixel size as seen in the first equation)

## Z-sensitivity

Z-sensitivity refers to the effective imaged slice width.

### Factors affecting z-sensitivity

##### 1. Detector slice thickness
• The wider (in the z-axis) the detector row, the lower the resolution
##### 2. Overlapping samples
• Acquiring the data using overlapping slices can improve Z-sensitivity. This is achieved by using a low spiral pitch i.e. pitch <1.
##### 3. Focal spot
• A fine focal spot improves the z-sensitivity

#### Importance of slice thickness

##### 1. Noise
• The thinner the slice the better the resolution BUT the worse the noise
##### 2. Partial volume effect
• Thicker slices increase the partial volume effects
##### 3. Isotropic scanning
• Thin slices allow isotropic scanning, i.e. the pixels in the axial and the z-axis are the same size (cubes). The advantages of this are:
• Reduced partial volume effect
• Better multi-planar reformatting
• Improved volume rendering e.g. displaying 3D representations of the data (e.g. cardiac imaging, vascular imaging, CT colonography etc)

## Noise

Even if we image a perfectly uniform object (e.g. a water filled object) there is still a variation in the Hounsfield units about a mean. This is due to noise. Noise degrades the image by degrading low contrast resolution and introducing uncertainty in the Hounsfield units of the images.

We can measure noise in any uniform region of the image e.g. with a water phantom. The standard deviation of the Hounsfield Units in a selected region-of-interest gives the mean noise measurement.

There are three sources of noise:

1. Quantum noise
2. Electronic noise
3. Noise introduced by the reconstruction process e.g. backprojection.

#### Stochastic noise

This is the dominant source of noise in an image. Photon registration by the detectors is a stochastic process. The number of photons detected will vary randomly about a mean value and that variation is the noise. The noise in the final image is given by:

Noise (standard deviation) ∝ 1/√(no. of photons)

From this equation we can say that increasing the number of photons reduces the amount of noise and, therefore, anything that increases the number of photons (increases the photon flux) will reduce the noise. If we double the number of photons we will reduce the noise by √2 (i.e. increasing the number of photons by a factor of 4 will halve the noise).

Doubling the number of photons can be achieved by:

• Doubling the tube current (mA)
• Doubling the rotation time (s)
• Doubling the slice thickness (mm)

Increasing the tube kilovoltage (kV) also increases the photon flux but it is not directly proportional (output is approximately ∝ kV2).

## Contrast

Factors influencing contrast:

• Noise: a higher noise will obscure any contrast between objects
• Tube current: a higher tube current reduces the noise in the image
• Inherent tissue properties: the difference in the linear attenuation coefficient of adjacent imaged objects will determine the contrast between those objects
• Beam kilovoltage: a higher beam energy will generally reduce the contrast between objects
• Use of contrast media

### Σ  Summary

#### Resolution

Transaxial resolution

• Scanner factors
• Focal spot size
• Flying focal spot
• Focus detector distance
• Focus isocentre distance
• Detector size
• Quarter detector offset
• Scan parameters
• Number of projections
• Reconstruction filter
• Pixel size (d, mm) given by d = FOV/n (FOV=field of view, n=image matrix size)
• Highest spatial frequency (fmax) = 1/2d
• Not affected by:
• Tube current
• Tube kilovoltage

Z-sensitivity

• Equals effective slice thickness
• Affected by:
• Detector slice thickness
• Overlapping samples
• Focal spot size
• Importance
• Smaller the slice, greater the noise
• Smaller the slice, the less the partial voluming artefact
• Isotropic scanning enables better 3D reconstruction and MPR

#### Noise

Quantum noise

• Dominant source of noise
• Noise ∝ 1 / √no. of photons
• Doubling the number of photons will decrease the noise by a factor of √2
• Doubling number of photons done by:
• Doubling tube current (mA)
• Doubling rotation time (s)
• Doubling slice thickness (mm)
• Increasing the tube kilovoltage (kV) also increases the photon flux but it is not directly proportional

Others:

• Electronic noise in detection system
• Noise introduced by reconstruction e.g. backprojection

#### Contrast

Affected by:

• Noise: higher noise = worse contrast differentiation
• Tube current: lower tube current = more noise (see above)
• Inherent tissue properties: difference in linear atteunation coefficient of adjacent imaged objects determines contrast
• Beam kilovoltage: higher beam energy generally reduces contrast
• Use of contrast media: increases contrast between objects e.g. blood vessels and surrounding tissue