Vertical Profile and Corresponding Fitted Curve

The profile plotted below is a line profile from a vertical line across the uniformity module. The points on the plot are the average over 5 columns of pixels. The plot is then smoothed further to reduce noise before the fitted curve is completed. 

Figure 8.2: A graph of the pixel intensity profile from the vertical line across the uniformity module. The vertical line analyzed typically starts and ends 1cm from the edge of the module, and consists of 5 columns of pixels. At every vertical distance from the center, the measured CT numbers from a 5-pixel row will be averaged, and plotted.

 

Horizontal Profile and Corresponding Fitted Curve

The profile plotted below is a line profile from a horizontal line across the uniformity module. The points on the plot are the average over 5 rows of pixels. The plot is then smoothed further to reduce noise before the fitted curve is completed. 

Uniformity and Noise ROI Size and Positioning

The ROIs for measuring uniformity and noise follow the guidance in the International Electrotechnical Commission (IEC) 61223. The uniformity ROIs are 10% of the phantom’s diameter. Noise measurements are made on an ROI with a diameter of 40% of the phantom’s diameter. 

The peripheral uniformity ROIs are positioned so that the outer edge of the ROI lies 10mm from the border of the uniformity module. The center uniformity and noise ROIs are centered on the phantom.

The phantoms in the Catphan® line use various uniformity modules. The table below shows the module part number for each Catphan® model.

 Table 8.1: Catphan® Model and corresponding Uniformity Module part number.

The uniformity modules have different dimensions, and consequently, the size and position of the ROIs will vary by model. The critical dimensions are given below.

Table 8.2: Dimensions [mm] for the 3 different Uniformity Module parts, their ROIs, and corresponding Noise ROIs. Since each module has a different diameter, the diameters of the noise and uniformity ROIs will vary according to the 10% uniformity ROI rule and 40% noise ROI rule.

With the varying phantom and ROI dimensions and positions, it is impossible to directly compare uniformity and noise results between phantoms using different uniformity modules.

Mean CT Value - Center Region

The mean CT number value in the center region of interest (ROI) is used as a reference for other uniformity calculations and can be viewed in the "Noise and Mean Values Plot". 

Noise and Mean Values Plot

In this plot, the mean CT number [HU] for each region of interest (ROI) is displayed as the blue column. The noise, displayed as the red column, is the standard deviation of HU values within each ROI. The upper and lower limits, indicated by the green horizontal lines, are +/- 4HU from the mean HU value of the center ROI as required by the IEC standards. 

Figure 8.4: Example of the Noise and Mean Values plot containing upper and lower limits which is included in the Uniformity and Noise analysis on Smári. Colors of the columns in the plot could be displayed differently than seen above, but each of the five regions seen above are included.

Absolute Difference from Center in Regions of Interest 

The absolute difference in mean CT number from the center ROI is calculated for each ROI. 

Noise

Noise is calculated as the standard deviation of CT numbers from a center ROI that encompasses 40% of the uniformity module. 

Noise Power Spectrum

The noise power spectrum (NPS), also known as the power spectral density, of a signal, is the Fourier transform of the noise autocorrelation. For CT volumetric image data, NPS can be evaluated in 3D using volumetric regions of interest (ROI), in 2D using 2D ROIs, or in 1D using a radially averaged 2D NPS. In the Catphan analysis report, the 3D noise power (HU²mm³) as a function of spatial frequency (mm^-1) is plotted. Since the NPS measures magnitude and the spatial correlation of noise (noise texture or noise grain size), it is a more useful measure of noise than the simple standard deviation. This becomes especially useful when the magnitude of noise is the same for two images that appear dramatically different from one another due to differences in noise texture. NPS is useful for evaluating fan and cone beam CT (CBCT) and comparing reconstructions. 

ROI Selection 

NPS is calculated for the uniformity module identified in the scan. For the uniformity module, 44 overlapping (20x20x20mm) ROI volumes are extracted at a radius of 70mm from the axial center of the phantom. The ROI volumes straddle the z-center of the module. This positioning avoids non-uniform areas of the phantom.

Figure 8.5: Axial CT image with an overlay of the arrangement of ROI volumes used to calculate the NPS. The blue square shaped ROIs have a green plus sign, +, in the center. The centers of the ROIs are arranged on the circular red line, which has a radius of 70mm from the axial center of the phantom. NPS sampling is typically performed at a constant radius as shown above. 

ROI Detrending 

For each z slice in the ROI, the overall mean of the ROI is subtracted from the pixel values in the ROI. Detrending is a method used to reduce the impact of the cupping artifact, which results in lower HU values towards the center of a homogenous object compared to the periphery. This phenomenon manifests as a spike in the NPS curve at low frequencies. By subtracting out low-frequency artifacts of the NPS, only the noise remains. 

NPS Calculations 

NPS is calculated for each ROI according to the formula below and then averaged over all the ROIs.

Where: N_x, N_y, and N_z are the dimensions of the ROI in pixels. This is dependent on the axial pixel spacing and the slice thickness. 

〈...〉is the ensemble mean, DFT is the Discrete Fourier transform and a_x, a_y, and a_z are the dimensions of the ROI in mm (i.e., 20x20x20mm).

This produces an NPS volume.

Figure 8.6: 3D NPS volume. The ROI volumes are 20x20x20mm. 

The NPS plot results are visualized in the axial plane (Figure 8.7a), along the z-axis (Figure 8.7b), and as a 3D rendering (Figure 8.7c).

Figure 8.7: Visualizations of the 3D NPS from the 3D ROI volumes that display the distribution of noise power in the (a) axial (f_x,f_y) plane, (b) sagittal (f_x,f_z) plane, and (c) 3D rendering (f_x,f_y,f_z).

The 3D NPS renderings above are from the Journal of the ICRU, Noise Assessment in CT [1]. Due to rotational symmetry of the noise ROIs, this 3D NPS in the sagittal (NPS(f_x, f_z)) plane is essentially identical to the 3D NPS projection of the coronal plane (NPS(f_y, f_z)).

The axial NPS(f(x,y)) curve, shown in Figure 8.8a below, is a radial average of the NPS values. The z-direction NPS curve, Figure 8.8b, is a circumferential average taken at a radius of half the Nyquist frequency. In both figures below, the NPS increases relatively linearly in the low spatial frequency due to the ramp filter, but then the low-pass smoothing filter causes the high-frequency roll off. The magnitude of the area under the 3D NPS curve is equal to the overall noise variance, σ², in the image.

Figure 8.8: (a) The axial NPS curve and (b) the z-direction NPS curve.

Uniformity Index (Vertical/Horizontal) 

Note: This method is not used by the algorithm but can be used manually.  

To calculate the uniformity index for the horizontal and vertical profiles, the maximum and minimum y-axis CT values [HU] from the fitted curve are entered into the following equation: 1 - [(CTmax-CTmin) / (CTmax+CTmin)].

The closer a value is to "1", the more uniform the image.  

Elekta GammaKnife Uniformity Calculation 

A different calculation is specified for GammaKnife than is used for a standard CT. The maximum percentage deviation between measured values in the five uniformity regions is used. 

The formula is: [((high + 1000)-(low + 1000))/(high + 1000)] x 100%

References

[1] 11. Noise Assessment in CT. Journal of the ICRU. (2012); 12(1): 121-134. Oxford University Press. doi:10.1093/jicru_ndt002