Topics covered in this article include:

Introduction
Vertical Profile and Corresponding Fitted Curve
Horizontal Profile and Corresponding Fitted Curve
Uniformity and Noise ROI Size and Positioning
Mean CT Value - Center Region
Noise and Mean Values Plot
Absolute Difference from Center in Regions of Interest
Noise
Noise Power Spectrum
Uniformity Index (Vertical/Horizontal)
Elekta GammaKnife Uniformity Calculation

Introduction

The image uniformity module is cast from a uniform material. The material’s CT number is designed to be within 2% (20H) of water’s density at standard scanning protocols. The typically recorded CT numbers range from 5H to 18H. This module is used for measurements of spatial uniformity, mean CT number and noise value.

The precision of a CT system is evaluated by the measurement of the mean value and the corresponding standard deviations in CT numbers within a region of interest (ROI). These measurements are taken from different locations within the scan field.

The algorithm provides vertical and horizontal line profiles across the uniformity module. The points on the plot are an average over 5 columns of pixels. The plot is then smoothed further to reduce noise before the fitted curve is completed. 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.

The phenomenon of “cupping” or “capping” of the CT number may indicate the need for calibration.

In the graph below, the upper limit is determined by adding 40 HU to the Mean CT number of the Center ROI. The lower limit is determined by subtracting 40 HU from the Mean CT number of the Center ROI.

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 an average over 5 columns of pixels. The plot is then smoothed further to reduce noise before the fitted curve is completed.

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 an 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 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.

Catphan Model	Uniformity Module Part Number
CTP500	CTP486
CTP503	CTP486
CTP504	CTP486
CTP600	CTP486
CTP604	CTP729
CTP605	CTP729
CTP606	CTP729
CTP700	CTP712

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.

Dimension (all dimensions in mm)	CTP486	CTP729	CTP712
Uniformity module diameter	150	201	200
Uniformity ROI diameter	15	20.1	20
Peripheral uniformity ROI radial distance from the center of the phantom	57.5	80.45	80
Noise ROI Diameter	60	80.4	80

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 value) 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.

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. It gives the intensity of noise as a function of spatial frequency. NPS is useful for evaluating fan beam CT 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.

ROI detrending

For each z slice in the ROI, the overall mean of the ROI is subtracted from the pixel values in the ROI.

NPS Calculations

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

Where :

ax, ay, and az are the dimensions of the ROI in mm (i.e., 20x20x20mm)

Nx, Ny, and Nz are the dimensions of the ROI in pixels. This is dependent on the axial pixel spacing and the slice thickness.

This produces an NPS volume.

The results are visualized in the axial plane and along the z-axis.

The axial (f(x,y)) curve is a radial average of the NPS values.

The z-direction NPS curve is a circumferential average taken at a radius of half the Nyquist frequency.

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)