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ORIGINAL ARTICLE
Year : 2023 | Volume
: 38
| Issue : 1 | Page : 23-33
Estimating center of rotation of single-photon emission computerized tomography projection images using MATLAB for standardization and calibration
Anil Kumar Pandey1, Jagrati Chaudhary1, Gagandeep Kaur1, Priya Yadav1, Param Dev Sharma2, Chetan Patel1, Rakesh Kumar1
1 Department of Nuclear Medicine, All India Institute of Medical Sciences, New Delhi, India
2 Department of Computer Science, SGTB Khalsa College, University of Delhi, New Delhi, India
Correspondence Address:
Dr. Anil Kumar Pandey
Department of Nuclear Medicine, All India Institute of Medical Sciences, New Delhi - 110 029
India
Source of Support: None, Conflict of Interest: None
CheckDOI: 10.4103/ijnm.ijnm_110_22
Abstract
Objective: The objective of the study was to develop a Personal Computer (PC) based tool to estimate the center of rotation (COR) offsets from COR projection datasets using methods mentioned in IAEA-TECDOC-602. Materials and Methods: Twenty-four COR studies were acquired on Discovery NM 630 Dual head gamma camera fitted with parallel hole collimator, and COR offsets were estimated with the software available at the terminal for processing a COR study. These COR projection images were exported in DICOM. A MATLAB script (software program) was written to estimate COR offset using Method A (using opposite pair of projections) and Method B (using curve fitting method) as mentioned in IAEA-TECDOC-602. Our program read the COR study (in DICOM) and estimated COR offsets using Method A and Method B. The accuracy of the program was verified using simulated projection dataset of a point source object acquired at 6° interval in the range of 0°–360° angle. Bland Altman plot was used for analyzing the agreement between the COR offsets estimated using (1) Method A and Method B mentioned in IAEA-TECDOC-602, and (2) Our program and vendor program available at Discovery NM 630 acquisition terminal. Results: On simulated data, offset from center of gravity (COG) in X direction (COGX) and COG in Y direction (COGY) estimated using Method A was constant (same) at each pair of angles while using Method B, it was found to be in the range (−2 × 10−10, 1 × 10−10) which is negligible. Most of the differences (23 out of 24) between the result of Method A and Method B, and between the results of our program and vendor program was found to be within 95% confidence interval (mean ± 1.96 standard deviation). Conclusions: Our PC-based tool to estimate COR offsets from COR projection datasets using methods mentioned in IAEA-TECDOC-602 was found to be accurate and provides results in agreement with vendor's program. It can be used as an independent tool to estimate COR offset for standardization and calibration purposes.
Keywords: Center of rotation, COR offset, single-photon emission computerized tomography
Introduction 
Single-photon emission computerized tomography (SPECT) image quality is affected by number of factors, out of which the accurate determination of the center of rotation (COR) of reconstruction is more critical[1],[2],[3],[4],[5],[6],[7],[8],[9] because small changes in COR may cause significant artifacts in the reconstructed images. For each camera head the accuracy of COR alignment should be checked weekly, unless indicated otherwise by the manufacturer. Usually, manufacturers recommend to follow a specific protocol for the determination and recalibration of the COR. Some manufacturers allow the COR calibration to be performed by service engineers only; however, all systems should be checked for correct COR calibration.[10]
It is essential that COR errors be checked for each collimator that is to be used clinically.[1] New COR calibrations should be performed after servicing of the camera, after power surges or outages, and after hardware and software upgrades. It is important to verify that the correct COR information is applied following service of any type by simply repeating the acquisition of new COR information, and then verifying that a tomographic acquisition of a point source produces a trans axial image correctly that is also a point source.[10] If the COR test results are not within acceptable limit, remedial action should be taken, before conducting routine clinical SPECT studies. An alignment error between the center of the electronic matrix of the camera and the mechanical COR (i.e. COR offset) can result in a characteristic ''doughnut'' (if a 360° orbit and a point source are used) or ''tuning fork'' artifact (if a 180° orbit is used) in the transverse images.[11] COR offsets also result in loss of spatial resolution leading to blurred clinical images, and finally might influence the clinical decision.
Under the subsection of acceptance and reference tests on SPECT systems, IAEA-TECDOC-602[12] provides detailed guidance on how to acquire a study to test the COR offset, and perform the data analysis. There is no mandatory guideline to be followed regarding the procedure used for the determination of COR offset from the projection data. Thus, SPECT gamma camera vendors can use any one of the methods existing in the literature for the determination of COR offset from the projection data and implement the method in software for processing the COR studies. If no specific COR acquisition protocol is recommended by the manufacturer, American Society of Nuclear Cardiology guideline also recommends a COR acquisition and processing protocol to be followed.[10] Whatever method manufacturer might follow, it is expected that software must accurately estimate the COR offset.
Nuclear Medicine Physicist might adopt the method described in the IAEA-TECDOC-602 for the estimation of COR offset from the SPECT projection data. COR offset estimated using this procedure can be taken as gold standard to verify the COR offset estimated by the vendor's software.
The objective of the study was to develop a personal computer (PC)-based software program using MATLAB that estimates COR offsets from the projection data sets. The program reads the projection data written in DICOM format and calculates the COR offsets using methods described in IAEA-TECDOC-602. We have verified the accuracy of the program using both the simulated and real COR study data.
Materials and Methods COR is the point at which the axis of rotation and the perpendicular from the center of the detector plane intercept. The trans-axial alignment of acquired projection images with the system's mechanical COR is critical for the accurate generation of tomographic images reconstructed from acquired projection images.
Two methods of estimation of COR offset mentioned in IAEA-TECDOC-602 are described briefly as follows:
Method A
Projection image is denoted by a matrix named img. The size of the image is the size of the matrix img and is determined by the width M (number of columns) and the height N (number of rows) of the image matrix img. The img (i, j) represent the pixel value of the image at the location i and j; the index i runs from 1 to M and index j runs from 1 to N.
For each projection image, the center of gravity (COG) of point source is calculated in x and y directions using the formula:
where i is the index along X direction and j is the index along Y direction.
The COG of the image of the point source, angle by angle, was calculated using equations 1 and 2 to estimate the position of the COR. The values of COGX and COGY were estimated to be a fraction of a pixel. The offset from the center of the rotation was calculated using the formula:
where,
X0 is the value of the COGX at 0°.
X180 is the number of pixels across the image (64 pixels for 64 × 64 image matrix size)
R0 is the offset from the COR. This value was calculated for each pair of angles θ separated by 180° to generate a set of values R (θ).
Method B
The COG of the X position is plotted as a function of angles over the total angle of rotation. A sine function A + B Sin(θ + ∅) is fitted to this curve, where θ is the angle of rotation, and where A, B, and ∅ are fitting constants. The value of A is compared to the expected center of the matrix (which was (N + 1)/2). The difference between the constant A and the COR is the mean offset. The fitted function is subtracted from the observed curve to get the residuals. This indicates the variation in the COR as a function of the angle of rotation. R (θ) is given by these residuals plotted against angle θ.
The value of R (θ) was converted into millimeters by using the known value of pixel size for the camera, for the corresponding matrix size.
We have developed a matlab script whose name is “COR offset Estimation.” The readymade “subfunction” that has been used are: The MATLAB function “radon” simulates the projection dataset of a two-dimensional (2D) object at various angles.[13] Step-by-step description of our program written in MATLAB (“9.10.0.1684407 [R2021a] Update 3.” The MathWorks Inc.) and Other MATLAB functions used to calculate COR offset in X and Y directions, are given in [Table 1].
In order to verify the accuracy of our program, we simulated the projection data of a point source image. We created an image of a point source object [Figure 1] by setting the value equal to 1 at the position (118, 138) in a 256 × 256 image matrix, while all other pixel locations have value equal to 0. The projection data sets (60 projection images generated at 6°- interval for total angle of 360°) of the point source image was generated using “radon” function.
Figure 1: Left side: Simulated point source image and Right side: Sixty projection image data sets displayed as sinogramIt is to be remembered that there should not be COR offset in the projection dataset generated by radon function. That is, estimated COR offset in either X or Y-direction should be 0 at each angle of projection.
The program was also validated with 24 COR studies (real data) acquired on Discovery NM 630 dual head SPECT gamma camera.
Experimental setup and acquisition protocol
The point source was placed in the source holder and the source holder was placed on the edge of the pallet. The source holder and table height were adjusted until the image of the point source was visible inside the ROI circle on detector 1 and also inside the ROI circle on detector 2 on the persistence scope. Then COR acquisition was started. After the completion of the study, the program automatically processed the COR study and displayed the report. The acquisition protocol used for these COR studies is summarized in [Table 2].
Data processing and statistical analysis
These 24 COR studies were exported in DICOM 3.0 format. Our developed program read these DICOM files one by one and calculated the COR offsets in X and Y directions for detector 1 and detector 2 using both Method A and Method B. The program also generated plots of COGX, plots of COGY, plots of offsets from COGX, and plots of offsets from COGY estimated from the projection images acquired at 6° interval in the range of angles between 0 and 360.
For each study, the program was executed 30 times. For each run, time required to process were recorded. Since we had 24 COR studies, we got 720 instances of time involved in the processing of COR study (i.e. the time involved in the time of COR estimation and the time of plotting of the graphs of COR offset estimation in X and Y direction using both the Method A and Method B). This experiment was performed on LAPTOP (Device name: LAPTOP-568R779P, Processor: Intel® Core™ i7-10870H CPU @2.20 GHz 2-21 GHz, Installed RAM: 16.0 GB [15.9 GB usable], 64-bit operating system, ×64 based processor, Windows 10 Home Single Language version 21H1).
We have applied the Bland Altman plot to assess the agreement between the COR offset estimated by our program and vendor program available at Discovery NM 630 acquisition terminal.[14] The analysis is based on the quantification of agreement between these two measurements by studying the mean difference and constructing limits of agreement. The resulting graph is a scatter plot XY, in which the Y axis shows the difference between the two paired measurements (COR offset estimated by our program-COR offset estimated by GE program) and the X axis represents the average of these measures ([COR offset estimated by our program + COR offset estimated by GE program]/2). The statistical limits of agreement were calculated by using the mean and the standard deviation (SD) of the differences between the two measurements. The limits of agreement were mean −1.96 SD and mean + 1.96 SD That is 95% of the data points should lie within ± 1.96 SD of the mean difference.
Results We verified the accuracy of our program with simulated projection data set. The 2-D image [[Figure 1] Left side] used for generating the projection dataset, and its sinogram [[Figure 1] Right side], the plot of COGX, the plots of COGY at various angle of projection [Figure 2]b and [Figure 2]c. The plot of offsets from COGX and COGY estimated by Method A [Figure 2]d and [Figure 2]e and plot of offset from COGX estimated by Method B [Figure 2]a shows that our program estimates the COR offset accurately on simulated projection data. Inspection of the plot of COR offset by Method A [Figure 2d and e] and Method B [Figure 2]a, shows the constant value of COR offset in both X and Y direction (i.e. no change in COR offset at various angles of projection verifies the accuracy of our program). This is expected from the Radon function for no change in COR offset in projection data.
Figure 2: (a): Offsets from COGX at various angles estimated using Method B (b): Plots of COGX at various angles of projection (c): Plots of COGY at various angles of projection (d): Offsets in pixels estimated using each opposite pairs of angles by Method A from COGX plot and (e): Offsets in pixels estimated using each opposite pairs of angles by Method A from COGY plot. COGX: Centre of gravity X direction, COGY: Centre of gravity Y directionOne real COR study acquired on GE SPECT gamma camera and COR offsets in X and Y direction were estimated by our program. Plot of COGX versus angle of projection [[Figure 3] Top left], plot of COGY versus angle of projection [[Figure 3] Top right], plot of COR offset in X-direction estimated with Method A versus angle of projection [[Figure 3] Bottom left] and plot of COR offset in Y-direction versus angle of projection [[Figure 3] Bottom right], For detector 1, [Figure 4] shows one sample of the COR offset report produced by our program. The COR offset estimated using Method B for detector 1 in X-direction [[Figure 4] Top left] and in Y-direction [[Figure 4] Top Right]. The COR offset estimated using Method B for detector 2 in X direction [[Figure 4] Bottom left] and in y direction [[Figure 4] Bottom right].
Figure 3: Top Left: Plot of COGX versus angle of projection. Top Right: Plot of COGY versus angle of projection. Bottom left: Plot of COR offset in X-direction estimated with Method A versus angle of projection. Bottom Right: Plot of COR offset in Y-direction estimated with Method A versus angle of projection. COGX: Centre of gravity X direction, COGY: Centre of gravity Y direction
Figure 4: Top Left: COR offset estimated using Method B for detector 1 in X-direction. Top Right: COR offset estimated using Method B for detector 1 in Y-direction. Bottom Left: COR offset estimated using Method B for detector 2 in X-direction. Bottom Right: COR offset estimated using Method B for detector 2 in Y-direction. COR: Centre of rotationThe three lines in [Figure 5] and [Figure 6] represent the mean of differences-called bias and rest two lines are limits of agreement mean +1.96 SD and mean −1.96 SD. In Figures 5 and 6, only one point lies outside mean + 1.96 SD limit. It is to be noted that the Bland Altman plot system does not say if the agreement is sufficient or suitable to use a method or the other indifferently. It simply quantifies the bias and a range of agreement, within which 95% of the differences between one measurement and the other are included.
Figure 5: Comparison of Method A and B: From left to right: Detector 1, X offset between Method A and Method B; Y offset between Method A and Method B: Detector 2 X offset between Method A and Method B; Y offset between Method A and Method B
Figure 6: Top row: From Left to Right: For detector 1: Comparison of Method A and GE program offset from COGX, Comparison of method B and GE program offset from COGX, Comparison of Method A and GE program offset from COGY and, Comparison of Method B and GE program offset from COGY: Bottom row: From Left to Right: For detector 2: Comparison of Method A and GE program offset from COGX, Comparison of Method B and GE program offset from COGX, Comparison of Method A and GE program offset from COGY and, Comparison of method B and GE program offset from COGY. COGX: Centre of gravity X direction, COGY: Centre of gravity Y directionAfter inspecting the Bland Altman plot [Figure 5] following inferences can be drawn: (a) In comparison to Method A, Method B overestimates the value of COR offset as the mean lies little below the line of equality (indicated by 0 on the Y-axis) when the COR offset was estimated from COGX for detector 1 and detector 2, and (b) in comparison to Method A, Method B underestimates the value of COR offset as the mean lies little above the line of equality (indicated by 0 on the Y-axis) when the COR offset was estimated from COGY for detector 1 and detector 2, (c) all expect one measured value of COR offset was within the limits of agreement indicating very good agreement.
Similarly, after inspection of [Figure 6], the following information can be obtained: (a) In comparison to Method A and Method B (our program), GE program underestimates the value of COR offset as the mean lies little above the line of equality (indicated by 0 on the Y-axis) when the COR offset was estimated from COGX for detector 1 and while for detector 2, GE program overestimated because the mean lies little below the line of equality, and (b) In comparison to Method A and Method B (our program), GE program underestimates the value of COR offset as the mean lies above the line of equality (indicated by 0 on the Y-axis) when the COR offset was estimated from COGY for detector 1 and detector 2, (c) All expect one measured value of COR offset was within the limits of agreement indicating very good agreement.
Our study results show that our program accurately estimates COR shifts in X and Y directions using Method A and Method B given in IAEA-TECDOC-602 on simulated data. Thus, our program can be used as tool for verification of the vendor software that estimates the COR offset in x and y directions.
The COR offset (in mm) in X and Y directions calculated using our program (using Method A) and with the GE software program have been given in [Table 3].
Table 3: Comparison of centre of rotation shift estimated by our program using Method A and with GE softwareThe COR offset (in mm) in X and Y directions calculated using our program (using Method B) and with the GE software program have been given in [Table 4], respectively.
Table 4: Comparison of centre of rotation shift estimated by our program using Method B and with GE softwareThe mean and SD of the time required to process a single set of COR studies were found to be 0.7939372 s and 0.02492115 s, respectively.
Discussion There are a large number of factors that affect the SPECT image quality, including uniformity, resolution, collimation, count rate capability, system COR, gantry and collimator hole angulation, rotational stability of the detector head, and the integrity of the reconstruction algorithm. Accurate COR correction is important for high quality of SPECT images. Inaccurate COR correction can result in artifacts, image degradation, and erroneous values when quantitative analysis is performed.[3] As small as 0.5-pixel errors in COR in a128 × 128 matrix have been reported to cause degradation in image quality.[1] Thus, it is important to use the correct value of COR. Besides this, it is also essential that the COR value remain constant as a function of angle.
Alignment between the computer digital image matrix and mechanical axis of rotation is performed either mechanically or electronically. Mechanical alignment is complex because it requires a level system base, parallel alignment of the detector head and the axis of rotation, absence of sag or excessive flexibility of the gantry, and perpendicular alignment between the collimator holes and the collimator face for parallel hole collimators.[15],[16],[17]
Electronic alignment is performed by making the appropriate adjustment of the X and Y voltage offsets and gains of the positional amplifier to place the centre of the camera crystal at the centre of the computer matrix. If the mechanical and electronic axis of rotations are aligned, then a single COR measurement is applicable for the entire field of view (FOV).[1] A correction for an COR offset error must be made. In modern SPECT systems the acceptable limit for COR offset is ± 1 mm.[2]
For standardization and calibration, there was a need for a software program to estimate the COR offset at the end of each acquisition to see the COR offset is within acceptable limit. In this study, we developed a PC-based software program to estimate COR offset. The program takes the COR projection data (in DICOM file format) as input and produces six plots as the output for each detector. The six plots are: (1) COGX versus Angles (Degrees) Plot [[Figure 3] Top Left], (2) COGY versus Angles (Degrees) Plot [[Figure 3] Top Right], (3) Offset from COGX Plot [[Figure 3] Bottom Left] estimated using Method A, (4) Offset from COGY Plot [[Figure 3] Bottom Right] estimated using Method A, (5) Residual versus Angles (Degrees) which provides offset from COGX Plot [[Figure 4] Top left] estimated using Method B, (6) Residual versus Angles (Degrees) which provides offset from COGY Plot [[Figure 4] Top right] estimated using Method B. The accuracy of the program was verified with simulated projection data and the program was found to deliver the accurate results. The COR offset estimated by our program was in good agreement with the COR offset estimated by GE program as all estimated COR offset values except one, were within the limit of agreement [Figure 5] and [Figure 6].
Bland Altman plots show how far the value we get from our software might be away from the value we get from the GE software. The plot tells us that for a reading from our software, what would be the differences between the two-software reading, with both an average difference-central line-and the 95% confidence interval of the difference-outer lines. The bias is small in the range of 0.01–0.03 mm [Figure 6] when COR offset was estimated from Method A and Method B (from our program) and GE program when estimated from COGX for Detector 1 and Detector 2. Whereas bias is approximately in the range of 1–2 mm [Figure 6] when COR offset was estimated from COGY for Detector 1 and Detector 2. In this [Figure 5] and [Figure 6], only one point lies outside agreement limits indicating very good agreement.
The reason for high variance noted in COGY between Method A and Method B in one of the 24 studies might be the variation in the position of the point source during the acquisition of the COR study. The plot of COGX and COGY versus angle of projection, of the study whose COR offset value was outside the agreement limit on Bland and Altman plot is shown in [Figure 7]. The value of average COGX and average COGY were found to be 128.436549368600 pixel and 135.755448544913 pixel shown by straight red line in [Figure 7]. Ideally expected value of (COGX, COGY) would have been (128, 128) in pixel unit. Thus, there was an error of-7.25544854491272 pixel from the ideal COGY was found in estimation of the average COGY. Since the COR offset estimation is based on the value of the COGY estimated at various angle of projection, thus bias of − 7.25544854491272 pixel (i.e. approximately − 16.0275034991685 mm) was introduced in the COR offset estimated value; and that is why this value appeared as outlier. Rest in all other 23 studies, the value of average COGY was within 1–2 pixels, thus all appeared scattered within the agreement limit of the Bland Altman plot.
Figure 7: Variation of COGX (left) and COGY (right) with angle of projection. COGX: Centre of gravity X direction, COGY: Centre of gravity Y directionAn ideal situation/model would have been that the value of COR offset obtained by our program or GE software gave exactly the same results. However, any measurement of variables (in our case, it is COR offset) may always include some degree of error.
The estimation of COR, in our case is from the data of the acquired image only. It is possible that vendor software might be factoring-in some internal instrumentation related information as well, not available to us. Thus, there is good chance that some difference between the value of COR offset estimated by our Program and GE program would exist. [Table 3] and [Table 4] have been included in the manuscript to detail the differences we found.
Farrell et al. had observed the shift in COR with collimator and have emphasized that the COR must be checked whenever a collimator is changed.[2] Li et al.[18] have developed new algorithm to correct mechanical shift by incorporating mechanical shift into the algorithm for the COR displacement in a cone beam single-photon emission computed tomography. They have evaluated the new algorithm using both Monte Carlo simulated data and experimentally acquired data and demonstrated that the algorithm was able to correct for blurring and the “doughnut” type artifacts caused by system mechanical shift and improve the image resolution.
Cerqueira et al.[1] have tested the variation from the mean COR across the FOV in four different collimators using multiple point source acquisitions and found that the mean COR was different for each collimator and two of the four had a >0.5 pixel difference from the mean COR on some area of the FOV. This variation makes these collimators unacceptable for SPECT acquisition. Their recommendations are: “initial acceptance testing of SPECT collimators should verify a uniform COR across the full FOV and collimators with a variability from the mean COR >0.5 pixels should be rejected.”
Saw has investigated the effects of COR shift of SPECT system on tomographic images.[19] They measured the contrast and spatial resolution variations as a function of COR shift for all shifts <1 pixel, in steps of 0.1 pixels. In addition, the validity of the limit imposed on the allowable COR shift, as utilized in the current SPECT quality control protocols, was examined. The value of either ± 0.5 or ± 0.25 pixels is presently in use as the limit. From this study, both limits result in the loss of resolution. For a COR shift of 0.25 pixels, the spatial resolution loss is approximately 5%. For a COR shift of 0.1 pixels, there is no observed loss of resolution.
Saw have studied the influence of zoom factor on COR and on the resolution of tomographic images.[20] They measured the COR values as function of zoom factor varying from × 1.0 to × 3.0. The COR was observed to shift linearly with zoom factor. The influence of zooming on COR depends on the location and deviation from the COR from the axis of rotation.
Blue have developed simple methods for COR determination so that the technologist can use their simple method for accurately determining the COR that can be used to determine the accuracy of and/or replace the current method of COR determination being used.[21]
Most manufacturers have software designed to analyze the acquisition and determine if the COR is within acceptable limits.
Our program does not provide identical result compared with vendor software. However, based on Bland Altman plot analysis, it was found that the COR offset estimated by our program is in very good agreement with GE software program.
Our program can be used as independent tool to compare the COR measurements across different institutions and within institution across different SPECT gamma camera. Our program can also be used to verify another program which estimates the COR offset from the SPECT projection data considering the procedure of estimation of COR offset given in IAEA-TECDOC 602 document as a gold standard. The test data was not acquired as per IAEA Protocol. The COR Studies used in the study were acquired using the protocol recommended by the manufacture of the Discovery NM 630 SPECT gamma camera. The program was found to provide accurate result on the simulated projection data and also was in agreement with the result produced with vendor program.
The limitation of our program is that it cannot be used to update the estimated COR offset values in the system in order to get the good clinical image. Only the vendor's program can update the value of COR offset in the system. Such corrections by way of other software apart from the vendor's will obviously need a relevant Application Programming Interface (API) provided by the vendor, about which we are not aware.
Use-case of our software
Vendor terminal offers vendor specific correction protocol for COR corrections. Our program can be used to (a) identify a problem and point to a suitable correction step, though, its integration with vendor software will require an open-ended API from the vendor, and (b) help the machine operators (and users) get some insight into the IAEA's standard about COR estimation and correction, which may empower them to look deeper into this or other such activities performed routinely. It may be noted that above mentioned identification and correction will be in offline-mode only (i.e. on stored image data), until there is a possibility of optional integration into vendors terminal software.
Conclusions Our PC-based tool to estimate COR offsets from COR projection datasets using methods mentioned in IAEA-TECDOC-602 was found to be accurate and provides results in agreement with vendor's program. Program can be used as independent tool to estimate COR offset as per method mentioned in IAEA-TECDOC-602, however, cannot be used for correction purpose.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References 
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