Estimation of primary radiation output for wide‐beam computed tomography scanner

Abstract Purpose To estimate in‐air primary radiation output in a wide‐beam multidetector computed tomography (CT) scanner. Materials and methods A 6‐cc ionization chamber was placed free‐in‐air at the isocenter, and two sheets of lead (1‐mm thickness) were placed on the bottom of the gantry cover, forming apertures of 40–80 mm in increments of 8 mm. The air‐kerma rate profiles were measured with and without the apertures (K˙w-A, K˙w/o-A) for 4.8 s at tube potentials of 80, 100, 120, and 135 kVp, tube current of 50 mA, and rotation time of 0.4 s. The nominal beam width was varied from 40 to 160 mm in increments of 40 mm. Upon completion of data acquisition, the K˙w/o-A were plotted as a function of the measured beam width, and the extrapolated dose rates (K˙0-w/o-A) at zero beam width were calculated by second‐order least‐squares estimation. Similarly, the K˙w-A were plotted as a function of the radiation field (measured beam width × aperture size at the isocenter), and the extrapolated dose rates (K˙0-w-A) were compared with the K˙0-w/o-A. Results The means and standard errors of the K˙w/o-A with 40‐, 80‐, 120‐, and 160‐mm nominal beam widths at 120 kVp were 10.94 ± 0.01, 11.13 ± 0.01, 11.22 ± 0.01, and 11.31 ± 0.01 mGy/s, respectively, and the K˙0-w/o-A was reduced to 10.67 ± 0.02 mGy/s. The K˙0-w-A of 40‐, 80‐, 120‐, and 160‐mm beam widths were reduced to 10.6 ± 0.1, 10.6 ± 0.2, 10.5 ± 0.1, and 10.6 ± 0.1 mGy/s and were not significantly different from the K˙0-w/o-A. Conclusions A method for describing the in‐air primary radiation output in a wide‐beam CT scanner was proposed that provides a means to characterize the scatter‐to‐primary ratio of the CT scanner.

for 160-mm wide x-ray beam is now less valid because (a) the beam width exceeds (is wider than) the length of the pencil chamber, (b) the use of just one CTDI phantom is not long enough in z-axis to adequately provide scatter tails from CTDI phantom, and (c) the CTDI vol is not conceptually appropriate for stationary cone beam CT or for perfusion studies or CT fluoroscopy. 3 Additionally, the higher gantry rotation speed also decreases the accuracy of CTDI 100 measurement. 4 .
One of the solutions for the evaluation of radiation output in a wide-beam CT scanner is to use a farmer-type ionization chamber and measure the air-kerma rate free-in-air ( _ K air ) at the isocenter without CTDI phantom. 2,5 Because these measurements are carried out with little scattered radiation, they are utilized not only for the determination of _ K air , but also for characterization of the half-value layer (HVL) 6,7 and the bow tie filter profile. 8 However, since _ K air increases as a function of the beam width while the tube potential and tube current remain constant, it must still include the scattered radiation. 9 Although the reduction in scattered radiation is an important factor for measurement of _ K air , to the best of our knowledge, there have been no published studies extracting the scattered radiation from the measured _ K air . The ionization chamber placed at the isocenter simultaneously detects the primary and the scattered radiation.
The scattered radiation increases as a function of the beam width, while the primary radiation remains constant. Conversely, it can be hypothesized that the contribution of scattered radiation could be removed through extrapolation of _ K air at the zero beam width ( _ K 0 ). 10 Then, the _ K 0 at any beam width would be independent of the beam width and would represent the primary radiation output of the CT system.

2.A | Measurement of x-ray beam width
The x-ray beam width is necessary to extrapolate _ K 0 in this study. It can be determined with conventional film, Gafchromic film, or computed radiography (CR) photostimulable phosphor plate. 11 13 The relation between the CR pixel value and the radiation dose was then investigated.
The CR plate was placed at the isocenter on the patient table   with the lead side down. The radiation exposure was taken under   axial scanning (tube potential 80 kVp, tube current between 10 and   40 mA at 5-mA intervals, rotation time 0.275 s, nominal beam width 80 mm, small focus, and medium bow tie filter). Upon completion of the radiation exposures, the CR plate was processed with a fixed mode with a latitude of 4 and sensitivity of 5 using the AVE4.0 test menu in the CR system to avoid any manipulation of raw data. 12 The CR pixel values at the beam center were measured using ImageJ (National Institute of Mental Health, Bethesda, MD, USA) and plotted as a function of the tube current.
After the relation between the CR pixel value and the tube current was verified for the CR system, the relation between K air and tube current was investigated. A 6-cc ionization chamber (10X6-6, Radcal, Monrovia, CA, USA) calibrated for RQR-5 beam quality was suspended free-in-air at the isocenter of the CT system, and K air was measured under the exact same scanning protocol. Upon completion of these data acquisitions, K air was superimposed on the graph of the CR pixel value at the beam center as a function of the tube current. After applying a logarithmic transformation of K air , the coefficient of determination (R 2 ) for log-linear relationship between CR pixel value and K air was calculated below the saturation level.

2.A.2 | Measurement of radiation profile
After linearity between the CR pixel value and K air had been verified for the CR system, the nominal beam widths of 40, 80, 120, and 160 mm were evaluated. The CR plate was placed at the isocenter on the patient table with the lead side down, and the exposures were taken under axial scanning (tube potential 80 kVp, tube current 10 and 20 mA, rotation time 0.275 s, and bow tie filter medium).
The two-exposure technique was utilized for the determination of full width at half maximum (FWHM), which represents the beam width. 14 The first exposure (20 mA) was taken for determination of the maximum CR pixel value at the beam center. The second exposure (10 mA) was one-half of the first exposure and was performed for determination of the half-maximum exposure level in the first profile. Finally, the FWHM was measured as the distance of the half-maximum CR values in the first profile.

2.B | Estimation of beam width independent in-air radiation output
A 6-cc ionization chamber (10X6-6, Radcal, Monrovia, CA, USA) calibrated for RQR-9 beam quality was employed in this study. The sensitive volume is 38 mm × 25 mmφ, and the sampling rate is 10 kHz.
It was suspended free-in-air at the isocenter of the CT system (see (IEC60601-2-44 ed3.1) was recorded. 15 Because the Accu-Gold electrometer with a 6-cc ionization chamber works as a real-time dosimeter, the profiles can be divided into two phases, with ( _ K wÀA ) and without ( _ K w=oÀA ) the apertures. The _ K wÀA is measured while the x-ray tube passes at the bottom of the gantry where the aperture is located. The _ K w=oÀA is the dose rate while the x-ray tube passes between 7 and 5 o'clock. The _ K w=oÀA and _ K wÀA were determined using the cursor and magnification tool in Accu-Gold2 software.
Upon completion of data acquisition, the _ K w=oÀA were plotted as a function of the measured beam width, and second-order leastsquares estimation was applied to calculate the extrapolated dose rates ( _ K 0Àw=oÀA ) at zero beam width. We also calculated the scatterto-primary ratio (SPR) given as a percentage (%), which is defined as Similarly, the _ K wÀA were also plotted as a function of the radiation field at the isocenter, which was calculated as measured beam width × aperture size at the isocenter. Then, the aperture size at the isocenter was calculated from the geometrical data (focus isocenter distance of 600 mm 2 and bore diameter of 780 mm). Finally, the extrapolated dose rates ( _ K 0ÀwÀA ) were compared with the _ K 0Àw=oÀA .

2.C | Statistical analysis
Tukey's multiple comparison test was used to evaluate the statistical differences among the _ K 0Àw=oÀA and the _ K 0ÀwÀA measured in the CT system. P-values of 0.05 or less were considered to indicate statistically significant differences. All statistical analyses were carried out using the R software package for Windows version 3.5.0 (R Core Team (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria). 16 3 | RESULTS  K wÀA . A 6-cc ionization chamber was suspended free-in-air at the isocenter of the CT system, and two sheets of lead (160 mm × 160 mm × 1 mm) were placed on the bottom of the gantry cover to form apertures (40, 48, 56, 64, 72, and 80 mm). The apertures were set to collimate the radiation beam along the x-axis.

3.A | Measurement of x-ray beam width
The CR pixel value as a function of K air or tube current. CR cassettes (24 cm × 30 cm) in conjunction with a photostimulable phosphor plate were exposed under axial scanning at 80 kVp and rotation time of 0.275 s and were processed with a fixed mode with a latitude of 4 and sensitivity of 5 using the AVE4.0 test menu in the CR system that can avoid any raw data manipulation. It shows a log-linear relationship between the CR pixel value and K air for CT exposure parameters less than or equal to 30 mA (8.25 mAs).
3.B | Estimation of beam width independent in-air radiation output Figure 4 shows the dose rate profile at 120 kVp with 40-mm aperture (x-axis) and 160-mm beam width (z-axis). A rectangular area is magnified to show the _ K w=oÀA and _ K wÀA , respectively (see the inset).
There are 12 _ K wÀA peaks for 4.8 s, and the data in the fourth to eighth rotations were employed to calculate the means and the standard errors of the _ K w=oÀA and _ K wÀA . Figure 5 shows the _ K w=oÀA at 80, 100, 120, and 135 kVp as a function of the measured beam width. The means and standard errors of the _ K w=oÀA with 40-, 80-, 120-, and 160-mm nominal beam widths at 120 kVp were 10.94 ± 0.01, 11.13 ± 0.01, 11.22 ± 0.01, and 11.31 ± 0.01 mGy/s, respectively, and the _ K 0Àw=oÀA was reduced to 10.67 ± 0.02 mGy/s. The CTDI vol , _ K w=oÀA , _ K 0Àw=oÀA , and SPR at 80, 100, 120, and 135 kVp as a function of the nominal and measured beam widths are summarized in Table 1. All _ K w=oÀA , as well as the SPR, were reduced with decreasing beam width. Figure 6 and Table 2 show the _ K wÀA of 40-, 80-, 120-, and 160mm nominal beam widths at 120 kVp as a function of the radiation field at the isocenter. These _ K wÀA were also reduced with decrease in the radiation field, and the _ K 0ÀwÀA were extrapolated as 10.6 ± 0.1, 10.6 ± 0.2, 10.5 ± 0.1, and 10.6 ± 0.1 mGy/s, respectively. These rates did not significantly differ between beam widths and were comparable to the _ K 0Àw=oÀA of 10.67 ± 0.02 mGy/s (no significant differences). However, it is worth mentioning that the standard errors of the _ K 0ÀwÀA are ten times larger than those of the _ K 0Àw=oÀA , because the ionization chamber is exposed during a much shorter time during the _ K wÀA part of the acquisition compared to _ K w=oÀA . The measurement of the _ K 0ÀwÀA is also tedious and timeconsuming compared with measurement of the _ K 0Àw=oÀA .

| DISCUSSION
We measured the _ K 0ÀwÀA and _ K 0Àw=oÀA to verify that the K 0 at any beam width is independent of the beam width in a wide-beam CT scanner. As shown in Tables 1 and 2, the _ K 0Àw=oÀA and _ K 0ÀwÀA at 40-, 80-, 120-, and 160-mm beam widths were not significantly different. From the above examinations, our new technique showed that (a) K 0 indicates the primary radiation output of the CT system, which is independent of the beam width; (b) it can reduce scatter contamination, which affects the accuracy of _ K air measurement; and (c) the _ K 0Àw=oÀA is straightforward compared with the _ K 0ÀwÀA . Additionally, because the unit of the _ K 0Àw=oÀA and _ K 0ÀwÀA is mGy/s, K 0 is F I G . 3. Measurement of 160-mm beam width by the doubleexposure technique. The half-maximum CR pixel value in the first exposure (20 mA) is the maximum CR pixel value in the second exposure (10 mA). FWHM was determined as the distance between the half-maximum CR pixel values in the first exposure (20 mA). FWHM, full width at half maximum.
F I G . 4. _ K air profile for 40-mm aperture (x-axis) and 160-mm beam width (z-axis) at 120 kVp. The inset shows a magnified view of the rectangle on the waveform showing the _ K w=oÀA and _ K wÀA . The _ K w=oÀA is the dose rate while the x-ray tube passes between 7 and 5 o'clock. The _ K wÀA is measured while the x-ray tube passes by the aperture, which is located on the bottom of the gantry. _ K w=oÀA , air-kerma rate without aperture; _ K wÀA , air-kerma rate with aperture.  Beam width measurement is necessary to extrapolate the _ K 0Àw=oÀA and _ K 0ÀwÀA , and we employed the double-exposure technique, the accuracy of which is within the CR system pixel spacing (0.1 mm). 14 The CR system is accurate for determination of the beam width; however, performing the measurement is tedious and time-consuming. Some authors have reported radiation dose profiles measured by a small-cavity ionization chamber or a liquid ionization chamber. 2,9 Unlike image analysis, such as the CR system, these chambers allow simultaneous measurement of both _ K air and the radiation dose profile to obtain the beam width.
The SPR increased as a function of tube potential and beam width, as shown in Table 1. One reason for the increase may be the F I G . 5. _ K w=oÀA at 80, 100, 120, and 135 kVp as a function of measured beam width. These _ K w=oÀA were reduced with decrease in the beam width. _ K w=oÀA , air-kerma rate without aperture.
F I G . 6. _ K wÀA for 40-, 80-, 120-, and 160-nominal beam widths at 120 kVp as a function of the radiation field at the isocenter. These _ K wÀA were reduced with a decrease in the radiation field, and almost the same _ K 0ÀwÀA were also extrapolated. These values did not significantly differ between beam widths and were comparable to the _ K 0Àw=oÀA of 10.67 ± 0.02 mGy/s (no significant differences). _ K wÀA , air-kerma rate with aperture; _ K 0ÀwÀA , air-kerma rate with aperture extrapolated at the zero radiation field at the isocenter; _ K 0Àw=oÀA , air-kerma rate without aperture extrapolated at the zero beam width.
T A B L E 1 CTDI vol , _ K w=oÀA , _ K 0Àw=oÀA , and SPR at 80, 100, 120, and 135 kVp as a function of nominal and measured beam widths. Data are given as means and standard errors. Note that CTDI vol is displayed under scanning at tube current of 50 mA and rotation time of 0.4 s. CTDI vol, volume computed tomography dose index; _ K w=oÀA , air-kerma rate without aperture; _ K 0Àw=oÀA , air-kerma rate without aperture extrapolated at the zero beam width; SPR, scatter-primary ratio.
Tube potential (kVp) probability of Compton scattering in the energy range of diagnostic radiology. The scattered radiation generated in the x-ray tube assembly increases with opening of the collimator. In addition, backscattered radiation from the imaging detector assembly contributes as the beam width is increased. We found that up to 5.8% of the scattered radiation is included in the measurement of _ K air for the widebeam CT scanner. These results are considered to have a minor impact on the estimation of _ K air with 80 mm beam width or less.
However, because the measurement uncertainties are increased as a function of the beam width and tube potential, medical physicists should take the SPR into account for the accurate _ K air measurement with 160 mm beam width at tube potentials of 120 and 135 kVp.
Because the photon energy of the scattered radiation is lower than that of primary radiation, theoretically, the average incident energy at the isocenter is shifted toward lower as the beam width is reported with the small aluminum cage because of scatter contamination in this geometry. Our beam width independent in-air radiation output measurement may also be applicable to reduce the scatter in this geometry. Second, the _ K air was recently used to assess the HVL in a dual-source, dual-energy CT system. 7 Because the two tube potentials were concurrently used for this scanner, the probability of scattered radiation is complicated. Our beam width independent in-air radiation output measurement enables scatter contamination to be analyzed and reduces the uncertainty of the _ K air measurement. This study had some limitations. The length of the 6-cc ionization chamber employed in the study was 38 mm. Therefore, beam widths less than 40 mm could not be measured with this ionization chamber. Bujila et al. used a 0.002-cc liquid ionization chamber to characterize the dose profile along the z-axis. 9 Because the length of the chamber was 0.35 mm, the _ K 0Àw=oÀA and _ K 0ÀwÀA for beam widths less than 40 mm could be measured.
De Denaro et al. reported the radiation dose profile free-in-air along the z-axis measured by Gafchromic film and pointed out the obvious dose gradient (heel effect) along the z-axis. 5 Because the _ K 0Àw=oÀA and _ K 0ÀwÀA indicate only the primary radiation output detected by the ionization chamber, the dose gradient along the zaxis is not accommodated.
Finally, three different bow tie filters can be selected in the CT system. Because the _ K 0Àw=oÀA and _ K 0ÀwÀA indicate the primary radiation output at the isocenter, these indices cannot characterize the peripheral radiation output. At this point, measurement of bow tie profiles using a real-time dosimeter would be a pragmatic approach. 8

| CONCLUSION
A new beam width independent in-air radiation output dosimetry in a modern CT system was introduced. Our new method can (a) measure the primary radiation output of the CT system, which is independent of the beam width; and (b) reduce scatter contamination, which affects the accuracy of _ K air measurement. The new method requires neither the conventional 100-mm-long ionization chamber nor the CTDI PMMA phantoms, but only requires the farmer-type ionization chamber. Our proposed dose index, _ K 0Àw=oÀA , has the potential of providing information about the primary component of CT irradiations which cannot be acquired using other conventional dose metrics.

ACKNOWLEDG MENTS
This work was supported by JSPS KAKENHI Grant Number JP18K15656.

CONFLI CTS OF INTEREST
The authors have no relevant conflicts of interest to disclose.