Applying three different methods of measuring CTDIfree air to the extended CTDI formalism for wide-beam scanners (IEC 60601-2-44): A comparative study.

PURPOSE
The weighted CT dose index (CTDIw ) has been extended for a nominal total collimation width (nT) greater than 40 mm and relies on measurements of CTDIfreeair. The purpose of this work was to compare three methods of measuring CTDIfreeair and subsequent calculations of CTDIw to investigate their clinical appropriateness.


METHODS
The CTDIfreeair, for multiple nTs up to 160 mm, was calculated from (1) high-resolution air kerma profiles from a step-and-shoot translation of a liquid ionization chamber (LIC) (considered to be a dosimetric reference), (2) pencil ionization chamber (PIC) measurements at multiple contiguous positions, and (3) air kerma profiles obtained through the continuous translation of a solid-state detector. The resulting CTDIfreeair was used to calculate the CTDIw , per the extended formalism, and compared.


RESULTS
The LIC indicated that a 40 mm nT should not be excluded from the extension of the CTDIw formalism. The solid-state detector differed by as much as 8% compared to the LIC. The PIC was the most straightforward method and gave equivalent results to the LIC.


CONCLUSIONS
The CTDIw calculated with the latest CTDI formalism will differ most for 160 mm nTs (e.g., whole-organ perfusion or coronary CT angiography) compared to the previous CTDI formalism. Inaccuracies in the measurement of CTDIfreeair will subsequently manifest themselves as erroneous calculations of the CTDIw , for nTs greater than 40 mm, with the latest CTDI formalism. The PIC was found to be the most clinically feasible method and was validated against the LIC.


| INTRODUCTION
Computed tomography (CT) is associated with relatively high radiation doses. The accurate estimation of radiation exposure is therefore a major priority within the medical physics community.
The CT dose index (CTDI) is a ubiquitous dose quantity used in CT. The CTDI represents an approximation of the average absorbed dose in a standard geometry (PMMA cylinder with a diameter of 32 cm for body scans or 16 cm for head scans and a length of approximately 14 cm) in a central rotation, including scatter contributions from adjacent rotations. 1 Since the CTDI represents the average absorbed dose in a standard geometry, it should not be confused with patient dose; however, it does provide useful and comparative information about the output of CT scanners. 2 In practice, the CTDI is determined by integrating the dose profile from a single axial scan along the z-direction, D z ð Þ, and normalizing that integral with the nominal total collimation width (nT) of the scan. When the CTDI was first proposed in 1981 3 and subsequently became a standard dose quantity in CT, 4 it was common with relatively narrow beam CT scanners. In 1999, the International Electrotechnical Commission (IEC) published the European Standard "Particular requirements for the safety of X-ray equipment for computed tomography" where the integration length of the CTDI was fixed to z ¼ AE50 mm (CTDI 100 ) and it also stated that D z ð Þ should be measured in air kerma (K air ). 5 A 100-mm pencil ionization chamber is appropriate to use according to this definition of the CTDI. In that same European Standard, equations for calculating the weighted CTDI (CTDI w,100 ) from central and peripheral CTDI 100 measurements in the reference phantoms is given. The CTDI w,100 represents the average CTDI 100 across a reference phantom in the axial plane. 4 Nowadays, there are CT scanners with wide-beam geometries that facilitate axial scans with a detector coverage up to 160 mm in a single a rotation. This technique allows for entire organs to be obtained in a single volume with short acquisition times (commensurate with the CT scanner's rotation time). This type of scanning is useful when imaging dynamic processes including, among other types of studies, brain perfusion, as well as coronary CT angiograms. 6,7 Take note that perfusion scans often require many passes and the accumulated radiation doses can be high.
Boone calculated the CTDI efficiency e CTDI ¼ CTDI100 CTDI1 for a number of nTs in both the reference head and body phantoms and found that the CTDI 100 underestimated CTDI ∞ appreciably, even for narrow nTs, due to the truncation of D z ð Þ; the underestimation becomes more apparent as nT increases. 8 For that reason, applying the first definition of the CTDI to scans with wide nominal total collimation widths would severely underestimate the radiation output of a widebeam acquisition.
In order to provide more accurate determinations of the output of CT scanners with wide nTs, Geleijns et al. 9 proposed extending the integration length of CTDI measurements by using a 300-mm pencil ionization chamber and 350-mm wide reference phantoms (CTDI 300 ) for scanners with wide nTs; however, this method never saw widespread adoption in clinic practice. In its third edition of the aforementioned European Standard, the IEC modified the definition of the CTDI 100 (to accommodate widebeam scanners) as the integral of D z ð Þ (100 mm integration length) normalized by nT or 100 mm, whichever is less. 10 This definition of the CTDI 100 has been shown to approximate the CTDI 300 within AE10% for both the reference head and body phantoms for a wide range of tube voltages and shaped filters with an nT of 160 mm. 9 In the third edition of the European Standard, the IEC also defined the CTDI free air as the CTDI 100 measured in the center of the axial plane without a phantom. 10 In 2012, the IEC further modified the definition of the CTDI 100 for nominal total collimation widths that exceed 40 mm, in a first amendment to the third edition of its European Standard. 11 It should be noted that for nominal total collimation widths that are less than or equal to 40 mm, the definition of the CTDI 100 remains the same as previous editions of the European Standard. The redefinition of the CTDI 100 for wide beams utilizes the assumption that the ratio of CTDI free air (with appropriate integration lengths to capture D z ð Þ) between two nominal total collimation widths is equal to the ratio of CTDI 100 with the same nTs. 12 Using this relationship, the CTDI 100, nT>40 mm is approximated by multiplying a measured CTDI 100,nT≤40 mm with the ratio of CTDI free air;nT [ 40 mm and CTDI free air;nT 40 mm .
To the best of our knowledge, no one has compared different methods of measuring CTDI free air and their subsequent calculation of the CTDI w per the extended formalism. The purpose of this work was to use three different methods of measuring CTDI free air and apply those measurements to the latest amendment of the IEC Standard, 11 for a range of nTs up to 160 mm. The CTDI free air was first determined using an advanced method, high-resolution step-andshoot translation of a liquid ionization chamber, which is considered to be a dosimetric reference. The advanced method was compared to more clinically feasible methods of determining the CTDI free air , namely, (1) using multiple contiguous positions to extend the integration length of a 100-mm pencil ionization chamber and (2) continuous translation of a real-time solid-state detector.

2.A | CTDI formalism
When first proposed, the CTDI was defined as, where D z ð Þ is a dose profile along the longitudinal axis, z, centered at z = 0. The number of detector channels and the width of each channel are n and T, respectively. 3 Note that nT represents the nominal total collimation width of the scan and in the early days of CT it was common with single slice scanners (n = 1). In the first edition of IEC 60601-2-44, 5 the CTDI was defined for an integration length of 100 mm as, In that same edition of the IEC standard, the weighted CTDI was defined as, where c and p denote measurements of the CTDI 100 in the central and peripheral holes of the CTDI reference phantoms, respectively.
In practice, the CTDI 100,p is the mean CTDI 100 from the four peripheral holes in the reference CTDI phantoms. In the first amendment to the third edition of IEC 60601-2-44, 11 where the subscript ref represents a reference nT that is equal to or less than 40 mm. In that same European Standard, 11 the CTDI measured in free air was defined as, where L is at least the nT of a single scan plus an additional 40 mm divided on both sides (nT þ 40 mm). Furthermore, it is stated that the CTDI free air should not be calculated with an integration length below 100 mm. 11 Contemporary CT scanners are obligated to present the volume CTDI (CTDI vol ) in accordance with the first amendment to the second edition of IEC 60601-2-44. 13 The CTDI vol accounts for

2.B | CT scanner
All measurements were made on a Revolution CT (GE Healthcare, Waukesha, WI, USA). In addition to this scanner being able to perform volume scans with nTs up to 160 mm, the CTDI is reported with the formalism from the first amendment to the 3rd edition of IEC 60601-2-44 in the scanner's latest software releases (since version 15MW43.x). The technique parameters used in this study, Table 1, reflect parameters that are given in the acceptance testing section of the scanner's Technical Reference Manual (TRM). 14 All measurements were made in clinical mode. Note that the reference nT in Eq. (4) is 5 mm on this scanner.

2.C | Determination of CTDI 100,nT,w
In this work, the CTDI 100,nT>40 mm , Eq. (4), is calculated using CTDI free air;nT that is measured with three different measurement systems. The three different measurement systems used to obtain CTDI free air;nT are subsequently used to determine CTDI 100,nT,w . The packaged LIC was coupled to a linear actuator that provided a stepwise translation in the longitudinal direction with a positioning accuracy better than 0.2 mm. Prior to the air kerma measurements, the carbon fiber rod was extended fully (500 mm) and a 160-mm volume scan (256 images) was taken to ensure that the stepwise translation was centered (x = 0, y = 0) and was free from rotational pitch and yaw (rotation about the x-and y-axes of the scanner, respectively). Depending on the nT, different profile lengths and step intervals were used (see Table 2). The profile measurements did not have equal step intervals, the interval was tighter at locations where the air kerma varied greatly, at, for example, step locations in the BUJILA ET AL. The type A uncertainty associated with this method was estimated by measuring 5 air kerma profiles using the technique parameters in Table 1 and a 5-mm nT. The number of measurement points was reduced to 40 and covered a length of 100 mm (À50 mm to 50 mm). The step interval was adapted to parts of the profile that increased or decreased rapidly. It would not have been feasible to estimate the type A uncertainty for all nTs.  Table 3. These recommended positions from IAEA are consistent with recommendations by Platten et al. 16   Using the same measurement method that was employed for the CTDI 100; 5 mm;w , the CTDI 100; nT;w was measured for the remainder of the collimations according to the third edition of IEC 60601-2-44, 10 where nT in Eq. (2) is equal to the nT or 100 mm, whichever is less.
Measurements of the CTDI 100; nT;w are compared using both the third edition and the first amendment to the third edition of IEC 60601-2-44. 11

| RESULTS
The air kerma profiles that were obtained using a step-and-shoot methodology with the LIC is presented in Fig. 3(a). Figure 3(b) presents air kerma profiles that were obtained using the continuous translation of the CTDP (solid-state detector). Note that the air kerma profiles in Fig. 3   The CTDI 100; nT;w was calculated with Eq. (4) using the CTDIfree air;nT CTDIfree air;ref ratios (Table 4) measured with the three different methods in this study. These results of the CTDI 100; nT;w are presented in Table 6.
Equation (4) is intended for nTs greater than 40 mm. For that reason, CTDI 100; nT;w for nTs of 5 and 40 mm are not presented in Table 5. Take note that the CTDI 100; nT;w , for an nT of 5 mm, (Table 5) is used as the CTDI 100; ref;w for the calculations presented in Table 6. Alongside the CTDI 100; nT;w in Table 6, expectation values from the scanner's TRM have also been included. There is a slight The greatest difference between any of the PIC, LIC, and CTDP measurements in Table 6 to the scanner's TRM is À7.5% for the PIC (IAEA Positions), with an nT of 120 mm. The greatest difference between any of the PIC results, both GE and IAEA positions, compared to the LIC results in Table 6 is 0.8%. However, the greatest difference between any of the CTDP results compared to the LIC results in Table 6 is 4.5% with an nT of 160 mm.
The relative standard uncertainty of CTDI free air; nT for the PIC and CTDP measurements steadily decreased as the nT increased. Take note, the relative standard uncertainty of CTDI free air; nT that required multiple PIC positions was calculated using a standard error propagation. The PIC measurement method, both the GE and IAEA positions, had a relative standard uncertainty between 0.04 and 0.01% for all nTs. The CTDP method had a relative standard uncertainty between 0.6 and 0.1% for all nTs. The relative standard uncertainty for the LIC method was estimated to be 0.2% for an nT of 5 mm. For nTs greater than 5 mm, the uncertainty is expected to be lower, since there are more measurement points along the air kerma profiles (better statistics).

| DISCUSSION
In this work, different methods of measuring CTDI free air;nT have been investigated and subsequently used to calculate the CTDI w; nT for F I G 3 . Air kerma profiles along the z-direction for different nominal total collimation widths (nT) using (a) LIC and a step-and-shoot methodology and (b) CTDP and a continuous translation with the RTI Mover. of the CTDI free air to the LIC (within 2%), the CTDP method consistently yielded results that were 6%-8% higher than the LIC for nTs greater than 40 mm. Table 5 shows that for nTs that are less than 100 mm, the CTDI 100; nT;w decreases as nT increases, which is consistent with the third edition of IEC 60601-2-44. 10 When the nT is greater than 100 mm, the CTDI 100; nT;w increases as the nT increases. This can be attributed to the CTDI phantom only having a length of 14 cm. As the nT increases, more and more scatter will contribute to the air kerma that the pencil ionization chamber measures. However, the normalization factor (nT) in Eq. (2) will remain constant (100 mm) for nTs greater than 100 mm. With the first amendment to the third edition of IEC 60601-2-44, 11 the CTDI 100; nT;w continues to decrease as the nT increases above 100 mm. Comparing the third edition with the first amendment to the third edition of IEC 60601-2-44 shows that there will be a slight increase in CTDI 100; nT;w for an nT of 80 mm (+5%) and a decrease in CTDI 100; nT;w for an nT of 160 mm (À19%) when using the latest definition of the CTDI 100; nT;w with the LIC and PIC methods. However, the difference is +7% (80 mm) and

T A B L E 4 The ratio
À14% (160 mm) for the CTDP method. The values from the TRM for the different versions of the CTDI formalism yields +7% (80 mm) and À20% (160 mm). A difference of À20% between the measured CTDI 100; nT;w and the CTDI 100; nT;w displayed on the scanner's console is considered to be a trigger to take remedial action by the Nordic Association of Clinical Physicists (NACP). 17 It is important to reflect upon that even though the CTDI 100; nT;w may decrease by 19% using the latest CTDI formalism and an nT of 160 mm, the exposure to the patient (and image quality of the examination) will remain the same using the previous CTDI formalism. This should be considered when optimizing, for example, wholeorgan perfusion protocols where the accumulated radiation doses can be high. In the context of patient dose, the CTDI metric has disadvantages in specificity with regard to characterizing the x-ray beam and the individual patient undergoing an examination. However, the evolution of applied CT dosimetry is built upon the CTDI, most notably in the form of size-specific dose estimates (SSDE). 18,19 It is therefore important to continue discussing the theoretical and practical aspects of the CTDI. Further refinements of CT dosimetry, beyond the SSDE, where the x-ray beam characteristics and contributions from scattered radiation are completely taken into account will require new reference geometries and more detailed descriptions of exposure. 20 Each of the measurement methods was associated with a relatively low type A uncertainty (below 1% for the CTDP method, below 0.2% for the LIC method and below 0.05% for the PIC method). However, this uncertainty evaluation does not factor in uncertainties in, for example, air kerma calibration factors. In the scope of this work, the step-and-shoot method of acquiring air kerma profiles with the LIC is considered to be the most accurate method that was used to obtain CTDI free air;nT for the range of nTs, both dosimetrically and spatially. The LIC has appreciable energy dependence when compared to other instruments, such as pencil ionization chambers, over a range of radiation qualities. However, the LIC used a calibration (RQT-9), which closely matches the radiation quality that was used during the measurements. The HVL associated with the RQT-9 radiation quality is 8.7 mm Al and the HVL along the central ray of the Revolution CT for 120 kVp with the Large shaped filter is 7.6 mm Al. 14 Table 4), as well as the expectation value in the scanner's technical documentation. 14 Note that the integration length of CTDI free air;nT for the LIC method was 300 mm compared to 100 mm (one position) using the PIC. Calculating CTDI free air;nT with the LIC, but using a 100 mm integration length (À50 to 50 mm) yields a value of 74.44 mGy or alternatively a CTDIfree air;nT CTDI free air;ref ratio of 0.62 (the same ratio that was measured using the PIC). Extending the integration length of CTDI free air for the 40 mm collimation to 200 mm using 2 PIC positions (À50 and 50 mm) yields a value of 76.94 mGy or a CTDI free air;nT CTDIfree air;ref ratio of 0.63 which is closer to the value that was obtained using the full integration length (300 mm) of the air kerma profile for the LIC measurement. This could possibly indicate that an integration length of 100 mm for CTDI free air measurements for a 40 mm collimation might not include the entire air kerma profile along the longitudinal direction. The additional contribution to the CTDI free air;nT that was observed when using an air kerma profile integration length greater than 100 mm, for the 40 mm nT, can be caused by several factors including the geometric efficiency (actual beam width is wider than the nominal total collimation width), extra focal radiation, as well as penetration of radiation through the collimator edges.

| CONCLUSION S
As CT is associated with relatively high radiation doses, it is therefore important for medical physicists to be able to accurately estimate the output from CT scanners. If the radiation output from a scanner is erroneously measured or reported, this could inadvertently lead to unnecessary radiation exposure or degraded image quality, both having unintended consequences. An amendment to the third edition of IEC 60601-2-44 has been made to further extend the concept of the CTDI w to CT scanners with nominal total collimation widths (nT) greater than 40 mm. This amendment has recently been implemented on certain CT scanners and clinical Medical Physicists need to update their measurement methodologies accordingly. The amendment relies on measurements of CTDI free air with integration lengths that exceed the length of a standard 100mm pencil ionization chamber. In this work, three methods of acquiring air kerma profiles to calculate the CTDI free air , for a range of nTs, were implemented and subsequent calculations of the CTDI w were compared. The measurement methods consisted of: 1. high-resolution air kerma profiles using a step-and-shoot translation of a liquid ionization chamber (considered to be a dosimetric reference), 2. the sum of multiple 100-mm pencil ionization chamber measurements where the chamber is placed at different contiguous locations in the z-direction, 3. continuous translation of a real-time solid-state detector.
The liquid ionization chamber results suggested that the latest CTDI formalism should also be extended to a nTs of 40 mm. The CTDI w calculated with the latest CTDI formalism was found to differ by À20% compared to the previous CTDI formalism, for an nT of 160 mm (used in, e.g., whole-organ perfusion); however, it is important to consider that the radiation exposure to the patient and the image quality of the examination will remain the same, using the latest CTDI formalism. The real-time solid-state detector method provided results that differed by as much as 8% (CTDI free air Þ compared to the liquid ionization chamber method. The pencil ionization chamber was considered to be the most clinically feasible method that was tested and provided results that closely matched, within 2%, the liquid ionization chamber method (dosimetric reference).

CONF LICT OF I NTEREST
Love Kull is a majority shareholder in LoniTech AB. Mats Danielsson has a research collaboration with GE Healthcare and is a shareholder in Prismatic Sensors AB. The remaining authors have no conflicts of interest.

ACKNOWLEDGMENTS
We thank the Department of General Radiology at the Karolinska University Hospital for allowing us to acquire measurements on their scanner. We thank the Swedish National Metrology Laboratory for assistance in calibrating the pencil ionization chamber and the liquid ionization chamber as well as GE Healthcare and RTI Electronics for helpful discussions about their equipment.