Comparison of methods to estimate water‐equivalent diameter for calculation of patient dose

Abstract Modern CT systems seek to evaluate patient‐specific dose by converting the CT dose index generated during a procedure to a size‐specific dose estimate using conversion factors that are related to patient attenuation properties. The most accurate way to measure patient attenuation is to evaluate a full‐field‐of‐view reconstruction of the whole scan length and calculating the true water‐equivalent diameter (D w) using CT numbers; however, due to time constraints, less accurate methods to estimate D w using patient geometry measurements are used more widely. In this study we compared the accuracy of D w values calculated from three different methods across 35 sample scans and compared them to the true D w. These three estimation methods were: measurement of patient lateral dimension from a pre‐scan localizer radiograph; measurement of the sum of anteroposterior and lateral dimensions from a reconstructed central slice; and using CT numbers from a central slice only. Using the localizer geometry method, 22 out of 35 (62%) samples estimated D w within 20% of the true value. The middle slice attenuation and geometry methods gave estimations within the 20% margin for all 35 samples.


| INTRODUCTION
The volumetric Computed Tomography Dose Index (CTDI vol ) provided by CT scanners is a calculated quantity representing the dose delivered to a standardized, homogeneous calibration phantom of a specified size based on CT parameter settings used during the scan. 1 Because the CTDI vol does not account for an individual patient's size or attenuation properties, it therefore is not a direct measurement of the absorbed dose delivered to a patient. 2 To address this, the size-specific dose estimate (SSDE), which modifies CTDI vol using a factor related to patient size, was introduced by the American Association of Physicists in Medicine (AAPM) in 2011. 3 As part of this effort, the AAPM Task Group 204 developed size-specific conversion factors (k) to better estimate patient radiation absorption properties and size-specific doses. These conversion factors are multiplied by CTDI vol to obtain the SSDE. Members of AAPM Task Group 220 4 further developed the technique by using the attenuation of x rays through the body, as measured by the CT scanner, to calculate patient water-equivalent diameter (D w ), the diameter of a cylindrical volume of water with equivalent mean attenuation. D w is a more precise metric of body size for the selection of a conversion factor because it accounts for radiation absorption directly by using attenuation information. 5,6 D w may be calculated directly from a full-field-of-view reconstruction, 7 or estimated using the geometric measurement methods of TG204. Geometric estimation requires the use of additional corrections based on the body region scanned to account for differences in attenuation of abdominal and thoracic anatomy. Calculation of D w using reconstructed attenuation values is more patient-specific and uses data directly relevant to the metric of interest. It is therefore the preferred method for determining the appropriate conversion factor. 4 The reconstructed region is ideally the full scan range, though Leng et al. showed that D w calculation from a central slice can be an acceptable substitute. 8 Anam et al. demonstrated that a fully automated image processing and D w calculation method can match manual calculation across a range of scan regions in both phantoms and human patients. 9 The purpose of this paper is to compare D w values from three estimation methods to a reference standard D w value calculated using a full-field-of-view, full scan range reconstruction. The first

2.A | Selection of image data sets
CT scan data from 35 sets of anonymized patient scan images were used to test each calculation method. Of these data, 18 were abdomen scans and 17 were thorax scans. The selected scans had a localizer radiograph with no truncation of tissue. Sets of axial "noncontrast" or "soft tissue" slices were used for attenuation analysis.
Slices were mostly from full-field-of-view reconstructions, with a few exceptions that had a small amount of skin truncation.

2.B | Calculation and comparison of D w values
Calculation of D w values using the whole scan range and center-slice attenuation methods, as well as the center-slice geometry method, was carried out by scripts written in MATLAB (Natick, MA). D w values from a localizer geometry method developed by Philips Healthcare (Andover, MA) were also compared.
Each method used involved the use of an edge detection image analysis algorithm to separate patient anatomy from background structures such as the table and padding. In each MATLAB script, Sobel edge detection was used, as shown in Fig. 1. The threshold for determining the pixel value difference that defined the outside of the patient was varied by data set and edge detection was inspected visually to confirm that it matched the visual border. The localizer analysis process was not available and proper edge detection could not be confirmed.

2.B.1 | Implementation of attenuation measurement methods
Each pixel in a reconstructed image contains information of the attenuation (attenuation coefficient l) of x rays through the corresponding volume in the form of a CT number. AAPM TG220 4 outlines a method for using these data to calculate D w , which is an ideal metric for estimating a patient's radiation absorption properties because it uses the patient's attenuation information directly.
CT numbers are defined relative to the attenuation coefficient of water, so they can be used to calculate the cross-sectional area (A w ) of a cylinder of water with average attenuation equivalent to that of the body in the analyzed slices [eqs.
In these equations, l water and lðx; yÞ are the attenuation coefficients of water and of the tissue in the voxel denoted by the coordinates (x, y) of the slice, respectively. A pixel is the area of one pixel, recorded in the DICOM data, and A ROI is the area of the region of interest, determined by image analysis. CTðx; yÞ is the CT number of voxel (x,y), and CTðx; yÞ is the average CT number value of the slice.
D w is then related to a correction factor using tables from AAPM Task Group 220. 4 The reported patient D w is the average D w of all slices of the desired analysis range.

Full scan range attenuation measurement
The reference method, to which the three other estimation methods were compared, used attenuation data from all slices along the full scan length. Using complete attenuation information from the whole scan provided the most accurate D w value. The D w of each slice was DAUDELIN ET AL.  The processing of each image using this method was not observed in this study. Only the initial localizer image and the final D w value were available.

2.C. | Comparison of methods
Estimation method D w values and the reference D w obtained using the full scan attenuation data were compared directly using the mean difference (signed) and mean absolute difference (positive).
The distribution of each set of differences was compared using a nonparametric two one-sided test of equivalence (TOST) adopted from Mara et al. 11 and carried out using Microsoft Excel. A TOST does not assume no difference as the null hypothesis, but rather presents the burden of proving equivalence. TOSTs can also indicate whether a method has a bias upward or downward compared to the reference method. The TOST provides left-side and right-side zscores, for which values greater than 2.58 correspond to significant results (P < 0.01). Both sides must show significance to conclude equivalence within a specified margin.
Task Group 220 stated that D w calculation using attenuation data from a localizer radiograph should be within 20% of the reference value. 4 We use this 20% margin as the basis for comparison between estimated D w values and the reference value, as well as for the equivalence margin of the two one-sided test.

4.A.2 | Availability of complete attenuation information
In clinical situations, a physician may only require reconstruction of a small internal region. When a reconstruction of the patient along the whole scan range is not available, the method of calculating D w from attenuation data will not yield an accurate result. Using the attenuation data from an incomplete reconstruction will produce a smaller D w , and overestimate the final SSDE value. A localizer radiograph image of the full scan area is always available, so a method that accurately estimates patient size using this image would not be subject to truncation issues.
Any D w estimation method that averages data or uses a smaller data set to represent the whole is susceptible to inaccuracy when analyzing a patient with large variations in anatomical shape along the scan range. A method that measures one to three central slices is especially vulnerable to this error, so caution should be taken when dealing with such cases.

4.B | Impact of measurement inaccuracy on SSDE
Error in SSDE increases with the error of the measured value used to determine the CTDI vol -to-SSDE conversion factor. However, conversion factors given by tables in TG220 scale differently depending on the dimension that is considered. Figure 6 shows how the percent difference between consecutive conversion factors changes with the value of the measured dimension. These differences accumulate when measurement error is >1 cm.  Potential errors under 10% may not be worth considering in a clinical setting, but methods that can incorrectly measure patient dimensions by many centimeters introduce substantial error in dose estimation.

| CONCLUSIONS
This study demonstrates that D w estimation methods using the geometry or attenuation data from a central, full-field-of-view reconstructed slice consistently produce results within 20% of their reference values and comply with the guidelines set by TG220. However, the localizer radiograph geometry method resulted in a considerable number of scans (13 of 35, 37%) that deviated by more than 20% of the reference value. The authors suggest that edge detection methods employed by localizer radiograph geometry methods should be fully evaluated prior to implementation in a clinical setting.
Although the method using reconstructed images are more accurate, full-field-of-view reconstructions are not always available, and incomplete reconstructions can lead to SSDE overestimation. Localizer geometry-based methods do not calculate D w exactly, but a proper implementation could produce sufficiently accurate dose estimates using the localizer radiograph, which is already available, while avoiding outliers caused by varying reconstruction practices. This is especially true for smaller patients, since there is less variation in SSDE conversion factors at low values of the lateral dimension when it is the sole metric for patient size. When both AP and LAT localizer images are available, a localizer geometry analysis method could meet or exceed the accuracy of a central slice geometry method, which is already highly accurate for patients with uniform anatomy.

CONFLI CTS OF INTEREST
Andrew Daudelin was a paid intern of Philips Healthcare (Andover, MA), which provided data from their localizer radiograph analysis method, during this study. Chris Martel is an employee of Philips Healthcare.