Technical Note: Model-based magnification/minification correction of patient size surrogates extracted from CT localizers

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1 Technical Note: Model-based magnification/minification correction of patient size surrogates extracted from CT localizers Christiane Sarah Burton Department of Radiology, University of Wisconsin-Madison, 1111 Highland Avenue, Madison WI 53705, USA Annie Malkus Department of Medical Physics, University of Wisconsin-Madison, 1111 Highland Avenue, Rm 1005, Madison WI 53705, USA Frank Ranallo Departments of Medical Physics and Radiology, University of Wisconsin-Madison, 1111 Highland Avenue, Madison WI 53705, USA Timothy P. Szczykutowicz a) Departments of Radiology, Medical Physics, and Biomedical Engineering, University of Wisconsin-Madison, 1111 Highland Avenue, Madison WI 53705, USA (Received January 018; revised August 018; accepted for publication 11 September 018; published 0 November 018) Purpose: Patient size-specific dose estimate (SSDE) calculations require knowledge of a patient s size. Errors in patient size propagate through SSDE calculations. AAPM Reports 04 and 0 recommend that a magnification correction be applied to patient size surrogates extracted from CT localizer radiographs. This technical note presents a novel approach for such a magnification correction. Methods: In our model-based magnification correction, we assume that the patient s cross sections are elliptical with minor and major axes defined using the anterior posterior (AP) and lateral (LAT) patient dimensions. We parameterize the problem by modeling a line emanating from the source, grazing the patient (i.e., the ellipse), and then terminating onto the detector plane. We model tangent lines on each side of the ellipse on both the LAT and AP CT localizer radiographs. We also account for vertical mispositioning with table offset. We compared our correction model to the actual AP and LAT dimensions to the vendor-supplied CT localizer images that only received a geometric magnification correction, and to other methods described in the literature. We compare our model to the others using direct size to size comparisons as well as SSDE conversion factor. Results: Our model-based method provides consistent accurate results (less than 1.8 error for absolute size and 1. error for SSDE for all measurement conditions) for all positions and patient sizes. Existing literature-based methods had maximum errors for absolute size and SSDE of 7.5 and 5., and for the vendor, they were 30.9 and 17.0, respectively. Conclusion: We presented a new model-based geometric size correction method that outperforms a simple geometric correction as well as other methods presented in the literature. By modeling the patient cross section and beam geometry using information all derived from the DICOM header and CT localizer views, we demonstrated SSDE correction factor improvements from 17.0 (vendor correction) to 1. (model base). These changes correspond directly into changes in SSDE itself and also represent clinically realistic patient sizes and mispositioning amounts. 018 American Association of Physicists in Medicine [ Key words: CT Localizer radiograph, SSDE, Geometric Magnification, CT Dose 1. INTRODUCTION The size-specific dose estimate (SSDE) uses a normalized dose coefficient to scale the CTDIvol and this scale depends on the patient s body size. Therefore, having an accurate estimation of SSDE depends on having and accurate estimate of the patient size. The dose received by the patient depends on the scanner output and on the patient s size. Turner et al. 11,1 demonstrated that by using CTDIvol as a normalization factor, organ dose estimates can be obtained for a specific patient size, 11 and the relationship between normalized dose and patient size was consistent across scanner models. 1 Hence, obtaining accurate information about patient size is crucial for estimating patient dose in CT. To determine the size-specific dose estimate (SSDE), the American Association of Physicists in Medicine (AAPM) Task Group (TG) Report 04 states that patient size be measured based on their dimensions including anterior posterior pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (AP), lateral (LAT), and effective diameter ð LAT APÞ. Estimating patient surrogates from axial CT images can only be performed after the CT scan is finished and tomographic images are reconstructed. However, knowledge of patient size may be desirable in order to calculate SSDE prior to tomographic scanning or in cases when only CT localizer radiograph 165 Med. Phys. 46 (1), January /019/46(1)/165/8 018 American Association of Physicists in Medicine 165

2 166 Burton et al.: CT localizer size correction 166 images and dose information are available such as with the American College of Radiology (ACR) dose index registry. AAPM TG Report 0 6 recommends that to accurately estimate AP and LAT from CT localizers (might also be referred to as Scanned Projection Radiograph, SPR) 10,13,14 a magnification/minification correction should be applied. To our knowledge, all known magnification correction methods proposed including the magnification correction believed to be used by all vendors are illustrated in Fig. 1. The vendor correction is a simple geometric magnification correction which assumes that the patients widest width is located at isocenter and that they have a thickness of zero extent. With these assumptions, the vendor correction is simply a similar triangles based on SID over SOD correction. Where SOD stands for source to object distance which is the difference from the source to the center of the idealized ellipse. The SID represents the source to image/detector distance. Therefore, the vendor applies the same magnification/ minification scaling factor to all images regardless of their actual position within the gantry. Methods by Christensen, 4 Li et al., 5,10 and Raupach et al. 9 (also implemented by McMillan et al. 7 ) aim to modify the vendor correction scheme by estimating the actual patient position within the gantry in order to obtain a true SID over SOD correction. This is commonly accomplished by assuming that the patient s center is offset from isocenter along the y-direction (same orientation as AP, shown in Fig. 1) by an amount determined using the table height and patient thickness. The patient thickness term allows the distance between the center of the patient and the table top to be taken into account. While the methods essentially use the same equation, they differ in their processing methods needed to obtain the table height and projected patient thickness (AP dimension). For example, Li et al. 5 use an orthogonal CT localizer radiograph to estimate the table height and correct for patient miscentering relative to the isocenter. Raupach et al. 7,9 estimate the lateral dimension taking into account the DICOM table height field to modify their geometric magnification as Li et al. did. The commonality of these methods is that they do not model the actual intersection of the x-ray beam with the patient (as shown in Fig. 1). These methods assumption of the x-ray intersecting the patient at their widest extent, solely defined using the knowledge of table height and patient thickness, is incorrect. This paper will investigate the effect of assuming a patient to be a flat line, and the x-ray beam first intersecting the patient at their widest point to provide a new model-based magnification/minification correction scheme as shown in Fig. 1. y x Christensen 1990 Raupach et al. 007 Li et al. 01 Vendor Model-based x 1, y 1 Isocenter Phantom Grazing occurs at this y value x, y FIG. 1. Illustration of the difference in lateral projections between the modelbase, Christensen , Raupach et al. 9, and Li et al. 5, and the vendor s geometric magnification correction approaches. In this illustration, the patient s major cross section defined by LAT is not located at isocenter. The table height, h, is defined here as the difference between the table top and isocenter. The vendor assumes that the patient s lateral dimension is located at isocenter. Previously reported geometric correction methods allow the maximum patient lateral dimension to be at a table position other than isocenter, but do not model the nonzero patient thickness (here defined by AP). Our model-based approach models the patient as an ellipse (or circle if AP = LAT) with a line representing x rays emanating from the source striking the first point of contact on the patient (grazing) and striking the detector which in the CT localizer image would be the edges of LAT M. [Color figure can be viewed at wileyonlinelibrary.com]. MATERIALS AND METHODS In our model-based magnification correction, the patient is assumed to have an elliptical cross section. We assume that there exists an x-ray line path that emanates from the source which touches the ellipse at only one point on each side of the patient and intersects the detector plane. We call this point of contact between the x-ray beam and the patient as grazing as shown in Fig. 1. Table I describes our method for obtaining the true lateral and anterior posterior patient TABLE I. Previously reported magnification correction methods and our model-based approach. In the publication by Li et al., the addition of a square root was an error in the original paper and that has been corrected here. The model-based method lists the general solution to the intersection between a line characterized by the focal spot and edge of the patient s extent on a localizer view and the patient parameterized by their offset from isocenter and extent in the vertical and horizontal directions. See the Section 6 for more details on the model-based method. Method Inputs Equations Geometric SID/ SOD Christensen/ Raupach/ Limethods Model-based (present study) SOD, SID h, SOD, AP M h, SOD, AP M ; LAT M LAT ¼ LAT M SOD SID LAT ¼ LAT SOD ðh 1 APMÞ M SOD System of equations for the intersection of a line (i.e., x-ray projection grazing the patient as shown in Fig. 1) and an ellipse (i.e., the patient parametrized by an offset from isocenter calculated using the table height and the AP thickness with major and minor dimensions given by the LAT and AP dimensions)

3 167 Burton et al.: CT localizer size correction 167 thicknesses. The full mathematical description is given in Section 6. Variables AP M and LAT M (M meaning measured from the CT localizer with the vendor s SOD SID correction applied) are measured from the CT localizer radiograph using digital calipers (ImageJ, National Institutes of Health, Bethesda, MD, USA), and AP and LAT are the true dimensions. In Section 6, we also describe a source of error inherent to measuring flat objects in a flat plane using a curved detector. We experimentally validated our model-based method by imaging three phantoms with known dimensions at various table heights. The three phantoms included: (a) a 30 mm CTDI phantom, (b) a 15 mm cylindrical water phantom, and (c) a 3: ratio elliptical phantom with three differently sized regions: large 350 and 33 mm, medium 300 and 00 mm, and small 50 and mm, respectively, for the major and minor phantom diameters. 8 In our experimental validation, we kept all phantoms centered in the lateral direction while varying the table height in the y-direction. The images in this study were acquired using a 64 slice MDCT scanner (Discovery HD 750, GE Healthcare, Chicago, IL, USA). There are vendors where TCM is directly affected by patient centering, and others that are not. The accurate size calculation of the patient from the CT localizer may be more important for SSDE calculations than TCM control for some CT vendors. 8 From the CT localizer radiographs, we used digital calipers to measure the AP and LAT dimensions of the phantoms from AP and LAT. We repeated AP M and LAT M measurements five times and took the average of the AP M and LAT M dimensions measured for each phantom. As phantom edges were well-defined, there was not a significant variation in width measurements; therefore, we did not include error bars in this study. Measurement maximum deviations between the five measurements of AP M and LAT M were submillimeter for all phantom sizes and positioning. We compare our methods to other magnification corrections summarized in Table I for both absolute sizes and also for SSDE conversion factors. The latter allows for the dosimetric impact of the different geometric correction methods to be compared. Absolute size differences were quantified by calculating the percent difference in size between the geometric correction algorithm and the known ideal phantom size. SSDE was calculated for all methods using the equations provided in AAPM TG report 04 [Eq. (A1), parameters a p= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , b = ] for effective diameter ( LAT AP) to conversion factor. 3. RESULTS Figure shows LAT and AP estimation using magnification correction methods for 30 mm CTDI and 15 mm water cylinder phantoms. The dashed lines represent the actual AP and LAT dimensions. Figure 3 shows how close each magnification correction is to the actual measured diameter for elliptical phantoms. The dashed lines represent the actual AP and LAT dimensions. Figures and 3 demonstrate how the experimental points are closest to the dashed lines (actual thickness) for the modelbase approach, particularly for larger phantoms relative to the other methods. Table II summarizes the worst and best conditions for each phantom and correction method shown in Figs. and 3. Figure 4 shows the calculation pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of correction factors using the effective diameter ð LAT APÞ from the magnification correction approaches. Table III summarizes the worst and best conditions for SSDE determination for each phantom and correction method shown in Fig DISCUSSION We demonstrate that our magnification correction method gives a more accurate estimate of the phantom size for both the lateral (LAT) and anterior (a) 400 Lateral dimension [mm] mm 15 mm 150 (b) Anterior-posterior dimension [mm] mm 15 mm 150 FIG.. Magnification correction for 30 and 15 mm cylindrical phantom dimensions estimated from CT localizer images. Measurements are shown from a variety of table heights using the University of Wisconsin (UW) model-based, the geometric, and the methods. (a) and (b) show the lateral anterior posterior dimensions, respectively. The dashed lines across the graphs show the ideal 30 and 15 mm dimensions. [Color figure can be viewed at wileyonlinelibrary.com]

4 168 Burton et al.: CT localizer size correction 168 (a) 500 Lateral dimension [mm] mm 300 mm 50 mm 00 (b) Anterior-posterior dimension [mm] mm 00 mm mm FIG. 3. Magnification correction for three different regions of the elliptical phantom dimensions. Measurements are shown from a variety of table heights using the University of Wisconsin (UW) model-based, the geometric, and the methods. (a) and (b) show the lateral anterior posterior dimensions, respectively. The three different lateral (LAT) and anterior posterior (AP) regions of the elliptical phantom are as follows for the major to minor axis: large mm, medium mm, and small mm. The dashed lines across the graph show the actual size of these dimensions for both lateral and anterior posterior measurements. [Color figure can be viewed at wileyonlinelibrary.com] TABLE II. Summary of best and worst results for absolute size determination from the various correction schemes for each phantom. The subscripts max and min on LAT and AP indicate that the measurement is the worst or best, respectively. Offset of difference between center of patient and isocenter refers to the table heights corresponding to the best and worst results, respectively. LAT max LAT min AP max AP min Length Offset max Length Offset min Length h max Length h min Vendor (30 mm) vendor (15 mm) Vendor (large) Vendor (medium) Vendor (small) Christensen/Raupach/ Li (30 mm) Christensen/Raupach/ Li (15 mm) Christensen/Raupach/ Li (large) Christensen/Raupach/ Li (medium) Christensen/Raupach/ Li (small) Model-based (30 mm) Model-based (15 mm) Model-based (large) < Model-based (medium) < Model-based (small) posterior (AP) dimensions shown in Figs. and 3 relative to the other methods. Our model, as discussed in the Section 6, assumes that there is no vertical mispositioning present in the lateral CT localizer radiograph. This explains why our model shows a slight increase in error as the mispositioning increases for Figs. (b) and 3(b). This also explains the slight downward slope in our corrected LAT measurements as seen in Figs. (a) and 3(a). Our data show that the UW modelbased method provides consistent accurate results, less than 1.8 error for absolute size for all measurement conditions relative to 30.9 and 7.5 for the vendor and Christensen/ Raupach/Li approaches. Using the

5 169 Burton et al.: CT localizer size correction 169 (a). (b). Correction factor mm 30 mm Correction factor small medium large 0.8 table difference from isocenter [mm] 1 FIG. 4. SSDE correction factor estimated from CT localizer images using the University of Wisconsin (UW) model-based, the geometric, and the magnification corrections. Correction factors as shown as a function of table height for (a) the cylindrical phantoms and (b) the three different sized sections of the elliptical phantom. Dashed lines across the each graph show the ideal SSDE correction factor derived using the known phantom effective diameter. [Color figure can be viewed at wileyonlinelibrary.com] approach for the largest elliptical phantom, the SSDE correction factor differed by approximately 5.0 and for the vendor s correction the maximum table height gave a difference of Our model-based method only differed by 1. for the largest elliptical section for SSDE correction factor. While determining D W was not done in this technical note, our method can be applied to CT localizer-based methods for calculating D W. Li et al. 5 demonstrate how the effective diameter (D E ) can be related to the waterequivalent diameter (D W ) by measuring the mean pixel value of the phantom area with the product of the width and normalizing it to the attenuation coefficient of water. Anam et al. 1 have recently reported a method for calculating D W which involves determining a linear relationship between pixel value and water thickness and then solving for water-equivalent area (A W ) by integrating over the x- axis of the CT localizer. Both Li et al. and Aman et al. s methods rely on accurate geometric size information to TABLE III. Summary of best and worst results for SSDE CF, where the subscript CF stands for conversion factor, for the various correction schemes for each phantom. The subscripts max and min on LAT and AP indicate that the measurement is the worst or best, respectively. Offset of difference between center of patient and isocenter refer to the table heights corresponding to the best and worst results, respectively. SSDE max SSDE min SSDE CF Offset max SSDE CF Offset min Vendor (30 mm) Vendor (15 mm) Vendor (large) < Vendor (medium) Vendor (small) ( mm) ( mm) (large) (medium) (small) Model-based (30 mm) Model-based (15 mm) Model-based (large) Model-based (medium) Model-based (small)

6 170 Burton et al.: CT localizer size correction 170 obtain D W and should therefore benefit from a geometric correction such as that described in this note. A source of error in using this method for future patient studies would come from not accounting for miscentering in the lateral (i.e., x-direction). This is due to not being able to estimate the patient s miscentering along the lateral dimension using information from the DICOM header. Similar to the postprocessing method by Li et al., one could calculate largest center of mass along each column in the image and subtract that location from the center of the image to estimate patient offset. Not accounting for this miscentering in the magnification/minification correction would result in either an under or overdose to the patient for calculating the effective diameter or for TCM response. We should note that our methods may not be needed for correcting geometric magnification on AEC algorithms by all vendors. Some vendors, as shown by Merzan et al. 8, are not effected by patient mispositioning. Albeit a SSDE derived using a CT localizer radiograph from such vendors may still experience error from geometric magnification. 5. CONCLUSIONS We have shown that our model-based magnification correction method is more accurate than the current vendor geometric SID over SOD based correction algorithms. We have also compared our method to all previously known reported methods in the literature and demonstrated our method to be superior. Our method requires no actual tomographic CT images, it only uses CT localizer radiograph and DICOM header information, making it amenable to large dose registries. APPENDIX (A1) The model-based approach models the patient as an ellipse and takes into account when the x-ray beam first grazes the anatomy (Fig. 1). In this section, we show derivation of two common points on the ellipse and a line using a system of two equations. The patient is modeled as an ellipse which is parameterized as ðx bþ ðy kþ 1 ¼ þ (A1) LAT AP where variables AP and LAT represent the anterior posterior and lateral dimensions of the patient or phantom, respectively, and variables k and b represent the table offset from isocenter in the anterior posterior (i.e., y-direction or vertical) and lateral (i.e., x-direction or horizontal) direction, respectively. In this note, we assume that the patient is centered along the isocenter in the x-direction; therefore, b = 0. The distance between the source and isocenter is referred to as the sourceto-object distance (SOD). We solve for AP and LAT using a system of two equations. We refer to these equations as the anterior posterior and lateral equation, named because they are set up using the geometry of the anterior posterior and lateral CT localizer radiographs, respectively. The two equations are set up by modeling the geometry of a ray emanating from the source, grazing ( grazing is defined in Fig. 1) the patient at a single point, and then progressing to strike the detector. In such a geometry, a grazing ray can be parameterized using the source as the origin and defining the slope of the line as the ratio of half the projected patient width to SOD. The projected patient thickness is given by either LAT M or AP M depending on if the CT localizer radiograph is a AP/PA or lateral view, respectively. For the anterior posterior equation, the line grazing the side of the patient ellipse model can be represented as y = mx + c where c = 0 as the source location is taken at the origin and m ¼ SOD. For the lateral LATM equation, m ¼ SOD. APM We assume that the effect of geometric magnification on the size of the lateral CT localizer radiograph is negligible and therefore set k to SOD for the lateral equation. The error introduced by not modeling the vertical offset present in the lateral equation for the 30 mm phantom used in this study was quite small. For table offsets of 65.0, 3.5, 0.0, 31.5, and 63.5 mm from isocenter the measured size of the phantom using only the vendor geometric calibration was 33, 335, 335, 334, and 33 mm. In other words, while our model assumed a constant AP M, in reality, it changed by a maximum of 3 mm for the 30 mm phantom over the table heights we analyzed. For larger patients, this error will increase slightly; however, in such cases, the patient will quickly become truncated in the CT localizer radiograph view. Therefore, we feel that simplifying the mathematics by not modeling the vertical mispositioning in setting up the lateral equation is justified. For the anterior posterior equation, k is given by SOD þ h AP which is not an assumption, but the actual off set. The solution between a line and an ellipse has a known closed-form solution for intersection points x 1; and y 1;. The points x 1; and y 1; are intersection points in the x- and y- planes, and equations for these points are provided here. The solution is given by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 1; ¼ ba ml LA L m þ A d k þ dk L m þ A (A) and pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y 1; ¼ A d kl m LAm L m þ A d k þ dk L m þ A (A3) where e = c k, d = c + mb, L ¼ LAT AP, and A ¼. In our geometry, the y-value of the intersections is equal making solution for the y-coordinates simpler by forcing the term to zero. Exploiting this fact for both the anterior posterior and lateral equations provides two equations with only two unknowns. Therefore, our system of equations is constructed by using the anterior posterior and lateral equation geometry to set the inside of the square root term to zero. Equations (A) and (A3) are not reduced so that the entire equation may be used in future studies to account for patient offset in the x-

7 171 Burton et al.: CT localizer size correction 171 Arc of Detectors SID d C' B C Isocenter SOD θ Focal Spot SOD/SID correction for that point at which B and C touch, the measured length of B will simply be the length of C. If h is the half angle of the Arc C. Then, C ¼ðSODÞh (A4) B ¼ðSODÞ tan h; (A5) where h ¼ arctan B ðsodþ; (A6) FIG. 5. Illustration of the geometric image distortion inherent to projecting a straight object onto a curved detector surface. The Arc C is centered on the focal spot and B is a straight line tangent to it at the iso-ray. Assume B is a straight metric ruler passing through the center of the scanned field of view (SFOV) and centered at the iso-ray. However B, as shown, does not necessarily pass through the isocenter. The SID/SOD correction applied to B to correct for its magnification at the detector is actually only correct at its center. The measured length of the cm increments on B will progressively decrease at positions farther away from its center. This is due to two effects; (1) the parts of B away from its center are closer to the detectors and their geometric magnification is less; () these parts of B are no longer parallel to the detector and are appear foreshortened to the detector. [Color figure can be viewed at wileyonlinelibrary.com] direction. Once the term was set to zero, we inserted Equations (A) and (A3) into a Matlabâ function (vpasolver, The Mathworks, Natwick, MA, USA) which provided us with a numerical approximation to the solution of the system of equations. In this system, AP and LAT are unknown, h is determined from the DICOM header (tag ID:0018,1130), SOD may be determined from the DICOM header (tag ID: 0018,940) or may be found in the vendor s technical manual if not provided in the DICOM header, and LAT M =AP M are measured from CT localizer radiograph images. In this note, we used digital calipers to manually determine LAT M =AP M ; however, in practice, they can be determined using automated methods. 3 In practice, the patient model-based magnification approach is useful for cases that require two CT localizers such as abdomen and chest cases for both adult and pediatric patients. However, since this approach requires two CT localizers, it might not be useful in determining size surrogates for extremity and head scans where only one CT localizer is more commonly acquired. In addition to modeling the grazing effect, there is an image distortion that should be taken into account for most scanners. It derives from the attempted mapping of a straight line through the scan field of view to the detectors which form an arc of a circle. Distances measured in the CT localizer radiograph are relative to this arc of detectors but with a minification correction factor of SOD/SID. This correction is accurate for distances along the Arc C. However, as shown in Fig. 5, the distances measured along B are progressively minified for distances measured farther from the iso-ray (the ray from the focal spot passing through the isocenter). At the isoray, measurements along B and C are equal. Using a single thus, C ¼ ðsodþarctanbðsodþ; (A7) gives the measured length of the ruler, which will always be less than its actual length, B. To somewhat counteract this overall minification of the measured length of the ruler, the length given above can be multiplied by a factor greater than one (f), or equivalently the SOD/SID correction can be increased (SOD is increased to SOD + d). In this case, the central part of the ruler is magnified while the outside remains minified, relative to the true distance. You can see this effect in increasing the SOD in the Arc C in Fig. 5. In this case, we can modify the measured length of B to be B : B 0 B ¼ ðfþðsodþarctan (A8) ðsodþ or B 0 B ¼ ðsod þ dþ arctan (A9) ðsodþ For the scanner used in this paper: f = or d = 1.3 cm. With these values B = B when B = 15 cm. In other words, for a ruler with a length of 30 cm, its measured length in the CT localizer will be 30 cm, if the center of the ruler is at isocenter. In the case of our system, for actual lengths ranging from 0 to 36 cm, the error in the measured lengths in the CT localizer will be less than mm. Thus, in this paper, no correction needed to be applied. If these corrections needed to be applied, one would simply adjust the measured distances from the localizer radiographs (LAT M and AP M ) using Eqs. (8) and (9). a) Author to whom correspondence should be addressed. Electronic mail: tszczykutowicz@uwhealth.org. REFERENCES 1. Anam C, Fujibuchi T, Toyoda T, et al. 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