Radiol Phys Technol (2012) 5:166–171 DOI 10.1007/s12194-012-0150-9
Application of CT-PSF-based computer-simulated lung nodules for evaluating the accuracy of computer-aided volumetry Ayumu Funaki • Masaki Ohkubo • Shinichi Wada Kohei Murao • Toru Matsumoto • Shinji Niizuma
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Received: 13 September 2011 / Revised: 7 March 2012 / Accepted: 11 March 2012 / Published online: 25 March 2012 Ó Japanese Society of Radiological Technology and Japan Society of Medical Physics 2012
Abstract With the wide dissemination of computed tomography (CT) screening for lung cancer, measuring the nodule volume accurately with computer-aided volumetry software is increasingly important. Many studies for determining the accuracy of volumetry software have been performed using a phantom with artificial nodules. These phantom studies are limited, however, in their ability to reproduce the nodules both accurately and in the variety of sizes and densities required. Therefore, we propose a new approach of using computer-simulated nodules based on the point spread function measured in a CT system. The validity of the proposed method was confirmed by the excellent agreement obtained between computer-simulated nodules and phantom nodules regarding the volume measurements. A practical clinical evaluation of the accuracy of volumetry software was achieved by adding simulated nodules onto clinical lung images, including noise and artifacts. The tested volumetry software was revealed to be accurate within an error of 20 % for nodules [5 mm and with the difference between nodule density and background (lung) (CT value) being 400–600 HU. Such a detailed analysis can provide clinically useful information on the use of volumetry software in CT screening for lung A. Funaki M. Ohkubo S. Wada (&) Graduate School of Health Sciences, Niigata University, 2-746 Asahimachi-dori, Chuo-ku, Niigata 951-8518, Japan e-mail:
[email protected] K. Murao Fujitsu, Ltd., Tokyo, Japan T. Matsumoto Kensei Clinic, Chiba, Japan S. Niizuma Plaka Health Care Center, Niigata, Japan
cancer. We concluded that the proposed method is effective for evaluating the performance of computer-aided volumetry software. Keywords Computed tomography (CT) Point spread function (PSF) Slice sensitivity profile (SSP) Volumetry Computer-aided diagnosis (CAD)
1 Introduction Lung cancer is the primary cause of cancer-related deaths, in the world [1]. Although advances have been made in surgical, radiotherapeutic, and chemotherapeutic approaches, the long-term survival rate has remained low. The advent of low-dose helical computed tomography (CT) altered the landscape of lung cancer screening, with studies indicating not only that low-dose CT detects many tumors at an early stage but also that it increases lung cancer curability [2]. The National Cancer Institute (USA) has released the initial results of the National Lung Screening Trial, which is a large-scale randomized controlled trial (RCT) of screening methods for reducing mortality from lung cancer [3]. The trial was launched during 2002 for determination whether screening with low-dose CT could reduce lung cancer mortality. The preliminary results of the RCT indicated that lung cancer deaths were reduced 20 % more by CT screening than by screening with chest radiography. The wide dissemination of high-quality CT screening is expected to improve the situation regarding mortality due to lung cancer. An accurate estimation of tumor growth is essential with such high-quality CT screening, i.e., accurate measurement of tumor volume is one of the key issues for minimizing overdiagnosis [4–6]. Computer-aided software
Application of CT-PSF-based simulation to evaluate the accuracy of nodule volumetry
is increasingly being utilized for these volumetric measurements [7–10], and there have been many studies on the accuracy of the volumetry software used. It is essentially required to evaluate the volumetric accuracy using actual nodules in patients. However, using actual nodules is difficult because of requirements of determining the true volume in clinical studies; studies with actual nodules have mainly investigated the intra- and interobserver variability of volume measurements [11–13], not the accuracy compared to the true volume. Also, many studies have employed a phantom with artificial nodules which enabled the evaluation of volumetric accuracy by the comparison with a known volume (true value) [13–18]. Whereas those methods with artificial nodules were valid as a basic approach, they have a limitation in that numerous nodules must be fabricated accurately in a variety of sizes and densities. Some investigators have also reported methods for generating computer-simulated (virtual) nodules [19– 21]. Those virtual nodules were obtained by computation with arbitrary modeling and filtering so that the resultant nodules were seemingly similar to real nodules (i.e., not depending accurately on the characteristics of the spatial resolution in a CT system). To evaluate the accuracy of the volumetric measurements, we propose a new approach that uses computersimulated nodules based on the point spread function (PSF) measured in a CT system. With this approach, numerous simulated nodules can be generated by computation of a variety of sizes (arbitrary known volumes) and densities, which are added to CT images. We validated the application of these simulated nodules regarding their use for evaluating the accuracy of computer-aided volumetry software instead of the commonly used artificial nodules included in a phantom. We then demonstrated the accuracy of the volumetry software by adding the computer-simulated nodules to clinical CT screening images.
2 Materials and methods 2.1 Computer-simulated nodules Blurring of the CT image can be described by the PSF of a system [22]. In the present study, we assumed that the PSF is separable into a two-dimensional (2D) PSF in the xy scan plane and the slice sensitivity profile (SSP) in the z direction perpendicular to the scan plane [23–26]. The threedimensional (3D) CT image I (x, y, z) is then expressed as [25–28] I ðx; y; zÞ ¼ ½Oðx; y; zÞPSFðx; yÞSSPðzÞ;
ð1Þ
where O (x, y, z) is the object function, PSF (x, y) and SSP (z) are the 2D PSF and SSP, respectively; and ** and *
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are 2D and 1D convolutions, respectively. Noise and artifact components are neglected in this representation. The 2D PSF and SSP were measured in a CT scanner and were applied to the calculation in Eq. (1). The 2D PSF measurement was done by a method that determined the 2D PSF in the scan plane by one scan of a commercial phantom, accompanied by verification [29, 30]. The SSP measurement was done with a delta phantom. Object functions were generated numerically as ideal spheres with uniform density by assumption of solitary pulmonary nodules. Using Eq. (1), we computed the CT image from the object function using the measured 2D PSF and SSP, i.e., we generated a computer-simulated nodule image based on the spatial resolution characteristics of the system. Then, we made an image data set by adding the computersimulated nodules onto a CT image data set obtained by scanning. Detailed descriptions of the image simulation based on Eq. (1) have been published previously [25, 28]. A brief description of one example is given in Fig. 1. The simulated nodule image (Fig. 1d) was computed from the object function (Fig. 1c) using 2D PSF (Fig. 1a) and SSP (Fig. 1b). The image simulation studies have been performed extensively [23–25, 28], and the validity of the simulation technique could be verified. 2.2 Comparison of computer-simulated nodules and phantom nodules We validated the computer-simulated nodules for evaluating the accuracy of computer-aided volumetry software for use as an alternative to the commonly used phantom with artificial nodules. The phantom (high-contrast CT test phantom, MHT-type; Kyoto Kagaku, Kyoto, Japan) was one that contained spherical objects of known diameter that were assumed to represent nodules. This phantom was scanned on a four-detector row CT scanner (Asteion; Toshiba, Tokyo, Japan) using the parameters 120 kV and 200 mA, a 4 9 1 mm detector configuration, and a pitch factor of 0.75. The image reconstruction was performed with a kernel of ‘‘FC50’’ (for standard lung imaging), a field of view (FOV) of 137 mm, and a slice thickness of 1 mm. The 2D PSF was obtained for a reconstruction kernel of FC50 (Fig. 1a), and the SSP was obtained for a slice thickness of 1 mm (Fig. 1b). The object function in Eq. (1) was generated as an ideal sphere that corresponds to the size and density of each spherical object in the phantom (Fig. 2). We obtained data for the computer-simulated nodules from the object functions using the measured 2D PSF and SSP and made an image data set by adding the simulated nodules onto the phantom images, as indicated in Fig. 2. We then measured the volumes of computer-simulated nodules and phantom
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Fig. 2 Computed tomography (CT) image of the phantom. Spherical objects with diameters of 2, 3, 5, 7, and 10 mm (arrows) were the only objects employed in this study. The computer-simulated nodules were added onto the image (arrowheads)
Fig. 1 Generation of a computer-simulated nodule. a The 2D PSF in the xy scan plane obtained for an image reconstruction kernel of FC50. b The SSP obtained for a slice thickness of 1 mm. c Images of the object function in the scan plane (left) and in the xz plane (right), which was generated as an ideal sphere with a diameter of 5 mm. d Images of a computer-simulated nodule in the scan plane (left) and in the xz plane (right), which was obtained from the object function using 2D PSF and SSP
nodules using volumetry software (Fujitsu, Tokyo, Japan) [7, 13]. The volumes measured for the computer-simulated nodules were compared with those measured for the phantom nodules. 2.3 Accuracy evaluation of volumetry software Images obtained from CT screening for lung cancer were obtained on a 16-detector row CT scanner (Aquilion; Toshiba) with the parameters of 120 kV and 60 mA and 16 9 1 mm detector configuration. The image reconstruction was performed using a kernel of ‘‘FC51’’ (for higher-resolution lung imaging), FOV 320 mm, and slice thickness 1 mm. The 2D PSF was obtained for the reconstruction kernel of FC51, and the SSP was obtained for the slice thickness of 1 mm. We obtained the computer-simulated nodules by Eq. (1) from the object functions (ideal spheres) using the 2D PSF
and SSP measured in the scanner. The simulated nodules were obtained by changes in the nodule size (diameter) and density, i.e., we changed the object function. The diameter was changed from 3 to 10 mm, and the DCT—the difference between the nodule density and the background (lung) density—was changed from 300 to 700 HU. This setting of the object function was decided on with consideration of a clinical practice for lung cancer screening. We made an image data set by adding the simulated nodules onto clinical images for lung cancer screening, as indicated in Fig. 3. The simulated nodules were located at both central and peripheral regions in the lung. Because of the simple addition of the simulated nodule, the components of noise and artifact included in the clinical image were seen on the nodule. Using the image data set, we measured the volumes of the nodules with volumetry software [7, 13] and compared them with the volumes of the corresponding object functions (i.e., the true volume).
3 Results With the phantom image data set, including the computersimulated nodules (as indicated in Fig. 2), the volumes for the computer-simulated nodules and for phantom nodules were measured with the volumetry software. The results are compared in Fig. 4. The volumes for the computer-simulated nodules showed excellent agreement with the volumes for phantom nodules, suggesting that the
Application of CT-PSF-based simulation to evaluate the accuracy of nodule volumetry
Fig. 3 Two computer-simulated nodules (arrows) added onto the clinical image obtained during CT screening for lung cancer. These nodules were located at both central and peripheral regions in the lung. The simulated nodules were obtained from the object function with a diameter of 5 mm and a difference between nodule density and the background (lung) density (DCT) of 300 HU
Fig. 4 Measured volumes of the computer-simulated nodules compared with those of the phantom nodules for five nodule diameters (2, 3, 5, 7, and 10 mm) (see Fig. 2)
computer-simulated nodules could be used as an alternative to the artificial phantom nodules for evaluation of the accuracy of the volumetry software. The volumes for the computer-simulated nodules added onto the clinical lung image data set (Fig. 3) were
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Fig. 5 Error in nodule volume measurements by the computer-aided volumetry software, in which the computer-simulated nodule was located at the central region in the left lung (see Fig. 3)
measured with the volumetry software. The results for nodules located at the central region in the lung are shown in Fig. 5, in which the percentage errors of the measured volumes to the true volumes [(measured volume - true volume)/true volume 9 100 %] were obtained. The accuracy of the measured volume was depended on the nodule size and density. When the nodule diameter was increased to more than approximately 5 mm, the absolute value of the percentage error tended to decrease (or remain constant) for each nodule density. The absolute values for the percentage errors in nodules with DCT values of 400–600 HU were \20 % for diameters of more than approximately 5 mm. The results for nodules located at the peripheral region in the lung are shown in Fig. 6; whereas the overall results are similar to those in Fig. 5, the values of the volume measurement percentage error tended to increase slightly compared with the values in Fig. 5 for each nodule density. The volumetry software did not work well for some of the nodules that had low density and small diameters, and those data were excluded.
4 Discussion The computer simulation of CT images based on the spatial resolution of a CT system has been applied previously to the investigation of the accuracy of size and density measurement. The object functions used in those image simulations were designed to simulate a cortical bone [23], small high-density structures (calcifications and stented
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Fig. 6 Error in nodule volume measurements by the computer-aided volumetry software, in which the computer-simulated nodule was located at the peripheral region in the right lung (see Fig. 3)
vessels) [24], and lung nodules [25]. The validity of such image simulations could be verified. In the present study, we applied this simulation technique to evaluate the accuracy of computer-aided volumetry software for lung nodules. Its validity was confirmed, as indicated by the results shown in Fig. 4. This technique can generate numerous simulated nodules by calculating variety of sizes and densities, thereby overcoming the limitation of previous studies that used phantom nodules [13–18]. Although the methods for obtaining computer-simulated nodules by arbitrary modeling and filtering have also been investigated [19–21], those nodules were not determined accurately based on the spatial resolution in a CT system. Our proposed method generates nodules that depend on the characteristics of the spatial resolution measured in each CT system, which, in turn, are based on the image-generating system itself. For a quantitative analysis study, such as evaluating the accuracy of volumetry software, the proposed method is the most appropriate in computer techniques that can generate simulated nodules. We demonstrated a method that evaluated the accuracy of volumetry software (Figs. 5, 6) in which computersimulated nodules were added onto CT screening images. Because of the simple addition of simulated nodules, the components of noise and artifacts included in the clinical image were unchanged. Therefore, a practical clinical evaluation was achieved; this is not possible with a technique that uses artificial nodules in a phantom [13–18]. The tested volumetry software was revealed to be accurate within an error of 20 % for nodules [5 mm and with a
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DCT value of 400–600 HU. Also, it was suggested that there was a possible difference in the accuracy of volume measurements of nodules located at the central and peripheral regions in the lung. Such a detailed analysis with many nodules (in total, eighty nodules) provides clinically useful information regarding the use of volumetry software for CT screening for lung cancer. Our study has some limitations. First, the computersimulated nodules were calculated from the object functions determined as ideal spheres with constant density. However, nodules in patients are more complicated, and numerous simulated nodules of heterogeneous density with various shapes would be necessary for a closer clinical approach. Second, we assumed that the PSF was separable into 2D PSF and SSP, and did not depend on the position within the image (i.e., was shift-invariant). However, it has been reported that the PSF has a complicated, nonseparable three-dimensional shape [31]. Also, the PSF might depend on the position within the image (i.e., might be shift-variant) [31]. However, from the present result (Fig. 4), we consider that these potential PSF errors would have little effect on the generation of computer-simulated nodules. Third, accurate measurement of the spatial resolution in a CT system was essential for generating the accurate computer-simulated nodules by Eq. (1). We recommend the use of the 2D PSF measurement method accompanied by verification [29, 30], which was used in the present study, leading to a good result (Fig. 4).
5 Conclusions A new approach using computer-simulated nodules based on the PSF is proposed for evaluating the accuracy of computer-aided volumetry software for the study of lung nodules. Its validity was confirmed. By addition of the simulated nodules onto clinical lung images, including noise and artifacts, a practical clinical evaluation of the accuracy of volumetry software was achieved. The proposed method can be useful for evaluating the performance of computer-aided volumetry software. Acknowledgments This study was supported in part by a Grant-inAid for Cancer Research (19–25) from the Ministry of Health, Labor and Welfare, Japan, and by a Grant-in-Aid for Scientific Research (C) (23602005). This research was also supported by a joint study undertaken between Niigata University and Fujitsu Limited.
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