Abstract
Surface morphology is an important indicator of malignant potential for solid-type lung nodules detected at CT, but is difficult to assess subjectively. Automated methods for morphology assessment have previously been described using a common measure of nodule shape, representative of the broad class of existing methods, termed area-to-perimeter-length ratio (APR). APR is static and thus highly susceptible to alterations by random noise and artifacts in image acquisition. We introduce and analyze the self-overlap (SO) method as a dynamic automated morphology detection scheme. SO measures the degree of change of nodule masks upon Gaussian blurring. We hypothesized that this new metric would afford equally high accuracy and superior precision than APR. Application of the two methods to a set of 119 patient lung nodules and a set of simulation nodules showed our approach to be slightly more accurate and on the order of ten times as precise, respectively. The dynamic quality of this new automated metric renders it less sensitive to image noise and artifacts than APR, and as such, SO is a potentially useful measure of cancer risk for solid-type lung nodules detected on CT.
Similar content being viewed by others
References
Ferlay J, Shin H, Bray F, et al: Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008. Int J Cancer 127:2893–2917, 2010
MacMahon H, Austin JH, Gamsu G, Herold CJ, Jett JR, Naidich DP, Patz Jr, EF, Swensen SJ: Fleischner Society: guidelines for management of small pulmonary nodules detected on CT scans: a statement from the Fleischner Society. Radiology 237:395–400, 2005
Gurney JW, Lyddon DM, McKay JA: Determining the likelihood of malignancy in solitary pulmonary nodules with Bayesian analysis. Part II. Application. Radiology 186:415–422, 1993
Travis WD, Brambilla E, Noguchi M, et al: International Association for the Study of Lung Cancer/American Thoracic Society/European Respiratory Society International Multidisciplinary Classification of Lung Adenocarcinoma. J Thorac Oncol 6:244–285, 2011
Detterbeck FC, Boffa DJ, Tanoue LT: The new lung cancer staging system. Chest 136:260–271, 2009
Travis WD: Pathology of lung cancer. Lung Cancer 23:65–81, 2002
Godoy MC, Naidich DP: Subsolid pulmonary nodules and the spectrum of peripheral adenocarcinomas of the lung: recommended interim guidelines for assessment and management. Radiology 253:606–622, 2009
Kostis WJ, Yankelevitz DF, Reeves AP, et al: Small pulmonary nodules: reproducibility of three-dimensional volumetric measurement and estimation of time to follow-up CT. Radiology 231:446–452, 2004
Kostis WJ, Reeves AP, Yankelevitz DF, et al: Three-dimensional segmentation and growth-rate estimation of small pulmonary nodules in helical CT images. IEEE Trans Med Imaging 22:1259–1274, 2003
Li F, Sone S, Abe H, Macmahon H, Doi K: Malignant versus benign nodules at CT screening for lung cancer: comparison of thin-section CT findings. Radiology 233(3):793–798, 2004
Kim HY, Shim YM, Lee KS, Han J, Yi CA, Kim YK: Persistent pulmonary nodular ground-glass opacity at thin-section CT: histopathologic comparisons. Radiology 245(1):267–275, 2007
Lee HJ, Goo JM, Lee CH, Park CM, Kim KG, Park EA, Lee HY: Predictive CT findings of malignancy in ground-glass nodules on thin-section chest CT: the effects on radiologist performance. Eur Radiol 19(3):552–560, 2009
Ko JP, Rusinek H, Jacobs E, et al: Volume measurement of small pulmonary nodules on chest CT: a phantom study. Radiology 228:864–870, 2003
Ko JP, Berman EJ, Kaur M, et al: Pulmonary nodules: growth rate assessment in patients by using serial CT and three-dimensional volumetry. Radiology 262:662–671, 2012
Petkovska I, Shah SK, McNitt-Gray MF, et al: Pulmonary nodule characterization: a comparison of conventional with quantitative and visual semi-quantitative analyses using contrast enhancement maps. Eur J Radiol 59:244–252, 2006
Shah SK, McNitt-Gray MF, Aberle DR, et al: Computer-aided diagnosis of the solitary pulmonary nodule. Acad Radiol 12:570–575, 2005
McNitt-Gray MF, Wyckoff N, Sayre JW, et al: The effects of co-occurrence matrix based texture parameters on the classification of solitary pulmonary nodules imaged on computed tomography. Comput Med Imaging Graph 23:339–348, 1999
McNitt-Gray MF, Hart EM, Wyckoff N, et al: A pattern classification approach to characterizing solitary pulmonary nodules imaged on high resolution CT: preliminary results. Med Phys 26:880–888, 1999
Suzuki K, Li F, Sone S, Doi K: Computer-aided diagnostic scheme for distinction between benign and malignant nodules in thoracic low-dose CT by use of massive training artificial neural network. IEEE Trans Med Imaging 24:1138–1150, 2005
Huang YL, Chen DR, Jiang YR, et al: Computer-aided diagnosis using morphological features for classifying breast lesions on ultrasound. Ultrasound Obstet Gynecol 32:562–572, 2008
Muhammad MN, Raicu, DS, Furst JM, et al.: Texture versus shape analysis for lung nodule similarity in computed tomography studies. Medical Imaging 2008: PACS and Imaging Informatics, Proceedings of the SPIE 6919:69190I-69190I-7, 2008
Iwano S, Nakamura T, Kamioka Y, et al: Computer-aided diagnosis: a shape classification of pulmonary nodules imaged by high-resolution CT. Comput Med Imaging Graph 29:565–570, 2005
Minavathi, Murali S, Dinesh MS: Curvature and shape analysis for the detection of spiculated masses in breast ultrasound images. Int J Mach Intell 3:333–339, 2011
Agam G, Armato SG, Wu CH: Vessel tree reconstruction in thoracic CT scans with application to nodule detection. IEEE Trans Med Imaging 24:486–499, 2005
Wu C, Agam G, Roy AS, et al: Regulated morphology approach to fuzzy shape analysis with application to blood vessel extraction in thoracic CT scans. Proc SPIE 5370:1262–1270, 2004
Kubo T, Lin PJ, Stiller W, et al: Radiation dose reduction in chest CT: a review. AJR Am J Roentgenol 190:335–343, 2008
Yap MH, Edirisinghe EA, Bez HE: A novel algorithm for initial lesion detection in ultrasound breast images. J Appl Clin Med Phys Am Coll Med Phys 9:181–199, 2008
Christe SA, Vignesh M, Kandaswamy A: An efficient fpga implementation of MRI image filtering and tumour characterization using Xilinx system generator. Int J VLSI Des Commun Syst 2:95–109, 2012
Kim HJ, Kim WH: Automatic detection of spiculated masses using fractal analysis in digital mammography. Comput Anal Image Patterns Proc 3691:256–263, 2005
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Appendix 1
We seek a threshold function Θ that turns μ′(i) into a binary matrix whose entries are equal to 1 if they exceed the assigned threshold value and are 0 otherwise, i.e.
where H is the Heaviside step function and T(μ′(i)) is the threshold-generating function for blurred nodule i's image matrix μ′(i). The latter function is defined by
where \( \mathrm{att}_{\mathrm{low}}^{(i) } \) is the attenuation value below which approximately 10 % of the attenuation values for nodule i lie. In other words, for a frequency distribution \( {f_i}\left( {\mathrm{at}{{\mathrm{t}}^{(i) }}} \right) \) of nodule i's attenuation values, \( \mathrm{att}_{\mathrm{low}}^{(i) } \) satisfies
where \( \left\{ {\mathrm{att}_j^{(i) }} \right\}_{j=1}^{{{N_{\mathrm{rows}}}\times {N_{\mathrm{cols}}}}}=\mathrm{vec}\left( {{\mu^{(i) }}} \right) \) is the set of attenuation values in μ (i). Similarly, \( \mathrm{att}_{\mathrm{high}}^{(i) } \) is the attenuation value above which the highest 10 % of attenuation values for nodule i reside, so that
The hope is that by using this 10 % margin, the attenuation value \( T\left( {{\mu^{(i) }}} \right) \) accurately reflects a typical value characterizing the attenuation distribution for nodule i and is not unduly influenced by aberrantly large or small attenuation values, as these can represent for example pieces of bone or air that are caught in the nodule image slice.
Appendix 2
According to the generalized linear model, we can write any expected value for a dependent variable Y in terms of the independent variable X with parameter set β:
where E(Y) is the expected value for Y and g is the link function. In our case, the outcome Y i is smoothness i , a continuous quantity that expresses the likelihood that nodule i is smooth or not smooth, and X is the self-overlap SO. Since we are interested in predicting whether a given nodule is smooth or not, our distribution is binomial, and we will denote the binary counterpart to smoothness to be “smooth” sm. When sm i = 1, we can say that nodule i is smooth, while sm i = 0 is a statement that nodule i is not smooth. Thus, the link function is given by
with corresponding mean function
The smooth values \( \left\{ {\mathrm{s}{{\mathrm{m}}_i}} \right\}_{i=1}^{{{N_{\mathrm{nods}}}}} \) were assigned by an experienced radiologist (JPK and DN). Together with \( \left\{ {\mathrm{S}{{\mathrm{O}}_i}} \right\}_{i=1}^{{{N_{\mathrm{nods}}}}} \), we can compute \( \left\{ {\beta_0, {\beta_1}} \right\} \) by least squares regression applied to the system of equations
called in Matlab as glmfit. Then we can compute \( \left\{ {\mathrm{smoothnes}{{\mathrm{s}}_i}} \right\}_{i=1}^{{{N_{\mathrm{nods}}}}} \) via the mean function (Eq. 14). Finally, using a threshold
we can assign a predicted smooth value
where H is the Heaviside step function.
Using the same fitting technique, we generate smooth values predicted from area-to-perimeter-length ratio \( \left\{ {\mathrm{sm}_i^{\mathrm{APR}}} \right\}_{i=1}^{{{N_{\mathrm{nods}}}}} \) for comparison with the smooth values \( \left\{ {\mathrm{sm}_i^{\mathrm{SO}}} \right\}_{i=1}^{{{N_{\mathrm{nods}}}}} \) predicted from the self-overlap method.
Appendix 3
We test for robustness by permuting the nodule μ (i) into \( {{\widetilde{\mu}}^{(i) }} \), which now has noise on top of the simulation image. We introduce noise by generating N rp = 200 randomly positioned trial points and subjecting them to the probability distribution \( {p_{\mathrm{flip}}}=\exp \left( {-{d_{\mathrm{bd}}}} \right) \), where p flip is the probability of a trial point's being accepted (thus flipping the sign of the pixel in that position), and d bd is the distance of the trial point from the nearest point on the nodule–air interface/boundary. This probability distribution weights noise toward the boundary, so that the added noise affects predominantly surface morphology. For each value of l, we generate N perm = 1,000 permuted nodules \( \left\{ {\widetilde{\mu}_m^{(l) }} \right\}_{m=1}^{{{N_{\mathrm{perm}}}}} \) by this approach, giving us sets of nodules that are distorted in various places and to various degrees.
Rights and permissions
About this article
Cite this article
Stember, J.N., Ko, J.P., Naidich, D.P. et al. The Self-Overlap Method for Assessment of Lung Nodule Morphology in Chest CT. J Digit Imaging 26, 239–247 (2013). https://doi.org/10.1007/s10278-012-9536-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10278-012-9536-9