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* Scientific Direction, Istituto Clinico Humanitas, IRCCS,
Via Manzoni 56, Milan, Rozzano 20089, Italy.
e-mail: fabio.grizzi@humanitas.it
Department of Medical-Diagnostic Sciences and Special Therapies,
University of Padua and IRCCS-IOV, Padova, Italy.
Editor:
We read with interest the article by Dr Matsuoka and colleagues that was published online before print in Radiology on February 16, 2005 (1). Although the study by Dr Matsuoka and colleagues is a noteworthy contribution, we made the following two observations:
First, several factors may affect the interpretations of the computed tomographic (CT) scans by radiologists, including the subtle nature of radiographic findings, poor image quality, eye fatigue, interpretation error, and even simply oversight. To overcome these problems we need not only compulsory advanced technical screening methods but also answers to the still unsolved question: What makes a good radiologist? At a basic level, the practice of radiology involves looking at an image (visual perception) and interpreting what is seen (cognition) (2). Experience gives the radiologist the perceptual and cognitive skills to know what information to look for and how to interpret that information on the basis of the accumulation and integration of information processed from previous encounters with the same types of images. What makes the task difficult is the fact that, although the basic anatomy is fundamentally the same from image to image, the degree of natural anatomic dissimilarity is high, and radiologists will never be able to recognize all possible variations no matter how long they practice and how many images they see. The need to find a new way of observing, classifying, and measuring the anatomic forms and their dynamic changes has prompted many investigators to develop computer-aided diagnosis algorithms based on fractal geometry (3). Dr Matsuoka and colleagues applied these principles to distinguish benign and malignant peripheral solitary pulmonary nodules in patients with and those without emphysema. However, it was not clearly described in their article whether the fractal dimension, which indexes the space-filling property of an irregular object, is a helpful quantitative parameter for classifying the morphologic complexity of peripheral solitary pulmonary nodules identified at CT. Furthermore, it could be interesting to verify whether emphysema affects the geometry (ie, the irregular interface) of solitary pulmonary nodules and whether benign and malignant pulmonary nodules may be affected differently by emphysema.
Second, in the context of neoplastic disease, the word "benign" means that the cells making up the tumor show no tendency to irregularly invade the adjacent tissue and never spread to distant sites. On the contrary, the absolute principle of malignancy is invasiveness, that is, cancer cells grow irregularly in the surrounding tissue. In geometric terms, the irregular shape of a neoplastic lesion can be quantified in two dimensions with the Euclidean circularity index. Moreover, an estimate of the irregular tumor edge can be obtained from the computation of the proper "dimension." We recently (4) showed that the Euclidean circularity index measures the irregular expansion of the neoplastic surface, while the fractal dimension gives a quantitative index of the irregular increasing cell proliferation and tissue infiltration. Like all natural objects, the measure of their outline length and surface extension is dependent on the level of magnification of the object for the appearance of new features unseen at lower scales of observation. Dr Matsuoka and colleagues used the box-counting algorithm for the estimation of fractal dimension for benign and malignant pulmonary nodule boundaries. However, in the Materials and Methods section of their article (1), it was not reported how the scaling window, in which the fractal dimension was invariant with respect to changes in magnification, had been evaluated.
The scaling window is a key marker of the scale-invariance characteristic of every fractal property, in contrast with Euclidean parameters, which vary greatly, changing the scale of observation (5–8).
The authors (1) discussed important points and, while the clinical application seems to be notable, we, as well as other morphologists, need these additional details if we are to replicate the results.
References
Department of Radiology, St Marianna University School of Medicine, 2-16-1 Sugao, Miyamae-Ku, Kawasaki City, Kanagawa216–8511, Japan. e-mail: shinma@d9.dion.ne.jp
We thank Drs Grizzi and Muzzio for their interest in our research (1), and their constructive comments are well taken. We would like to respond to their comments as follows.
Kido et al (2) reported that fractal dimensions reflected characteristics of the interfaces of small peripheral pulmonary nodules and could be used to distinguish between benign and malignant pulmonary nodules. Referring to this report, we applied fractal analysis for distinguishing benign and malignant peripheral solitary pulmonary nodules in patients with or those without emphysema. In additional data of all 81 patients with or without emphysema, the mean fractal dimension was significantly greater in malignant nodules than in benign nodules (1.62 vs 1.54, P < .001, Mann-Whitney U test). Thus, "the value of fractal dimension" may be a helpful quantitative parameter for classifying the morphologic complexity of solitary pulmonary nodules to some degree. However, we think that the classification of benign or malignant pulmonary nodule is not regulated only in the nodule shape. Furthermore, in our study, we found no significant differences in fractal dimension between malignant and benign nodules associated with emphysema. For the quantitative analysis of the pulmonary nodules, the innovative method of considering not only the shape of the nodule but also preexisting lung disease is desired. We welcome any suggestions that may resolve this issue.
In biologic tissues, fractal patterns or self-similar structures are usually observed within a scaling window of the measure length. For fractal analysis, we used a computer algorithm of the box-counting method to calculate the fractal dimension of the nodules without magnification. Subsequently, log-log plots were constructed of the reciprocal box size against the number of nodule outlines–containing boxes. The slope of the linear segment of the graph represents the fractal dimension of the image. The coefficient of determination of this relationship was assessed, and values greater than 0.95 were obtained in each case, indicating that the nodules were included within a scaling window.
References
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