In this work we studied the relationship between parameters that describe the texture and fractal dimension of endobronchial ultrasonographic images of mediastinal nodes and the likehood for malignancy. In both raw images as well as enhanced ones it was found that there is a statistical difference between malignant and non-malignant nodes in terms of fractal dimension.
The introduction of EBUS-TBNA has provided a significant advance in the staging and diagnosis of lung cancer and other malignancies in a safe and minimally invasive procedure . The analysis of the ultrasonographic appearance of the nodes has been applied to predict malignancy. Fujiwara et al. studied morphologic characteristics of lymph nodes by means of a multivariable analysis that included round shape, distinct margin, heterogeneous echogenicity and presence of coagulation necrosis . The authors found that these morphologic characteristics are independent predictive factors for predicting malignancy. Echogenicity was the parameter with the most validated punctuation. The authors did not apply the automatic process of the image, but only qualitative subjective evaluation. Nguyen et al. applied for the first time the second order grayscale texture feature analysis in EBUS . In their study, 52 malignant nodes and 48 benign ones were analyzed. They found that malignant nodes have a higher difference in first and second order texture parameters in relation with benign nodes, using as distinctive features in texture parameters based on first and second order statistics. It should be noted that images were not pre-processed in order to maintain the same real time quality image. On the other hand, the differences in textures after enhancing the image were not significant. This can be attributed to the fact that the processing smoothed the image, eliminated spurious peaks, and enhanced the inner structures of the nodules. This processing that improved the visual appearance of the details of the nodes, changed the texture of the image.
An interesting aspect of the proposal in this paper of introducing the fractal index α, is that this index is complementary with respect to the texture parameters. This complementariness arises from the fact that the fractal index is adapted to the shape of the internal structures of the nodule, and therefore appears as significant after the enhancement of the image. On the other hand the raw image has too much noise, which gives rise to artifacts when computing the fractal index. The fractal dimension is a real number that generalizes the concept of ordinary dimension for geometric objects. This process also provides data regarding phenomena like deformation, remodeling, breakup and repair. Cancer in general is associated with a disruption of tissue architecture due to the interaction between cells and stroma , and fractal-shape parameters could be descriptors of the cell-stroma system. On the other hand, there is a fractal relationship between the degree of apparent heterogeneity of local tissue and the resolution of the measurement, when heterogeneity provides no uniformity in the cell organs examined.
Fractal dimension has been applied in ultrasound echo signals to detect tissue tumors [14, 15]. Texture parameters and fractal Higuchi dimension of the ultrasound series detected prostate cancer in small tissue regions with an accuracy of 91% . Zheng et al.  applied fractal Brownian motion and k means cluster analysis to detect breast cancer with a recognition rate of 94.5% for malignant tumors. In the present work, we analyzed 23 nodes (12 of them malignant), and applied an algorithm to compute the inner area (white space) and its perimeter. We assume a power model between the perimeter of the inner structure of the ganglia and the area. Difference of fractal dimension between malignant and non malignant nodes was significant, and less in malignant nodes. A possible cause of this slight reduction in fractal dimension of malignant nodes is that cell membranes spread to take the form of a lower energy structure like a circle, therefore, diminishing the fractal dimension of a neoplasic node . In this way, Kikuchi et al.  showed that sonography of solid components in cystic epithelial ovarian cancers had a fractal structure, and the mean fractal dimension decreased from 1.26 for serous intracystic components to 1.18 for clear cell adenocarcinoma. In our study the mean fractal dimension was more than 1, meaning the topological line dimension, and it decreased from 1.53 for benign nodes to 1.47 for malignant nodes, the same proportion of the Kikuchi study.
We believe that the principal limitation of our study is the relatively small number of analyzed nodes, but the objective was to describe the fractal nature of the ultrasonographic images of mediastinal nodes. A future application and validation of the present technique could be developed to distinguish between malignant nodes and other non-malignant pathologies that affect mediastinal nodes (such as tuberculosis and chronic inflammatory diseases like sarcoidosis). We should always try to obtain pathological reference diagnosis from suspicious lymph nodes, but in the future, image analysis could assist the bronchoscopist regarding the likelihood to malignancy of the node, as well as the most suspicious region of the node to sample. In consequence, we believe that fractal dimension can constitute a new EBUS parameter to take into account. To our knowledge, this is the first study that applies fractal dimension analysis to EBUS images.