Quantification of interstitial lung abnormalities with chest radiography: comparison of radiographic index and fractal dimension

The fractal geometry of bronchial trees differs by strain in mice

Fractal biological structures are pervasive throughout the plant and animal kingdoms, with the mammalian lung being a quintessential example. The lung airway and vascular trees are generated during embryogenesis from a small set of building codes similar to Turing mechanisms that create robust trees ideally suited to their functions. Whereas the blood flow pattern generated by these fractal trees has been shown to be genetically determined, the geometry of the trees has not. We explored a newly established repository providing high-resolution bronchial trees from the four most commonly studied laboratory mice (B6C3F1, BALB/c, C57BL/6 and CD-1). The data fit a fractal model well for all animals with the fractal dimensions ranging from 1.54 to 1.67, indicating that the conducting airway of mice can be considered a self-similar and space-filling structure. We determined that the fractal dimensions of these airway trees differed by strain but not sex, reinforcing the concept that airway branching patterns are encoded within the DNA. The observations also highlight that future study design and interpretations may need to consider differences in airway geometry between mouse strains.NEW & NOTEWORTHY Similar to larger mammals such as humans, the geometries of the bronchial tree in mice are fractal structures that have repeating patterns from the trachea to the terminal branches. The airway geometries of the four most commonly studied mice are different and need to be considered when comparing results that employ different mouse strains. This variability in mouse airway geometries should be incorporated into computer models exploring toxicology and aerosol deposition in mouse models.

Computerized characterization of prostate cancer by fractal analysis in MR images

PURPOSE

To explore the potential of computerized characterization of prostate MR images by extracting the fractal features of texture and intensity distributions as indices in the differential diagnosis of prostate cancer.

MATERIALS AND METHODS

MR T2-weighted images (T2WI) of 55 patients with pathologic results detected by ultrasound guided biopsy were collected and then divided in two groups, 27 with prostate cancer (PCa) and 28 with no histological abnormality. Texture fractal dimension (TFD) and histogram fractal dimension (HFD) were calculated to analyze complexity features of regions of Interest (ROIs) selected from the peripheral zone. Two-sample t-tests were performed to evaluate group differences for both parameters. Receiver operating characteristic (ROC) analysis was used to estimate the performance of TFD and HFD for discriminating PCa.

RESULTS

Significant differences were found in both TFD and HFD between the two patient groups. The areas under the ROC curves of TFD and HFD were 0.691 and 0.966, respectively, in distinguishing prostatic carcinoma from normal peripheral zone. As characterized by the fractal indices, cancerous prostatic tissue exhibited smoother texture and lower variation in intensity distribution than normal prostatic tissue.

CONCLUSION

The study suggests that TFD and HFD depict the changes in texture and intensity distribution associated with prostate cancer on T2WI. Both TFD and HFD provide promising quantitative indices for cancer identification. HFD performs better than TFD offering a more robust MR-based indicator in the diagnosis of prostatic carcinoma.

Fractal Analysis for Quantitative Evaluation of Diffuse Lung Abnormalities on Chest Radiographs: Use of Sub-ROIs

We evaluated the usefulness of fractal analysis for quantitative evaluation of diffuse lung abnormalities seen on chest radiographs. Regions of interest (ROIs) with 296 x 296 matrix size were selected in the right upper and lower lung zones of digitized chest radiographs. We selected ROIs of 50 mild and 50 severe diffuse lung abnormalities and 50 ROIs of normal lungs. The fractal dimension (FD) for each ROI was defined as the mean value of those obtained from sub-ROIs in each ROI. In the sub-ROIs with 256 x 256, 128 x 128, and 64 x 64 matrix size, the mean values of FDs obtained from the patients with diffuse lung abnormalities were significantly higher than those obtained from the patients with normal lungs (P < 0.001, respectively). The performance of FDs obtained from the sub-ROIs with 256 x 256 matrix size was equal to that obtained from the sub-ROIs with 128 x 128 matrix size (P = 0.980). However, the performance of FDs obtained from the sub-ROIs with 128 x 128 matrix size was superior to that obtained from the sub-ROIs with 64 x 64 matrix size (P = 0.0001). Fractal analysis is useful for quantitative evaluation of diffuse lung abnormalities seen on chest radiographs. From our results, the sub-ROIs whose matrix sizes were greater than or equal to 128 x 128 were suggested to be suitable for quantitative evaluation of diffuse lung abnormalities seen on chest radiographs.

Fractal analysis of small peripheral pulmonary nodules in thin-section CT: evaluation of the lung-nodule interfaces

OBJECTIVES

To analyze the lung-nodule interfaces on small peripheral pulmonary nodules (<2 cm) in thin-section CT (HRCT) images with fractal analysis.

METHODS

Thin-section CT images from 70 patients with bronchogenic carcinomas (61 adenocarcinomas and 9 squamous cell carcinomas) and 47 patients with benign pulmonary nodules (23 hamartomas, 13 organizing pneumonias, and 11 tuberculomas) were used. For calculation of fractal dimensions (FDs), the authors used a box-counting method for binary- and gray-scale images of nodules. FD(two-dimensional [2D]) was an FD obtained from the binary image, and FD(three-dimensional [3D]) was an FD obtained from the gray-scale image.

RESULTS

The FD(2D)s of hamartomas were smaller than those of other nodules ( < 0.05). The FD(3D)s obtained from the gray-scale images of organizing pneumonias and tuberculomas were greater than those of bronchogenic carcinomas ( < 0.0001) and hamartomas ( < 0.0001). In bronchogenic carcinomas, FD(3D)s of adenocarcinomas were greater than those of squamous cell carcinomas ( < 0.05).

CONCLUSIONS

Fractal dimensions reflect the characteristics of the lung-nodule interfaces of small peripheral pulmonary nodules. The FD(2D)s revealed the irregularities of the contours. On the other hand, FD(3D)s revealed the complexities of the heterogeneous textures. With use of FD(2D) and FD(3D), it may be possible to distinguish bronchogenic carcinomas from benign pulmonary nodules. Moreover, FD(3D) may make it possible to distinguish between adenocarcinomas and squamous cell carcinomas.

Computerized classification of interstitial lung abnormalities on chest radiographs with normalized radiographic index and normalized fractal dimension

OBJECTIVE

To evaluate the performance of two kinds of physical measures, the normalized radiographic index (R) and the normalized fractal dimension (F), for computerized classification of interstitial lung abnormalities on chest radiographs.

METHODS AND MATERIAL

The values of R were obtained as the normalized percent area of extracted opacities in selected regions of interest (ROIs). The values of F were calculated with a box-counting algorithm and then normalized. To extract linear opacities on chest radiographs selectively, we processed ROIs by four-directional Laplacian-Gaussian filtering and binarization (4LG/B), linear opacity judgment (LOJ), and linear opacity subtraction (LOS). We used the ROIs of 50 mild and 50 severe interstitial lung abnormalities. In both groups, all cases were divided into H (n=21, honeycombing opacities were found to be dominant) and Non-H (n=79, abnormal opacities were found, but these were excluded from H). We obtained three types of normalized physical measures of R and F in one ROI from 4LG/B, LOJ, and LOS images, and the combined indices, R(COM) and F(COM) were calculated.

RESULTS

The values of F(LOJ) could differentiate H from Non-H in the mild-and the severe-abnormality group. However, all Rs could not differentiate H from Non-H in the severe-abnormality group. The combined indices of both R and F could differentiate H from Non-H in the mild-abnormality group; however, these could not differentiate H from Non-H in the severe-abnormality group.

CONCLUSION

The values of F(LOJ) seem to be useful in the classification of interstitial lung abnormalities on chest radiographs.