Appendix Materials and Methods Fractal dimension analysis The 附錄材料分形維數(shù)分析方法

1、.AppendixMaterials and MethodsFractal dimension analysisThe blanket algorithm is an iterative process in which each pixelin the ROI of an imageis compared with its surrounding pixels in order to estimate the gray level variation in the area around pixel (13). Using the assumption that the set that r

2、epresents all the points at distance fromfor. The set is a “blanket” of thickness that covers the surface and can be represented as the union of all the balls of radius centred on. The fractal dimension of surface is related to its surface area through the following equationwhere is a constant (12).

3、 The surface area is estimated as the difference in the volume occupied by the blankets for radius and divided by. Mathematically, this can be expressed as (35): where, is the size of the examined region around pixel. The volume of the blanket of the surface for radius is calculated by its upperand

4、lower surface bounds, i.e.,where andThe points included in a blanket are all the points that lie between the upper and the lower surface of the blanket. According to Equation (2), the blanket of the surface for radius includes all the points of the blanket for radius, together with all the points wi

5、thin radius from the upper and lower surfaces of that blanket.Estimating the surface area for different values of the radius () yields a set of points which form a line on the bilogarithmic plane. The slope of this line is the fractal dimension of the image area around pixel. In this study, radius v

6、alues up to () have been considered for the fractal dimension estimation and the examined region around each pixel has been a window of size pixels (corresponding to mm) of the predefined ROI. The size of the examined window should be large enough to enable the integration of information from neighb

7、oring pixels and small enough to preserve the local characteristics of the examined point. In the proposed work the window length was set to pixels ( of the image length) in order to ensure it covers the whole width of the ROI (pixels), even for the examined pixels at the edges of the ROI.Lung densi

8、ty analysisThe method identified high-density structures within the lung parenchyma to be excluded (such as extra-pulmonary areas, blood vessels and airways) prior to lung density calculation (13). The structures to be excluded were isolated by thresholding the gray-scale values on the CT images at

9、the five levels in order to keep the areas that correspond to high gray-scale values. The hysteresis thresholding approach was used instead of applying a global threshold to the CT image. The hysteresis method employed two threshold values. The high threshold was used to find “seeds” for the structu

10、res to be excluded, i.e., points that correspond to vessels or nodules with high probability among all the points on the parenchyma. Then, each point on the parenchyma which was connected to a “seed” and lies above the lower threshold, was marked as vessel or airway. The lowest and highest threshold

11、s of the gray-scale values were set equal to 330 and 550, respectively, according to the threshold values suggested in 14.The lung density was estimated at each predefined level as the mean lung attenuation in the examined ROI:whereis the segmented ROI where structures such as extra-pulmonary areas, blood