Asymptotic fractals in the context of grey‐scale images

Jp, Rigaut; Schoëvaërt-Brossault, D.; Am, Downs; Landini, Gabriel

doi:10.1046/j.1365-2818.1998.00284.x

Cited by 27 publications

(16 citation statements)

References 25 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, Horsfield found fractal properties in the relationship between the generation number and mean diameter of airways in the bronchial tree (11). The perimeter of alveolar wall sections (12) and pulmonary blood flow (13,14) also were reported to have fractal properties. Additionally, Gilliard et al reported that surfactant administered transbronchially to rabbit lungs showed a fractal distribution (15).…”

mentioning

confidence: 99%

Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease

Mishima

Hirai²,

Itoh³

et al. 1999

Proc. Natl. Acad. Sci. U.S.A.

317

341

View full text Add to dashboard Cite

Increases in the low attenuation areas (LAA) of chest x-ray computed tomography images in patients with chronic obstructive pulmonary disease (COPD) have been reported to ref lect the development of pathological emphysema. We examined the statistical properties of LAA clusters in COPD patients and in healthy subjects. In COPD patients, the percentage of the lung field occupied by LAAs (LAA%) ranged from 2.6 to 67.6. In contrast, LAA% was always <30% in healthy subjects. The cumulative size distribution of the LAA clusters followed a power law characterized by an exponent D. We show that D is a measure of the complexity of the terminal airspace geometry. The COPD patients with normal LAA% had significantly smaller D values than the healthy subjects, and the D values did not correlate with pulmonary function tests except for the diffusing capacity of the lung. We interpret these results by using a large elastic spring network model and find that the neighboring smaller LAA clusters tend to coalesce and form larger clusters as the weak elastic fibers separating them break under tension. This process leaves LAA% unchanged whereas it decreases the number of small clusters and increases the number of large clusters, which results in a reduction in D similar to that observed in early emphysema patients. These findings suggest that D is a sensitive and powerful parameter for the detection of the terminal airspace enlargement that occurs in early emphysema.High-resolution computed tomography (CT) is a sensitive and noninvasive tool for assessing alterations in lung structure induced by various disease processes. Increases in the low attenuation areas (LAA) in the lung regions of chest x-ray CT images in patients with chronic obstructive pulmonary disease (COPD) have been reported to reflect the development of pathological emphysema (1-4). Nevertheless, previous methods of analyzing lung CT images are limited for general clinical diagnostic purposes (5) because the size and spatial distribution of LAAs are not taken into account. Recently, Uppaluri et al. (6) found that a texture-based adaptive multiple feature method could differentiate between normal and emphysematous tissue with 100% accuracy. However, it is not clear whether this method would detect early emphysema. More recently, Shimizu et al. (7) proposed a promising fractal analysis method for assessing ground-glass opacities in lung CT images. Their approach was able to successfully differentiate between fibrotic and nonfibrotic disease processes.The concept of fractal geometry was developed by Mandelbrot (8) to quantitatively describe the random variations in size and shape seen in natural objects. A fractal object is said to be scale-free because its characteristics are invariant under isotropic scale transformations. Such scale-invariance can be achieved if the object is formed by parts that are similar to the whole. In other words, fractals are self-similar and hence are characterized by power law functions (the only mathematical functions obeying s...

show abstract

mentioning

confidence: 99%

Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease

Mishima

Hirai²,

Itoh³

et al. 1999

Proc. Natl. Acad. Sci. U.S.A.

317

341

View full text Add to dashboard Cite

show abstract

“…The collagen islets forming fibrosis (Figure 1-C) were measured in linear meters; the result was corrected by the fractal dimension [5] to include details of the irregularity of their shapes The fractal dimension was obtained by means of the box counting method because the objects to be measured were “truncated fractals” [6], the fractal dimension was used as a dilation factor rather than an exponent [7] Three classes of islet magnitude were arbitrarily identified: area from 10 and 10 3 μm 2 , from 10 3 to 10 4 μm 2 and over 10 4 μm 2 .…”

Section: Resultsmentioning

confidence: 99%

Automatic measurement of the evolutionary process dynamics of primary of biliary cirrhosis

et al. 2013

View full text Add to dashboard Cite

“…We derived the fractal dimension using the box-counting method [20,21,28,29] . Since the biological objects has been classified as "truncated fractals" [20,21,30] we used the fractal dimension to correct the reference units as a dilation factor [20,21] . Table 2 shows the differences between the uncorrected and fractal dimension-corrected IS measurements.…”

Section: Fractal Dimension Correction Of the Is Metermentioning

confidence: 99%

Metrically measuring liver biopsy: A chronic hepatitis B and C computer-aided morphologic description

Dioguardi¹,

Grizzi²,

Fiamengo³

et al. 2008

WJG

View full text Add to dashboard Cite

CONCLUSION:The results are the first standardized metrical evaluation of the geometric properties of the parenchyma, inflammation, fibrosis, and alterations in liver tissue tectonics of the biopsy sections. The present study confirms that biopsies are still valuable, not only for diagnosing chronic hepatitis, but also for quantifying changes in the organization and order of liver tissue structure. INTRODUCTIONThe main purpose of this paper is to describe a rigorous method based on the fundamentals of measurement theory [1] , which metrically defines the changes in magnitude of liver tissue prime basic structural elements that occurring during the course of chronic hepatitis B and C.Each available score to evaluate hepatic lesions is characterized by some methodological inaccuracy [2][3][4] . In fact, transient elastography (Fibro-Scan) [5,6] is limited by the skill of the operator and because liver stiffness is not only dependent from fibrosis, and serological assays not directly involved in tissue evolution, but in patient diagnosis [7][8][9][10][11] . In addition to the inherent risks of excising a liver specimen [12] , current morphometric analyses [13][14][15][16][17] are timeconsuming, depend on subjective choices of the regions of interest, involve the interactive elimination of Glisson's capsule and staining artefacts, and use the International System (IS), which is unsuitable for measuring the irregular shapes found in histology [18][19][20][21] . The study concerning the status of the liver tissue affected by chronic viral hepatitis was suggested by three Abstract AIM:To describe a quantitative analysis method for liver biopsy sections with a machine that we have named "Dioguardi Histological Metriser" which automatically measures the residual hepatocyte mass (including hepatocytes vacuolization), inflammation, fibrosis and the loss of liver tissue tectonics. METHODS: We analysed digitized images of liver biopsy sections taken from 398 patients. The analysis with Dioguardi Histological Metriser was validated by comparison with semi-quantitative scoring system. RESULTS: The method provides: (1) the metrical extension in two-dimensions (the plane) of the residual hepatocellular set, including the area of vacuoles pertinent to abnormal lipid accumulation; (2) the geometric measure of the inflammation basin, which distinguishes intra-basin space and extra-basin dispersed parenchymal leukocytes; (3) the magnitude of collagen islets, (which were considered truncated fractals and classified into three degrees of magnitude); and (4) the tectonic index that quantifies alterations (disorders) in the organization of liver tissue. Dioguardi Histological Metriser machine allows to work at a speed of 0.1 mm 2 /s, scanning a whole section in 6-8 min.

show abstract

Asymptotic fractals in the context of grey‐scale images

Cited by 27 publications

References 25 publications

Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease

Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease

Automatic measurement of the evolutionary process dynamics of primary of biliary cirrhosis

Metrically measuring liver biopsy: A chronic hepatitis B and C computer-aided morphologic description

Contact Info

Product

Resources

About