Fractal Analysis Based on Hierarchical Scaling in Complex Systems

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (= coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17 ± 0.05 (mean ± SD) for the left hemisphere and 1.15 ± 0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04 ± 0.03 than in healthy controls. Conclusion: Within the limits of spatial resolution of SPECT, the heterogeneity of brain blood flow is well characterized by a fractal dimension. Fractal analysis may help brain scientists to assess age-, sex- and laterality-related anatomic and physiological changes of brain blood flow and possibly to improve precision of diagnostic information available for patient care.

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Air Pollution Attributable Deaths: A Global View Through Fractal Analysis

Recoletos Multidisciplinary Research Journal ◽

10.32871/rmrj1402.01.16 ◽

2014 ◽

Vol 2 (1) ◽

pp. 149-162

Author(s):

Melvin de Castro ◽

◽

Tonette Villanueva ◽

Grace Arcamo ◽

Rayna Lynn de Castro ◽

...

Keyword(s):

Air Pollution ◽

Fractal Analysis ◽

Global View

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Structure characterization of ground calcium carbonate flocs by fractal analysis and their effects on handsheet properties

TAPPI Journal ◽

10.32964/tj12.3.17 ◽

2013 ◽

Vol 12 (3) ◽

pp. 17-23 ◽

Cited By ~ 3

Author(s):

WANHEE IM ◽

HAK LAE LEE ◽

HYE JUNG YOUN ◽

DONGIL SEO

Keyword(s):

Fractal Analysis ◽

Structural Characteristics ◽

Fractal Dimensions ◽

Strength Loss ◽

Structure Characterization ◽

Uniform Size ◽

Cross Sectional ◽

Floc Size ◽

Mass Fractal ◽

Handsheet Properties

Preflocculation of filler particles before their addition to pulp stock provides the most viable and practical solution to increase filler content while minimizing strength loss. The characteristics of filler flocs, such as floc size and structure, have a strong influence on preflocculation efficiency. The influence of flocculant systems on the structural characteristics of filler flocs was examined using a mass fractal analysis method. Mass fractal dimensions of filler flocs under high shear conditions were obtained using light diffraction spectroscopy for three different flocculants. A single polymer (C-PAM), a dual cationic polymer (p-DADMAC/C-PAM) and a C-PAM/micropolymer system were used as flocculants, and their effects on handsheet properties were investigated. The C-PAM/micropolymer system gave the greatest improvement in tensile index. The mass fractal analysis showed that this can be attributed to the formation of highly dense and spherical flocs by this flocculant. A cross-sectional analysis of the handsheets showed that filler flocs with more uniform size were formed when a C-PAM/micropolymer was used. The results suggest that a better understanding of the characteristics of preflocculated fillers and their influence on the properties of paper can be gained based on a fractal analysis.

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From Quasicrystals to More Complex Systems

10.1007/978-3-662-04253-3 ◽

2000 ◽

Cited By ~ 7

Keyword(s):

Complex Systems

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