A fractal approach to the distribution function of a paramagnetic system

1995 ◽  
Vol 99 (1) ◽  
pp. 137-141 ◽  
Author(s):  
Fevzi Büyükkiliç ◽  
Doĝan Demirhan
Keyword(s):  
Distribution Function ◽  
Fractal Approach ◽  
Paramagnetic System

Heterogeneity of Cerebral Blood Flow: a Fractal Approach

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Fractal Dimension ◽  
Frontal Lobe ◽  
Fractal Analysis ◽  
Relative Dispersion ◽  
Emission Computed Tomography ◽  
Brain Blood Flow ◽  
Healthy Controls ◽  
Fractal Approach

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.

Influence of extinction phenomenon on determination of the orientation distribution function

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 175-180
Author(s):  
G. Gómez-Gasga ◽  
T. Kryshtab ◽  
J. Palacios-Gómez ◽  
A. de Ita de la Torre
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

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