A fractal analysis of cell images

Smith, Thomas G.; Marks, W. B.; Lange, G. David; Sheriff, W.H.; Neale, Elaine A.

doi:10.1016/0165-0270(89)90100-3

Cited by 236 publications

(151 citation statements)

References 13 publications

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“…Grid measures the coastline by placing grids of different grid sizes on the coastline and counting the number of non-empty boxes (which is the same as box counting the coastline). Measuring the coastlines of neurons and other objects with calipers of various sized openings was found to produce less linear graphs by Smith et al (1989) than the other methods. By analyzing only the coastline or perimeter of a neuron, instead of the space inside the coastline we obtained a higher fractal dimension.…”

Section: Methodology Of Fractal Analysi~mentioning

confidence: 88%

“…Three methods of measuring neuronal coastline length were compared by Smith et al (1989). The methods were caliper, disk, and grid.…”

Section: Methodology Of Fractal Analysi~mentioning

confidence: 99%

“…Fractal analysis has also been used to describe how completely a neuron fills its dendritic field or the straightness of individual dendrites (Montague and Friedlander,199 1). However, previous studies have used the following different methods for calculating the fractal dimension (d,) of a neuron: cumulative-mass (Caserta et al, 1990), box counting (Morigiwa et al, 1989) and coastline measurement (Smith et al, 1989). The use of different methods of fractal analysis has made comparison of results difficult because each method of determination can give slightly different results when used to analyze the same structure.…”

Section: Introductionmentioning

confidence: 99%

“…We did this by analyzing several neurons in both 2 and 3 dimensions using the cumulative-mass method, and comparing the results. Finally, previous fractal analysis studies have largely been performed on neurons whose physiological A properties have not been directly assessed Friedlander, 1989, 1991;Morigiwa et al, 1989;Smith et al, 1989;Caserta et al, 1990). This left open the question of whether there is a correlation between the fractal dimension and physiology of a given cell.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Caserta

Eldred

Fernández

et al. 1995

Journal of Neuroscience Methods

155

126

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Although there is a growing interest in the application of fractal analysis in neurobiology, questions about the methodology have restricted its wider application. In this report we discuss some of the underlying principles for fractal analysis. we propose the cumulative-mass method as a standard method and we extend the applicability of fractal analysis to both 2 and 3 dimensions. We have examined the relationship between the method of log-log Sholl analysis and fractal analysis and have found that they correlate well. Measurements of physiologically characterized retinal ganglion cells indicate that different cell types can have significantly different fractal dimensions. Such differences may allow the correlation of the physiological type of a neuron with its morphological fractal dimension.

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Section: Methodology Of Fractal Analysi~mentioning

confidence: 88%

“…Three methods of measuring neuronal coastline length were compared by Smith et al (1989). The methods were caliper, disk, and grid.…”

Section: Methodology Of Fractal Analysi~mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Caserta

Eldred

Fernández

et al. 1995

Journal of Neuroscience Methods

155

126

View full text Add to dashboard Cite

show abstract

“…2, step 5) was preferred among the different fractal techniques at disposal (e.g. caliper and box counting methods) because of its simplicity and lower susceptibility to pixelization effects (Smith et al, 1989(Smith et al, , 1996Maria and Carey, 2002). The principle of the dilation method is that the single-pixel particle outline is progressively widened (and thus, smoothened) in steps of one pixel at each side of the outline not occupied by a pixel.…”

Section: Fractal Analysesmentioning

confidence: 99%

Eifel maars: Quantitative shape characterization of juvenile ash particles (Eifel Volcanic Field, Germany)

Rausch

Grobéty

Vonlanthen

2015

Journal of Volcanology and Geothermal Research

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The Eifel region in western central Germany is the type locality for maar volcanism, which is classically interpreted to be the result of explosive eruptions due to shallow interaction between magma and external water (i.e. phreatomagmatic eruptions). Sedimentary structures, deposit features and particle morphology found in many maar deposits of the West Eifel Volcanic Field (WEVF), in contrast to deposits in the East Eifel Volcanic Field (EEVF), lack the diagnostic criteria of typical phreatomagmatic deposits. The aim of this study was to determine quantitatively the shape of WEVF and EEVF maar ash particles in order to infer the governing eruption style in Eifel maar volcanoes. The quantitative shape characterization was done by analyzing fractal dimensions of particle contours (125-250 μm sieve fraction) obtained from Scanning electron microscopy (SEM) and SEM micro-computed tomography (SEM micro-CT) images. The fractal analysis (dilation method) and the fractal spectrum technique confirmed that the WEVF and EEVF maar particles have contrasting multifractal shapes. Whereas the low small-scale dimensions of EEVF particles (Eppelsberg Green Unit) coincide with previously published values for phreatomagmatic particles, the WEVF particles (Meerfelder Maar, Pulvermaar and Ulmener Maar) have larger values indicating more complex smallscale features, which are characteristic for magmatic particles. These quantitative results are strengthening the qualitative microscopic observations, that the studied WEVF maar eruptions are rather dominated by magmatic processes. The different eruption styles in the two volcanic fields can be explained by the different geological and hydrological settings found in both regions and the different chemical compositions of the magmas.

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Loss of 'Complexity' and Aging

Lipsitz

Goldberger²

1992

JAMA

931

345

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The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.

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A fractal analysis of cell images

Cited by 236 publications

References 13 publications

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Eifel maars: Quantitative shape characterization of juvenile ash particles (Eifel Volcanic Field, Germany)

Loss of 'Complexity' and Aging

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