Is the brain cortex a fractal?

Kiselev, Valerij G.; Hahn, Klaus; Auer, Dorothee P.

doi:10.1016/s1053-8119(03)00380-x

Cited by 151 publications

(117 citation statements)

References 12 publications

Supporting

Mentioning

113

Contrasting

Unclassified

Order By: Relevance

“…Various physical phenomena such as the growth of cancers and arterial and bronchial trees show the features of fractals, and fractal theory has already provided clinically useful information to differentiate pathological tissue from healthy tissue (Baish and Jain, 2000;Mauroy et al, 2004;Zamir, 1999). The application of fractal theory to the neuroimaging field has also provided novel and useful information in clinical medicine (Kiselev et al, 2003;Yoshikawa et al, 2003a,b). In contrast to simple fractals, the concept of ''multifractal phenomena'' holds that different regions of an object have different local fractal properties that quantify local singular behavior (Halsey et al, 1986).…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of deep white matter microstructural changes on MRI in relation to early-stage atherosclerosis

et al. 2006

View full text Add to dashboard Cite

Multifractal analysis based on generalized concepts of fractals has been applied to evaluate biological tissues composed of complex structures. This type of analysis can provide a precise quantitative description of a broad range of heterogeneous phenomena. Previously, we applied multifractal analysis to describe heterogeneity in white matter signal fluctuation on T2-weighted MR images as a new method of texture analysis and established Da as the most suitable index for evaluating white matter structural complexity (Takahashi et al. J. Neurol. Sci., 2004; 225: 33À37). Considerable evidence suggests that pathophysiological processes occurring in deep white matter regions may be partly responsible for cognitive deterioration and dementia in elderly subjects. We carried out a multifractal analysis in a group of 36 healthy elderly subjects who showed no evidence of atherosclerotic risk factors to examine the microstructural changes of the deep white matter on T2-weighted MR images. We also performed conventional texture analysis, i.e., determined the standard deviation of signal intensity divided by mean signal intensity (SD/MSI) for comparison with multifractal analysis. Next, we examined the association between the findings of these two types of texture analysis and the ultrasonographically measured intima -media thickness (IMT) of the carotid arteries, a reliable indicator of early carotid atherosclerosis. The severity of carotid IMT was positively associated with Da in the deep white matter region. In addition, this association remained significant after excluding 12 subjects with visually detectable deep white matter hyperintensities on MR images. However, there was no significant association between the severity of carotid IMTand SD/MSI. These results indicate the potential usefulness of applying multifractal analysis to conventional MR images as a new approach to detect the microstructural changes of apparently normal white matter during the early stages of atherosclerosis. D

show abstract

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of deep white matter microstructural changes on MRI in relation to early-stage atherosclerosis

et al. 2006

View full text Add to dashboard Cite

show abstract

“…On the right, an original picture of the main elevation This geometric concept is applied in several scientific fields. For example, in medicine, when considering neuronal networks and their pathologies; in electronics, when considering the physical behavior of circuits on smaller manufacturing scales; in chemistry, when obtaining different properties of substances depending on their roughness (Kiselev et al 2003). This concept is also used in architecture, when seeking evidence of the objective influence between buildings designed by renowned architects, or in order to obtain mathematical evidence with regard to whether or not certain important architects respected the compositional continuity of the artificial or natural environment in which their design was intended to be constructed (Bechhoefer and Bovill 1994;Batty and Longley 1997;Hammer 2006;Sala 2006;Joye 2007;Rian and Park 2007;Bovill 2008;Ostwald 2001;Ostwald et al 2008;Ostwald and Vaughan 2009;Ostwald 2009, 2011).…”

Section: Mathematical Background: Fractal Parametermentioning

confidence: 99%

A Study of the Roughness of Gothic Rose Windows

Samper

Herrera

2015

Nexus Netw J

View full text Add to dashboard Cite

The rose window is one of the most representative elements of Gothic art and architecture. In this work we analyze fifteen rose windows from fifteen Gothic cathedrals using fractal geometry. Specifically, we examine the texture and roughness of these rose windows focusing on three factors, their designs, glass areas and solid areas. In this investigation we generate parameters which provide a measure of roughness of the rose windows in order to find out if they show a general non-random fractal pattern. The paper concludes that statistically, there is a characteristic fractal pattern in the solid and glass areas of the rose windows of the Gothic style, but not necessarily in their overall design.Keywords Rose windows Á Gothic architecture Á Fractal geometry Á Fractal parameter Historical Background: Light in the Gothic CathedralThe Gothic style signaled a veritable revolution in architecture as a result of its technical innovations which challenged the conventional concepts of construction at the time and also changed the manner in which large indoor spaces were conceived. Louis VI, King of France, aspired to rule all of the vast territories which had formed the Carolingian Empire three centuries before. To achieve this aspiration he was assisted in this task by Abbot Suger of Saint-Denis, an advisor with both intelligence and diplomatic skills. In gratitude for the services rendered, Louis VI granted the abbey of Saint-Denis great privileges so that they would have a competitive advantage and be able to hold their prosperous annual fair, which gathered both the faithful and merchants providing major benefits for the abbey. As a result of this, Saint-Denis became the richest Benedictine monastery in France after Cluny. Influenced by the Neoplatonic thoughts which spread amongst scholars of the early twelfth century in the Paris region, Suger was fascinated by light as a means to connecting with God. With this concept as an intellectual guide, Suger inferred that the House of God, the Christian church, had to become a temple of light and even more: ''a city bathed in the light of God'' (Berger 1906;Panofsky 1970). In order to achieve this ideal, it was necessary to modify and improve the construction system of the great Romanesque churches. That is, it was imperative to remove some walls and tear others from top to bottom in order to place large windows in them which would capture the sunlight. The name of the architect who found the solution to Suger's problem is unknown. Perhaps it was the master builder who directed the construction of the Romanesque structure in the abbey of Saint-Denis. Regardless, shortly before finishing this work, Suger ordered the following inscription to be places, in Latin verses on the main door of the abbey church. ''Portarum quisquis attolere quaeris honorem, Aurum nec sumptus, operis mirare laborem. Nobile claret opus, sed opus quod nobile claret, Clarificet mentes, ut eant per lumina vera, Ad verum lumen, ubi Christus jaunua vera. Quale sit intus in his determinat aurea p...

show abstract

“…The concept of the mammalian brain as a fractal structure was presented by Hofman in 1991 who provided a strong case in favor of the fractal geometry of the human cortex based on the surface-to-volume relations [21]. Studies on the human cortex, external cortex surface and the interface between human white and grey matter confirm their fractal dimensions [22][23][24][25]. Fractal measures have been used as measures of complexity in dendritic arborization of spinal cord neurons [26] and in the characterization of the complexity of grey matter and white matter structures of the brain [27][28][29].…”

Section: Cns Fractal Spatial Structurementioning

confidence: 99%

“…There are several methods for computing the fractal dimension of objects including caliper methods [30,31], box-counting algorithms [30,32], dilation methods [33], and spatial frequency analysis [25]; however, for structural analysis of the CNS, the most prevalent method appears to be box-counting algorithms used on magnetic resonance imaging (MRI) of the brain. The traditional box-counting method functions by repeatedly covering the fractal image with different-sized boxes and then evaluating the number of boxes needed to cover the fractal completely, resulting in a logarithmic function whose slope is the fractal dimension (FD) [30].…”

Section: Cns Fractal Spatial Structurementioning

confidence: 99%

Fractal Structure and Entropy Production within the Central Nervous System

Seely

Newman

Herry

2014

Entropy

View full text Add to dashboard Cite

Abstract:Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS). Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer's and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.

show abstract

Is the brain cortex a fractal?

Cited by 151 publications

References 12 publications

Multifractal analysis of deep white matter microstructural changes on MRI in relation to early-stage atherosclerosis

Multifractal analysis of deep white matter microstructural changes on MRI in relation to early-stage atherosclerosis

A Study of the Roughness of Gothic Rose Windows

Fractal Structure and Entropy Production within the Central Nervous System

Contact Info

Product

Resources

About