Fractal anatomy of the hippocampal formation

Aceves, Guillermo Axayacalt Gutiérrez; López, Miguel Ángel Celis; Alonso-Vanegas, Mario; Marrufo-Melendez, Oscar René; Moreno-Jiménez, Sergio; Cruz, Juan Carlos; Peregrino, Roberto Díaz; Aguilar, Alberto González; González, José Alfredo Herrera

doi:10.1007/s00276-018-2077-2

Cited by 4 publications

(4 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Just as the spatial configuration of atoms within bulk or lattice materials express alternative physical properties despite identical, homogeneous atomic constituents, the morphological properties and resultant functional consequences of the cerebral cortices could be determined by similar organizational principles and constraints. Consistent with many previous observations of the fractal-like organization of brain structure [30][31][32][33], we will present a hypothesis that positions the cortical column as a periodic and self-similar structure that emerges spontaneously from spatial frequencies intrinsic to neural tissue patterning.…”

Section: The Cortical Column Conundrumsupporting

confidence: 87%

“…Inputting wavelengths, wavenumbers can be computed within the spatial boundaries of the cerebral cortices. Assuming an average cortical column width of 500 µm [30], a wavenumber of 2 cycles per mm is achieved. When the average column's wavenumber is multiplied over the average human neocortical thickness of 2.69 mm [43], the result is 5.38 cycles per average cortical thickness (Figure 2A).…”

Section: Spatial Periodicities Within Columns Predict Observed Lamina...mentioning

confidence: 99%

See 1 more Smart Citation

Self-Similarity and Spatial Periodicity in Cerebral Cortical Patterning: Structural Design Notes for Neural Tissue Architects

Rouleau

Murugan

2023

Anatomia

View full text Add to dashboard Cite

Tissue engineering is a powerful tool with which to systematically identify the determinants of biological functions. Applied to the design and fabrication of biomimetic brains, tissue engineering serves to disentangle the complex anatomy of neural circuits and pathways by recapitulating structure-function relationships in simplified model systems. The complex neuroanatomy of the cerebral cortex, with its enigmatic columnar and stratified cytoarchitectonic organization, represents a major challenge toward isolating the minimal set of elements that are required to assemble neural tissues with cognitive functions. Whereas considerable efforts have highlighted important genetic and physical correlates of early cortical tissue patterning, no substantive attempt to identify the determinants of how the cortices acquire their relatively conserved, narrow range of numbered layers is evident in the literature. Similarly, it is not yet clear whether cortical columns and laminae are functionally relevant or epiphenomena of embryonic neurodevelopment. Here, we demonstrate that spatial frequencies (m−1) derived from the width-to-height ratios of cerebral cortical columns predict sinusoids with a narrow range of spatial cycles over the average cortical thickness. The resulting periodicities, denoted by theoretical wavenumbers, reflect the number of observed cortical layers among humans and across several other species as revealed by a comparative anatomy approach. We present a hypothesis that cortical columns and their periodic layers are emergent of the intrinsic spatial dimensions of neurons and their nested, self-similar aggregate structures including minicolumns. Finally, we discuss the implications of periodic tissue patterns in the context of neural tissue engineering.

show abstract

Section: The Cortical Column Conundrumsupporting

confidence: 87%

Section: Spatial Periodicities Within Columns Predict Observed Lamina...mentioning

confidence: 99%

Self-Similarity and Spatial Periodicity in Cerebral Cortical Patterning: Structural Design Notes for Neural Tissue Architects

Rouleau

Murugan

2023

Anatomia

View full text Add to dashboard Cite

show abstract

“…Concerning the complexity of the DCs, as noted above, it was quantified by measuring the fractal dimensions. The fractal dimension is an index widely applied in biology and medicine, quantifying the complexity of a pattern (Alberich‐Bayarri et al, 2010; Bruner et al, 2006; Di Ieva, 2016; Gutierrez Aceves et al, 2018; Mandelbrot, 1982). In fractal geometry, the fractal dimension of a linear 2D pattern can vary between 1.0 and 2.0.…”

Section: Methodsmentioning

confidence: 99%

The diploic venous system in Homo neanderthalensis and fossil Homo sapiens: A study using high‐resolution computed tomography

Hui,

Balzeau

2023

American Journal of Biological Anthropology

View full text Add to dashboard Cite

ObjectivesThe diploic venous system has been hypothesized to be related to human brain evolution, though its evolutionary trajectory and physiological functions remain largely unclear. This study examines the characteristics of the diploic venous channels (DCs) in a selection of well‐preserved Homo neanderthalensis and Upper Paleolithic Homo sapiens crania, searching for the differences between the two taxa and exploring the associations between brain anatomy and DCs.Materials and MethodsFive H. neanderthalensis and four H. sapiens fossil specimens from Western Europe were analyzed. Based on Micro‐CT scanning and 3D reconstruction, the distribution pattern and draining orifices of the DCs were inspected qualitatively. The size of the DCs was quantified by volume calculation, and the degree of complexity was quantified by fractal analyses.ResultsHigh‐resolution data show the details of the DC structures not documented in previous studies. H. neanderthalensis and H. sapiens specimens share substantial similarities in the DCs. The noticeable differences between the two samples manifest in the connecting points surrounding the frontal sinuses, parietal foramina, and asterional area.DiscussionThis study provides a better understanding of the anatomy of the DCs in H. neanderthalensis and H. sapiens. The connection patterns of the DCs have potential utility in distinguishing between the two taxa and in the phylogenetic and taxonomic discussion of the Neandertal‐like specimens with controversial taxonomic status.

show abstract

“…Moreover, fractal objects possess a crucial characteristic, whereby the patterns defining them are consistently replicated at decreasing magnitudes, and this leads to their constituent parts, which exhibit a likeness to the whole structure, irrespective of their dimensions: this feature is commonly known as "selfsimilarity". Many anatomical structures have been shown to demonstrate self-similarity properties [15], and lungs, with their bronchioalveolar ramifications, can be one of them. Such an approach has been successfully used by radiologists to characterize the spatial patterns of disease progression in ILD, and we believe that this approach, implemented using digital pathology, could also be successful at the histological level, with fractal morphometry assessing architectural distortion and correlating with a specific pattern, thus enforcing histologic pattern recognition [16].…”

Section: Introductionmentioning

confidence: 99%

Histologic Analysis of Idiopathic Pulmonary Fibrosis by Morphometric and Fractal Analysis

Mancini¹,

Bargiacchi²,

Vitis

et al. 2023

Biomedicines

View full text Add to dashboard Cite

Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive fibrotic lung disorder, ultimately leading to respiratory failure and death. Despite great research advances in understanding the mechanisms underlying the disease, its diagnosis, and its treatment, IPF still remains idiopathic without known biological or histological markers able to predict disease progression or response to treatment. The histologic hallmark of IPF is usual interstitial pneumonia (UIP), with its intricate architectural distortion and temporal inhomogeneity. We hypothesize that normal lung alveolar architecture can be compared to fractals, such as the Pythagoras tree with its fractal dimension (Df), and every pathological insult, distorting the normal lung structure, could result in Df variations. In this study, we aimed to assess the UIP histologic fractal dimension in relationship to other morphometric parameters in newly diagnosed IPF patients and its possible role in the prognostic stratification of the disease. Clinical data and lung tissue specimens were obtained from twelve patients with IPF, twelve patients with non-specific interstitial pneumonia (NSIP), and age-matched “healthy” control lung tissue from patients undergoing lung surgery for other causes. Histology and histomorphometry were performed to evaluate Df and lacunarity measures, using the box counting method on the FracLac ImageJ plugin. The results showed that Df was significantly higher in IPF patients compared to controls and fibrotic NSIP patients, indicating greater architectural distortion in IPF. Additionally, high Df values were associated with higher fibroblastic foci density and worse prognostic outcomes in IPF, suggesting that Df may serve as a potential novel prognostic marker for IPF. The scalability of Df measurements was demonstrated through repeated measurements on smaller portions from the same surgical biopsies, which were selected to mimic a cryobiopsy. Our study provides further evidence to support the use of fractal morphometry as a tool for quantifying and determining lung tissue remodeling in IPF, and we demonstrated a significant correlation between histological and radiological Df in UIP pattern, as well as a significant association between Df and FF density. Furthermore, our study demonstrates the scalability and self-similarity of Df measurements across different biopsy types, including surgical and smaller specimens.

show abstract

Fractal anatomy of the hippocampal formation

Abstract: The hippocampal complex is a fractal. The fractal analysis must be an objective measurement that can help us as a descriptive tool in hippocampal anatomy and maybe in a close future in the diagnosis of anatomical alterations.

Cited by 4 publications

References 26 publications

Self-Similarity and Spatial Periodicity in Cerebral Cortical Patterning: Structural Design Notes for Neural Tissue Architects

Self-Similarity and Spatial Periodicity in Cerebral Cortical Patterning: Structural Design Notes for Neural Tissue Architects

The diploic venous system in Homo neanderthalensis and fossil Homo sapiens: A study using high‐resolution computed tomography

Histologic Analysis of Idiopathic Pulmonary Fibrosis by Morphometric and Fractal Analysis

Contact Info

Product

Resources

About