A comparative fractal analysis of various mammalian astroglial cell types

Fractal Analysis in Neurodegenerative Diseases

Neurodegenerative diseases are defined by progressive nervous system dysfunction and death of neurons. The abnormal conformation and assembly of proteins is suggested to be the most probable cause for many of these neurodegenerative disorders, leading to the accumulation of abnormally aggregated proteins, for example, amyloid β (Aβ) (Alzheimer's disease and vascular dementia), tau protein (Alzheimer's disease and frontotemporal lobar degeneration), α-synuclein (Parkinson's disease and Lewy body dementia), polyglutamine expansion diseases (Huntington disease), or prion proteins (Creutzfeldt-Jakob disease). An aberrant gain-of-function mechanism toward excessive intraparenchymal accumulation thus represents a common pathogenic denominator in all these proteinopathies. Moreover, depending upon the predominant brain area involvement, these different neurodegenerative diseases lead to either movement disorders or dementia syndromes, although the underlying mechanism(s) can sometimes be very similar, and on other occasions, clinically similar syndromes can have quite distinct pathologies. Non-Euclidean image analysis approaches such as fractal dimension (FD) analysis have been applied extensively in quantifying highly variable morphopathological patterns, as well as many other connected biological processes; however, their application to understand and link abnormal proteinaceous depositions to other clinical and pathological features composing these syndromes is yet to be clarified. Thus, this short review aims to present the most important applications of FD in investigating the clinical-pathological spectrum of neurodegenerative diseases.

A Self-Similarity Logic May Shape the Organization of the Nervous System

From the morphological point of view, the nervous system exhibits a fractal, self-similar geometry at various levels of observations, from single cells up to cell networks. From the functional point of view, it is characterized by a hierarchical organization in which self-similar structures (networks) of different miniaturizations are nested within each other. In particular, neuronal networks, interconnected to form neuronal systems, are formed by neurons, which operate thanks to their molecular networks, mainly having proteins as components that via protein-protein interactions can be assembled in multimeric complexes working as micro-devices. On this basis, the term "self-similarity logic" was introduced to describe a nested organization where, at the various levels, almost the same rules (logic) to perform operations are used. Self-similarity and self-similarity logic both appear to be intimately linked to the biophysical evidence for the nervous system being a pattern-forming system that can flexibly switch from one coherent state to another. Thus, they can represent the key concepts to describe its complexity and its concerted, holistic behavior.

Fractal analysis of the macular region in healthy eyes using swept-source optical coherence tomography angiography

PURPOSE

This cross-sectional observational study evaluated the relationship between retinal vascular fractal dimension (FD) and age, as well as other vascular parameters in healthy eyes using swept-source optical coherence tomography angiography (SS-OCTA).

METHODS

The study cohort consisted of 222 eyes of 116 healthy participants with no ocular or systemic disease. SS-OCTA images were captured and analyzed using the Plex Elite 9000 and software tools available in the advanced retinal imaging (ARI) network hub. The retinal vascular layers were defined by the instrument's automatic retinal layer segmentation. The fractal analysis was performed on the superficial capillary plexus (SCP), deep capillary plexus (DCP), and the whole retina. Grayscale OCTA images were standardized and binarized using ImageJ and fractal box-counting analyses were performed using Fractalyse software. Pearson's correlation was used to analyze the correlation between FD and retinal vascular parameters.

RESULTS

The results showed that FD values were significantly higher in the 6 mm ring and the whole 6 × 6 scan region when compared to the 1 mm ETDRS central subfield. The correlation between age and FD was weak with a significant positive correlation between age and FD of the SCP in the 6 mm ring and between age and FD of the DCP in the 1 mm ring. Overall, differences in FD values in these healthy eyes were extremely small regardless of age or macular location.

CONCLUSION

FD values in normal eyes show little variation with age and are relatively stable across the macula. This suggests that FD values may not need adjustment for age or location when evaluated in the context of retinal disease.

Dopamine, Immunity, and Disease

The neurotransmitter dopamine is a key factor in central nervous system (CNS) function, regulating many processes including reward, movement, and cognition. Dopamine also regulates critical functions in peripheral organs, such as blood pressure, renal activity, and intestinal motility. Beyond these functions, a growing body of evidence indicates that dopamine is an important immunoregulatory factor. Most types of immune cells express dopamine receptors and other dopaminergic proteins, and many immune cells take up, produce, store, and/or release dopamine, suggesting that dopaminergic immunomodulation is important for immune function. Targeting these pathways could be a promising avenue for the treatment of inflammation and disease, but despite increasing research in this area, data on the specific effects of dopamine on many immune cells and disease processes remain inconsistent and poorly understood. Therefore, this review integrates the current knowledge of the role of dopamine in immune cell function and inflammatory signaling across systems. We also discuss the current understanding of dopaminergic regulation of immune signaling in the CNS and peripheral tissues, highlighting the role of dopaminergic immunomodulation in diseases such as Parkinson's disease, several neuropsychiatric conditions, neurologic human immunodeficiency virus, inflammatory bowel disease, rheumatoid arthritis, and others. Careful consideration is given to the influence of experimental design on results, and we note a number of areas in need of further research. Overall, this review integrates our knowledge of dopaminergic immunology at the cellular, tissue, and disease level and prompts the development of therapeutics and strategies targeted toward ameliorating disease through dopaminergic regulation of immunity. SIGNIFICANCE STATEMENT: Canonically, dopamine is recognized as a neurotransmitter involved in the regulation of movement, cognition, and reward. However, dopamine also acts as an immune modulator in the central nervous system and periphery. This review comprehensively assesses the current knowledge of dopaminergic immunomodulation and the role of dopamine in disease pathogenesis at the cellular and tissue level. This will provide broad access to this information across fields, identify areas in need of further investigation, and drive the development of dopaminergic therapeutic strategies.

Evaluation of early microstructural changes in the R6/1 mouse model of Huntington's disease by ultra-high field diffusion MR imaging

Diffusion MRI (dMRI) has been able to detect early structural changes related to neurological symptoms present in Huntington's disease (HD). However, there is still a knowledge gap to interpret the biological significance at early neuropathological stages. The purpose of this study is two-fold: (i) establish if the combination of Ultra-High Field Diffusion MRI (UHFD-MRI) techniques can add a more comprehensive analysis of the early microstructural changes observed in HD, and (ii) evaluate if early changes in dMRI microstructural parameters can be linked to cellular biomarkers of neuroinflammation. Ultra-high field magnet (16.7T), diffusion tensor imaging (DTI), and neurite orientation dispersion and density imaging (NODDI) techniques were applied to fixed ex-vivo brains of a preclinical model of HD (R6/1 mice). Fractional anisotropy (FA) was decreased in deep and superficial grey matter (GM) as well as white matter (WM) brain regions with well-known early HD microstructure and connectivity pathology. NODDI parameters associated with the intracellular and extracellular compartment, such as intracellular ventricular fraction (ICVF), orientation dispersion index (ODI), and isotropic volume fractions (IsoVF) were altered in R6/1 mice GM. Further, histological studies in these areas showed that glia cell markers associated with neuroinflammation (GFAP & Iba1) were consistent with the dMRI findings. dMRI can be used to extract non-invasive information of neuropathological events present in the early stages of HD. The combination of multiple imaging techniques represents a better approach to understand the neuropathological process allowing the early diagnosis and neuromonitoring of patients affected by HD.

Implication of cerebral astrocytes in major depression: A review of fine neuroanatomical evidence in humans

Postmortem investigations have implicated astrocytes in many neurological and psychiatric conditions. Multiple brain regions from individuals with major depressive disorder (MDD) have lower expression levels of astrocyte markers and lower densities of astrocytes labeled for these markers, suggesting a loss of astrocytes in this mental illness. This paper reviews the general properties of human astrocytes, the methods to study them, and the postmortem evidence for astrocyte pathology in MDD. When comparing astrocyte density and morphometry studies, astrocytes are more abundant and smaller in human subcortical than cortical brain regions, and immunohistochemical labeling for the astrocyte markers glial fibrillary acidic protein (GFAP) and vimentin (VIM) reveals fewer than 15% of all astrocytes that are present in cortical and subcortical regions, as revealed using other staining techniques. By combining astrocyte densities and morphometry, a model was made to illustrate that domain organization is mostly limited to GFAP-IR astrocytes. Using these markers and others, alterations of astrocyte densities appear more widespread than those for astrocyte morphologies throughout the brain of individuals having died with MDD. This review suggests how reduced astrocyte densities may relate to the association of depressive episodes in MDD with elevated S100 beta (S100B) cerebrospinal fluid serum levels. Finally, a potassium imbalance theory is proposed that integrates the reduced astrocyte densities generated from postmortem studies with a hypothesis for the antidepressant effects of ketamine generated from rodent studies.

Enteric glia: the most alimentary of all glia

Glia (from Greek γλοία meaning 'glue') pertains to non-neuronal cells in the central (CNS) and peripheral nervous system (PNS) that nourish neurons and maintain homeostasis. In addition, glia are now increasingly appreciated as active regulators of numerous physiological processes initially considered exclusively under neuronal regulation. For instance, enteric glia, a collection of glial cells residing within the walls of the intestinal tract, regulate intestinal motility, a well-characterized reflex controlled by enteric neurons. Enteric glia also interact with various non-neuronal cell types in the gut wall such as enterocytes, enteroendocrine and immune cells and are therefore emerging as important local regulators of diverse gut functions. The intricate molecular mechanisms that govern glia-mediated regulation are beginning to be discovered, but much remains unknown about the functions of enteric glia in health and disease. Here we present a current view of the enteric glia and their regulatory roles in gastrointestinal (GI) (patho)physiology; from GI motility and epithelial barrier function to enteric neuroinflammation.

Reliability of Using Retinal Vascular Fractal Dimension as a Biomarker in the Diabetic Retinopathy Detection

The retinal fractal dimension (FD) is a measure of vasculature branching pattern complexity. FD has been considered as a potential biomarker for the detection of several diseases like diabetes and hypertension. However, conflicting findings were found in the reported literature regarding the association between this biomarker and diseases. In this paper, we examine the stability of the FD measurement with respect to (1) different vessel annotations obtained from human observers, (2) automatic segmentation methods, (3) various regions of interest, (4) accuracy of vessel segmentation methods, and (5) different imaging modalities. Our results demonstrate that the relative errors for the measurement of FD are significant and FD varies considerably according to the image quality, modality, and the technique used for measuring it. Automated and semiautomated methods for the measurement of FD are not stable enough, which makes FD a deceptive biomarker in quantitative clinical applications.

Morphology and functions of astrocytes cultured on water-repellent fractal tripalmitin surfaces

In the brain, astrocytes play an essential role with their multiple functions and sophisticated structure, as surrounded by a fractal environment which has not been available in our traditional cell culture. Water-repellent fractal tripalmitin (PPP) surfaces can imitate the fractal environment in vivo, so the morphology and biochemical characterization of astrocytes on these surfaces are examined. Water-repellent fractal PPP surface can induce astrocytes to display sophisticated morphology with smaller size of cell area, longer and finer filopodium-like processes, and higher morphological complexity. The super water-repellent fractal PPP surface with water contact angle of 150°∼160° produces the maximal effects compared with other surfaces at lower water contact angles. The trends of characteristic protein expression, including that of nestin, vimentin, GFAP and glutamine synthetase, for astrocytes cultured on super water-repellent fractal PPP surfaces approximate more to in vivo pattern. The super water-repellent PPP surface also render astrocytes to perform more pronounced promotion of neurogenesis by increasing the release of nerve growth factor in a co-culture system. Altogether, our results suggest that the super water-repellent fractal PPP surface facilitates the astrocytes to mimic their in vivo performance, thus provides a closer-to-natural culture environment for experimental assessment of glial structure and functions.

FGF2 deficit during development leads to specific neuronal cell loss in the enteric nervous system

The largest part of the peripheral nervous system is the enteric nervous system (ENS). It consists of an intricate network of several enteric neuronal subclasses with distinct phenotypes and functions within the gut wall. The generation of these enteric phenotypes is dependent upon appropriate neurotrophic support during development. Glial cell line-derived neurotrophic factor (GDNF) and fibroblast growth factor-2 (FGF2) play an important role in the differentiation and function of the ENS. A lack of GDNF or its receptor (Ret) causes intestinal aganglionosis in mice, while fibroblast growth factor receptor signaling antagonist is identified as regulating proteins in the GDNF/Ret signaling in the developing ENS. Primary myenteric plexus cultures and wholemount preparations of wild type (WT) and FGF2-knockout mice were used to analyze distinct enteric subpopulations. Fractal dimension (D) as a measure of self-similarity is an excellent tool to analyze complex geometric shape and was applied to classify the subclasses of enteric neurons concerning their individual morphology. As a consequence of a detailed analysis of subpopulation variations, wholemount preparations were stained for the calcium binding proteins calbindin and calretinin. The fractal analysis showed a reliable consistence of subgroups with different fractal dimensions (D) in each culture investigated. Seven different neuronal subtypes could be differentiated according to a rising D. Within the same D, the neurite length revealed significant differences between wild type and FGF2-knockout cultures, while the subclass distribution was also altered. Depending on the morphological characteristics, the reduced subgroup was supposed to be a secretomotor neuronal type, which could be confirmed by calbindin and calretinin staining of the wholemount preparations. These revealed a reduction up to 40 % of calbindin-positive neurons in the FGF2-knockout mouse. We therefore consider FGF2 playing a more important role in the fine-tuning of the ENS during development as previously assumed.

Quantification of echodensities in tuberculous pericardial effusion using fractal geometry: a proof of concept study

Background

The purpose of this study was to quantify the heterogeneous distribution of echodensities in the pericardial fluid of patients with tuberculous pericarditis using echocardiography and fractal analysis, and to determine whether there were differences in the fractal dimensions of effusive-constrictive and effusive non-constrictive disease.

Methods

We used fractal geometry to quantify the echocardiographic densities in patients who were enrolled in the Investigation of the Management of Pericarditis in Africa (IMPI Africa) Registry. Sub-costal and four chamber images were included in the analysis if a minimum of two clearly identified fibrin strands were present and the quality of the images were of a standard which allowed for accurate measurement of the fractal dimension. The fractal dimension was calculated as follows: D_f = limlog N(s)/[log (l/s)], where D_f is the box counting fractal dimension of the fibrin strand, s is the side length of the box and N(s) is the smallest number of boxes of side length s to cover the outline of the object being measured. We compared the fractal dimension of echocardiographic findings in patients with effusive constrictive pericarditis to effusive non-constrictive pericardial effusion using the non-parametric Mann–Whitney test.

Results

Of the 14 echocardiographs from 14 participants that were selected for the study, 42.8% (6/14) of images were subcostal views while 57.1% (8/14) were 4-chamber views. Eight of the patients had tuberculous effusive constrictive pericarditis while 6 had tuberculous effusive non-constrictive pericarditis. The mean fractal dimension Df was 1.325 with a standard deviation (SD) of 0.146. The measured fibrin strand dimension exceeded the topological dimension in all the images over the entire range of grid scales with a correlation coefficient (r²) greater than 0.8 in the majority. The fractal dimension of echodensities was 1.359 ± 0.199 in effusive constrictive pericarditis compared to 1.330 ± 0.166 in effusive non-constrictive pericarditis (p = 0.595).

Conclusions

The echocardiographic densities in tuberculous pericardial effusion have a fractal geometrical dimension which is similar in pure effusive and effusive constrictive disease.

Radial glia: progenitor, pathway, and partner

Radial glia (RG) are a glial cell type that can be found from the earliest stages of CNS development. They are clearly identifiable by their unique morphology, having a periventricular cell soma and a long process extending all the way to the opposite pial surface. Due to this striking morphology, RG have long been thought of as a transient substrate for neuron migration in the developing brain. In fact, RG cells, far from exclusively serving as a passive scaffold for cell migration, have a remarkably diverse range of critical functions in CNS development and function. These include serving as progenitors of neurons and glia both during development as well as in response to injury, helping to direct axonal and dendritic process outgrowth, and regulating synaptic development and function. RG also engage in extensive bidirectional signaling both with neurons and one another. This review describes the diversity of RG cell types in the CNS and discusses their many important activities.

Cell surface topology creates high Ca2+ signalling microdomains

It has long been speculated that cellular microdomains are important for many cellular processes, especially those involving Ca²⁺ signalling. Measurements of cytosolic Ca²⁺ report maximum concentrations of less than few micromolar, yet several cytosolic enzymes require concentrations of more than 20 μM Ca²⁺ to be activated. In this paper, we have resolved this apparent paradox by showing that the surface topology of cells represents an important and hitherto unrecognized feature for generating microdomains of high Ca²⁺ in cells. We show that whereas the standard modeling assumption of a smooth cell surface predicts only moderate localized effects, the more realistic “wrinkled” surface topology predicts that Ca²⁺ concentrations up to 80 μM can persist within the folds of membranes for significant times. This intra-wrinkle location may account for 5% of the total cell volume. Using different geometries of wrinkles, our simulations show that high Ca²⁺ microdomains will be generated most effectively by long narrow membrane wrinkles of similar dimensions to those found experimentally. This is a new concept which has not previously been considered, but which has ramifications as the intra-wrinkle location is also a strategic location at which Ca²⁺ acts as a regulator of the cortical cytoskeleton and plasma membrane expansion.

Fractal Analysis of the Vascular Tree in the Human Retina

The retinal circulation of the normal human retinal vasculature is statistically self-similar and fractal. Studies from several groups present strong evidence that the fractal dimension of the blood vessels in the normal human retina is approximately 1.7. This is the same fractal dimension that is found for a diffusion-limited growth process, and it may have implications for the embryological development of the retinal vascular system. The methods of determining the fractal dimension for branching trees are reviewed together with proposed models for the optimal formation (Murray Principle) of the branching vascular tree in the human retina and the branching pattern of the human bronchial tree. The limitations of fractal analysis of branching biological structures are evaluated. Understanding the design principles of branching vascular systems and the human bronchial tree may find applications in tissue and organ engineering, i.e., bioartificial organs for both liver and kidney.

Characterization of Melanophore Morphology by Fractal Dimension Analysis

Fractal or focal dimension (FD) analysis is a valuable tool to identify physiologic stimuli at the cellular and tissue levels that allows for quantification of cell perimeter complexity. The FD analysis was determined on fluorescence images of caffeine- or epinephrine-treated (or untreated control) killifish Fundulus heteroclitus (Linneaus) melanophores in culture. Cell perimeters were indicated by rhodamine-phalloidin labeling of cortical microfilaments using box-counting FD analysis. Caffeine-treated melanophores displayed dispersed melanosomes in cells with less serrated edges and reduced FD and complexity. Complexity in epinephrine-treated cells was significantly higher than the caffeine-treated cells or in the control. Cytoarchitectural variability of the cell perimeter is expected because cells change shape when cued with agents. Epinephrine-treated melanophores demonstrated aggregated melanosomes in cells with more serrated edges, significantly higher FD and thus complexity. Melanophores not treated with caffeine or epinephrine produced variable distributions of melanosomes and resulted in cells with variably serrated edges and intermediate FD with a larger SE of the regression and greater range of complexity. Dispersion of melanosomes occurs with rearrangements of the cytoskeleton to accommodate centrifugal distribution of melanosomes throughout the cell and to the periphery. The loading of melanosomes onto cortical microfilaments may provide a less complex cell contour, with the even distribution of the cytoskeleton and melanosomes. Aggregation of melanosomes occurs with rearrangements of the cytoskeleton to accommodate centripetal distribution of melanosomes. The aggregation of melanosomes may contribute to centripetal retraction of the cytoskeleton and plasma membrane. The FD analysis is, therefore, a convenient method to measure contrasting morphologic changes within stimulated cells.

Astroglial interlaminar processes in human cerebral cortex: variations in cytoskeletal profiles

Among mammalian species, astroglial interlaminar processes are unique features of the primate cerebral cortex. The morphological diversity in the immunocytochemical expression of their cytoskeleton was analyzed. For this purpose, samples from normal human cerebral cortex from autopsy cases were used. While Fractal dimension failed to represent the actual complexity of interlaminar processes, Compression analysis allowed classification of these profiles according to their relative tortuosity. Conversion of Compression values into estimates of membrane surface suggested that profile changes could not only affect the directionality of dynamic events, but also the amount of glial cell membrane exposed to the local neuropil. Terminal segments of interlaminar processes were usually more tightly twisted than the cytoskeleton stalk, and enlarged in aged individuals. If not aberrant structures, these so-called 'terminal masses' may provide an additional means to increase local membrane availability. Based on Compression analysis, categories of the geometric variability of the cytoskeleton of cerebral cortex interlaminar glial processes are presented.

Rapid morphological changes in astrocytes are accompanied by redistribution but not by quantitative changes of cytoskeletal proteins

Astrocytes have the potential to acquire very different morphologies, depending on their regional location in the CNS and on their functional interactions with other cell types. Morphological changes between a flat or a fibroblast-like and a stellate or process-bearing appearance, and vice versa, can occur rapidly, but very little is known as to whether morphological transformations are based on quantitative changes of cytoskeletal proteins in microfilaments, intermediate filaments, and/or microtubules. Using a cell culture of selective type 1 astrocytes, we compared the distribution and protein amounts of a number of cytoskeletal proteins both during primary process growth induced by specific media conditions and after secondary transformations induced by dBcAMP. Our data presented in this report support the idea that astrocytes can undergo dramatic changes in their morphology requiring subcellular redistribution of most cytoskeletal proteins but no quantitative modifications of the amount of the respective proteins. After pharmacological treatment with lysophosphatic acid and genistein we show that astrocytes can acquire intermediate morphologies reminiscent of both fibroblast and stellate-like cells. These experiments demonstrate that the recently described RhoA-mediated signaling cascade between the cell surface and cytoskeletal proteins is only one of several signaling pathways acting on the astrocytic cytoskeleton.

Identification of living oligodendrocyte developmental stages by fractal analysis of cell morphology

The Mandelbrot's fractal dimension (D), a measure of shape complexity, has been used to quantify the complex morphology of living cells. Previous studies on glial cells have shown that as cells increase in morphological complexity, their "D" value increases, suggesting that "D" could be used to estimate their stage of differentiation. In the present study the box-counting method was used to calculate the "D" values of rat cerebellar oligodendrocytes during their differentiation in primary culture. These values were correlated with the immunoreactivity of cells to antigenic markers commonly used for assessing their stages of differentiation: A2B5, O4 and anti-galactocerebroside (Gal-C). Our results show that changes of the fractal dimension during differentiation follow the well known pattern of markers expression by these cells. These results demonstrate that A2B5-, O4-, and Gal-C-expressing oligodendrocytes can be confidently estimated from their respective fractal dimension values. Based on this immunocytochemical calibration, the calculation of "D" allows an easy and fast determination of the developmental stage of living (unstained) oligodendrocytes before the study of their physiological characteristics. Using this method we precisely identified living oligodendrocyte progenitors and early pro-oligodendrocytes expressing voltage-activated sodium currents that is a common characteristic of these two immature developmental stages (Sontheimer et al. [1989b] Neuron 2:1135-1145).

The effect of type 1 astrocytes on neuronal complexity: a fractal analysis

Embryonic, ventral spinal cord neurons were grown on poly(d-lysine) (PDL) or on a monolayer of type 1 astrocytes. At various times from 6 h to 2 weeks postplating, cells were fluorescently labeled and fixed with 4% paraformaldehyde. The cell surface immunoreaction allowed visualization of neurons in their entirety, namely, cell bodies and various membranous extensions that included lamellipodia, growth cones, axons, and dendrites. Outlines were drawn for individual neurons and their fractal dimension (D) was calculated. Neurons on poly(d-lysine) reached a peak D at 3 days in vitro, 1 day later than neurons on astrocytes (2 days in vitro). The maximum D was greater for cells on poly(d-lysine) when compared with neurons on astrocytes. In a second experiment the maximum D was similar for neurons on both surfaces but neurons on PDL maintained a higher D for a much longer period than neurons on astrocytes. An examination of fluorescent images revealed that neurons on poly(d-lysine) exhibited lamellipodia and large growth cones for several days and these structures were likely responsible for the high D seen in these cells. These structures were rarely observed in neurons plated on astrocytes. Interestingly, D on both surfaces decreased to a similar value at between 1 and 2 weeks in vitro. The trend for D in these cultures, an initial increase to a peak value followed by a decrease to a stable value, is discussed in light of the chemical nature of the two surfaces and synapse formation and stabilization.

Surface fractal computation and its application to immunofluorescent histochemical studies of calpain and calpastatin in PC12 cells

The purpose of this report is to present a method which can be used to parameterize patterns of immunofluorescent staining in cultured neural cells. The algorithm is based on the observation that the variance in pixel intensity of the image is a power function of the magnitude of the area in immunofluorescently stained PC12 cells. This property is used to derive the fractal dimension (D) of the region of interest (ROI), and corresponds to the complexity of the pixel intensity associated with the ROI, which is analogous to a fractal surface. We show that the measure is useful in characterizing immunofluorescent staining patterns, and apply this measure to study the effects of ethanol exposure on mu-calpain and calpastatin-associated immunoreactivity. Exposure of PC12 cells to ethanol (80 mM)x48 h resulted in alterations in immunofluorescent signal (Control vs ethanol) associated with actin, calpastatin and mu-calpain: 2289+/-166 vs 1709+/-69, P<0.01; 1681+/-38 vs 2224+/-95, P<0.001; 1823+/-39 vs 2841+/-68, P<0.0001 respectively, magnitudes being pixel intensity units on a scale of 0-4095. D-values for the three proteins in the same order were: 2.32+/-0.01 vs 2.31+/-0.03, NS; 2.31+/-0.01 vs 2.32+/-0.01, NS; 2.16+/-0.03 vs 2. 24+/-0.02, P<0.01, with a possible D-value range of 2-3.

Microdomains for neuron-glia interaction: parallel fiber signaling to Bergmann glial cells

Astrocytes are considered a reticulate network of cells, through which calcium signals can spread easily. In Bergmann glia, astrocytic cells of the cerebellum, we identified subcellular compartments termed 'glial microdomains'. These elements have a complex surface consisting of thin membrane sheets, contain few mitochondria and wrap around synapses. To test for neuronal interaction with these structures, we electrically stimulated parallel fibers. This stimulation increased intracellular calcium concentration ([Ca2+]i) in small compartments within Bergmann glial cell processes similar in size to glial microdomains. Thus, a Bergmann glial cell may consist of hundreds of independent compartments capable of autonomous interactions with the particular group of synapses that they ensheath.

Fractals in pathology

Many natural objects, including most objects studied in pathology, have complex structural characteristics and the complexity of their structures, for example the degree of branching of vessels or the irregularity of a tumour boundary, remains at a constant level over a wide range of magnifications. These structures also have patterns that repeat themselves at different magnifications, a property known as scaling self-similarity. This has important implications for measurement of parameters such as length and area, since Euclidean measurements of these may be invalid. The fractal system of geometry overcomes the limitations of the Euclidean geometry for such objects and measurement of the fractal dimension gives an index of their space-filling properties. The fractal dimension may be measured using image analysis systems and the box-counting, divider (perimeter-stepping) and pixel dilation methods have all been described in the published literature. Fractal analysis has found applications in the detection of coding of coding regions in DNA and measurement of the space-filling properties of tumours, blood vessels and neurones. Fractal concepts have also been usefully incorporated into models of biological processes, including epithelial cell growth, blood vessel growth, periodontal disease and viral infections.

Fractal methods and results in cellular morphology--dimensions, lacunarity and multifractals

This paper discusses the concepts of fractal geometry in a cellular biological context. It defines the concept of the fractal dimension. D, as a measure of complexity and illustrates the two different general ways of quantitatively measuring D by length-related and mass-related methods. Then, these several Ds are compared and contrasted. A goal of the paper is to find methods other than length-related measures that can distinguish between two objects that have the same D but are structurally different. The mass-related D is shown potentially to be such a measure. The concept of lacunarity, L, is defined and methods of measuring L are illustrated. L is also shown to be a potentially distinguishing measure. Finally, the notion of multifracticality is defined and illustrated to exist in certain individual nerve and glial cells.

Complexity analysis of oligodendroglial processes expressing myelin-associated glycoprotein

Oligodendroglia synthesize myelin in the mammalian central nervous system. Mature oligodendroglia have been identified in culture by two criteria; the expression of molecules characteristic of myelin, such as galactocerebroside (galC) and myelin-associated glycoprotein (MAG), and the elaboration of complex processes. Myelin gene expression can be documented by the binding of specific antibodies and antisera to the myelin-specific molecules; process complexity can be described by the fractal dimension, D. In this study, anti-MAG antisera was used to document MAG expression in the processes of oligodendroglia. Eighty percent of the galC+ oligodendroglia bound anti-MAG antiserum. With time in culture, MAG immunoreactivity seemed to extend from the cell soma into the oligodendroglial processes. To quantify this observation, fractal dimensions were calculated using either galC or MAG immunoreactivity to visualize oligodendroglial processes. A fractal dimension of 1.5 was calculated for O1+ processes by day 4 of culture; this value for D remained constant over the course of 1 month in culture. The fractal dimension calculated for MAG+ processes increased from 1.2 to 1.5 over the course of 28 days in culture. This change in fractal dimension confirms our visual impression that galC-containing processes acquire MAG slowly over the course of several weeks in culture.

Quantification of tight junction complexity by means of fractal analysis

The concept of fractal geometry provides an elegant tool for the quantitative and objective structural description of various objects, the fractal analysis. Fractal analysis quantifies the structural complexity of objects by a characteristic singular value, the fractal dimension (FD). It can be estimated, e.g. by the box-counting method and provides a highly integrated measure in the range 1 < FD < 2 for curves extending within a plane. In this study, fractal analysis is used for the first time to evaluate the complexity of the tight junction network between adjoining cells. Bovine brain endothelial cells were cultured under various experimental conditions and the tight junctions were drawn to scale as visualized by the freeze fracture technique. These drawings were analyzed by fractal analysis, and by two other methods commonly used in this field, viz. the strand counting (SC) and complexity index (CI) methods. In contrast to the latter methods, the FD shows no directional preference and therefore no assumptions on the dynamic properties of the network's complexity are required. Thus, FD is demonstrated to provide the most sensitive, reliable and complete measure of tight junction complexity. In combination with SC and CI, additional information can be achieved concerning the directionality of the altered arrangement of tight junctional strands. Our analysis allows for the following conclusions. (1) Defined experimental influences can modify the complexity of tight junctions that are formed between endothelial cells in vitro, and (2) these structural modifications of the tight junctions are mainly due to an altered strand branching pattern.

Morphology of horseradish peroxidase (HRP)-injected glial cells in the myenteric plexus of the guinea-pig

Glial cells of the myenteric plexus from guinea pig small intestine were intracellularly filled with horseradish peroxidase (HRP), and histochemically stained. Camera lucida-like drawings of twenty cells were morphologically and morphometrically analyzed. The cells have very small ellipsoid somata (8.5 +/- 0.7 microns equivalent diameter, i.e., about 330 micron3 volume), and send up to 20 thin and short processes (less than 26 to about 110 microns in length). The morphology of the cells appears to depend on their location within the plexus. Glial cells located within the ganglia are similar to CNS protoplasmic astrocytes; they are star-shaped, and their very short processes are irregularly branched. In contrast, glial cells within the interganglionic fiber tracts resemble CNS fibrous astrocytes. They extend longer processes that are parallel to the fiber tracts, and show less tendency to branch. We propose that the morphology of enteric glia is determined by the structure of the microenvironment. Both cell types form several flat endfeet at a basal lamina either surrounding blood vessels or at the ganglionic border. Furthermore, the occurrence of "holes" in the glial cell processes suggests that particular neuronal cell processes may be enwrapped in a specific manner. Fractal analysis of camera lucida-like drawings of the cells showed that the cells have a highly complex surface structure, comparable to that of protoplasmic astrocytes in the brain. These tiny cells may possess a membrane surface area of approximately 2000 micron2, almost 90% of which are contributed by the cell processes.(ABSTRACT TRUNCATED AT 250 WORDS)

Fractal geometric analysis of colorectal polyps

Colorectal polyps have a subjectively self-similar structure which suggests that these structures may have fractal elements and that the fractal dimension may be a useful morphometric discriminant. The fractal dimensions of images from haematoxylin and eosin-stained sections of 359 colorectal polyps (214 tubulovillous adenomas, 41 'pure' tubular adenomas, 29 'pure' villous adenomas, 68 metaplastic polyps, and 7 inflammatory polyps) were measured using a box-counting method implemented on a microcomputer-based image analysis system. Results were assessed using polychotomous logistic regression, confusion matrices, and kappa statistics. All examined polyps were shown to have a fractal structure in the range of scales examined. The fractal dimension was significantly different between different diagnostic categories (P < 0.0001) and was a useful discriminant between these categories (kappa statistic 0.60 for the confusion matrix with size as the other variable). The fractal dimension did not shown any significant correlation with the grade of epithelial dysplasia (P > 0.05). This study shows that colorectal polyps have a fractal structure over a defined range of magnification and Euclidean morphometric measurements will be invalid outside precisely defined conditions of resolution and magnification. The fractal dimension is a better way of quantitating the polyp shape and is a useful morphometric discriminant between diagnostic categories.

Comparative fractal analysis of cultured glia derived from optic nerve and brain demonstrate different rates of morphological differentiation

O-2A progenitor cells derived from neonatal rat cerebral hemispheres or optic nerves, were induced to differentiate in culture into either oligodendrocytes or type 2 astrocytes. The fractal dimensions, a measure of morphological complexity, of the differentiating glial cells were measured over time. Analysis of the changes in fractal dimension (D) with respect to time revealed specific rates of growth for each glial phenotype and a specific final D. The time course of these changes is well fit by a simple mathematical model. While brain-derived oligodendrocytes matured faster than the astrocytes, they ultimately attained comparable levels of complexity, with similar maximum fractal dimensions. Oligodendrocytes from nerve also matured faster than nerve derived astrocytes, in contrast, however, they attained a greater morphological complexity than nerve astrocytes. While the brain-derived oligodendrocytes showed a faster rate of maturation than their optic nerve counterparts, astrocytes from both regions had similar rates of morphological differentiation. Self-similarity, a defining property of fractal objects was investigated, by determining the fractal dimension of cells over a range of magnifications. The calculated fractal dimension remained constant over a 10-fold range in optical magnification, illustrating that cultured glial cells exhibit this important characteristic of fractal objects. In addition, we analyzed the branching patterns of glial processes by the Sholl method and found that the results were not as interpretable or meaningful as those of fractal analysis.

The application of fractal geometric analysis to microscopic images

Fractal geometry is a relatively new tool for the quantitative microscopist that is a more valid way of measuring dimensions of complex irregular objects than the integer-dimensional geometries (such as Euclidean geometry). This review discusses the theory of fractal geometry using the classic examples of the Von Koch curve, the Cantor set and the Sierpinski gasket. The problems of describing the dimensions of these objects are discussed and the concept of fractal dimensionality is introduced. Methods for measuring fractal dimensions are discussed, including their implementation on microcomputer-based image analysis systems . The advantages and problems of fractal geometric analysis are discussed and current applications in the field of microscopy are reviewed.

Early dendrite development in spinal cord cell cultures: a quantitative study

Neurons in dissociated cell culture provide a favorable system for the quantitative analysis of structural changes and the examination of structure-function relationships during development. Fragment C of tetanus toxin was used to label neurons in murine spinal cord cell cultures and dendrite outgrowth was monitored by a number of measures. The dissociated neurons increased in morphologic complexity from approximate spheres to highly branched structures during the first week in culture. Much of the structural complexity of the dendrite arbor, as quantified by fractal dimension, was established within 48 hr after plating, i.e., prior to the development of interneuronal contacts. During the first few days in culture, dendrite branching complexity increased more rapidly than dendrite size, whereas after 4 days, fractal dimension remained relatively constant while dendrites continued to grow. Fractal analysis has provided data which suggest that the early development of dendrite branching complexity is determined intrinsically. Fractal dimension, as an effective index of morphologic complexity, should be a useful tool for the further study of extrinsic signals which might modify the generation or stabilization of dendrite form.