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

The Morphology of Brain Neurons: The Box-Counting Method in the Quantitative Analysis of 2D Images

This chapter begins by showing the difference between fractal geometry and fractal analysis. The text shows the difference between mathematical and natural fractals and how they are best defined by explaining the concept of fractal analysis. Furthermore, the text presents the most famous technique of fractal analysis: the box-counting method. Defining this method and showing the methodology that leads to the precise value of the fractal (i.e., the box) dimension is done by demonstrating the images of human dentate neurons. A more detailed explanation of the methodology was presented in the previous version of this chapter.This version promotes the notion of monofractal analysis and shows how three types of the same neuronal images can quantify four image properties. The results showed that monofractal parameters successfully quantified four image properties in three nuclei of the cerebellum. Finally, the author discusses the results of this chapter and previously published conclusions. The results show how the monofractal parameters discriminate images of neurons from the three nuclei of the human cerebrum. These outcomes are discussed along with the results of previous studies.

New morphological features based on the Sholl analysis for automatic classification of traced neurons

BACKGROUND

This article addresses the automatic classification of reconstructed neurons through their morphological features. The purpose was to extend the capabilities of the L-Measure software.

METHODS

New morphological features were developed, based on modifications of the conventional Sholl analysis. The lengths of the compartments, as well as their volumes, were added to the features used in the classical analysis in order to improve the results during automatic neuron classification. FSM were used to obtain subsets of lower cardinality from the full feature sets and the usefulness of these subsets was tested through their use in supervised classification tasks. The study was based on two types of neurons belonging to mice: pyramidal and GABAergic interneurons. Furthermore, a set of pyramidal neurons belonging to Later 4 and Layer 5 was analyzed.

RESULTS

RF classifier shown the best performance combined with a Wrapper method.U-WNAD set allowed to obtain higher values than WN, A and D in all cases and better results than LM for the filters and wrappers FSM. U-LM-WNAD set, led to the highest AUC values for all the FSM studied. Similar results for different regions of cortex were obtained. Comparison with Existing Methods The new features exhibited high discriminatory power with which the values of AUC and Acc obtained in the experiments exceeded those obtained using only the features provided by L-Measure.

CONCLUSIONS

The highest values of AUC and Acc were obtained from the sets U-WNAD and U-LM-WNAD, evidencing the discriminatory power of the new proposed features.

Fractal dimension analysis reveals skeletal muscle disorganization in mdx mice

Duchenne Muscular Dystrophy (DMD) is characterized by muscle extracellular matrix disorganization due to the increased collagen deposition leading to fibrosis that significantly exacerbates disease progression. Fractal dimension analysis is a method that quantifies tissue/cellular disorganization and characterizes complex structures. The first objective of the present study was use fractal analysis to evaluate extracellular matrix disorganization in mdx mice soleus muscle. Next, we mimic a hyper-proliferation of fibrogenic cells by co-culturing NIH3T3 fibroblasts and C2C12 myoblasts to test whether fibroblasts induce disorganization in myoblast arrangement. Here, we show mdx presented high skeletal muscle disorganization as revealed by fractal analysis. Similarly, this method revealed that myoblasts co-cultured with fibroblast also presented cellular arrangement disorganization. We also reanalyzed skeletal muscle microarrays transcriptomic data from mdx and DMD patients that revealed transcripts related to extracellular matrix organization. This analysis also identified Osteoglycin, which was validated as a potential regulator of ECM organization in mdx dystrophic muscles. Our results demonstrate that fractal dimension is useful tool for the analysis of skeletal muscle disorganization in DMD and also reveal a fibroblast-myoblast cross-talk that contributes to "in vitro" myoblast disarrangement.

Box-Counting Method of 2D Neuronal Image: Method Modification and Quantitative Analysis Demonstrated on Images from the Monkey and Human Brain

This study calls attention to the difference between traditional box-counting method and its modification. The appropriate scaling factor, influence on image size and resolution, and image rotation, as well as different image presentation, are showed on the sample of asymmetrical neurons from the monkey dentate nucleus. The standard BC method and its modification were evaluated on the sample of 2D neuronal images from the human neostriatum. In addition, three box dimensions (which estimate the space-filling property, the shape, complexity, and the irregularity of dendritic tree) were used to evaluate differences in the morphology of type III aspiny neurons between two parts of the neostriatum.

Fractal analysis of dendrite morphology using modified box-counting method

The box-counting dimension of a non-stellate neuron changes continuously with its rotation. During preprocessing for box-counting, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel. A non-stellate neuronal picture should have the smallest fractal dimension when the angle between the horizontal axis and its major diameter is about 45°. The box-counting method does not consider the position of a picture on the computer screen. Therefore a dispersion of the box dimension values of a neuronal sample is rather large and their mean value is with larger variance. Modified box-counting method partly diminishes these findings. To improve a dependence of neuronal rotation on the box-counting dimension of non-stellate neurons, prior to applying box-counting method, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel.

Nano-volume drop patterning for rapid on-chip neuronal connect-ability assays

The ability of neurons to extend projections and to form physical connections among them (i.e., "connect-ability") is altered in several neuropathologies. The quantification of these alterations is an important read-out to investigate pathogenic mechanisms and for research and development of neuropharmacological therapies, however current morphological analysis methods are very time-intensive. Here, we present and characterize a novel on-chip approach that we propose as a rapid assay. Our approach is based on the definition on a neuronal cell culture substrate of discrete patterns of adhesion protein spots (poly-d-lysine, 23 ± 5 μm in diameter) characterized by controlled inter-spot separations of increasing distance (from 40 μm to 100 μm), locally adsorbed in an adhesion-repulsive agarose layer. Under these conditions, the connect-ability of wild type primary neurons from rodents is shown to be strictly dependent on the inter-spot distance, and can be rapidly documented by simple optical read-outs. Moreover, we applied our approach to identify connect-ability defects in neurons from a mouse model of 22q11.2 deletion syndrome/DiGeorge syndrome, by comparative trials with wild type preparations. The presented results demonstrate the sensitivity and reliability of this novel on-chip-based connect-ability approach and validate the use of this method for the rapid assessment of neuronal connect-ability defects in neuropathologies.

Effects of fractal surface on C6 glioma cell morphogenesis and differentiation in vitro

Neurons and glial cells in the brain are surrounded by a fractal environment. A fractal alkylketene dimmer (AKD) surface was shown to provide such a biomimetic environment for glial cell culture. However, little is known about the effects of fractal surface on the complexity of cell morphology. In particular, whether fractal surface induces glial cell differentiation remains to be elucidated. The present work, thus determined the fractal dimension (FD) of cell complexity with a geometrically calculational parameter, the expressions of GFAP gene and protein in C6 glioma cells on fractal AKD, non-fractal AKD and PLL-coated surfaces. Fractal surface suppressed the proliferation of glioma cell, and significantly increased the length and number of cell process. Furthermore, the enhanced values of FD were accompanied with the expressions of GFAP gene and protein, especially that of gene. However, cells on non-fractal and PLL surface proliferated gradually along with the culture time, showing the fibroblast-like morphology, and accompanied with the consistent expressions of GFAP gene and protein. These results suggested that C6 glioma cell differentiation can be induced by fractal AKD surface.

Cell image area as a tool for neuronal classification

The measurement of the area of a shapeless plane region is one of the basic problems in traditional calculus. In order to calculate the 'true' area of such a region, we have superimposed a net of identical squares on this region, counted the squares containing at least one point of the region, and calculated the sum of the areas of said squares. This sum represents an approximation of the region's area. By mathematical modelling and computational techniques we have investigated the law governing the decrease of these areas with the decrease of the length of the square's side. In theory, the prediction of the 'true' area could then be performed if the side of the net's squares tend to zero. Of course, the accuracy of the calculated area strongly depends on the computational potential and the statistical possibilities. Several morphometric parameters are currently in use for the quantitative analysis of the morphology of neuronal cell images. The cell image area has not yet been used and evaluated as a classification parameter - but it has the potential to be chosen over some other alternatives due to the high mathematical accuracy at which it is defined. By adopting mathematical modelling and computational techniques we show that this parameter can lead to successful distinction between 2 types of morphologically very similar cells (large boundary neuron and large asymmetrical neuron) in the dentate nucleus of the rhesus monkey (Macaca mulatta), while some other parameters failed to achieve positive results.

Mathematical modelling of neuronal dendritic branching patterns in two dimensions: application to retinal ganglion cells in the cat and rat

Sholl's analysis has been used for about 50 years to study neuron branching characteristics based on a linear, semi-log or log-log method. Using the linear two- dimensional Sholl's method, we call attention to a relationship between the number of intersections of neuronal dendrites with a circle and the numbers of branching points and terminal tips encompassed by the circle, with respect to the circle radius. For that purpose, we present a mathematical model, which incorporates a supposition that the number of dendritic intersections with a circle can be resolved into two components: the number of branching points and the number of terminal tips within the annulus of two adjoining circles. The numbers of intersections and last two sets of data are also presented as cumulative frequency plots and analysed using a logistic model (Boltzmann's function). Such approaches give rise to several new morphometric parameters, such as, the critical, maximal and mean values of the numbers of intersections, branching points and terminal tips, as well as the abscissas of the inflection points of the corresponding sigmoid plots, with respect to the radius. We discuss these parameters as an additional tool for further morphological classification schemes of vertebrate retinal ganglion cells. To test the models, we apply them first to three groups of morphologically different cat's retinal ganglion cells (the alpha, gamma and epsilon cells). After that, in order to quantitatively support the classification of the rat's alpha cells into the inner and outer cells, we apply our models to two subgroups of these cells grouped according to their stratification levels in the inner plexiform layer. We show that differences between most of our parameters calculated for these subgroups are statistically significant. We believe that these models have the potential to aid in the classification of biological images.

Interaction of Cochlear Nucleus Explants With Semiconductor Materials

OBJECTIVE/HYPOTHESIS

Implantable hearing devices such as cochlear implants and auditory brainstem implants deliver auditory information through electrical stimulation of auditory neurons. The combination of microelectronic electrodes with auditory nerve cells may lead to further improvement of the hearing quality with these devices. Whereas several kinds of neurons are known to grow on semiconductor substrates, interactions of cochlear nucleus (CN) neurons with such materials have yet to be described.

MATERIALS AND METHODS

To investigate survival and growth behavior of CN neurons on different semiconductor materials. CN explants from postnatal day 10 Sprague-Dawley rats were cultured for 96 hours in Neurobasal medium on polished and unpolished silicon wafers (p-type Si [100] and p-type Si3N4[100]) as well as plastic surface. These surfaces had been coated with poly-L-lysine and laminin. Neuronal outgrowth was examined using image analysis software after immunohistologic staining for neurofilament. Neurite length and directional changes were quantified. Additionally, neurite morphology and adhesion to the semiconductor material was evaluated by scanning electron microscopy.

RESULTS

Although proper adhesion of CN explants was seen, no neurite growth could be detected on unpolished silicon wafers (Si and Si3N4). Compared with the other test conditions, polished, laminin-coated Si3N4 wafers showed best biocompatibility regarding neurite length and number per explant. CN explants developed a mean of eight neurons with an average length of 236 mum in 96 hours of culture on these wafers.

CONCLUSION

The results of this study demonstrate the general possibility of CN neuron growth in culture on semiconductors in vitro. The differences in neuron length and number per explant indicate that the growth of CN neurons is influenced by the semiconductor substrate as well as extracellular matrix proteins, with laminin-coated p-type Si3N4[100] being a preferable material for future hybrid experiments on auditory-neuron semiconductor chips.

The Sholl analysis of neuronal cell images: Semi-log or log–log method?

Although the Sholl analysis is a quantitative method for morphometric neuronal studies and its application provides many benefits to neurobiology since it is obvious, common and meaningful, there are many unresolved theoretical issues that need to be addressed. Nevertheless, it can be practiced without much background or sophistication. The two different methods of the Sholl analysis--log-log and semi-log--have been applied previously without a clear basis as to what to use. To make an adequate choice of the method, one should try and accept that one which gives a better result. We consider that some of the underlying principles, assumptions and limitations for the Sholl analysis can be found in basic mathematics. In order to compare the results of applications of the semi-log and log-log methods to the same neuron, we introduce the concept of determination ratio as the ratio of the coefficient of determination for the semi-log method and that for the log-log method. If the semi-log method is better as related to the log-log method, the value of this parameter is larger than 1. Having in mind that dendrites exhibit enormously diverse forms, we point out that the semi-log Sholl method is more frequently utilizable in practice. Only the neurons, whose dendritic trees have one or a few sparsely ramified dendrites being much longer than the rest ones, could be successfully and exactly analysed using the log-log method. We also compare the Sholl analysis with fractal analysis for the characterization of neuronal arborization patterns and found that between the Sholl and fractal analysis exist various and important analogies.

A fast and accurate procedure for deriving the Sholl profile in quantitative studies of neuronal morphology

The growth and elaboration of neural processes underpins the establishment of neural architecture during development and is a key facet of neural plasticity throughout life. Sholl analysis is a valuable and widely used method for quantifying the extent and complexity of neural processes in the vicinity of the neuronal soma, such as the dendritic arbors of individual neurons in vivo and neuritic arbors of individual neurons in vitro. It consists of tracing a series of concentric rings with regular radial increments centred in the neuronal soma and counting the number X(i) of processes intersecting each ring. This is a laborious and time-consuming procedure that consequently can only be applied to relatively small numbers of neurons. We propose a simpler and accurate method for deriving exactly the same information based only on the relative position, with respect to the cell soma, of the bifurcation (B(i)) and terminal points (T(i)) of processes. By means of the iterative equation X(i)=X(i-1)+B(i)-T(i,) it is possible to automatically reconstruct the complete pattern of intersections between neurites and the concentric rings. We compared our method with the conventional Sholl analysis and found that our simplified procedure is approximately five times faster permitting numerically larger samples to be analyzed. We further tested the sensitivity of our method of analysis by looking at the effect of preventing NF-kappaB signaling on BDNF-dependent neuritic growth in sensory neurons.

Application of modified Sholl analysis to neuronal dendritic arborization of the cat spinal cord

The drawings of Golgi-impregnated neurons from laminae I to VI in dorsal horn of the cat spinal cord were analysed morphometrically with a modified Sholl method of concentric circles. In order to advance the Sholl analysis of neuronal dendritic arborization patterns, we developed a new method of data presentation using polynomial regression and defining three parameters: the critical value of the circle radius (which defines the place of a possible circle intersecting maximum number of dendrites), the maximum number of dendritic intersections with the circles (counted for consecutive circles placed starting at the cell body to the border of the dendritic tree), and the mean value of the fitted polynomial function (which describes an average property concerning numbers of branches of dendritic tree over the whole region occupied by the dendritic arbor). For that purpose we also used the Sholl regression coefficient as well as the Schoenen ramification index. As an illustration of our model, we demonstrate that proposed modification of the Sholl method can successfully discriminate neuronal populations among different laminae of the cat spinal cord.

Quantification of the fractal nature of mycelial aggregation in Aspergillus niger submerged cultures

Background

Fractal geometry estimates have proven useful in studying the growth strategies of fungi in response to different environments on soil or on agar substrates, but their use in mycelia grown submerged is still rare. In the present study, the effects of certain important fermentation parameters, such as the spore inoculum level, phosphate and manganese concentrations in the medium, on mycelial morphology of the citric acid producer Aspergillus niger were determined by fractal geometry. The value of employing fractal geometry to describe mycelial structures was examined in comparison with information from other descriptors including classic morphological parameters derived from image analysis.

Results

Fractal analysis of distinct morphological forms produced by fermentation conditions that influence fungal morphology and acid production, showed that the two fractal dimensions D_BS (box surface dimension) and D_BM (box mass dimension) are very sensitive indexes, capable of describing morphological differences. The two box-counting methods applied (one applied to the whole mass of the mycelial particles and the other applied to their surface only) enabled evaluation of fractal dimensions for mycelial particles in this analysis in the region of D_BS = 1.20–1.70 and D_BM = 1.20–2.70. The global structure of sufficiently branched mycelia was described by a single fractal dimension D, which did not exceed 1.30. Such simple structures are true mass fractals (D_BS = D_BM = D) and they could be young mycelia or dispersed forms of growth produced by very dense spore inocula (10⁸–10⁹ spores/ml) or by addition of manganese in the medium. Mycelial clumps and pellets were effectively discriminated by fractal analysis. Fractal dimension values were plotted together with classic morphological parameters derived from image analysis for comparisons. Their sensitivity to treatment was analogous to the sensitivity of classic morphological parameters suggesting that they could be equally used as morphological descriptors.

Conclusion

Starting from a spore, the mycelium develops as a mass fractal and, depending on culture conditions, it either turns to a surface fractal or remains a mass fractal. Since fractal dimensions give a measure of the degree of complexity and the mass filling properties of an object, it may be possible that a large number of morphological parameters which contribute to the overall complexity of the particles, could be replaced by these indexes effectively.

Fractal analysis of the laminar organization of spinal cord neurons

Images of Golgi impregnated neurons from different laminae of the human and rat dorsal horns were subjected to a quantitative analysis to support the Rexed's laminar scheme in mammals. Four methods of fractal analysis were performed in the proceedings: box-counting, mass-radius, cumulative intersection, and vectorized intersection. The results show that the box-counting method is more precise than the other fractal methods performed, and offers support for the conclusion that fractal analysis can successfully discriminate the neuron populations among different laminae. The analysis supports the concept of Rexed's cytoarchitectonic lamination of the dorsal horn.

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.

Morphological development of microglia in the postnatal rat brain

Morphological transformation of lectin-positive microglia/macrophages in the developing rat cerebral hemisphere was analysed using quantitative methods. During the first postnatal month, the cells showed increases in their size and fractal dimension accompanied by a simultaneous decrease in their solidity. Regional variations in dynamics of the process indicated the existence of spatio-temporal developmental gradients within the cerebral hemisphere wall which might correspond with regional patterns of neuronal differentiation. Results of the present study prove that the quantitative methods can be the source of reliable data replacing subjective cell typologies.

Morphological transformations of cells immunopositive for GFAP, TrkA or p75 in the CA1 hippocampal area following transient global ischemia in the rat. A quantitative study

Transient global ischemia induces intensive neuronal degeneration in the hippocampal CA1 pyramidal layer, accompanied by reactive transformation of glial cells. Previously, we have shown using the double immunostaining method that the NGF receptors (NGFR) p75 and TrkA are expressed mainly on subpopulations of GFAP+ astrocytes, and this expression increases progressively after ischemia. In the presented study, we analyzed quantitatively the morphological transformations of cells immunopositive for GFAP or NGF receptors in the stratum radiatum of the CA1 hippocampal area in different survival periods after ischemia, evoked by 10-min cardiac arrest in adult rats. In control brains, NGF receptors were expressed only on small cells with poorly ramified processes. After ischemia, the NGFR+ cells increased in size and morphological complexity (measured using fractal analysis). However, even 2 weeks after ischemia these cells did not reach the size and value of the fractal dimension typical of the largest GFAP+ astrocytes. Moreover, the reaction of NGFR+ cells was significantly delayed in comparison with the total astrocyte population. The obtained results suggest that NGF receptors are expressed mainly by immature astrocytes and ischemia induces the maturation of these cells.

GABA-induced neurite outgrowth of cerebellar granule cells is mediated by GABA(A) receptor activation, calcium influx and CaMKII and erk1/2 pathways

During neuronal development, GABAA-mediated responses are depolarizing and induce an increase in the intracellular calcium concentration. Since calcium oscillations can modulate neurite outgrowth, we explored the capability of GABA to induce changes in cerebellar granule cell morphology. We find that treatment with GABA (1-1000 microm) induces an increase in the intracellular calcium concentration through the activation of GABA(A) receptors and voltage-gated calcium channels of the L-subtype. Perforated patch-clamp recordings reveal that this depolarizing response is due to a chloride reversal potential close to - 35 mV. When cells are grown in depolarizing potassium chloride concentrations, a shift in reversal potential (Erev) for GABA is observed, and only 20% of the cells are depolarized by the neurotransmitter at day 5 in vitro. On the contrary, cells grown under resting conditions are depolarized after GABA application even at day 8. GABA increases the complexity of the dendritic arbors of cerebellar granule neurons via a calcium-dependent mechanism triggered by voltage-gated calcium channel activation. Specific blockers of calcium-calmodulin kinase II and mitogen-activated protein kinase kinase (KN93 and PD098059) implicate these kinases in the intracellular pathways involved in the neuritogenic effect of GABA. These data demonstrate that GABA exerts a stimulatory role on cerebellar granule cell neuritogenesis through calcium influx and activation of calcium-dependent kinases.

Contribution of Ca2+ calmodulin-dependent protein kinase II and mitogen-activated protein kinase kinase to neural activity-induced neurite outgrowth and survival of cerebellar granule cells

In this report we describe our studies on intracellular signals that mediate neurite outgrowth and long-term survival of cerebellar granule cells. The effect of voltage-gated calcium channel activation on neurite complexity was evaluated in cultured cerebellar granule cells grown for 48 h at low density; the parameter measured was the fractal dimension of the cell. We explored the contribution of two intracellular pathways, Ca2+ calmodulin-dependent protein kinase II and mitogen-activated protein kinase kinase (MEK1), to the effects of high [K+ ]e under serum-free conditions. We found that 25 mm KCl (25K) induced an increase in calcium influx through L subtype channels. In neurones grown for 24-48 h under low-density conditions, the activation of these channels induced neurite outgrowth through the activation of Ca2+ calmodulin-dependent protein kinase II. This also produced an increase in long-term neuronal survival with a partial contribution from the MEK1 pathway. We also found that the addition of 25K increased the levels of the phosphorylated forms of Ca2+ calmodulin-dependent protein kinase II and of the extracellular signal-regulated kinases 1 and 2. Neuronal survival under resting conditions is supported by the MEK1 pathway. We conclude that intracellular calcium oscillations can triggered different biological effects depending on the stage of maturation of the neuronal phenotype. Ca2+ calmodulin-dependent protein kinase II activation determines the growth of neurites and the development of neuronal complexity.

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.

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.

Use of fractal theory in neuroscience: methods, advantages, and potential problems

Fractal analysis has already found widespread application in the field of neuroscience and is being used in many other areas. Applications are many and include ion channel kinetics of biological membranes and classification of neurons according to their branching characteristics. In this article we review some practical methods that are now available to allow the determination of the complexity and scaling relationships of anatomical and physiological patterns. The problems of describing fractal dimensions are discussed and the concept of fractal dimensionality is introduced. Several related methodological considerations, such as preparation of the image and estimation of the fractal dimensions from the data points, as well as the advantages and problems of fractal geometric analysis, are discussed.

Morphology of reactive microglia in the injured cerebral cortex. Fractal analysis and complementary quantitative methods

The present study focuses on application of quantitative methods measuring differences between particular morphological types of microglial cells as well as between their proliferating and non-proliferating examples. On the basis of subjective classification, microglial cells of three morphological types (ramified, hypertrophied and bushy) were selected from the neocortex of injured rat brain. Thereafter, the morphological complexity of each cell was assessed by calculation its fractal dimension as well as its form factor, convexity, ramification factor and solidity. The fractal dimension seemed a good parameter for detecting small changes in the space-filing capacity of cells, for example, it shows differences between ramified cells from control and injured brains. This measure seemed insensitive to some aspects of cell morphology. To obtain precise quantification of observed changes other morphological parameters had to be applied. Proliferating and non-proliferating microglial cells displayed significant differences in their solidity and ramification factors, but not in fractal dimension and convexity. The results indicated that proliferating microglia were more massive and less-ramified but they did not reduce their spatial complexity.

Neuronal sensitivity to tetanus toxin requires gangliosides

Tetanus toxin produces spastic paralysis in situ by blocking inhibitory neurotransmitter release in the spinal cord. Although di- and trisialogangliosides bind tetanus toxin, their role as productive toxin receptors remains unclear. We examined toxin binding and action in spinal cord cell cultures grown in the presence of fumonisin B(1), an inhibitor of ganglioside synthesis. Mouse spinal cord neurons grown for 3 weeks in culture in 20 microM fumonisin B(1) develop dendrites, axons, and synaptic terminals similar to untreated neurons, even though thin layer chromatography shows a greater than 90% inhibition of ganglioside synthesis. Absence of tetanus and cholera toxin binding by toxin-horseradish peroxidase conjugates or immunofluorescence further indicates loss of mono- and polysialogangliosides. In contrast to control cultures, tetanus toxin added to fumonisin B(1)-treated cultures does not block potassium-stimulated glycine release, inhibit activity-dependent uptake of FM1-43, or abolish immunoreactivity for vesicle-associated membrane protein, the toxin substrate. Supplementing fumonisin B(1)-treated cultures with mixed brain gangliosides completely restores the ability of tetanus toxin to bind to the neuronal surface and to block neurotransmitter release. These data demonstrate that fumonisin B(1) protects against toxin-induced synaptic blockade and that gangliosides are a necessary component of the receptor mechanism for tetanus toxin.

GABA induces proliferation of immature cerebellar granule cells grown in vitro

The presence of GABA and its receptors early in rodent nervous system development has lead to speculation on the role of this transmitter system in neuroblast proliferation, migration and differentiation. We studied the effect of GABA and GABA agonists on immature cerebellar granule cell proliferation and survival. Cerebellar granule cell suspensions were obtained from 6-8-day-old rats and grown in culture for up to 7 days in serum-containing or serum-free medium. The addition of GABA (0.1-100 microM) or muscimol (0.01-10 microM) 2 h after inoculation and harvested 22 h later, lead to an increase in 3H-thymidine incorporation over control samples with the correspondent increase in granule cells number assayed 48 h later. The effect on cell proliferation exerted by GABAA agonists was blocked by MgCl2 and nifedipine, as well as by the chloride channel blocker, picrotoxin (50 microM), and the GABAA receptor specific blocker, bicuculline (50 microM). The increase on cell proliferation induced by GABA also was blocked by PD98059 (75 microM), a specific inhibitor of the mitogen-activated protein kinase kinase (MAPKK). GABAA receptor-mediated proliferation was consistently seen in cells inoculated in serum-containing medium supplemented with 25 mM KCl but not seen in serum-free medium, with 5 mM or 25 mM KCl. The presence of serum did not enhance the survival of cerebellar granule cells grown for 7 days in either 5 mM or 25 mM KCl. Additionally, neither GABA nor muscimol applied from day 2 to day 7 in vitro affected cell survival in any culture condition. We conclude that GABA and GABAA receptor agonists influence granule cell proliferation but not survival and that this effect is mediated by a calcium influx via voltage-dependent calcium channel activation, with a subsequent activation of the MAPK cascade.

TrkB signaling modulates spine density and morphology independent of dendrite structure in cultured neonatal Purkinje cells

Neurotrophins cooperate with neural activity to modulate CNS neuronal survival and dendritic differentiation. In a previous study, we demonstrated that a critical balance of neurotrophin and neural activity is required for Purkinje cell survival in cocultures of purified granule and Purkinje cells (Morrison and Mason, 1998). Here we investigate whether TrkB signaling regulates dendrite and spine development of Purkinje cells. BDNF treatment of purified Purkinje cells cultured alone did not elicit formation of mature dendrites or spines. In cocultures of granule and Purkinje cells, however, continuous treatment with BDNF over a 2 week postnatal culture period increased the density of Purkinje cell dendritic spines relative to controls without causing a shift in the proportions of headed and filopodia-like spines. The increase in spine number was blocked by adding TrkB-IgG to the medium together with BDNF. Although BDNF alone did not consistently modify the morphology of dendritic spines, treatment with TrkB-IgG alone yielded spines with longer necks than those in control cultures. None of these treatments altered Purkinje cell dendritic complexity. These analyses reveal a role for TrkB signaling in modulating spine development, consistent with recently reported effects of neurotrophins on synaptic function. Moreover, spine development can be uncoupled from dendrite outgrowth in this reductionist system of purified presynaptic and postsynaptic neurons.

Neurons and fractals: how reliable and useful are calculations of fractal dimensions?

In the past 15 years it has become possible to determine the fractal dimension (Df) of complex objects, including neurons, by automated image analysis methods. However, there are many unresolved issues that need to be addressed. In this paper we discuss how the Df calculated by different methods may vary and how fractal analysis may be of use for retinal ganglion cell characterization. The goal of this work was to acknowledge inherent sources of variation during measurement and evaluate current fractal analysis methods for describing structure. Our results show that different algorithms and even the same algorithm performed by different computer programs and/or experimenters may give different but consistent numerical values. All described methods demonstrated their suitability for classifying cat retinal ganglion cells into distinct groups. Our results reinforce the idea that comparison of measurements of different profiles using the same measurement method may be useful and valid even if an exact numeric value of the dimension is not realised in practice.

Extracellular potassium concentration regulates proliferation of immature cerebellar granule cells

The present study examines the effect of depolarizing potassium concentrations on the proliferation of immature rat cerebellar neurons. Cells inoculated in serum free medium and 5 mM KCl (5 K) showed a high degree of 3H-thymidine incorporation that decreased 24-48 h after plating as differentiation began. During the first 24 h after inoculation, cells grown in high potassium (25 K), showed a 34 +/- 3% increase (mean +/- S.E.M., n = 12) in 3H-thymidine incorporation as compared with the values observed in 5 K. After 24 h in vitro, cells grown in 25 K showed 23 +/- 3% (mean +/- S.E.M., n = 3) less DNA synthesis than those inoculated in 5 K. The increase in DNA synthesis due to 25 K was blocked by MgCl2 and nifedipine, but not by omega-conotoxin GVIA, suggesting that it is mediated by a Ca2+ influx via voltage-gated calcium channels (VGCC) of the L-subtype. High potassium-induced cell proliferation was blocked by the mitogen-activated protein kinase kinase (MEK1) inhibitor (PD98059, 75 microM). The number of neurons counted after 48 h in vitro in 25 K was 35-100% above of the number obtained with 5 K and this increase also was blocked by MgCl2 and nifedipine. These data support the hypothesis that depolarizing activity during neurogenesis plays a role in the modulation of cerebellar granule cells proliferation.

Properties of cochlear nucleus neurons in primary culture

Dissociated primary cell cultures were derived from the cochlear nuclei (CN) of postnatal rats using standard techniques. Cultured cells differentiated morphologically, but their dendritic profiles were generally less specialized than those of CN cells in vivo. Physiologically, cultured cells could be divided into three classes: tonic, phasic and non-spiking cells, which differed in many of their fundamental biophysical properties. The percentage of cultured cells that spiked repetitively increased over time to a maximum of 85% at 6 days. However, the percentage of cells that produced action potentials decreased with time in culture, from 91% during the first 8 days to less than 40% after 9 days. CN cells were successfully cultured in both serum-supplemented and serum-free (Neurobasal) media. More neurons survived at low plating densities in Neurobasal than in medium containing serum, although neuronal survival was similar at higher densities. Few neurons raised in the serum-free medium were spontaneously active; other response properties were similar to those of cells grown in the presence of serum. Although differentiation of CN cells in culture did not completely mirror the in vivo developmental pattern, these experiments demonstrate that primary culture represents a viable method for the in vitro study of CN neurons.

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.

The effect of X-radiation on cerebellar granule cells grown in culture. Ganglioside GM1 neuroprotective activity

In this paper we describe the effects of X-radiation on the viability of cerebellar granule cells grown in culture. Cell cultures were exposed to X-rays 2 h after plating and then grown for 1-7 days. Two days after X-ray exposure with a dose-range of 0.1-2 Gy (acute effect), a significant decrease in neuronal number was observed. The magnitude of the lethal effect was directly correlated to the dose of X-ray applied. When the interval between plating and irradiation was increased, the acute lethal effect of X-rays decreased. 3H-thymidine incorporation was maximal during the first 24 h in vitro and decreased to nearly blank levels, after 72 h. In some experiments, cells present in each culture dish were counted at day 2 and at day 7. We observed that the number of cells present in sham-irradiated cultures decreased from day 2 to day 7, reflecting cell death after several days in vitro. The cell loss observed in X-irradiated cultures was significantly greater as compared with sham-irradiated cultures, confirming the deleterious effect of X-ray on cell survival. This effect was completely prevented by GM1 (6.5, 10 and 30 microM) added 48 h after X-ray exposure, but not 1 h after plating. We conclude that X-rays induce two different effects: an acute effect related to impaired DNA synthesis which is very active during the first 24 h in vitro, and a long-term effect owing to a sublethal damage in the surviving neuronal population.

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.

Retinal neurons and vessels are not fractal but space-filling

Many branched patterns in nature are hypothesized to be fractal, i.e., statistically self-similar across a range of scales. We tested this hypothesis on the two-dimensional arbors of retinal neurons and blood vessels. First, we measured fractalness on synthetic fractal and nonfractal patterns. The synthetic fractal patterns exhibited self-similarity over a decade of scale, but the nonfractal "controls" showed hardly any self-similarity. Neuronal and vascular patterns showed no greater self-similarity than the controls. Second, we manipulated a synthetic fractal pattern to remove its self-similarity and found this to be reflected in a loss of measured fractalness. The same manipulation of the nonfractal control and also of the neural and vascular patterns did not alter their measured fractalness. Third, we "grew" patterns of branched line segments according to a variety of nonfractal algorithms. These patterns were, if anything slightly more fractal than the neural and vascular patterns. We conclude that the biological patterns studied here are not fractal. Finally, we measured extended versions of these patterns: a contiguous array of homotypic neuron arbors and a vascular pattern with a high degree of total detail. These patterns showed a "fractal dimension" of 2, which implies that down to some cut-off scale they fill space completely. Thus, neural and vascular patterns might best be described as quasi-regular lattices.

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.

Culture model for the study of cerebral malaria: antibodies from Plasmodium falciparum-infected comatose patients inhibit the dendritic development of Purkinje cells

The in vitro development of kitten Purkinje cells was inhibited by sera or IgG from cerebral malaria (CM) patients but not by sera from acute non-complicated malaria (NCM) cases. This inhibitory effect, quantified by computer-assisted methods, concerned the dendritic (though not the axonal) development and was found to be related to the presence of CM sera of self-reactive antibodies of the IgG class. These results suggest that protection acquired against the major complication of Plasmodium falciparum malaria may correspond to the repression of an abnormal stimulation of autoreactive B cells.

Quantitative phylogenetic constancy of cerebellar Purkinje cell morphological complexity

Golgi-stained material of cerebellar cortices from 17 species was examined by measuring the fractal dimensions of the borders of Purkinje cells, which is a quantitative, objective measure of morphological complexity. Nine species (from birds to man) were chosen for a comparison with ANOVA and no statistically significant differences were found in their fractal dimensions. In contrast, a wide range of differences was found in the membrane areas across species lines. The Sholl coefficient, a measure of branch formation and termination away from the soma, showed no consistent pattern for each cell. We interpret our results as indicating a constancy in morphological cellular complexity of Purkinje cells during late evolutionary time.