Biophysics of Computation

To the Editor: Neuroscientists measure the tree-like structures of neurons in order to better understand how neural circuits are constructed and how neural information is processed. In 1953, Donald Sholl published his well-known technique for quantitative analysis of the complex arbors of dendrites and axons1, but conventional methods still require reconstruction of arbors via time-consuming manual or semi-automated tracing from microscopy images. To bypass this reconstruction step and perform the Sholl technique directly on images instead, we developed Sholl Analysis (http://fiji.sc/Sholl), an open-source program for ImageJ/Fiji2 (Supplementary Fig. 1). The plug-in employs an improved algorithm to retrieve data from twoor three-dimensional (2D or 3D) bitmap images in any format supported by the Bio-Formats library (Supplementary Methods). It pairs this data retrieval with curve-fitting, regression analysis and statistical inference so that users can automatically extract a collection of Sholl-based metrics of arborization1,3 (Supplementary Note). Using individual cortical pyramidal neurons in 3D images, we found Sholl Analysis to be accurate when benchmarked against corresponding manual reconstructions (Supplementary Fig. 2). The method was also resilient to image degradation by simulated shot noise (Supplementary Fig. 3 and Supplementary Software). To further assess accuracy, and to explore the utility of Sholl Analysis in tackling neurons that are particularly slow to reconstruct manually, we studied cerebellar Purkinje cells in mice, which have large and intricate dendritic arbors. From tiled 3D image stacks of cerebellum (Fig. 1a), we selected seven Brainbow2.1-expressing Purkinje neurons and isolated their morphologies (Fig. 1b and Supplementary Note). We then used the Sholl Analysis software to retrieve ten metrics and found they were indistinguishable from those retrieved from manual reconstructions of the same 7 cells (Fig. 1c,d and Supplementary Methods). To probe the sensitivity of the Sholl Analysis software, we asked whether its metrics could be used to distinguish closelyrelated neocortical interneuron subtypes. Parvalbumin-positive (PV) interneurons in layer 5 of visual cortex can be morphologically classified into two subtypes on the basis of their axonal morphology: type 1 PV cells have ascending axons arborizing in layer 2/3, whereas axons of type 2 cells remain in layer 5 (ref. 4). Because their dendritic arbors are indistinguishable4, these two cell types otherwise appear highly similar (Fig. 1e,f). Using the Sholl Analysis software, we retrieved 18 metrics directly from 3D image stacks of 12 PV interneurons. We then used Ward’s hierarchical clustering based on these metrics to independently classify these cells (Fig. 1g and Supplementary Fig. 4). The 12 cells segregated into two groups: one group of five neurons and another of seven. We found that all the neurons but two were correctly classified, with one cell assigned incorrectly to each class (Fig. 1g). Thus, our use of the Sholl Analysis software to quantify arborization directly from bitmap images correctly identified 80–86% of cells. In agreement, linear Sholl plots of type 1 cells indicated more branching than was found for type 2 cells at a distance of 225–300 μm from the soma (Fig. 1h), which corresponds to check and inviting routine use. Second, the software can generate a summary report of the current system performance or a full report containing all individual PSF measurements and associated fitting parameters. Third, a table with the extracted resolution, planarity and colocalization data can be exported. This can be used for subsequent analysis, such as in an image processing or restoration pipeline. In addition, an average PSF from a user-selectable region of interest can be exported, for example, for image deconvolution. We used PSFj to quantify the performance of various high– numerical aperture (NA) objectives and to track day-to-day and system-to-system variation. The results showed substantial performance differences and allowed us to identify strengths and weaknesses of individual objectives as well as general shortcomings (Supplementary Figs. 1 and 2). In particular, we found that whereas lateral resolution performance generally fell short (~20–30%), axial resolution often met or exceeded expectations from the scalar approximation of the PSF commonly used in textbooks2 (Supplementary Note). Planarity was usually well corrected with variations over the FOV below the axial resolution and allowed for the detection of tilted slides caused, for example, by dust particles or misaligned slide holders or stages. Axial chromatic shifts were usually small, with little variation across the FOV (Supplementary Table 1). In contrast, chromatic shifts often showed circular symmetry and increased toward the edge of the FOV, which is a sign of lateral chromatic aberrations. Day-to-day performance variation of most objectives was relatively small (~2–6%) and comparable to single-measurement FOV variations (Supplementary Table 2). Furthermore, testing a limited number of identical objectives identified objective-toobjective and microscope-to-microscope variations of about 10% (Supplementary Tables 3 and 4). The PSFj software is open source and based on libraries from various sources, including ImageJ3 and μManager4, and it runs as a stand-alone application on the three major operating systems (using Java).

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Neuronal morphometry directly from bitmap images

https://escholarship.org/content/qt9xb8q5z6/qt9xb8q5z6.pdf?t=q7c1km

Psychedelics Promote Structural and Functional Neural Plasticity

The ever decreasing area of forests has lead to environmental and economical challenges and has brought with it a renewed interest in developing methodologies that quantify the extent of deforestation and reforestation. In this study we analyzed the deforested areas of the Apuseni Mountains, which has been under economic pressure in recent years and resulted in widespread deforestation as a means of income. Deforested surface dynamics modeling was based on images contained in the Global Forest Database, provided by the Department of Geographical Sciences at Maryland University between 2000 and 2014. The results of the image particle analysis and modelling were based on Total Area (ha), Count of patches and Average Size whereas deforested area distribution was based on the Local Connected Fractal Dimension, Fractal Fragmentation Index and Tug-of-War Lacunarity as indicators of forest fragmentation or heterogeneity. The major findings of the study indicated a reduction of the tree cover area by 3.8%, an increase in fragmentation of 17.7% and an increase in heterogeneity by 29%, while fractal connectivity decreased only by 0.1%. The fractal and particle analysis showed a clustering of forest loss areas with an average increase from 1.1 to 3.0 ha per loss site per year. In conclusion, the fractal and particle analysis provide a relevant methodological framework to further our understanding of the spatial effects of economic pressure on forestry.

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Dynamics of Forest Fragmentation and Connectivity Using Particle and Fractal Analysis

It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between "ramified resting" and "activated amoeboid" has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology.

/pdf/quantitating-the-subtleties-of-microglial-morphology-with-22cx7voyf5.pdf

Quantitating the subtleties of microglial morphology with fractal analysis.

Neurons of the rat spinal cord were stained using the Golgi impregnation method. Successfully impregnated neurons from laminae II, III, and VI were subjected to fractal and nonfractal analyses. Fractal analysis was performed using length-related techniques. Since an application of fractal methods to the analysis of dendrite arbor structures requires caution, we adopted as appropriate a nonfractal method proposing a generalized power-law model with two main nonfractal parameters: (i) the anfractuosity, characterizing the degree of dendritic deviation from straight lines; and (ii) an estimate of the total length of arbor dendrites. The anfractuosity can distinguish between two sets of drawings where the fractal methods failed. We also redefine some basic concepts of fractal geometry, present the ruler-counting method, and propose a new definition of fractal dimension.

Fractal and nonfractal analysis of cell images: comparison and application to neuronal dendritic arborization

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

Quantitative analysis of dendritic morphology of the alpha and delta retinal ganglion cells in the rat: A cell classification study

Fractal analysis in the neurosciences has advanced over the last twenty years to include measures such as lacunarity. Lacunarity assesses heterogeneity or translational and rotational invariance in an image. In general, measures of lacunarity correspond to visual impressions of uniformity, where low lacunarity conventionally implies homogeneity and high lacunarity heterogeneity. It is now necessary to review some of the new permutations of this analysis technique and what it can tell the neuroscientist. This paper outlines methodological considerations associated with three different types of lacunarity analysis applied to the classification of microglial cells.

Nebojša T. Milošević

Papers

Fractal and nonfractal analysis of cell images: comparison and application to neuronal dendritic arborization

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

Quantitative analysis of dendritic morphology of the alpha and delta retinal ganglion cells in the rat: A cell classification study

Reviewing lacunarity analysis and classification of microglia in neuroscience

Application of fractal analysis to neuronal dendritic arborisation patterns of the monkey dentate nucleus.