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.

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Quantitating the subtleties of microglial morphology with fractal analysis.

Aim: Breast cancer prognosis is in the spotlight owing to its potentially major clinical importance in effective therapeutic management. Following our recent prognostic establishment of the fractal features calculated on binary breast tumor histopathology images, this study aimed to accomplish the first optimization of this methodology by direct comparison of monofractal, multifractal and co-occurrence algorithms in analysis of binary versus grayscale image formats. Patients & methods: The study included 93 patients with invasive breast cancer, without systemic treatment and a long median follow-up of 150 months. Results: Grayscale images provided a better prognostic source in comparison to binary, while monofractal, multifractal and co-occurrence image analysis algorithms exerted a comparable performance. Conclusion: The critical prognostic importance of the grayscale texture is revealed.

Prognostic biomarker value of binary and grayscale breast tumor histopathology images

BACKGROUND/AIM Dentate nucleus (nucleus dentatus) is the most distant of the cerebellar nuclei and the major system for information transfer in the cerebellum. So far, dendritic branches of four different kinds of large neurons of dentate nucleus, have been considered mainly qualitatively with no quantification of their morphological features. The aim of the study was to test the qualitative hypothesis that the human dentate nucleus is composed of various types of the large neurons by quantitative analysis of their dendritic branching patterns. METHODS Series of horizontal sections of the dentate nuclei were taken from 15 adult human brains, free of diagnosed neurological disorders. The 189 Golgi-impregnated images of large neurons were recorded by a digital camera connected to a light microscope. Dendritic branching patterns of digitized neuronal images were analyzed by modified Sholl and fractal analyses. RESULTS The number of intersections (N(m)), critical radius (r(c)) and fractal dimension (D) of dendritic branching pattern for four types of the large neurons were calculated, statistically evaluated and analyzed. The results show that there is a significant difference between four neuronal types in one morphometric parameter at least. CONCLUSION The present study is the first attempt to analyze quantitatively the dendritic branching pattern of neurons from the dentate nucleus in the human. The hypothesis that the four types of the large neurons exist in this part of human cerebellum is successfully supported.

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Quantitative analysis of dendritic branching pattern of large neurons in human cerebellum

Aggressive posterior retinopathy of prematurity: Fractal analysis of images before and after laser surgery

The morphology and cell classification in the human dendate nucleus: A fractal analysis study

The morphology of neurons from the human dentate nucleus was analyzed estimating the size and shape of the dendritic field, shape of the neuron, space-filling property and the degree of dendrite aberrations. Among them, the last three morphological properties were investigated using the most popular technique of fractal analysis: the box-count method. The box dimensions of binary images and dendritic field area were statistically investigated in order to test whether the binary box dimension can quantify the size of the neuron. The same analysis was carried out using the box dimension of outline images and image circularity. The parameters, presented in this study have proved to be a useful means for quantifying the morphology of dentate neurons as they provide a robust means of differentiating between neuron subtypes in the dentate nucleus. The findings of the present study are in accordance with previous qualitative data.

Nebojša T. Milošević

Papers

Prognostic biomarker value of binary and grayscale breast tumor histopathology images

Quantitative analysis of dendritic branching pattern of large neurons in human cerebellum

Aggressive posterior retinopathy of prematurity: Fractal analysis of images before and after laser surgery

The morphology and cell classification in the human dendate nucleus: A fractal analysis study

Neurons of the Human Dentate Nucleus: Box-Count Method in the Quantitative Analysis of Cell Morphology