Audrey Karperien

Quantitating the Subtleties of Microglial Morphology with 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.

Automated detection of proliferative retinopathy in clinical practice

Timely intervention for diabetic retinopathy (DR) lessens the possibility of blindness and can save considerable costs to health systems. To ensure that interventions are timely and effective requires methods of screening and monitoring pathological changes, including assessing outcomes. Fractal analysis, one method that has been studied for assessing DR, is potentially relevant in today’s world of telemedicine because it provides objective indices from digital images of complex patterns such as are seen in retinal vasculature, which is affected in DR. We introduce here a protocol to distinguish between nonproliferative (NPDR) and proliferative (PDR) changes in retinal vasculature using a fractal analysis method known as local connected dimension (Dconn) analysis. The major finding is that compared to other fractal analysis methods, Dconn analysis better differentiates NPDR from PDR (p = 0.05). In addition, we are the first to show that fractal analysis can be used to differentiate between NPDR and PDR using automated vessel identification. Overall, our results suggest this protocol can complement existing methods by including an automated and objective measure obtainable at a lower level of expertise that experts can then use in screening for and monitoring DR.

Fractal Analysis of Cervical Intraepithelial Neoplasia

Introduction Cervical intraepithelial neoplasias (CIN) represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN) and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. Methods Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologists neoplasia grades with the predicted groups obtained by fractal methods. Results Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologists grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. Conclusion Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.

Box-counting analysis of microglia form in schizophrenia, Alzheimer's disease and affective disorder.

In pathological brain, a variety of morphological forms exist that reflect differences in functional requirements. To better understand microglia function in neurological disease, it is important to identify and quantify microglia morphology associated with specific neuropathologies. Traditional feature parameters such as area or cell diameter are not sufficient. In this study microglia were quantified by the box-counting fractal dimension (DB). One hundred and four cells from post-mortem tissue were analyzed comprising cells of controls, Alzheimers disease, schizophrenia and affective disorder. The DB was significantly different from the control (1.36) compared to schizophrenia (1.41), Alzheimers disease (1.41) and affective disorder (1.43) with p < 0.01. Thus fractal analysis provides a useful quantitative and objective measure of microglial form associated with normal function and diverse neuropathology. The distribution of fractal dimensions associated with microglia structure and activation with disease progression also differs, suggesting a different etiology for these diseases.

Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation

Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

The fractal heart - embracing mathematics in the cardiology clinic.

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Fractal, Multifractal, and Lacunarity Analysis of Microglia in Tissue Engineering

Tissue engineering is currently one of the most exciting fields in biology (Grayson et al., 2009). Fractal analysis is equally exciting (Di Ieva et al., 2013), as is the study of microglia, the brain’s immuno-inflammatory cell, recently shown to be of considerably more importance than previously imagined in both healthy and diseased brain (Tremblay et al., 2011). Each of these fields is developing at a pace far outstripping our capacity to integrate and translate the information gained into clinical use (Karperien et al., 2008b, 2013; Jelinek et al., 2011, 2013), and the excitement more than trebles where these fields intersect. Three elements of fractal analysis – monofractal, multifractal, and lacunarity analysis – applied to microglia may contribute significantly to the next steps forward in engineered tissues and 3D models in neuroscience. Fractal analysis and lacunarity To define “fractal analysis” would take a volume, but for this commentary, it is sufficient to understand that fractal analysis in biology assesses the scaling inherent in biological forms or events, and turns out a statistical index of complexity having no units called the “fractal dimension” (DF). This number measures not length, width, height, or density, but scale-invariant detail. For a pattern to have fractal scale-invariant detail means that the pattern repeats itself infinitely as one inspects it at closer and closer resolution (magnifies it), where that detail is not trivial. To elaborate, as one magnifies a simple line, it infinitely repeats itself quite trivially as a simple line, but as one magnifies a fractal line, one finds it never resolves into straight pieces but rather each magnified segment repeats the initial fractal pattern infinitely. A DF measures this infinite scaling, quantifying complex patterns without rendering meaningless the relative numbers of large and small measurements within them. Without getting too technical, fractal analysis of a simple line yields a DF of 1.00, and the higher the “complexity,” the higher the DF (Mandelbrot, 1983; Takayasu, 1990). Building on this so-called monofractal analysis, multifractal analysis, to summarize, is a way of finding for a single pattern a spectrum of DFs, owing to a pattern having characteristically multiple degrees of scaling, such as could be imagined for a cascading fractal phenomenon (Jestczemski and Sernetz, 1996; Falconer, 2014). The word “lacuna” is derived from the word for lake, and refers to a gap or pool. In fractal analysis, lacunarity translates to measures of gappiness or “visual texture,” such as might be seen in the patchiness of forests, for instance (Plotnick et al., 1993). It has been defined as the degree of inhomogeneity and translational and rotational invariance in an image (Plotnick et al., 1993; Smith et al., 1996), where low lacunarity implies homogeneity and that rotating the image will not change it significantly. Thus, an image having mostly similarly sized gaps and little rotational variance would be expected to have low lacunarity, and one with much heterogeneity, many differently sized gaps, and notable rotational variance, would be expected to have high lacunarity (Karperien et al., 2011a). Lacunarity is frequently assessed during fractal analysis because the data on which it is based are easily collected by the same methods. The details and calculations behind fractal analysis are beyond the scope of this commentary but user-friendly, freely available software for biologists (Karperien, 2001, 2013) and in-depth explanations are available elsewhere (Smith et al., 1996).

Box-Counting and Multifractal Analysis in Neuronal and Glial Classification

Fractal analysis in the neurosciences has advanced over the past twenty years. The fractal dimension, besides its ability to discriminate among different cell types, can work as a reliable parameter in cell classification. A qualitative analysis of the morphology of neurons and glia cell types involves a detailed description of the structure and features of cells, and accordingly, their classification into defined classes and types. This paper outlines how fractal analysis can be used for further quantitative classification of these cell types using box-counting and multifractal analysis.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out elementary principles of fractal geometry underpinning much of the rest of this book. It assumes minimal mathematical background, defines key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to do fractal, lacunarity, and multifractal analyses. As a standalone reference, the chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate the exquisitely detailed fractal geometry of the brain.

ImageJ in Computational Fractal-Based Neuroscience: Pattern Extraction and Translational Research

To explore questions asked in neuroscience, neuroscientists rely heavily on the tools available. One such toolset is ImageJ, open-source, free, biological digital image analysis software. Open-source software has matured alongside of fractal analysis in neuroscience, and today ImageJ is not a niche but a foundation relied on by a substantial number of neuroscientists for work in diverse fields including fractal analysis. This is largely owing to two features of open-source software leveraged in ImageJ and vital to vigorous neuroscience: customizability and collaboration. With those notions in mind, this chapter’s aim is threefold: (1) it introduces ImageJ, (2) it outlines ways this software tool has influenced fractal analysis in neuroscience and shaped the questions researchers devote time to, and (3) it reviews a few examples of ways investigators have developed and used ImageJ for pattern extraction in fractal analysis. Throughout this chapter, the focus is on fostering a collaborative and creative mindset for translating knowledge of the fractal geometry of the brain into clinical reality.