To convert a chosen structural feature into such a pattern, the feature has to first be revealed by some method that can deliver a signal the software can make sense of. For box counting, as we alluded to earlier, the signal pattern is usually input as a still digital image; that input image is usually made from an original digital image. Microglia are not normally visible, so the digital image is constructed from a histological slide or other visualization method via some amplified signal marker. Such markers are specific for different cell parts and can reveal different features of microglial morphology. Electron microscopy, for instance, reveals exquisite intracellular and the finest membrane detail, the peripheral benzodiazepine receptor, used in live imaging studies, tracks events at the outer mitochondrial membrane, cytoskeletal protein markers reveal differently arranged networks of whichever particular filament is being exposed, antibodies to CD68 show binding on primarily lysosomes in the cytoplasm but also on the outer membrane, RCA-1 shows binding over the entire plasma membrane, and scanning electron microscopy shows gross morphological detail (Streit and Kreutzberg, 1987; Kreutzberg, 1995; Banati et al., 1999; Cross and Woodroofe, 2001). As an example, then, electron microscopy would be more suited to grayscale analysis of intracellular texture and lectin binding to binary analysis of ramification.

Another factor influencing the final pattern of the image is the original size of the region of interest. As their name suggests, microglia are typically smaller than most other cells found in the nervous system (i.e., neurons and other glia). A survey of published values suggests that for human microglia observed at all stages of their activation cycle and the human life span, grown in culture or found in tissue samples, nuclei average roughly 5–10 μm in diameter, cell bodies range from 7 to 20 μm in diameter, and cell branches (if present) radiate outward from the cell body so that an entire cell spans, on average, from 30 to 120 μm (de Groot et al., 1992, 2000; Rezaie et al., 1997, 1999, 2002; Andjelkovic et al., 1998; Sheng et al., 1998a; Stoll and Jander, 1999; Radewicz et al., 2000).

With such small subject matter, it is important to consider the level of detail analyzed and issues such as how well the staining, magnification, and resolution preserved information (e.g., terminal branches or fine membrane fringes). Indeed, despite that fractal dimensions are independent of object size, measured D_Bs are not entirely independent of imaging protocols, including staining methods and image size and resolution, which can affect the results of a fractal analysis to varying degrees. In practice, this limits the applicability of comparing fractal dimensions across paradigms. Over and above absolute differences owing to methodology or image size, however, as is discussed in section “One Fundamental Relative Pattern Across Paradigms,” when looking at branching and membrane detail at least, relative effects are preserved across many paradigms. More work is still needed to characterize issues related to specific methods of visualization and compare how different types of fractal analysis are affected by different visualization techniques.

A major challenge in any type of digital image analysis, pattern extraction itself is another element that must be understood to interpret results of fractal analysis studies. Pattern extraction means removing noise—that can mean overall background and can include other cells or structures. For grayscale box counting analysis, this is often less a challenge than for binary image analysis. Extracting a grayscale pattern is usually relatively straightforward, sometimes involving only isolating the relevant part and converting the original image to grayscale in an image processing program, in which case images of individual cells or entire fields with multiple cells can be processed rapidly. Grayscale analysis assumes that the image background is supposed to be processed along with any objects of interest; if not, grayscale pattern extraction becomes more involved.

Rather than grayscale analysis, however, most of the work published on microglia to date has used binary image analysis. Patterns have been extracted by either manual tracing or automated segmenting methods (Soltys et al., 2001; Jelinek et al., 2008). Both approaches incur their own level of bias. As an illustration, staining in unactivated cells may be splotchier than in activated cells owing to upregulation of the marker on activation, so the operator may interpolate in a “connect the dots” fashion; in automated thresholding, only the actual “dots” are rendered as signal. However, in both cases, a person, either a tracer or a programmer, decides what is background and what is foreground, a universal bias affecting any assessment of staining of biological cells. Also, in automated methods, there is a bias away from overlapping cells so that such methods are usually limited to investigations where clustering and overlap are considered part of the signal rather than noise.

The patterns extracted have typically been profiles or contours of single cells or of fields containing multiple cells. If the goal is to identify branching and membrane characteristics, the patterns generally exclude intracellular content; if the goal is to assess the actual pattern of distribution of a marker, then including inner detail can be appropriate. Depending on the feature being investigated, the final pattern can be filled or outlined; filled patterns of the same cell tend to have higher D_Bs. Ramification has been assessed using another method, skeletonizing (e.g., a function in ImageJ), which is especially suited to the dilation method (Orlowski et al., 2003; Soltys et al., 2005). Of note, the dilation method measures different features of the image so produces different values for the fractal dimension compared to box counting unless the image is Euclidean in which case all fractal dimensions are equal (Jelinek et al., 2005; Losa et al., 2005; Karperien et al., 2008a).

Little has been published on pattern acquisition per se for microglia, but one investigation carried out in our lab compared D_Bs for images of individual microglia obtained using a tracing and a thresholding method (Karperien, 2004). Operator bias within each method was minimizable by having clearly defined rules for the methods, and training operators over a few practice sessions. Although the tracing and thresholding results deviated somewhat from each other for certain images, overall the differences were not statistically significant. That is, the patterns from both methods were not identical, but the results imply that they contained essentially the same information relevant to the D_B. This investigation was very limited, however, and preprocessing is a contentious issue in digital image analysis (Jelinek and Fernandez, 1998; Jelinek et al., 2005).

Another finding of this work was that D_Bs were statistically significantly lower for images obtained from one compared to many focal planes (Karperien, 2004). This may be attributable to the point that the box counting method used to find the D_B from the extracted pattern was intended for 2-dimensional data rather than a sample from 3 dimensions.

Manual tracing methods have the distinct disadvantage of being potentially very time consuming, so have been considered impractical for some types of investigation (Donnelly et al., 2009; Kozlowski and Weimer, 2012). Nonetheless, they are well-suited to investigations of branching patterns and have been used to extract intricate patterns from images of microglia (Soltys et al., 2001; Karperien et al., 2008c).

Semi-automated segmentation methods have also been used (Jelinek et al., 2008; Karperien et al., 2008a); these are quicker, but depend more on suitable starting material. For example, with strong contrast and little overlap of cells an operator can preselect regions of interest, or, alternatively, algorithms have been designed to automatically segment and analyze images of individual microglia or fields of multiple cells without intervention (Karperien, 2001a; Karperien et al., 2008a; Kam et al., 2009). Fully automated segmentation of various shapes is a broad goal in digital image analysis (Kim et al., 2011). Kozlowski and Weimer (2012) have published a promising study in which they demonstrate an automated segmentation method designed specifically for identifying microglia visualized by a variety of protocols, although it is not clear if the method is likely to reveal fine branching patterns; future work is needed to find out if the method extracts patterns suitable for fractal analysis and how generally applicable it is.

Another issue one should be conversant in is how well the patterns typically analyzed represent actual microglia. There can be large gaps in the correspondence between overall visual impressions of cells in their original contexts and the final binary patterns, especially when using automated methods geared to identify only pixels corresponding to staining past a certain threshold. Such discrepancies may reflect losses, gains, or distortions of information, or they may be artefacts of perception. That is, regardless of the pattern extraction method used, the essential procedure is to take 3-dimensional, multiply motile, functional cells, and derive from them still, binary, 2-dimensional contours or silhouettes. In addition to containing information about the cell's actual morphology and orientation in space, the information available in the final image will depend on how the original image was acquired and encoded to digital format as well as how the information was extracted. In the case of microglia, detail lost, gained, or distorted could be in intracellular or nuclear features, soma shape, fine branches, membrane protrusions, information about how a cell cuts out its unique volume within the CNS at the moment the image is taken, etc.

Whereas changes to the information may cause the final pattern to bear little resemblance to the original cell or image, this perceptual disjunction has generally been deemed to be negligible based on conventions that have been widely applied to other biological cells. One is the assumption that the information of interest (e.g., in the branching of processes and the contour of the membrane) is sufficiently preserved at least on average (which means sample size and random selection should be considered in any investigation). Another is the assumption that objects contained in 3D without completely filling 3-dimensional space are adequately represented by projections onto 2-dimensional space (e.g., theoretically, a contour of a tree's branches should hold the same information as the tree) (Takayasu, 1990; Vicsek, 1992; Smith et al., 1996; Losa et al., 1997; Jelinek and Fernandez, 1998; Fernandez and Jelinek, 2001). As discussed in the next section, computer based modeling has been used to test the validity of these assumptions for branching patterns in microglia.

Modeling lets us test our understanding of and predict the behavior of biological systems. Work by Jelinek et al. (2002) and others from that laboratory demonstrated that increasing ramification in microglia can be modeled by increasing complexity. Changes in complexity input to models can, in turn, be accurately measured back from binary outlines extracted from in silico microglia. Jelinek's team created computer-simulated models from images of microglia in normal and pathological elderly human brain, as well as several other samples from humans and other animals. The models were specified by recursively applied rules derived from measuring microglial features. These included features associated with fractal geometry, such as process length and diameter, branching frequency, and branching angle, as well as other features, including the tortuousness of processes and size and shape of the soma, that were expected to influence the results. The models were generated as several 200-member populations of both idealized models and statistical models designed to emulate microglia in the 3D space they occupy under real circumstances, or at least in observed circumstances (Karperien, 2001c, 2004; Jelinek and Karperien, 2008).

Supporting the conclusion that binary contours from microglia realistically represent underlying scaling features, the average D_Bs of binary contours extracted from the model populations corresponded to the D_Bs that would be expected for theoretical fractal microglia having the same underlying scaling features (see Figure 5). Ramified microglia modeled on a population with a mean D_B of 1.423 for instance, had a mean D_B of 1.425. Furthermore, the D_Bs changed as would be expected for fractal patterns when the length or diameter of the modeled branches changed, but were not affected when the soma size or elongation changed. The results were robust under the emulations of 3D space, but only within limits (Jelinek et al., 2002; Karperien, 2004; Karperien et al., 2005; Jelinek and Karperien, 2008).

Overall, the in silico studies suggest that, in practice, some variation in calculated D_Bs is predictable even for cells in equivalent activation states having essentially the same branching ratios, attributable to the space the microglia occupy, and the orientation they assume at any point in time. The variation not related to scaling is small enough to conclude that binary contours represent microglial morphology for box counting fractal analysis, at least for the particular pattern extraction methods and large sample sizes used. However, a feature of the models that limits the applicability of these results is that the modeller could control the background and the degree of “staining,” and the models had very high contrast (Jelinek et al., 2002).

Empirical results add to the fundamental relative pattern that “most activated” means “least ramified,” but “least activated” is not necessarily “most ramified.” This is because the most complex microglial form seems to be ramified cells that are subtly activated.

Thus, the evidence suggests that the basic pattern is characterized by an initial increase in the D_B when unstimulated ramified cells start responding, followed by a decrease until the roundest forms are reached, then an increase back up to the ramified states. The amount of data available at this point is insufficient to establish normative ranges, but, as a rough guide and taking note that the actual values varied with the investigative protocol, the peak in D_B was typically around 1.42, and rarely above 1.50. The essential cycles illustrated in Figures 1 and 7 thus can be tentatively understood as cycles going from 1.00 at the bottom to 1.50 at the top, but establishing normative ranges for ramified cells is another challenge for future fractal analysts (Soltys et al., 2001, 2005; Karperien, 2004; Jelinek et al., 2008; Hinwood et al., 2012). Various studies have shown that the cells with the peak values for complexity are both highly ramified and in compromised environments (i.e., ramified cells in uncompromised environments had slightly lower D_Bs). In some studies these were cells with many medium to long, hypertrophied processes. This configuration may be in addition to, or related to, a phenomenon known as “hyper-ramification,” due to ramified cells subtly responding to noxious stimuli such as chronic stress (Hinwood et al., 2012).

Potentially relevant to quantitating hyper-ramification is that many methods depend on changes in markers constitutively expressed at low or undetected levels then upregulated during responses to compromise such as chronic stress. This opens up the possibility of morphological information being underrepresented in ramified cells being used as comparisons to identify activated cells. Further research about the extent to which a cell has become hyper-ramified, vice having possibly had more existing detail made visible (e.g., as revealed by upregulated MHC-II in the absence of actual morphological changes) is required (Kanaan et al., 2010; Kettenmann et al., 2011; Hinwood et al., 2012).

Over and above the finding of a fundamental relative pattern hangs the issue of the actual differences in fractal dimensions found with different investigations. There are important practical considerations in fractal analysis to consider that may underlie such differences. Accordingly, below we discuss several factors affecting microglial morphology that may be relevant to fractal analysis.

Downward shift in D_B for microglia grown in the laboratory. The D_B for cultured microglia showed the fundamental relative pattern for microglia described above, but actual values tended to be lower than for other protocols. This may be related to certain differences that distinguish these cells from other preparations due to the culture environment and have the potential to affect the results of fractal analysis. Such cells, depicted in the drawings in Figure 6, typically look different from other microglia. On ramified cells, secondary branches are often less apparent or appear as extremely fine extensions, and cellular contours generally appear smoother. Lamellopodia are frequently more evident, and hairy-looking fringes, not normally detected in light microscope examinations of microglia from tissue, may be seen. The drawings show morphologies from unstimulated (left) to becoming activated (right) but lack an initially rounded morphology that immature cells in culture often have before ramifying. In addition, depending on many conditions, cultured microglia adopt other morphologies not shown in these drawings (de Groot et al., 1992; Bohatschek et al., 2001; Kettenmann et al., 2011; Olah et al., 2011).

Some of the differences such as seen with lamellopodia translate into less detail than is typical of microglia in tissue and lead to a lower D_F for ramified cells in particular. Our lab did find in one investigation that the D_B of cultured cells increased as subjective ratings of activation increased. This result was attributed to a technical issue that rendered secondary branches invisible on many of the ramified cells (Karperien, 2004). The cytoskeletal reorganization seen in microglia is known to distinguish microglial ramification from ramification of other cells, so it might be informative to separate cytoskeletal rearrangements from strictly membrane features (Faff et al., 1996; Tanaka et al., 1999; Faff and Nolte, 2000; Ohsawa et al., 2000). Perhaps comparing cytoskeletal components in cultured and in vivo microglia would eliminate the difference, or perhaps the difference is indeed inherent to the spatial context of microglia in the culture environment. In this respect, there are a host of factors that influence microglial morphology in culture (e.g., the presence of astroglia). In general, work is needed to confirm if the D_F is lower in other types of fractal analysis and to further clarify quantifiable differences between in vitro and in vivo morphologies with respect to different microglia classes and interpretation of microglia cycling.

The unknown influence of species on the D_F. Another element that may have been a factor in different studies reporting different values from fractal analysis is species. Microglia are presumed to reside in all mammals and have been found in several other vertebrates and invertebrates (e.g., birds, frogs, fish, snails, and leeches) (Dowding et al., 1991; Dowding and Scholes, 1993; Sonetti et al., 1994; Magazine et al., 1996; Dobrenis, 1998; Bernhardi and Nicholls, 1999; McMenamin, 1999; Navascues et al., 2000), which has led many researchers to generally classify microglial morphology assuming the fundamentals apply across species. But this assumption is questionable because microglia from one species are not necessarily comparable to microglia from another. In some cases, significant differences in various features have been noted even between strains of one species (Humphrey and Moore, 1995; Klyushnenkova and Vanguri, 1997). Microglia differ in how they are distributed in any particular species (Hutchins et al., 1990; Andjelkovic et al., 1998; Maslinska et al., 1998; Rezaie and Male, 1999; Rezaie et al., 1999; Navascues et al., 2000; Male and Rezaie, 2001); the evidence suggests that some amphibians and rodents have smaller, and some fish considerably larger, proportions than humans (Lawson et al., 1990; Dowding et al., 1991; Sonetti et al., 1994). Other differences have been found in function and staining, as well as fundamental morphology (Chen et al., 2002; Hayakawa et al., 2005; Jinno and Yamada, 2011). A difference affecting ramified microglia in particular is that processes branch subtly differently according to species (Finch et al., 2002). Broadly speaking, any of a host of species-related differences in microglia may have accounted for some of the difference across paradigms, but the significance of species differences for fractal analysis is unknown. A future challenge for fractal analysts, then, is to explore differences amongst microglia from different species.

Branching angle. The difference noted above in microglial branching angle with species deserves further consideration. It is known that microglia tend to sprout essentially orthogonally near their middle and end, filling the outer portion of the spread of processes with nearly perpendicular branch points. They are more orthogonal than astroglia, for instance, which tend to branch more acutely (Karperien, 2001c, 2004; Jelinek and Karperien, 2008). Branching angle in general may have special relevance to fractal analysis of microglia, because not just the degree of branching but in particular branching angle influences both flow within branched structures and the D_B (Hahn et al., 2005).

Potential influences of texture and space. Another factor that may have contributed to differences in the D_F is texture. Microglia respond to textures such as glass and various biomaterials (Dobrenis, 1998; Tanaka et al., 1999; de Groot et al., 2000; Wollmer et al., 2001). Research into mechanisms behind the rejection of biomedical implants has shown that microglia respond to coatings used on electrodes and implants, for instance (Leung et al., 2008). Perhaps future applications of fractal analysis will move our understanding of biomedical implant rejection forward, but whether or not fractal analysis is sensitive to the effects of various textures is currently unknown.

Space may also have accounted for some differences. Some morphological variability of microglia grown in the laboratory and identified in tissue is known to be accounted for by 3-dimensional space and how microglia orient themselves in it. Given room, for instance, the processes of microglia grown in culture tend to avoid each other, and under astrocyte layers, whole microglia appear flatter than cells above, and rounder in more open than confined spaces (Dobrenis, 1998; Tanaka et al., 1999; de Groot et al., 2000; Wollmer et al., 2001). A topic currently being investigated is how microglia in the human CNS are oriented with respect to each other and with respect to neurons, and how this influences brain function (e.g., in autism in humans). Microglia are more dynamic in space and time than neurons and may therefore play important roles in real-time signal processing (Morgan et al., 2012). One study has used both 2D and 3D data to analyze the D_F of microglia in pathological scenarios, and as this technology continues to evolve (Sheets et al., 2010; Xiao et al., 2011), fractal analysis may prove valuable for modeling and understanding the significance of orientation in space and interdigitation amongst these mutually-existing branched structures (Pow et al., 1989; Hahn et al., 2005). Currently, however, this is another topic that needs to be explored.

Location and subtype. Other factors that affect microglial morphology are location and subtype. In CNS tissue samples, microglia adopt different conformations depending on where they are from and local characteristics within that area, to the extent that investigators formally classify subcategories based on location and different staining characteristics (Lawson et al., 1990; Mittelbronn et al., 2001). For instance, whereas microglia in gray matter are usually more stellate, hugging neuron cell bodies, sprawling alongside of oligodendroglia, or intertwining with astroglial processes, when in intra- and inter-cortical tracts, they are more often found in a bipolar, lengthwise orientation with a leading process, suggesting they may be in motion and giving them the appearance of a less ramified cell even though they are not “activated” (Kreutzberg, 1995; Rezaie et al., 1997; Rezaie and Male, 1997, 1999; Bayer et al., 1999; Radewicz et al., 2000; Male and Rezaie, 2001). Perivascular microglia, too, adopt conformations distinguishing them from other microglia. Characteristically elongated and conforming to the surfaces of the vessels they lie along like lichens clinging along branches, they are less stellate than ramified microglia networked throughout the CNS. A relatively sprawling and untortuous morphology of ramified microglia can be observed in the retina, where they may be found in a horizontal laminar distribution from the nerve fiber layer to the outer plexiform layer (Liu et al., 2012). One pilot investigation of differences reported in the literature suggests the D_B can be affected by the location at which microglia are found in the brain (Karperien, 2004). More and more phenoytpes of microglia are being proposed (Olah et al., 2011) and the details of such differences still need to be charted.

Studies of how D_Fs correspond to visually assigned morphological categories have so far yielded three main results. (1) Fractal dimensions discriminated between all categories in four-category systems. (2) D_Fs did not consistently discriminate three-category systems, failing to differentiate intermediate from ramified cells in some studies. And (3), despite failing to discriminate three-category systems, they nevertheless discriminated other subtle and visually undetectable differences within a category, ramified normal and ramified compromised (Soltys et al., 2001; Karperien, 2004; Karperien et al., 2005).

These results suggest that classifying microglia using a three-category system ignores differences in complexity that a four-category system detects. That is, where people subjectively group some “bushy” and some “hypertrophied” cells with ramified, the D_F objectively draws lines quantitating these categories (as well as activated). Moreover, that fractal dimensions discriminate between subtle differences within ramified cells from compromised vs. normal tissue suggests a fifth category, presumably the peak cells noted above, may be quantifiable.

These results may be particularly relevant to counting cells classified into a category. Because the changes in microglial morphology occur in so many domains and reflect so many influences and events, finding the same number of cells in a morphological category might obscure subtle but important differences between samples in what the cells are doing. By clarifying the functional and morphological correlates of differences in complexity within categories, fractal analysis may be a major contributor to making models of microglial function more quantitatively sensitive to subtle but meaningful changes in morphology. Further study of the quantifiable differences may also lead to identification of rules that will assist human observers in categorizing microglia.

Further work is necessary to verify and expand this small body of work, but the results so far suggest that the discriminating capacities of the D_B may be powerful for gauging microglial activation in incipient or ongoing responses associated with injury, disease, and drug use (Soltys et al., 2005). This could affect clinical decision-making as well as laboratory work. Based on the work described above, one application that could be explored is measuring the fractal dimension of microglia in spinal fluid to monitor and quantify pathological status, stages of an ongoing response after injury, or effects of drugs in patients (e.g., for schizophrenia) (Nikkila et al., 1999; Stoll et al., 2006; Blackbeard et al., 2007). Another area we can speculate that fractal analysis of microglia may be helpful in is in making mathematical models to predict drug responses. Whether or not average D_Bs or profiles of the distribution of complexity will be useful for differentiating different diseases or states by quantifiably characterizing the numbers of various types of morphology without the need for subjective classification is a question for future research.

Another area with promise for the future is building on recent work in tracking microglia with in vivo imaging.

Diabetes. In diabetes and glycemic status in human and animal models microglia have been implicated as playing important roles in pathological sequelae (Chahed et al., 2010; Polito et al., 2011). Liu et al. (2012), for example, have tracked the association of retinal microgliosis with retinal ganglion cell degeneration in rodents. Several studies of rodent models of diabetes have shown that the function and morphology of microglia in different areas of the CNS can be affected (e.g., marked shortening of processes) by compromised glycemic status without cells becoming activated (Gaucher et al., 2007; Arden and Sivaprasad, 2011). Based on work cited earlier in this paper describing how similar changes affect the D_B, it is likely that the types of changes that have been noted in diabetic sequelae are likely to influence the D_B, suggesting another potential use of fractal analysis that could be developed. This may be especially relevant with respect to diabetes research for live monitoring, but will depend on in vivo visualization techniques being further developed.

Alcohol and thiamine deficiency. The link to diabetes research brings up the point that diet and nutritional status in general are factors that can have multiple, compound effects on microglia. It is well documented that a host of factors in the milieu affect microglia (e.g., acidity and temperature) (Faff and Nolte, 2000; Rezaie et al., 2002). Researchers have shown that microglia in mice respond rapidly to a high fat diet by infiltrating the hypothalamic arcuate nucleus (Yi et al., 2012). Effects on microglia of thiamine deficiency, which may occur in alcoholics or nutritionally deprived people, have also been studied. Like all cells, microglia depend on energy, thus can become dysregulated by metabolic compromise (e.g., ATP may be unavailable or lactate may accumulate with reduced thiamine dependent enzymes) (Park et al., 1999). Researchers have shown that microglia in rats are exquisitely sensitive to such compromise, changing both their profile of proteins expressed and their morphology (Zhao et al., 1996), but not necessarily being classifiable as responding. It has been reported, for instance, that with thiamine deficiency, especially perivascular microglia become “plump,” although still have processes, prior to and probably mediating eventual overt neuronal damage (Sonetti et al., 1994; Dickson, 1999; Todd and Butterworth, 1999a,b; Calingasan and Gibson, 2000a,b). Again, because the changes noted are subtle and difficult to objectively classify but also the kinds typically quantifiable by the D_B, this may be another area that could be explored by fractal analysis.

Another subject in which fractal analysis has been used to quantitate typical changes in microglia is early development. Microglia play many roles in neurodevelopment, at different times, places, and forms. Proposed roles include “fine-tuning” CNS structure, promoting axonal growth, directing neuronal migration, determining neuronal phenotypes, interacting with oligodendrocytes in myelination, influencing vascularization, and disposing of debris and normally dying cells. Through epigenetic, structural, and other mechanisms, they may also contribute to developmental disruptions and subsequent neuropathology such as in fetal alcohol spectrum disorder, cerebral palsy, Down's syndrome, autism, and schizophrenia (Hao et al., 2001a,b; Aarum et al., 2003; McAllister and Miller, 2010; Maezawa et al., 2011; Paolicelli et al., 2011). There are many opportunities to test the ability of fractal analysis to contribute to our knowledge of early development.

In humans, rather than there being one general early microglial morphology, there are characteristic temporal and spatial patterns. Many of these appear to be very much the purview of fractal analysis. For instance, microglia appear very early and then colonize the CNS mainly during the second and to some extent the third trimester of fetal development (in rodents, microglia start to populate the CNS around or after birth). In tissue from humans gestated a few weeks, investigators first see “rounded” cells, then “intermediately ramified” cells migrating along white matter tracts and blood vessels; then, later in development, mainly fully ramified cells. This basic temporal pattern is superimposed on several spatial patterns—different brain areas are populated at different times but according to usually the same basic morphologic sequence. Orlowski et al. (2003) have demonstrated an elegant quantification of this progression using fractal analysis as cells becoming increasingly complex over time. There is evidence that distinct morphological and functional subtypes of microglia appear even in the earliest stages of development, which requires further investigation (Hutchins et al., 1990; Andjelkovic et al., 1998; Cuadros and Navascues, 1998; Maslinska et al., 1998; Alliot et al., 1999; Navascues et al., 2000; Rezaie et al., 2002).

Another topic that could be explored with fractal analysis is variation in different areas. Billiards et al. (2006) have found that human fetus and infant cerebral white matter is densely populated with “intermediate” and “amoeboid” microglia and that there is a transiently increased density of activated microglia (i.e., cells in the typical morphology marked by CD68) in the cerebral white matter prior to 37 weeks gestation. This peak has been proposed to translate into a window of increased vulnerability to injury mediated by microglia (e.g., hypoxic injury underlying cerebral palsy). Fractal analysis may add to our knowledge by quantitating such differences and providing a finer level of knowledge about what cells are doing in different places and times in development.

Rounded cells seen early on in development are generally considered to be “immature” rather than activated. Many authors call a cell “amoeboid,” regardless of its origins or maturity, as long as its cell body is amorphous, long, fine processes are absent, and pseudopodia are (usually) present, but other authors object, saying that immature and unbranched as opposed to reactive microglia differ. It is not clear if the microglia that are first seen as rounded cells are rounded because they are immature or because that is the morphology in which they are best able to migrate through, prune, and clean up the developing CNS. Further, the extent to which microglia deramify and reramify in developing CNS is not known. These are questions for which fractal analysis may be able to provide additional insight.

Not only do microglia change over early development, microglia in the very young are not the same as microglia in the very old. Microglia generally increase from sparse cells with few branches in infancy to a ramified network in adulthood to an increasingly dense network of increasingly “reactive looking” microglia in old age. Primary microglial processes are usually shorter, thicker, and more numerous in adults as compared to infants, and again in nonelderly adults compared to elderly adults. Researchers have also characterized a tendency toward more aberrant features, including twisting and fragmenting of processes, with age (Sheng et al., 1997a,b, 1998a,b; Rozovsky et al., 1998; Sheffield and Berman, 1998; Nichols, 1999; Sheffield et al., 2000; Finch et al., 2002; Yu et al., 2002; Olah et al., 2011).

Within the overall spectrum of age-related changes, other factors such as gender and brain region can further influence microglia and may be reflected in the morphology itself or at least how that morphology is revealed under the microscope. To illustrate, some researchers have found that HLA-DR expression is higher in normal elderly human males than females (but higher in females with Alzheimer's disease), and significantly so only in white matter. In a study of rodents, Morgan and colleagues (1999) found that food restriction lessened age-related increases in complement receptor expression but not MHC-II expression in microglia in the basal ganglia, but food restriction and age did not affect these two measures in the outer molecular layer of the dentate gyrus (Kreutzberg, 1995; Carson et al., 1998; Hurley et al., 1999; Morgan et al., 1999; Overmyer et al., 1999; Ren et al., 1999; Wierzba-Bobrowicz et al., 2000a,b; Cross and Woodroofe, 2001; Kanaan et al., 2010).

The changes of age are accompanied by functional changes in elderly adults, whereby from development to old age, microglia lose their ability to protect and become more likely to react or more likely to react abnormally. Why microglia become “senescent” or “dystrophic” is unknown, but it has been suggested that the changes may be at least partly mediated by and contribute to the changing hormonal environment of aging as well as a reflection of accumulating pathology.

Modeling studies suggest that the changes described in the literature would affect the D_B. For instance, in space-emulating models simulating process swelling in isolation from other changes—i.e., changing only the diameter of primary branches—as process diameter increased relative to soma diameter, the measured D_B decreased despite the fact that the complexity input to the models did not. Another factor relevant to age-related changes that affected results was the number of primary branches. The D_B tended to increase with the number of primary branches even when the fundamental complexity of the branches was not changed. Tortuousness was another factor having an effect: in keeping with results for known fractal patterns, the average D_B for more tortuous models generally deviated more from theoretical than for straighter patterns (e.g., ~5 vs. 3%) and models with curled rather than sprawled processes had higher D_Bs (Jelinek et al., 2002; Karperien, 2004; Karperien et al., 2005; Jelinek and Karperien, 2008).

Little research has been published describing actual measurements of these changes with fractal analysis. One investigation measuring the D_B for microglia from elderly human brain illustrated that the distribution of complexity in healthy elderly human brain differed from that for pathological elderly human brain (e.g., for the D_B range from 1.30 to 1.43, pathological brain had more cells, and for the range from 1.40 to 1.48 healthy elderly had more), and that microglia in the healthy brain had a different complexity profile than more typically noted for younger adult brain (Karperien, 2004). Future research exploring age-related changes in microglia and correlates in the D_B may shed light on the topic of age-related disease and dysfunction.

Virtually all of the fractal analysis studies in the literature compared D_Fs against other metrics. The utility of the D_F varied with different methods. In many cases where multiple measures were compared, the D_F was the most consistently useful measure of, and in some cases, the only measure refined enough to detect, the most subtle and difficult to identify changes. One consistent result was that D_Fs were generally complemented by various measures of lacunarity, where using them together gave the most sensitive correlation to morphological categories (Soltys et al., 2001, 2005; Orlowski et al., 2003; Karperien, 2004).

In some work, measures of the size and shape of the 2-dimensional space occupied by a cell were less sensitive to differences in microglial morphology, where the D_B was superior to Λ in detecting the subtlest changes, but in some studies Λ was shown to be especially good at detecting changes in soma shape and size that D_Fs did not detect (Soltys et al., 2001, 2005; Orlowski et al., 2003; Karperien, 2004).

Some investigations found some D_Fs to be correlated with certain features, but the D_B in particular was generally deemed not superfluous with other measures. In one study, the D_B was correlated with Λ, but only for cells at certain levels of activation. The DB was correlated with the number of pixels in some cases, but generally not strongly correlated with the density of pixels, and the number of pixels was not as useful an index of function-related change as was the DB. Modeling studies showed that Λ was sensitive to many of the changes affecting the D_B but as an independent measure; the two were not consistently correlated, except for tortuousness, for which they were strongly negatively correlated (Karperien, 2004; Karperien et al., 2008c; Jelinek et al., 2011).

Modeling and other studies using multifractal measures suggest mutlifractality and local dimension analysis may be useful for identifying particularly intermediate forms of microglia. Modeling studies have shown that microglia modeled with the same branching parameters on all branches did not scale as multifractals, but models with disparate parts were more likely to scale as multifractals and showed variation in the local dimension. These results are consistent with other results (Karperien, 2004; Karperien et al., 2011; Jelinek et al., 2013) indicating that multifractal scaling is rare overall but that ramified microglia are more likely than others to show multifractal scaling, and when they do, to have disparate parts. One challenge for the future, then, is to clarify the nature of multifractal scaling in microglia, and pursue the potential for multifractal analysis to reveal cells in a transitional state having elements of more than one typical level of activation.