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

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