Second‐order spatial analysis of epidermal nerve fibers

Abstract

Breakthroughs in imaging of skin tissue reveal new details on the distribution of nerve fibers in the epidermis. Preliminary neurologic studies indicate qualitative differences in the spatial patterns of nerve fibers based on pathophysiologic conditions in the subjects. Of particular interest is the evolution of spatial patterns observed in the progression of diabetic neuropathy. It appears that the spatial distribution of nerve fibers becomes more 'clustered' as neuropathy advances, suggesting the possibility of diagnostic prediction based on patterns observed in skin biopsies. We consider two approaches to establish statistical inference relating to this observation. First, we view the set of locations where the nerves enter the epidermis from the dermis as a realization of a spatial point process. Secondly, we treat the set of fibers as a realization of a planar fiber process. In both cases, we use estimated second-order properties of the observed data patterns to describe the degree and scale of clustering observed in the microscope images of blister biopsies. We illustrate the methods using confocal microscopy blister images taken from the thigh of one normal (disease-free) individual and two images each taken from the thighs of subjects with mild, moderate, and severe diabetes and report measurable differences in the spatial patterns of nerve entry points/fibers associated with disease status.

Spatial analysis improves the detection of early corneal nerve fiber loss in patients with recently diagnosed type 2 diabetes

“…These findings were explained by multifocal fiber loss along the length of nerves and sprouting [33]. Likewise, intraepidermal nerve fiber (IENF) loss due to neuropathy does not seem to occur in a random way, but rather, the remaining nerves seem arranged in ‘clusters’ and exhibit some spatial pattern, possibly due to collateral branching by the surviving nerve fibers [34,35]. Preliminary attempts to describe this pattern indicate that the spatial distribution of nerve fibers in the foot becomes more ‘clustered’ as neuropathy advances [35].…”

“…The resulting test statistic provides a measure for this deviation, and the results showed that MADPC was slightly more sensitive than MADL in discriminating between point patterns between control and diabetes subjects. Better applicability of non-cumulative pair-correlation functions and considerably lower reliability of cumulative L functions was already reported for the analysis of IENFs [35]. …”

Characterizing cross‐subject spatial interaction patterns in functional magnetic resonance imaging studies: A two‐stage point‐process model

“…First, rather than studying the interactions between different types of points on the same image (Eckel et al ., 2009; Diggle et al ., 2006), we study the interactions between the points from subject-pairs. Thus, our replicates are pairs of subjects instead of individual subjects, locations, or images (Myllymäki et al ., 2012; Waller et al ., 2011; Schladitz et al ., 2003; Diggle et al ., 2000; Baddeley et al ., 1993). This introduces a complicated dependence structure between our replicates that needs to be accounted for.…”

Comparison of the spatial organization in colorectal tumors using second-order statistics and functional ANOVA

“…All these functions consider the distribution of distances between pair of detected points representing the biological objects. They have been used in various biomedical contexts such as the description of the organisation of cancerous cells in breast [5], [6] or brain [7] tumors, or diabetic and non-diabetic epidermal nerve fibers [8]. However, in all these papers, these statistics are generally used in the simple context of comparing the organization of diseased and healthy data, which lead to studying images containing very different spatial organisations.…”

“…In addition, the object extraction in these works is either done manually [5], [8] or semi-automatically [7], [6]. A manual intervention leads to inter-and intra-operator variability and, being costly, limits the possible size of the study.…”