A semi-automated analysis method of small sensory nerve fibers in humanskin-biopsies

Kazuyuki Tamuraa,∗, Violet A. Magera,b, Lindsey A. Burnettc, John H. Olsond, Jeremy B. Browere,f, Ashley R.Casanof, Debra P. Baluchd, Jerome H. Targovnikg,d, Rogier A. Windhorsth,a, Richard M. Hermanf,e

aDepartment of Physics, Arizona State University, Tempe, Arizona, 85287-1504, USAbCarnegie Observatories, Pasadena, California, 91101-1232, USA

cMolecular and Cellular Biology Program, Arizona State UniversityTempe, Arizona, 85287-4601, USA

dSchool of Life Sciences, Arizona State University, Tempe, Arizona, 85287-4501, USAeHarrington Department of Bioengineering, Arizona State University,

Tempe, Arizona, 85287-9709, USAfClinical Neurobiology and Bioengineering Research Center,

Banner Good Samaritan Medical Center,Phoenix, Arizona, 85006-2666, USA

gCarl T. Hayden VA Medical Center, Phoenix, Arizona, 85012-1839, USAhSchool of Earth and Space Exploration, Arizona State University,

Tempe, Arizona, 85287-1404, USA

Abstract

Computerized Detection Method (CDM) software programs have been extensively developed in the field of astron-omy to process and analyze images from nearby bright stars totiny galaxies at the edge of the Universe. These object-recognition algorithms have potentially broader applications, including the detection and quantification of cutaneousSmall Sensory Nerve Fibers (SSNFs) found in the dermal and epidermal layers, and in the intervening basementmembrane of a skin punch biopsy. Here, we report the use of astronomical software adapted as a semi-automatedmethod to perform density measurements of SSNFs in skin-biopsies imaged by Laser Scanning Confocal Microscopy(LSCM). In the first half of the paper, we present a detailed description of how the CDM is applied to analyze theimages of skin punch biopsies. We compare the CDM results to the visual classification results in the second half ofthe paper. Abbreviations used in the paper, description of each astronomical tools, and their basic settings and how-tosare described in the appendices. Comparison between the normalized CDM and the visual classification results onidentical images demonstrates that the two density measurements are comparable. The CDM therefore can be used —at a relatively low cost — as a quick (a few hours for entire processing of a single biopsy with 8-10scans) and reliable(high-repeatability with minimum user-dependence) method to determine the densities of SSNFs.

Key words: Computerized detection method, Visual classification, Small sensory nerve fibers, Basement membrane,Confocal images

∗Corresponding author. Tel.:+1-480-965-0665; fax:+1-480-965-7954.

Email addresses:ktamura@asu.edu (Kazuyuki Tamura),vmager@ociw.edu (Violet A. Mager),lindsey.burnett@asu.edu (Lindsey A. Burnett),john.olson@asu.edu (John H. Olson),jeremy.brower@asu.edu (Jeremy B. Brower),ashley.casano@asu.edu (Ashley R. Casano),page.baluch@asu.edu (Debra P. Baluch),docglands@cox.net(Jerome H. Targovnik),rogier.windhorst@asu.edu (Rogier A.Windhorst),richard.herman@cox.net (Richard M. Herman)

1. Introduction

Damage to the peripheral nervous system can be idio-pathic, or can occur as a result of known causes, such asof pre- and post-diabetic disorder (e.g., Lacomis, 2002;Smith and Singleton, 2006). This damage can be char-acterized by pathology of Small Sensory Nerve Fibers(SSNFs: e.g., Dyck et al., 1981; Periquet et al., 1999;Verghese et al., 2001; Sumner et al., 2003; Malik et al.,2005; Smith and Singleton, 2006), which are difficult toassess functionally, and may be variable in symptoms

Preprint submitted to Journal of Neuroscience Methods October 9, 2009

(e.g., pain and tingle), signs (e.g., sensory loss), or dis-abilities.

The difficulty in diagnosing an SSNF neuropathy hasled to the development of histological analysis of skinpunch biopsy tissue, utilizing morphological surrogatemarkers and confocal, or conventional microscopy (e.g.,Dalsgaard et al., 1989; Karanth et al., 1991; Kennedyand Wendelschafer-Crabb, 1993). This technique is asafe, reliable, and reproducible method of quantifyingSSNF pathology. It also has been advocated for di-agnosing SSNF neuropathy from a variety of causes(Holland et al., 1997, 1998), and for assessing the de-gree of neuropathy from none to severe (Quattrini et al.,2007). A basis for such diagnostic procedure is thatthese biopsy tissues are rich in SSNFs (often referredto as C-fibers), that can be labeled by immunostainingwith a pan-neuronal marker (e.g., Protein Gene-Product(PGP) 9.5; Dalsgaard et al., 1989; Karanth et al., 1991),and quantified as density values (e.g., fibers mm−1) ofepidermal length, or as in this presentation, of basementmembrane length where fibers are counted in the base-ment membrane.

Under normal clinical conditions, the key issue in vi-sually measuring the density of SSNFs is the reliabil-ity. The use of multiple blind-study classifiers is usu-ally used to improve the reliability of the analysis. Sta-tistical studies show the correlation coefficients for re-peated observations by the same classifier is 0.80±0.06(McArthur et al., 1998), and for observations betweendifferent classifiers is 0.90±0.04 (Hirai et al., 2000).Smith et al. (2005) shows that the interobserver variabil-ity is 9.6%± 9.4 (in the form of relative intertrial vari-ability (RIV) ± standard deviation (SD)), and intraob-server variability is 9.6%± 8.9 for each biopsy, wherea RIV value of less than 10% indicates a high degreeof repeatability. Detail descriptions of how to calculatethe RIV and SD are provided by Smith et al. (2005). Toimprove the reliability, a number of computerized pro-grams have been adopted (e.g., Kennedy et al., 1996).One practical issue with these programs is the cost ofthe software. We therefore propose here: (1) alow-cost, novel, and semi-automated computerized detec-tion method, which can determine the density of SS-NFs in immunostained tissue images; and (2) that thismethod, with some adaptation, can be readily used todetect SSNFs, and to determine the presence of SSNFneuropathy in any kind of tissue.

In this paper, we present a quantitative semi-automated method of measuring the SSNF densitieswithin the basement membrane, using parts of exist-ing computer codes. These codes have been success-fully used for decades to analyze images of tiny galax-

ies in the field of extragalactic astronomy (e.g., Driveret al., 1995; Odewahn et al., 1996; Arnouts et al.,1997). Since the 1960’s, astronomers have developedmany techniques for detection of those tiny objects.As a result, current technology allows us to detect andanalyze from the surface of the Sun to objects 1022

times fainter than the Sun, and up to 10 million timessmaller than the angular size of the full Moon (e.g.,Tyson, 1988; Neuschafer and Windhorst, 1995; Pas-carelle et al., 1996; Windhorst et al., 1998, 2008). As-tronomers also have developed numerical techniques toobtain the best possible resolution through deconvolu-tion and other methods such as the Maximum EntropyMethod (MEM: Gull and Daniell, 1978, 1979), CLEAN(Hogbom, 1974), and Pixon methods (Pina and Puetter,1993; Puetter, 1997). Some of these (e.g., MEM andPixon methods) have been adapted for use in the med-ical field, such as the detection of breast cancer fromX-ray mammograms. For these reasons, we employthe rich expertise of astronomical image analysis soft-ware to detect SSNFs in the basement membrane of skinpunch biopsies of volunteer subjects.

2. Materials and Methods

All human studies have been approved by the In-stitutional Review Boards of two institutions: BannerGood Samaritan Medical Center, Phoenix, AZ and Ari-zona State University, Tempe, AZ. They have been per-formed in accordance with the ethical standards laiddown in the Declaration of Helsinki. All persons gavetheir informed consent prior to the investigation. Agroup of 27 subjects were recruited yielding 52 biop-sies. Skin punch biopsies were obtained from the prox-imal forearm and/or distal thigh of these subjects.

The intent of this work is to demonstrate that SSNFdensity values attained by computer analysis com-pares favorably to the visually-monitored density countswithin the same subject. Thus, in any one subject, ahealthy or unhealthy pool of subjects is not specificallyrelevant to the research question. Nevertheless, in thisstudy, we chose to examine SSNF densities in a repre-sentative cohort of obese subjects with no neuropathicsymptoms with the purpose to conduct a later study,which would examine the present cohort with anotherobese population with diabetes.

2.1. Sample preparation: Procedures

2.1.1. Biopsy techniqueA 2 cm circle was drawn around the hairy skin sites

of the proximo-lateral forearm and the disto-medial as-2

pect thigh. Each skin site was then sterilized with an al-cohol swab and anesthetized with 1 % lidocaine. Oncethe subject reported complete numbness in the area, askin punch biopsy was performed (3 mm diameter by3 mm depth). The sample was placed in fixative, anda small sample of gelfoam was placed on top of thewound to expedite healing. BacitracinR© (a topical an-tibiotic) was swabbed on a bandage and placed on topof the site. There were no reports of adverse events as aconsequence of these procedures.

2.1.2. Sectioning and stainingSkin punch biopsies were fixed overnight in modi-

fied Zamboni’s fixative (2 % formaldehyde, 15 % Picricacid in 0.1M PBS, pH 7.5); biopsies were equilibratedin 50 % sucrose in 0.01M PBS for 12 hours at 4◦C,and mounted in Tissue Tek OCT Compound (Miles Inc.,Elkhart, IN); 0.06 mm (60µm) thick sections were ob-tained by cryostat sectioning. Biopsy sections werethen blocked in blocking solution (0.1M PBS, 0.05 %Tween-20, 0.1 % Triton X-100, 5 % bovine serum al-bumin frac V) at 4◦C for 12 hours, then washed twiceby solution replacement with washing solution (0.1MPBS, 0.05 % Tween-20, 2 % BSA, pH 7.5). Primary an-tibodies to collagen IV (mouse anti-human collagen IVmonoclonal, Cat. # MAB1910, Chemicon International,Temecula, CA) and PGP 9.5 (rabbit anti-human PGP9.5 IgG purified polyclonal, Cat. # 7863-0507, BioGen-esis, Kingston, NH) were diluted 1:50 with antibodydilution buffer (0.1M PBS, 1 % BSA, pH 7.5). Sec-tions were immunolabeled for 24 hours at 4◦C in theprimary antibody solution. Sections were then washedtwice in washing solution. Secondary antibodies (AlexaFluor 488 goat anti-mouse IgG (H+L); Cat. # A11001,and Alexa Fluor 633 goat anti-rabbit IgG (H+L), Cat.# A21070, Molecular Probes, Eugene, OR) were diluted1:100 in antibody dilution buffer. Sections were incu-bated in this solution for 24 hours at 4◦C, and washedtwice with washing buffer.

2.1.3. Visualization and image acquisitionImmunofluorescently labeled sections were dehy-

drated in a graded ethanol series, transferred to methylsalicylate, and wet mounted for visualization using aLeica TCS-NT Laser Scanning Confocal Microscope(LSCM) at the W. M. Keck Bioimaging Facility (KeckLab) at the Arizona State University using Ar andHe/Ne lasers. For each sample, 32z-plane optical sec-tions were imaged every 0.00125mm (1.25µm) througha 0.040 mm (40µm) region with 0.16 mm×0.16 mm(160µm× 160µm) in the x–y dimensions (see Fig. 1).Serial sections of these images were obtained using

C o n f o c a l D a t a S e t o f T i s s u e B i o p s i e s1 m m x 1 m m x 1 m mt i s s u e “ b i o p s y ” 1 m m x 1 m m x 0 . 0 6 m mt i s s u e s e c t i o nC r y o s t a t c u ts e c t i o n C o n f o c a lo p t i c a l“ s c a n ”

0 . 0 0 1 2 5 m mb e t w e e n i m a g e s3 2 o p t i c a l“ l a y e r : i m a g e s ”

0 . 1 6 m m : x 0.16mm:yS i z e o f e a c h i m a g e i s1 0 2 4 x 1 0 2 4 p i x e l s .U p t o 1 2 s c a n s o f e a c hb i o p s y s a m p l e i sc o l l e c t e d b y t h e L a s e rS c a n n i n g C o n f o c a lM i c r o s c o p e ( L S C M ) .T h e f i n a l i m a g e i s a l i n e a r s t a c k o f3 2 l a y e r Q i m a g e s f r o m a s i n g l e s c a n .( “ b a s e m e n t m e m b r a n e i m a g e ” a n d“ S S N F i m a g e ” )Figure 1: A diagrammatical illustration at different stages of the im-age preparation and analysis. From a single “biopsy” sample, a thintissue section is prepared by immunostaining, then the LSCMtakesup to 12 “scans” of image-sets, each with a 63× magnification. Asingle “scan” consists of two sets of 32 “layer-images” — one for thebasement membrane and the other for the SSNFs — with a spacingof 0.00125 mm between layers. Only one set is illustrated here forsimplicity. These two sets of 32 “layer-images” are then distributed toindividual CDM and visual classifiers. Once distributed, each classi-fiers stacks these “layer-images” linearly to create a single projected“basement membrane image” and a single “SSNF image” for furtheranalysis.

Leica TCS-NT image software. Images were ob-tained at 63× magnification with an image resolutionof 1024×1024 pixels to increase the visibility of smalldiameter fibers to facilitate quantification of their den-sity.

2.1.4. Intraepidermal nerve fiber density quantificationFor each biopsy, up to 12 scans were observed man-

ually, and by up to four different observers. The num-ber of fibers embedded into or penetrating the basementmembrane was visually assessed by examination of thescans. Mean density for each biopsy were then deter-mined, based on the densities for each series of images,and recorded as a number of intraepidermal nerve fibersper mm of basement membrane length, yielding a meandensity value for the scans of a single biopsy.

Although the conventional method is to report epi-dermal length as the reference for calculating the den-sity value, whenthe purpose is to examine only the den-sity of intraepidermal nerve fibers, which are terminat-ing into or penetrating the basement membrane, we usebasement membrane length as the reference.

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2.2. Data and tools

2.2.1. Definition and terminologyThroughout our analysis, the data — in a form of dig-

ital images — are undergoing multiple processing steps.The images at different steps, and at different levels ofgrouping, therefore need to have specific names to beidentified. The structure of our data set is diagrammat-ically illustrated in Fig. 1, and is defined as follow: (1)there are a total of 52 skin punch biopsies, or “biopsies”;(2) eachbiopsyhas up to 12 LSCM “scans” at differ-ent locations along the basement membrane section(s);and (3) a single LSCMscancreates a set of 32 “layer-images” of basement membrane images and 32 “layer-images” of SSNF images. Theselayer-imagesare thendistributed to, and “stacked” into a single “basementmembrane image” and a single “SSNF image” by in-dividual classifiers for analysis.

2.2.2. Steps of Computerized Detection MethodIn this specific study, we use a Computerized Detec-

tion Method (CDM), derived from the field of astron-omy, to measure SSNF densities in skin punch biopsiesof our volunteer subjects. In the following sections, wedescribe the steps in the semi-automated CDM analysis,which include: (1) preparation of digitized images by:(a) converting the image format; (b) stacking two sets oflayer-images; (c) smoothing the stackedbasement mem-brane image; and (d) adding a small Gaussian noise-field to the stackedSSNF image, and similarly smooth-ing it; (2) determination of the location and length ofthe basement membrane in abasement membrane im-age; (3) detection of SSNF segments in anSSNF image;and (4) calculation of the median “SExtractor detectionrate” for each biopsy. Upon completion of these steps,the CDM results are compared to the visual classifica-tion results for normalization and proper intercompari-son — by converting fromSExtractor detection ratetoestimatedfiber density— and for assessment of the re-liability of our method.

2.2.3. Astronomical toolsIn our CDM, we use analysis tools, such as software

and computer languages, that are commonly used in thefield of astronomy. These tools have been developedand optimized over time for image analysis, especiallyfor detecting stars and small distant galaxies in a largefield of view, which somewhat resemble the appearanceof SSNF segments in a basement membrane. Since themajority of astronomical tools are developed primarilyunder the UNIX/Linux operating systems, all processesfor this study are performed using Red Hat LinuxR© or

the freely available Community ENTerprise OperatingSystemR© (CentOSR©). The astronomical tools used inthis study are distributed withno or at low cost, andmost of them can also be used with other operating sys-tems, such as Microsoft WindowsR© or MacintoshR©.Other tools, software, and computer languages could besubstituted, given the preference of a CDM user.

Astronomical image-processing tools have been de-veloped in the last three or four decades by the NationalAstronomical Observatories1, and astronomers all overthe world. New and improved astronomical softwarepackages and tools are continuously under developmentas well. These image-processing tools currently consistof many large software packages, each with 2–4 mil-lion lines of code, and many hundreds of person-yearsof software development. The main tools and softwareused in this project are, amongst others, the Smithso-nian Astrophysical Observatory Image DS9 (SAOIm-age DS9: Joye and Mandel, 2003), the Flexible Im-age Transport System (FITS: Wells et al., 1981), theNational Optical Astronomy Observatory (NOAO) Im-age Reduction and Analysis Facility (IRAF: Stefl, 1990,and references therein), the Interactive Data Language(IDL R©), the Source Extractor (SExtractor: Bertin andArnouts, 1996), SuperMongo (SM2), and FORTRAN77 (F77). More detailed descriptions of these tools andsoftware packages are given in the appendices. Most ofthese software packages and languages are distributedon the internet with low or no cost. Since these toolscould be substituted by many other free software pack-ages and languages, all of the CDM steps can be in prin-ciple constructedwithout any major software cost to theuser. In this paper, we present one well tested imple-mentation of this CDM.

2.3. Post-digitized image preparationIn this section, we give a high level review of all the

necessary steps of the CDM. The specific details, nec-essary to reproduce these steps, are given in the Appen-dices. Readers not interested in the high level steps maydirectly proceed to§2.4, or even to§3.

1National Optical Astronomy Observatory (NOAO):http://www.noao.edu/

National Radio Astronomy Observatory (NRAO):http://www.nrao.edu/

Space Telescope Science Institute (STScI):http://www.stsci.edu/

2The SM Reference Manual. Robert H. Lupton and Patricia Mon-ger (1977):http://www.astro.princeton.edu/∼rhl/sm/sm.html

http://www.supermongo.net/

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2.3.1. Image format conversion

The first step in the image preparation is convertingthe image file format as it arrives form the LSCM. Whilethe original layer-images obtained with the LSCM aresaved in the Tagged Image File Format (TIFF), theimage-displaying software, DS9, andall subsequentsoftware requires the FITS image format. To convert thefile format, a pre-written F77 program with a sequenceof various Linux commands and IRAF tasks is used.Once an original TIFF image is read in by this pro-gram, the signal (original image data) is recorded in oneof the Red-Green-Blue (RGB) channels of the portableanymap (PNM) format image, which are then separatedinto three independent PNM image files. Using IRAFtasks, the image file containing the data is saved intoa FITS image. As a result of this file format conver-sion, originally green- and red-colored TIFF images forthe basement membrane and SSNFs are converted intogray-scale images as shown in Figs. 2–4. During thisformat conversion, the original signals are rounded intointeger values in units of Data Numbers (DNs), with thelowest value set to zero. To avoid a systematic errordue to this zero-signal, a value of 1.0 DN is added to allpixels. Since the immunostained basement membraneand the SSNFs have large signal values (& 1000DN),adding 1.0 DN does not affect the final results.

While it would take a long time if all of these pro-cesses are performed manually, this pre-programed im-age conversion only takes a fraction of a second for animage on modern computers.

2.3.2. Stacking layer-images and smoothing the base-ment membrane image

The SSNFs are running through a basement mem-brane and surrounding tissue not two-dimensionally,but three-dimensionally. A single layer-image thereforecannot capture an entire SSNF, unless it happens to ex-actly line up with the scanning focal plane of the LSCM.By imaging at 32 different depths of a biopsy sectionfor a single scan, and by stacking these layer-images,we ensure that SSNFs are imaged. Stacking these 32layer-images also helps the CDM detection software byenhancing the total signal-to-noise (S/N) level of thebasement membrane and of SSNFs. The second stepin the preparation therefore includes: (1) stacking allthe basement membrane and SSNF layer-images froma single scan; and (2) smoothing the stacked basementmembrane image (see Fig. 2). The stacked SSNF im-age requires several more steps in this preparation, andhence they are treated separately in the following steps(§2.3.3).

The first process is to stack all of the layer-imagesinto a single image using an F77 program. Once a com-puter disk path to a single scan is provided, this pro-gram creates a new sub-folder and the necessary files forsubsequent analysis. The number of layer-images to becombined is set to 32 for our CDM, but this number canbe changed with a few easy modifications to the pro-gram if necessary. To actually stack the layer-images,the IRAF executable file created by the F77 program hasto be run in the directory where the IRAF parameter fileis stored (usually at the top working directory). Oncethis script has run, IRAF automatically starts up andstacks the 32 layer-images to create a single basementmembrane image and a single SSNF image. During thisprocess, 3σ-clipping — whereσ stands for the standarddeviation of the image noise — is applied to remove anyhot or bad pixels. These pixels usually have extremelyhigh or low values due to spontaneous electrical effectsof a photodetector, e.g., photomultiplier tubes (PMTs)or Charge-Coupled Devices (CCDs), used in the LSCM,and would cause a systematic error in the subsequentanalysis.

The next process is to outline the basement mem-brane in the stacked image. Fig. 2a shows the stackedbasement membrane image without any treatment (i.e.,smoothing), with green-colored contours drawn at a sig-nal level of 130.0DN. Without smoothing, the perimetercontours outlining the basement membrane have jaggededges, which will cause errors in subsequent SSNF de-tection at the edges of the basement membrane. Sincethe inner and outer edges of the basement membraneshould be ideally outlined by rather simple contours,we smooth the stacked basement membrane image toremove this graininess. Fig. 2b shows the smoothed im-age of Fig. 2a, with the green-colored contours appliedto the same signal level of 130.0 DN. While the origi-nal image (Fig. 2a) has a slightly sharper appearance,the edges in the smoothed image (Fig. 2b) are mucheasier to trace and visualize. Another important effectof smoothing is that it softens and removes, or shrinkthe regions of slightly lower signals within a basementmembrane. Without any treatment, these low-signal re-gions appear as small “bubbles” along edges or insideof basement membrane (see Fig. 2a), and would affectthe final results. In the same IRAF script to stack layer-images, another IRAF task —BOXCAR with a box-sizeof 7 pixels — is therefore used to smooth the stackedbasement membrane image.

As in the previous step, stacking multiple images, cre-ating folders and files, and smoothing the stacked base-ment membrane image only take at most a few secondson a∼ 2 GHz Linux box, while the same processes per-

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a b

Figure 2: Zoomed-in images of an example basement membrane:(a) without smoothing (i.e., an untreated stack of 32 layer-images of a singlescan of a biopsy); and (b) with smoothing applied. In the visualization software (DS9), the original basement membrane images are displayed asa gray-scale image, where the darker gray indicates the stronger signal. In both panels, green-colored contours are drawn at the same signal levelof 130 DN. While the edge of basement membrane is untraceableby the graininess of the original image (panela), this effect is removed in thesmoothed image (panelb), making the edges of basement membrane easily traceable. Scale bars at the bottom-left indicate 0.02 mm.

formed manually would take a much longer time.

2.3.3. Preparation of the SSNF imagesThe final step is to prepare the stacked SSNF image.

This step involves: (1) the treatment of the large flat-signal regions; and (2) the application ofunsharp mask-ing to the SSNF image.

The critical issue with the original (untreated) stackedSSNF image (Fig. 3a) is that the lightest gray-coloredregions in the background have a noiseless, flat signallevel of 32.0 DN, due to the simple stacking of 32 layer-images with 1.0 DN in these regions. If an area with aflat signal is relatively small, the subsequent processeswill not be affected. In most of stacked SSNF images,however, these regions usually extend over a significantfraction of an image (e.g., see Fig. 4). Since the SEx-tractor code uses the signal statistics of an entire image,a large region with a constant value has to be removedor modified. Without any treatment, these extended flat-signal regions would cause systematic errors in the auto-mated object detection by SExtractor in the subsequentanalysis. The optimal and easiest solution to this issue isto add a small Gaussian noise-field to the entire image,which simulates the regular electronic noise in CCD im-ages.

To create a simulated noise image, the IDL randomnumber generator function,RANDOMN, is used, whichcreates floating-point numbers in any specified multi-dimensional vector or matrix. In our study, we create a

set of random values in a two-dimensional matrix, cor-responding to the same size as LSCM scanned images.The values originally created have a Gaussian distribu-tion with a mean of 0.0 and a standard deviation of 1.0.To simulate the low-level noise of a CCD image, thisinitial noise matrix is multiplied by a factor of 25.0,which is determined from the signal statistics of SSNFimages to be about optimal. Once the noise matrix issaved as a FITS image, IRAF is used to linearly add thisnoise image to stacked SSNF images.

The SSNF images have another significant issue tobe solved. The cause of this problem stems from therelatively strong signal regions of immunostained tis-sues other than SSNFs. These regions affect the imagestatistics, and may cause the under-detection of SSNFsegments by SExtractor. Since these non-SSNF tissuesusually have physically larger appearances than SSNFs,“unsharp masking” is used to remove these larger struc-tures from the SSNF images. Removing these large-scale, high S/N structures ensures a much improved de-tection of the SSNF segments.Unsharp maskingis atechnique commonly used to sharpen digital images inmany different fields. In signal processing jargon, it op-timally separates the high spatial-resolution structuresfrom the low resolution ones. For the current project,this technique is used to bring out higher contrast ofthe small-scale structures, specifically the SSNFs. TheGaussian-noise-added SSNF image is smoothed withthe same IRAF task applied to the basement membrane

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a b c

Figure 3: Zoomed-in images of an example SSNF: (a) without any treatment (i.e., no smoothing nor unsharp masking was applied); (b) withsmoothing applied; and (c) with unsharp masking applied (i.e., smoothed image (panelb) is subtracted from the (noise-added) stacked image(panela)). As for the basement membrane images (Fig. 2), the original red-immunostained images are converted into a gray-scaleimage. Thetechnique of unsharp masking enhances the signals of SSNFs in small structures within an image (panelc). Scale bars at the bottom-left indicate0.02 mm.

images earlier, with a box-size of 9 pixels. Fig. 3bshows the smoothed version of Fig. 3a, where large-scale structures remain, and small-scale structures arediluted or faded away. The smoothed image is then sub-tracted from the noise-added, unsmoothed image. Thefinal image (Fig. 3c) shows that after theunsharp mask-ing process, the small-scale structures are now muchmore clearly recognizable. One caution about unsharpmasking is that the smoothing box-size has to be ad-justed, based on the apparent size of SSNFs and othernon-SSNF structures. The SSNFs will be subtracted outif the smoothing box-size is too small. On the otherhand, some non-SSNF structures will remain if the box-size is too large.

Since all the steps described above are pre-determined, and all the necessary parameter values arealready written inside the programs and codes, usingthe CDM does not only reduce the time for processing,but also significantly reduces the chance of making mis-takes.

2.4. Analysis

2.4.1. Determining the basement membraneThe first step in the analysis is identifying the base-

ment membrane using the smoothed basement mem-brane image (Fig. 2b). DS9 is used to display and in-teract with the image. A detailed description of howto set up and use DS9 is given in the appendix (§C.1).The contour level is adjusted manually (see details in§C.2), and DS9 automatically fits the contours to theentire image. Figs. 2b and 4a show how nice smoothcontours are fitted to the basement membrane, as wellas to some regions other than the basement membrane.While the green-colored contours are saved as a DS9

formatted contour-file (with a file extension “.con”), theactual contour level, indicated by a single value, is savedin a separate file to be read in by the subsequent pro-gram. At this point, if we do not distinguish the base-ment membrane from other regions marked by spuriouscontours, the subsequent program will detect any highS/N features (e.g., blood vessels) that still exist withinthe corresponding regions in the SSNF image. To ex-clude these spurious contours from subsequent analysis,black rectangular boxes are drawn around them as seenin Fig. 4a, and saved into a DS9 formatted region-file(with a file extension “.reg”).

Once the basement membrane is identified, blue linesegments are fitted along the ridge of the basementmembrane (see Fig. 4a), and saved into another region-file. These line segments are used to measure the lengthof a basement membrane, which is used later on tocalculate the SExtractor detection rate. An importantstep before tracing the basement membrane with theseline segments is that all of the previous markings (i.e.,black boxes) must be deleted from the DS9 image. Ifany markings other than blue-colored line segments areleft in the image, these will cause an error in sub-sequent analysis due to difference in the DS9 region-shape. Contours, which are treated differently from thebox- or line-markings by DS9 — and hence reside ina different file format — can be left overplotted in thebasement membrane image during this process.

2.4.2. Detecting SSNF segmentsSExtractor is used on the unsharp masked SSNF im-

age (Fig. 3c) to detect SSNF segments. Detailed set-tings of SExtractor parameters are described in ap-pendix (§C.4). The critical difference between the vi-sual measurement and the CDM is how SSNFs are rec-

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a b

Figure 4: The final set of: (a) the basement membrane image; and (b) the SSNF image, with marked regions relevant to each image overlaid. Inpanel (a), green contours outline the basement membrane (and other strong signal regions), black rectangular boxes exclude thespurious contours,and blue line-segments are used to measure the length of the basement membrane. In panel (b), red ovals indicate SExtractor detections of SSNFsegments, and green contours and black boxes are the same as in panel (a). Scale bars at the bottom-left indicate 0.02 mm.

ognized in an image. While a single SSNF is observedas “oneSSNF” by a visual observer, SExtractor usuallydetects “multiple segments” of an SSNF. This results ina chain of SExtractor detections for a single SSNF (e.g.,red ovals in Fig. 4b). A total number of SExtractor de-tections therefore not only depends on how many SS-NFs are physically present in a basement membrane, butalso depends on how long each SSNF is within a base-ment membrane. We will come back to this issue in alater section, where we compare the CDM results to thevisual results, and apply the appropriate normalizationto the CDM results.

Because SExtractor scans the entire image, SExtrac-tor detections are generally distributed all over the im-age. An IDL program is therefore used to select theSExtractor detections inside the basement membrane.This program reads in: (1) the smoothed basementmembrane image; (2) the saved contour level for thebasement membrane; (3) the SExtractor detection re-sults; and (4) the region-file of exclusion regions. Thecoordinates of the applied contours, exclusion regions,and SExtractor detections are compared, and the finalSSNF segment candidates are saved into a new DS9 for-mat region-file. A separate file with a simple numericalsummary of the final SExtractor detections is also cre-ated. Fig. 4 shows a final basement membrane image(Fig. 4a) and a final SSNF image (Fig. 4b), with all therelated markings overplotted. Fig. 4b shows the SEx-

tractor detections as a chain of small red-colored ovals,with green contours and black exclusion boxes from thebasement membrane image (Fig. 4a).

At this point in the CDM process, the selected SEx-tractor detections should be checked visually. It is pos-sible that some spurious SExtractor detections are leftinside a basement membrane, or visible SSNFs are sig-nificantly under-detected. In these cases, the CDM pro-cesses have to be repeated with adjusted SExtractor pa-rameters and locations of exclusion boxes until a sat-isfactory result is achieved. It is also important to re-analyze all scans from the same biopsy previously pro-cessed with the new SExtractor parameters. Since allimages from a single biopsy is scanned at a “fixed”LSCM settings, this helps to keep the personal bias by aCDM user to a minimum.

2.4.3. Calculating the SExtractor detection rate

After reasonable SExtractor detections are obtainedfor a set of SSNF images from a single biopsy, the finalstep in the CDM analysis is to calculate the SExtrac-tor detection rate. The calculation program, written inF77, reads in files containing a number of SExtractor de-tections and the length — region-file of fitted blue linesegments — of the basement membrane for each scan.Provided with the LSCM image scale of 0.0001551mmpixel−1, the SExtractor detection rate is calculated inunits of “detections mm−1”, and the median value of all

8

scans is selected as the representative detection rate ofa given biopsy. While a “mean withσ-clipping” statis-tic could provide a slightly more accurate representa-tive detection rate, this is better applicable if there ex-ists a large number of scans for a single skin-biopsy,or if a scatter in measurements is small. Since a typi-cal biopsy has only∼6–8 scans, and with a large scatterin measured SExtractor detection rates, the median isa more sensible representative value than aσ-clippedmean. Especially in the early-phase (see§3), and in thepre-early project phase — when the CDM was in devel-opment — a systematic error due to the specific LSCMsettings could cause a large scatter in the SExtractor de-tection rates among the scans for a single biopsy.

A file containing this result is then read by an SMscript for plotting as shown in Fig. 5a. This fig-ure — along with Fig. 5b — is recreated in IDL forthe consistency of figure styles. Fig. 5a shows theresults of all scans for a single biopsy. The blackdashed-line indicates the median SExtractor detectionrate (ρmedian= 53.97 detections mm−1) for this particu-lar biopsy. The error for the representative detectionrate (± 13.30 detections mm−1) is the standard error inthe distribution for a median. The brown dotted-line —which is added at the time of re-creating this figure inIDL — indicates aσ-clipped mean atρmean= 50.06 de-tections mm−1 with a standard deviation of 20.31 de-tections mm−1. Thisσ-clipped mean value is currentlynot used as a part of the CDM. Since aσ-clipped meandoes provide more accurate representative SSNF den-sities for visual classifiers, theσ-clipped mean of theSExtractor detection rate is added for comparison to thevisual SSNF densities obtained in the following section(§3).

Finally, another SM script is used to plot the rep-resentative SExtractor detection rates for the analyzedbiopsies. Fig. 5b, which is recreated by IDL, shows themedian (black asterisks) andσ-clipped mean (browndiamonds) of the SExtractor detection rates for the 52biopsies, which are used for the comparison to the vi-sual results in§3. While a few SExtractor detectiondensities are different by∼ 15 detections mm−1, mostof the biopsy’s median andσ-clipped mean values arevery similar. Hence, theσ-clipped mean of SExtractordetection rates can be compared to theσ-clipped meanof the visual SSNF densities in the following section.

One difference from the original SM plot — as a partof the CDM technique — is that while the original SMplot differentiates the biopsies from forearm and fromthigh, this differentiation is removed from the recreatedIDL plot (Fig. 5b). Since the main goal of this paper isto study the correlation between the CDM results and

visual classification densities, studying any correlationbetween the SExtractor detection rates and these bodyparts is beyond the scope of this paper. Also, to reducethe prejudice and personal bias by knowing the degreeof disease of each volunteer subject (and hence of eachbiopsy), this information is not provided to the visualand CDM classifiers at this time. A detailed study ofrelationships among the SExtractor detection rates, thebody parts, and the degree of disease are therefore de-ferred to a subsequent paper.

The representative SExtractor detection rate rangesfrom 0.0 detection mm−1 up to∼ 140 detections mm−1.Assuming that the segmentation by SExtractor is af-fecting all SSNFs equally, the SExtractor detection rateshould in general increase as a physical SSNF densityincreases. Yet, without knowing the results from visualclassifiers, we cannot asses how reasonable the CDMresults are to the actual SSNF densities.

3. Results

While the CDM technique was developed and ap-plied, no communication of the results between theCDM and visual classifiers was permitted to avoid anyprejudice. To study how our CDM results are related tothe actual SSNF density, we will now proceed to com-pare our results to those from the four expert visual clas-sifiers. In this section, we first have to ensure that theresults of visual classifiers are in agreement. Once thisagreement is confirmed, the mean visual SSNF densitiescan be compared to the CDM results. A conversion fac-tor, or formula, from the SExtractor detection rate to theestimated SSNF density are then determined to assessour results and the effect of the CDM on the measuredSSNF densities.

3.1. Visual classification resultsFig. 6a shows the results from four different visual

classifiers. Aσ-clipped mean and its standard deviationare used to show the measured visual SSNF densities.The results of the first visual classifier (blue asterisks)are also plotted as a light-blue bar-graph for easy visual-ization of which biopsy number is displayed. Except fora few biopsies, most visual classifiers agree with eachother within the range of the rms errors. When calcu-lating the representative density of all four visual classi-fiers for a single biopsy, we simply used the mean overall visual classifiers. These final representative visualdensities are plotted with orange triangles in Fig. 6b,with orange shaded bar-graph for better visualization.The error bars for mean visual densities represent themean standard deviations of all visual classifiers.

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Figure 5: The pre-normalized results of the CDM are shown. Panel (a) shows the result for a single biopsy with a total of 9 scans. The horizontalblack dashed-line indicates themedianSExtractor detection rate, and the horizontal brown dotted-line indicates theσ-clipped mean SExtractordetection rate. The error for the median is the standard error of the median (SEM), and the error of theσ-clipped mean is the standard deviation(σ) over the 9 scans. Panel (b) shows the results of 52 biopsies. The black asterisks are the median detection rates, and the brown diamonds areσ-clipped mean detection rates, with corresponding errors as described in panel (a).

3.2. Normalization of the CDM results

To compare the SExtractor detection rates to the vi-sual SSNF densities, a normalization has to be appliedto the original CDM results. As mentioned earlier, thereis no single constant, or a defined formula, to convertthe segmented SExtractor detection rate into an SSNFdensity. Instead, the amount of segmentation increasesas the length of a nerve fiber inside a basement mem-brane becomes longer. For a single SSNF, the numberof SExtractor detections can be only equal to one if theapparent length of an SSNF is really short, or it can beup to≫10 if this length is much longer. In other words,the normalization of the SExtractor detection rate de-pends on the CDM result itself.

Before determining this normalization, there is oneimportant issue that requires attention. In the course ofthis study, the settings of the LSCM has been changedin the Summer of 2005. Earlier biopsies with ID≤ 17(indicated by a gray background shading in Figs. 6aand 6b) were scanned with the LSCM before this date,and biopsies with ID≥ 18 (with no background shad-ing in the same figures) were scanned after that date.We define these two groups as the “early-phase” andthe “main-phase” of this study. In theearly-phase, theimages were scanned at lower PMT levels than dur-

ing themain-phase. This effect is clearly visible whenthe CDM results in Fig. 5b and the visual densities inFigs. 6a and 6b are compared. The CDM results arerelatively consistent over both phases in Fig. 5b, orthe early-phase have somewhat larger average detectionrate. On the other hand, Figs. 6a and 6b show that thebiopsies in the early-phase have, on average, smaller vi-sual densities than those in the main-phase biopsies. Wetherefore have to apply two different normalization toeach phase, since it is clear that the two different PMTsettings caused this difference.

To determine a normalization formula, we plot an-other figure of (normalization-in-process) CDM den-sities vs. mean visual densities (not shown here butsimilar to Fig. 6c), while various normalizations arebeing examined. The normalization is applied suchthat the SExtractor detection rate becomes an indica-tor of the SSNF density. The normalized CDM den-sities therefore should have one-to-one relation with themean visual SSNF densities in the ideal case. We firstplot regression lines — determined by the IDL func-tion ROBUST LINEFIT with the “bisect” option enabled— through datapoints for: (1) the early-phase biopsies(pink triangles in Fig. 6c); (2) the main-phase biopsies(black stars in Fig. 6c); and (3) all 52 biopsies. We

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Figure 6: Comparisons of the measured SSNF densities between visual classifiers and the normalized CDM. Panel (a) shows a comparison amongvisual classifiers for 52 biopsies. The first 17 biopsies (with a gray shaded background) are from the early-phase, and theother biopsies (withoutbackground shading) are from the main-phase of this project. Different colors and symbols — blue asterisks, red diamonds, green triangles, andblack squares — represent the four different visual classifiers. A light-blue shaded bar-graph is added for “Visual 1” for easier identification of thedensities and the corresponding biopsy ID. Panel (b) shows the comparison between themeanvisual densities (orange triangles) and thenormalizedmean CDM densities (purple asterisks) for each biopsy. Panel (c) shows a direct comparison between themeanvisual and thenormalizedmeanCDM densities. The black dotted-line represents the ideal one-to-one correlation (x= y) and the green dashed-line represents the best-fit regression.The pink triangles and black stars are from the early- and main-phase of the project, respectively. Panel (d) shows the residuals between thenormalized CDM and mean visual densities. The green dashed-line show the best-fit regression line, and the shaded regionrepresents the 1σdistribution around the regression line through the residuals. Error bar in all panels represent the standard error of the mean.

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then adjust the coefficient, power, and constant of eachterm in the normalization formula for both the early-and main-phases until all three regression slopes and y-intercepts become as close to 1.0 and 0.0 as possible, re-spectively. Fig. 6c shows the final regression line (greendashed-line) forall biopsies with a slope ofm=0.93and y-intercept ofb= 1.23 . The black dotted-line inFig. 6c shows the ideal one-to-one regression with aslope of 1.0 and y-intercept of 0.0 . The two lines arewithin the statistical errors and indistinguishable.

The normalization formula applied for the main-phase is:

ρCDM,norm = 1.4× [ln(ρCDM,orig)]2

+ ln(ρCDM,orig) , (1)

and that for the early-phase is:

ρCDM,norm = 1.1× [ln(ρCDM,orig)]2

+1.2× ln(ρCDM,orig) − 8.0 , (2)

whereρCDM,norm is the normalized SExtractor detectionrate (a converted CDM SSNF density),ρCDM,orig is theoriginal SExtractor detection rate, and “ln” stands forthe natural logarithm. Since a logarithm of 0.0 willcause an arithmetic error, any representative SExtrac-tor detection rate of 0.0 is replaced with 1.0 detec-tions mm−1, which is not affecting the results given thestatistical errors in Fig. 6c. Any resulting normalizedρCDM,norm with the negative values (ρCDM,norm< 0.0) —which is unrealistic for any SSNF density, and due tothe original SExtractor detection rate being equal to 0.0— are automatically replaced by 0.0 fibers mm−1 in thenormalization process.

3.3. Comparison to the visual densities

Figs. 6b–d shows the comparisons of normalizedCDM densities to the mean ofσ-clipped visual densi-ties. Fig. 6b shows the mean visual densities (orangetriangle) and the normalized CDM densities (purple as-terisks). Even though there are relatively large differ-ences between the CDM and visual densities, a trendtoward larger CDM densities for larger visual densi-ties, and toward smaller CDM densities for smaller vi-sual densities can be clearly recognized in this diagram.Fig. 6b also shows that, even though the pre-normalizedCDM results for the early-phase have larger SExtrac-tor detection densities than the main-phase in general(see Fig. 5b), the applied normalization (Eq. 2) clearlyreduces the normalized CDM densities to levels compa-rable with the visual SSNF densities.

To better visualize and analyze the correlation be-tween the normalized CDM and the visual classification

results, a direct comparison between these two quanti-ties is plotted in Fig. 6c. Pink triangles represent theearly-phase biopsies, and black stars represent the main-phase biopsies. Error bars are the standard deviationscalculated from all scans for each biopsy.

The calculated Pearson correlation coefficient for thedistribution in Fig. 6c isrPearson= 0.64 with ap-valueof pPearson<0.01. In all of our statistics, we selectp=0.05 as the minimum threshold for significance. ThepPearson<0.01 therefore indicates that the mean visualdensities and the normalized CDM densities are indeedcorrelated, yet as can be seen in Fig. 6c, with a largescatter. The cause of this scatter is discussed in detail inthe following section. We also performed a two-tailed,paired, Student T-test to see if their measurements aresignificantly different from each other. The calculatedp-value for this T-test ispT−test> 0.05, indicating thatthe two densities are non-significantly different. Com-bining these statistics, and the regression and y-interceptof 0.93 and 1.23, respectively, we conclude that the nor-malized CDM and the mean visual densities are not sig-nificantly different, and hence comparable to each other,as the best fitted green dashed regression-line and theblack dottedy= x line in Fig. 6c already indicated.

Fig. 6d shows theresidualsbetween the normalizedCDM and the mean visual classification densities, com-pared to the mean visual densities. The early-phasebiopsies and the main-phase biopsies are representedusing the same symbols and colors as in Fig. 6c. Thebest-fit regression line (green dashed-line) has a slopeof −0.42±0.10 and y-intercept of 7.19± 1.96, withthe gray shaded region represents the 1σ distributionaround the regression line. The Pearson correlation co-efficient is rPearson=−0.51, and thep-value associatedwith this Pearson correlation ispPearson< 0.01. There-fore, this negative correlation is a true feature. While theregression between the normalized CDM and the meanvisual densities is∼ 1.0 (see Fig. 6c), a negative corre-lation for these residuals (see Fig. 6d) indicates that theCDM tends to somewhat over-estimate the SSNF den-sity for low mean visual densities, and somewhat under-estimate the SSNF density for higher mean visual den-sities. Even though Fig. 6c indicates that there is in gen-eral good agreement between the normalized CDM andmean visual densities, Fig. 6d shows that there are stillsome systematic effects between the CDM detectionsand the visual classifications.

4. Discussion

Although the normalized CDM densities and themean visual classification densities show a fair corre-

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lation (Fig. 6c withrPearson=0.67 andpPearson< 0.01),there is still a fairly large scatter in Figs. 6c and 6d. Thisscatter is caused by the different nature of the CDM de-tection method, i.e., the segmentation by SExtractor, ascompared to the visual classification method,anddue toseveral important factors of the images themselves. Theobject segmentation by SExtractor has already been de-scribed in§2.4.2. Another important cause for the dis-crepancy between the two methods is the visibility —the PMT or the S/N level — of the SSNFs in the stackedSSNF images, as described in§3.2. Detecting SSNFsby eye, as performed by the visual classifiers, requiresSSNFs to have much stronger signals than other tissuestructures surrounding the SSNFs. In other words, thevisual classification method requires an absolutely highsignal-level. The CDM, on the other hand, uses theSSNF signal relative to the image noise, i.e., the S/Nlevel, allowing SSNF segments to be detected even if thestrongest signals are not available. The unsharp mask-ing technique helps the CDM detection by enhancingthe S/N-ratio in the SSNFs, and therefore their detectionlevels. Even though some SSNFs are difficult to recog-nize by eye, the CDM is therefore able to detect SSNFsat a lower (absolute) signal level. The physical size ofthe image may also be an important factor in the visualclassification method. The image size in the early-phasewas half the size of that in the main phase, making smalland narrow SSNFs appear even smaller and narrower inan early-phase image. The CDM, on the other hand,is able to detect small SSNF segments — even thoughtheir apparent image size is small — as long as an SSNFsegment is satisfying the SExtractor parameters.

Along with the segmented detection of SSNFs bySExtractor, another possible cause of scatter is the ori-entation of the SSNFs within a basement membrane rel-ative to the plane of the scanned image. The image hasphysical dimensions of∼0.16× 0.16 mm, and a depthof ∼ 0.04 mm, which is converted to a two-dimensionalimage of∼ 0.16× 0.16 mm. An SSNF running along theplane of the image therefore appears as a long fiber, andis detected both by SExtractor and by eye without anyproblem. On the other hand, some SSNFs are runningnear-perpendicular, or in thez-direction of the biopsysection (see Fig. 1). Such SSNFs appear short, or onlyas small oval shapes in extreme cases, and are mostlikely not recognized by the visual classifiers. Sincethe SExtractor algorithm used by the CDM detectsanysmall region, as long as it satisfies the provided mini-mum threshold parameters, these SSNFs running near-perpendicular to the plane of the imageare in fact de-tected by SExtractor. These detections are shown inFig. 4b, not as a chain of red ovals, but as isolated single

or as a few connected red ovals.Limitations to the measurement of the SSNF density

not only occur with the visual classification method.Some SSNFs are not detected by the CDM, if they donot reach the required signal level by SExtractor. Fur-thermore, even though the CDM is semi-automated, itsparameter values are still adjusted manually, and theseparameters settings can be slightly different dependingon a given CDM user. During this study, we observedthat small differences (. 10 %) in the parameter valuesaffect the final results only very slightly. This occurs,because the signal levels are generally much higher forthe basement membrane and for the SSNFs, comparedto other tissue structures after the smoothing and un-sharp masking procedures.

The reduction of processing time, the significant in-dependence of the user, and the nearly complete re-peatability of the results are the significant advantagesof the CDM, when compared to the visual classificationmethod.

5. Conclusion

A computerized method of quantifying immunos-tained SSNF densities in the basement membrane ofskin biopsies is presented, using astronomical imageprocessing and object detection tools and software. Theadvantage of our method over other medical software isthat the tools and software used in our CDM are dis-tributed without any cost, or at most with a minimumfee. There are also many other tools and software pack-ages available to CDM users, which can be substituted,based on the preference of the user. The actual analysisusing our specific implementation of the CDM involves:(1) preparation of the digitized skin-biopsy images; (2)determination of the location and length of the basementmembrane; (3) automated detection of the SSNF seg-ments; and (4) calculation of the segmented SSNF de-tection density in each biopsy.

The CDM also has significant advantages over thevisual classification method. While some of the stepsare time consuming if performed manually, using pre-written tasks and programs, most of the steps take onlya fraction of a second on an average desktop computer.In addition to the reduction of the processing time, theCDM keeps the effects of personal prejudice, bias, andmistakes at a minimum level. Even though the CDMrequires some manual input — such as determinationof the contour level for a basement membrane and ofthe SExtractor parameters — small differences in theseinputs have only a minimal effect on the final results.High repeatability, regardless of who or when the CDM

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is performed, is another major advantage. Other im-portant aspects of the CDM are: (1) the CDM is basedon therelativesignal levels of SSNFs, instead of strongabsolute signals required for the visual classificationmethod; and (2) the CDM is capable of detecting visu-ally hard-to-recognize SSNFs, such as SSNFs runningnear-perpendicular to the plane of a skin biopsy image.

Even though there is a fairly large scatter between theCDM and the visual classification results, this is due tothe different nature of the two detection methods. Con-sidering these differences, we conclude that our CDMis detecting SSNFs in a reasonable manner. At thispoint, our CDM is not yet ready to fully replace the vi-sual density measurements, but the CDM is at least ableto support or confirm the visual classification results.With further studies and improvements to the CDM pro-cess — e.g., automated determination of whether two ormore SExtractor detections are associated with the sameSSNF — the CDM has the capability of eventually re-placing the visual density measurement.

The current study shows that the CDM technique isdependable, and likely applicable to conventional stud-ies of intraepidermal nerve fiber densities in normal andneuropathic populations. This topic will be addressedin more detail in a future paper. Furthermore, our studyproves that the CDM can effectively reduce the cost andtime involved in detecting SSNFs, which are very im-portant constraints when analyzing a very large numberof medical images. In a future paper, we will also pur-sue ways of reducing the systematic and random errorsin the CDM, so as to further improve upon this method.This will require larger samples, so we can better mea-sure these errors, and make subsequent improvementsto the CDM software.

Acknowledgments

We thank Stephen Odewahn (McDonald Observatory, FortDavis, Texas, USA) for helping design the research. R.M.H.acknowledges Dr. William Kennedy (University of Min-nesota) for his advice and teaching. This work was supportedby a grant from the Palms Clinic and Hospital CorporationFoundation, the Arizona State University College of LiberalArts and Science, the Arizona State University Department ofPhysics, the Arizona State University Department of Bioengi-neering, and the Arizona State University Vice President forResearch funds.

A. Abbreviations in the paper

Here is an alphabetical list of abbreviations used inthis paper.CCD — Charge-Coupled DeviceCDM — Computerized Detection MethodDN — Data NumberDS9 (SAOImage DS9) — Smithsonian AstrophysicalObservatory Image DS9F77 — Fortran 77FITS — Flexible Image Transport SystemIDL — Interactive Data LanguageIRAF — Image Reduction and Analysis FacilityLSCM — Laser Scanning Confocal MicroscopeNASA — National Aeronautics and Space Administra-tionNOAO — National Optical Astronomy ObservatoryNRAO — National Radio Astronomy ObservatoryPGP 9.5 — Protein Gene-Product 9.5PMT — Photomultiplier tubesPNM — Portable anymapRGB — Red-Green-BlueSExtractor — Source ExtractorSM — SuperMongoS/N — Signal-to-NoiseSSNF — Small Sensory Nerve FiberTIFF — Tagged Image File FormatWCS — World Coordinate System

B. Astronomical tools

B.1. Smithsonian Astrophysical Observatory Image(SAOImage) DS9

DS9 is a standard image display tool used in the fieldof astronomy, and developed by the Smithsonian Astro-physical Observatory (Joye and Mandel, 2003). DS9is used by astronomers to visualize and analyze imagesspecifically in FITS format (see§B.2). With DS9, usersnot only can change the brightness and contrast of theimage on the computer screen, but also can change thegray scale stretch of the image (e.g., linear scale, logscale, square, or square-root stretch) and the range ofgray-scale values to be displayed. DS9 also lets the usermark regions in different colors and shapes (e.g., cir-cles, boxes, and lines), fit contours to an image, and savethe processed image in variety of image formats includ-ing the FITS, Postscript, and Joint Photographic ExpertsGroup (JPEG) formats. The important aspect of usingDS9 is that a user can visually interact with other as-tronomical tools, especially with IRAF (see§B.3), toselect a region or to specify a pixel location.

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B.2. Flexible Image Transport System: FITS

The FITS format3 (Wells et al., 1981) is also devel-oped in the field of astronomy, and provides a methodfor transportation of any (astronomical) image itself,and a virtually unlimited number of auxiliary parame-ters, which is called theimage headerthat is associatedwith that image. Some examples of parameters savedin the image header are the date, time, and location ofthe observation, name and settings of the instruments,image scale, and history of the image processing oper-ations performed on the image. DS9 and other astro-nomical tools require the image format to be this FITSformat.

B.3. Image Reduction and Analysis Facility: IRAF

IRAF4 (Stefl, 1990, and references therein) is a col-lection of software packages written by astronomers allover the world. The framework of IRAF is provided byNational Optical Astronomy Observatory (NOAO), andmany individual packages for specific IRAF tasks —most of which are publicly available — are developedand added by astronomers all over the world. IRAFis used to analyze and process images in a pixel arrayform, or more commonly knows as digital images takenby CCD cameras at astronomical telescopes. ManyIRAF tasks use DS9 as an interactive display to analyzeFITS images.

B.4. Interactive Data Language: IDL

IDL is a programming language commonly used inthe field of science. It is especially very popular in thefield of astronomy, and used for image analysis and the-oretical simulations. The basic function and task pack-age, IDL Astronomy User’s Library, is explained at anddownloadable from the National Aeronautics and SpaceAdministration’s (NASA’s) web page5. Additional IDL

3A detailed description of the FITS format is provided at NationalAeronautics and Space Administration’s (NASA’s) web pages:http://fits.gsfc.nasa.gov/

http://heasarc.gsfc.nasa.gov/docs/heasarc/fits.html

and at National Radio Astronomy Observatory’s (NRAO’s) webpage:http://www.cv.nrao.edu/fits/

4IRAF is maintained and distributed by the National Optical As-tronomy Observatory (NOAO), which is operated by the Associationof Universities for Research in Astronomy (AURA), Inc. under theNational Science Foundation (NSF).http://iraf.noao.edu/

5The IDL Astronomy User’s Library:http://idlastro.gsfc.nasa.gov/

function and task packages are also developed by as-tronomers all over the world, and different IDL func-tions and tasks are downloadable, and ready to use atvarious personal web pages, which can be found viavarious web search engines. The framework of IDL it-self is maintained and distributed by ITT Visual Infor-mation Solution (Research Inc.), and can be purchasedfrom there for a fixed fee per workstation, or via a site-license for an institution.

B.5. Source Extractor: SExtractorSExtractor6 is used to search any region of an im-

age with specified intensity thresholds that are specifiedthrough the parameter file (Bertin and Arnouts, 1996).Once detection and selection thresholds — the mini-mum S/N ratio and the size of the object area (consec-utive pixels) — are specified, SExtractor automaticallyselects all the image regions matching the specified cri-teria, and marks these regions with ovals of correspond-ing sizes in DS9.

B.6. SuperMongo: SMSM7 is a visualization program used to create plots

and figures. SM uses line graphics for simple, but fastand easy plotting. A plot can be made by providingcommands in a terminal window line-by-line, or by sim-ply reading in pre-written plotting scripts. In our study,the latter method is used for visualization of the results.SM also easily reads and plots text files, or ASCII tablesof data in any form.

B.7. FORTRAN 77: F77Another programming language used in our CDM is

FORTRAN 77 (F77). FORTRAN is The IBM’s Math-ematical Formula Translating System, and was origi-nally developed in the late 50’s. F77 was very pop-ular in the field of astronomy before IDL came out.Newer versions of FORTRAN, i.e., Fortran 90/95 andFortran 2003, are available today. In the field of astron-omy, however, F77 is still the most popular version usedby astronomers today, and its compilers have been up-graded to accommodate the current generation of Linux,Unix, and Mac OS workstations.

6SExtractor is developed and distributed by the TraitementElementaire, Reduction et Analyse des PIXels megacam (Terapix),Institute d’Astrophysique de Paris (IAP), France:http://terapix.iap.fr/rubrique.php?id rubrique=91

7The SM Reference Manual. Robert H. Lupton and Patricia Mon-ger (1977):http://www.astro.princeton.edu/∼rhl/sm/sm.html

http://www.supermongo.net/

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C. Settings for astronomical tools in the CDM

C.1. DS9 initial setting

Setting up DS9 properly is an important step to an-alyze the basement membrane and SSNF images cor-rectly. The most important step is the selection of thecorrect coordinate system. There are different selectionsof the coordinate system available in the “File Coordi-nate System” within the DS9 “Region”menu. Since noworld coordinate system (WCS) — a coordinate sys-tem on the sky, usually recorded in the right ascensionand declination — information has been recorded inthe header of LSCM scanned images, the only avail-able selections should be “Physical” and “Image”. Bothof these coordinate systems are based on image pixels,and the difference between these two is simply the zeropoints of the columns and rows. Programs used in theCDM assume that the lower left corner is the zero-point,hence the coordinate system should be set to “Image”.The zero points for the “Physical” coordinate system isbased on “how” the image is created and prepared, andhence it can be anywhere on the image or even outsideof the image if a smaller section of image is copied orcropped from an larger image.

Another important preparation step is the adjustmentof the screen and image size. Fitting the image to theframe can be performed in the DS9 “Zoom” menu. Thepixel-scale setting of “1” shouldnotbe used to avoid er-rors in the subsequent analysis. The zoom-scale of “1”matches the DS9 visualization window pixel-scale andimage pixel-scale, so that DS9 creates region-files onlywith integer coordinate values. Since some of the CDManalysis programs require floating point (decimal) val-ues for as input, these integer values could cause someerror in the analysis. Changing the zoom-scale by using“Zoom To Fit Frame” usually solves this problem. Ifnot, then re-sizing the DS9 window and fitting the im-age to the frame should be sufficient.

A minor step — depending on the preference of theCDM user — is to invert the color of the image fromwhite-on-black to black-on-white. This makes visu-alization of the high-signal regions — the basementmembrane and the SSNFs — much easier as shown inFigs. 2–4. In astronomical publishing, it is customaryto display images with objects in black and backgroundin white, since it gives the best contrast in the publishedjournal and on printed paper.

C.2. Contour parameter settings

The selection of “Contour Parameter...” within theDS9 “Analysis” menu brings up the control panel forfitting contours. This panel allows users to adjust the

parameters of the contour(s) fitted in the main windowof DS9, i.e., the number of contours, the contour lev-els, and their smoothness. For our CDM, we set theContour Levels to 5 (a default setting) andContourSmoothness to 1. If theContour Smoothness is leftat a larger number (the default setting is 4), the fittedcontour will be smoothed automatically by DS9. ThisDS9 smoothing is different from the IRAF smoothing,and may cause a systematic error later in the analysis.For this reason, we have to use theunmodifiedcontourswith a pre-smoothed image in the CDM.

Another parameter we need to manually change isthe Limits. Since we simply want to trace the edgeof the basement membrane in the pre-smoothed image,theLow and theHigh values should be set at the samelevel. If they are different, five contours — or any num-ber of contours equal to the number in theContourLevels — are fitted at equally spaced interval betweentheLow and theHigh settings. In future applications ofthe CDM, fitting multiple contours can be used to detectnot only the SSNFs in the basement membrane, but alsoin the epidermis and dermis of the skin tissue.

Once a satisfactory contour is fitted, it should besaved, so that it can be over-plotted later in the red im-age to indicate the location of the basement membrane.The most important step when saving the contour is tochoose the correct coordinate system. Even though theimage coordinate system is set to “Image” in the mainDS9 window, the default coordinate system for the con-tour parameter control panel isalways“WCS”, whichuses a specific coordinate keywords in the FITS imageheader. Since the FITS image used in this project doesnot contain these keywords in their header file, sav-ing the contours with the WCS may cause the DS9 tohang or crash. Therefore, the coordinate system mustbe changed to “IMAGE”every timea contour is saved.

C.3. Changing the shape and color of the DS9 regionmarking tool

When placing black rectangular boxes and blue linesin the basement membrane image, the CDM user has tomanually select the shape and color of the region mark-ing tool. The shape and color of a region marker can beselected from the sub-menu “Shape” and “Color”, re-spectively, within the DS9 “Region” menu. The “Color”in the main DS9 menu bar serves a different purpose,and is not used in our CDM. Once the correct shape andcolor are selected, the CDM user can create a box or aline by simply clicking-and-dragging. Once all mark-ings are completed, they can be saved with “Save Re-gions...” within the DS9 “Region” menu. The CDM userhas to make sure that all marked regions (boxes or lines)

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are deleted before starting the next set of markings. Thiscan be completed by simply using “Delete All Regions”within the DS9 “Region” menu. While the current CDMprograms use black excluding boxes and blue line seg-ments for region markings, the colors of these markingscan be changed by modifying the key-words in the anal-ysis programs.

C.4. SExtractor thresholds

To run a SExtractor, a parameter file specify-ing the different detection requirements are neces-sary. Within this file, the important parameters, whichrequire manual adjustments, areDETECT THRESH,ANALYSIS THRESH, andDETECT MINIMA. The first twoparameters,DETECT THRESH and ANALYSIS THRESH,must be set to the same value. These values indicatethe minimum S/N ratio required to be recognized as anobject. These threshold values are usually in a range ofS/N≃ 2.5 up to S/N≃ 5.0–7.0. If these values are cho-sen too small, SExtractor starts picking up noise spikesand residues of faint tissue structures in the unsharpedimage. If they are too large, SExtractor picks up onlythe strongest signal sections of SSNFs and won’t detectall of the SSNFs, or simply does not detect any SSNF atall. TheDETECT MINIMA parameter indicates the min-imum number of pixels above the signal threshold thatare required to be adjacent to each other. This value isset to 14 for 512×512 pixel images (a few images inthe early-phase), and 20 for 1024× 1024 pixel imagesin our CDM. If this value is too small, SExtractor startspicking up random noises in the image. If this value istoo large, some SSNFs might not be detected.

References

Arnouts S, de Lapparent V, Mathez G, Mazure A, Mellier Y, BertinE, Kruszewski A. The ESO-Sculptor faint galaxy redshift survey:The photometric sample. Astron. Astrophys. Sppl. Ser. 1997; 124:163–182.

Bertin E, Arnouts S. SExtractor: Software for source extraction. As-tron. Astrophys. Sppl. Ser. 1996; 117: 393–404.

Dalsgaard CJ, Rydh M, Haegerstrand A. Cutaneous innervation inman visualized with protein gene-product 9.5 (PGP-9.5) antibod-ies. Histochemistry 1989; 92: 385–389.

Driver SP, Windhorst RA, Ostrander EJ, Keel WC, Griffiths RE, Rat-natunga KU. The morphological mix of field galaxies tomI =24.25magnitudes (bJ ∼ 26 magnitude) from a deep Hubble Space Tele-scope WFPC2 image. Astrophys. J. 1995; 449: L23–L27.

Dyck PJ, Oviatt KF, Lambert EH. Intensive evaluation of referred un-classified neuropathies yields improved diagnosis. Ann. Neurol.1981; 10: 222–226.

Gull SF, Daniell GJ. Image reconstruction from incomplete and noisydata. Nature 1978; 272: 686–690.

Gull SF, Daniell GJ. The Maximum Entropy Method. Astrophys.Space Science Lib. 1979; 76: 219–226.

Hirai A, Yasuda H, Joko M, Maeda T, Kikkawa R. Evaluation of di-abetic neuropathy through the quantitation of cutaneous nerves. J.Neurol. Sci. 2000; 172: 55–62.

Hogbom JA. Aperture synthesis with a non-regular distribution ofinterferometer baselines. Astron. Astrophys. Sppl. Ser. 1974; 15:417–426.

Holland NR, Stocks A, Hauer P, Cornblath DR, Griffin JW, McArthurJC. Intraepidermal nerve fiber density in patients with painful sen-sory neuropathy. Neurology 1997; 48: 708–711.

Holland NR, Crawford TO, Hauer P, Cornblath DR, Griffin JW,McArthur JC. Small-fiber sensory neuropathies: clinical courseand neuropathology of idiopathic cases. Ann. Neurol. 1998;44:47–59.

Joye WA, Mandel E. New features of SAOImage DS9. In: Payne,H.E., Jedrzejewski, R.I., Hook, R.N. (Eds.), AstronomicalDataAnalysis Software and Systems XII: ASP Conf. Ser. 295. Astro-nomical Society of the Pacific 2003; 489–492.

Karanth SS, Springall DR, Kuhn DM, Levene MM, Polak JM. Animmunocytochemical study of cutaneous innervation and thedis-tribution of Neuropeptides and protein gene product 9.5 in man andcommonly employed laboratory animals. Am. J. Anat. 1991; 191:369-383.

Kennedy WR, Wendelschafer-Crabb G. The innervation of humanepidermis. J. Neurol. Sci. 1993; 115: 184–190.

Kennedy WR, Wendelschafer-Crabb G, Johnson T. Quantitation ofepidermal nerves in diabetic neuropathy. Neurology 1996; 47:1042-1048.

Lacomis D. Small fiber neuropathy. Muscle and Nerve 2002; 26:173-188.

Malik RA, Tesfaye S, Newrick PG, Walker D, Rajbhandari SM, Sid-dique I, Sharma AK, Boulton AJM, King RHM, Thomas PK, WardJD. Sural nerve pathology in diabetic patients with minimalbutprogressive neuropathy. Diabetologia 2005; 48: 578–585.

McArthur JC, Stocks EA, Hauer P, Cornblath DR, Griffin JW. Epider-mal nerve fiber density. Arch. Neurol. 1998; 55: 1513–1520.

Neuschaefer LW, Windhorst RA. Observation and reduction methodsof deep Palomar 200 inch 4-Shooter mosaics. Astrophys. J. Sppl.Ser. 1995; 96: 371–399.

Odewahn SC, Windhorst RA, Driver SP, Keel WC. Automated mor-phological classification in deep Hubble Space Telescope UBVIfields: Rapidly and passively evolving faint galaxy populations.Astrophys. J. 1996; 472: L13–L16.

Pascarelle SM, Windhorst RA, Keel WC, Odewahn SC. Sub-galacticclumps at a redshift of 2.39 and implications for galaxy formation.Nature 1996; 383: 45–50.

Periquet MI, Novak V, Collins MP, Nagaraja HN, Erdem S, Nash SM,Freimer ML, Sahenk Z, Kissel JT, Mendell JR. Painful sensoryneuropathy: Prospective evaluation using skin biopsy. Neurology1999; 53: 1641–1647.

Pina RK, Puetter RC. Bayesian image reconstruction – the pixon andoptimal image modeling. Pub. Astron. Soc. Pacific 1993; 105:630–637.

Puetter RC. Information, language, and pixon-based image recon-struction. Ann. N.Y. Acad. Sci. 1997; 808: 160–183.

Quattrini C, Tavakoli M, Jeziorska M, Kallinikos P, TesfayeS, Finni-gan J, Marshall A, Boulton AJM, Efron N, Malik RA. Surrogatemarkers of small fiber damage in human diabetic neuropathy. Dia-betes 2007; 56: 2148–2154.

Smith AG, Howard JR, Kroll R, Hauer P, Singleton JR, McArthurJ.The reliability of skin biopsy with measurement of intraepidermalnerve fiber density. J. Neurol. Sci. 2005; 228: 65–69.

Smith AG, Singleton JR. Ideopathic neuropathy, prediabetes and themetabolic syndrome. J. Neurol. Sci. 2006; 242: 9–14.

Stefl S. The IRAF software system and its use for UV-flux variabil-ity studies. Contrib. Astron. Observatory Skalnate Pleso 1990; 20:

17

161-162.Sumner CJ, Sheth S, Griffin JW, Cornblath DR, Polydefkis M. The

spectrum of neuropathy in diabetes and impaired glucose toler-ance. Neurology 2003; 60: 108–111.

Tyson JA. Deep CCD survey – Galaxy luminosity and color evolution.Astron. J. 1988; 96: 1–23.

Verghese J, Bieri PL, Gellido C, Schaumburg HH, Herskovitz S.Peripheral neuropathy in young-old and old-old patients. MuscleNerve 2001; 24: 1476–1481.

Wells DC, Greisen EW, Harten RH. FITS – a Flexible Image Trans-port System. Astron. Astrophys. Sppl. Ser. 1981; 44: 363–370.

Windhorst RA, Keel WC, Pascarelle SM. Deep Hubble Space Tele-scope/Planetary Camera imaging of a young compact radio galaxyat Z= 2.390. Astrophys. J. 1998; 494: L27–L31.

Windhorst RA, Hathi NP, Cohen SH, Jansen RA, Kawata D, DriverSP, Gibson B. High resolution science with high redshift galaxies.J. Adv. Space Res. 2008; 41; 1965–1971.

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