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Journal of Neuroscience Methods 51 (1994) 229-238

JOURNALOF NEUROSCIENCE METHODS

Automated nerve fibre size and myelin sheath measurement using microcomputer-based digital image analysis: theory, method and results R o l a n d N. A u e r * Departments of Pathology and Clinical Neurosciences, University of Calgary, 3330 Hospital Drive N~, Calgary, Alberta T2N 4N1, Canada (Received 7 July 1993; accepted 30 October 1993)

Abstract

In either clinical or research settings, manual measurement and counting of myelinated fibres in peripheral nerve is tedious and error-prone, yet fully automatic computerized counting and measuring of fibres fails to count small fibres and eliminate extraneous profiles in the tissue. This article describes an operator-interactive, semiautomated method for quantification of myelinated nerve fibre data using commercially available hardware and software on an inexpensive, yet full-featured image analysis system based on a microcomputer. Software macros automate the acquisition of data from the microscope images and the production of numerical and graphic data, with output to either paper hardcopy or 35 mm colour slides. User control is retained for dynamic thresholding, binary image creation and elimination of artifacts. In addition to generating the classic histogram showing the size distribution of nerve fibres, the thickness and variability of myelin sheaths are also graphically depicted. The method is based on measurement of myelin area and total perimeter, with calculation of equivalent circles and diameters for both axon and nerve fibre. Measured fibre sizes are thus somewhat larger than those resulting from manual methods using the minor diameter of an oval profile, or mean diameter of crenated or irregular profiles. The method allows the rapid measurement and counting of numbers of fibres previously impossible to assess manually, or using digitizing tablets. By increasing the speed and accuracy of data acquisition and processing using widely available microcomputers, the method may allow a better description of peripheral nerve changes in research and clinical settings.

Key words: Peripheral nerve; Morphometry; Biopsy; Axon; Myelin; Image analysis; Computer

I. Introduction

The analysis of a nerve biopsy includes consideration of quantitative data on the size distribution of myelinated nerve fibres and ideally also the thickness and variability of myelin sheaths. Prior to the wide availability of image analysis systems, it was necessary to obtain morphometric nerve biopsy data through manual measurements on enlarged photomicrographs of the biopsy. Various opto-mechanical methods have been used in the past (Espir and Harding, 1961), but are now only of historical interest. The advent of digitizing tablets and inexpensive microcomputers allowed the tracing of nerve fibre outlines, with storage of data in the microcomputer for subsequent calculation and analysis. However, any method requiring manual attention to individual nerve fibres involves considerable tedium and time-related * Corresponding author. Tel.: (403) 220-6887; FAX: (403) 283-2700. 0165-0270/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 1 6 5 - 0 2 7 0 ( 9 3 ) E 0 1 3 5 - 0

cost. Also several errors are prone to occur if manual measurement methods are employed. One error in manual measuring methods relates to the choice of the diameter measured on each fibre. Oblique, rather than transverse orientation in a section will lead to fibres that are oval rather than round in outline. Although choice of the least diameter may avoid the result of obtaining a spuriously large fibre size, the nerve fibre count per unit area of endoneurium will be spuriously low due to the unavoidable smaller number of fibres per unit area in oblique sections. Accurately transverse, rather than oblique sections must therefore be used in peripheral nerve morphometry. Transversely sectioned nerves are easily identified by the numerous oval outlines of nerve fibres with long axes of the ovals running in parallel. Even in transverse sections, however, a second source of error arises when a fibre is distorted into a very flat oval or into an irregular crenated outline. Such a fibre would be grossly undersized by the calcu-

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R.N. Auer /Journal of Neuroscience Methods 51 (1994) 229-238

lation derived from a minimum diameter (Karnes et al., 1977). Irregular crenated fibres are undersized even using a mean diameter, when compared to diameters based on dividing the measured perimeter by ~r (Karnes et al., 1977). Diameters derived from area measurements show the greatest precision and accuracy, with the least bias (Karnes et al., 1977). These results suggest that when fibres are distorted, as they often are even in transverse sections of the nerve, myelin area and perimeter are relatively preserved. The method described here calculates the equivalent circles based on myelin area and perimeter. A third source of error in any manual counting and measuring process relates to neglect of the small fibres. This can lead to a relative over-representation of large fibres in the data. Lastly, operator fatigue and e c o n o m i c / t i m e considerations may lead to examination of only a few microscopic fields, obtaining a sample of perhaps 100 or 200 fibres using manual counting and measuring methods. These factors together decrease the statistical reliability and usefulness of the data. The above considerations might suggest that fully automated, computerized image analysis systems could be ideally programmed to analyse myelinated fibre density in experimental or clinical specimens independent of a human operator. However, previous studies by Zimmerman et al. (1980), as well as my own pilot experiments, indicated that operator intervention was necessary to manually eliminate dark tissue elements such as pericytes, dark Schwann cell nuclei, or spuriously counted objects such as dust or crystals of stain. It thus seemed desirable to develop a widely applicable system which largely eliminated the above sources of error inherent in manual measurement techniques, using a relatively inexpensive, PC microcomputer-based image analysis system. Such a system can be based on the measurement of perimeters and areas of objects, after grey scale thresholding of digitized image data acquired directly from toluidine blue-stained, plasticembedded sections viewed through an oil immersion lens. The microcomputer-based image analysis system receives the data from a video camera mounted on the microscope and the respective diameters of equivalent circles for the nerve fibres and the contained axons are calculated from the measured myelin area and perimeter. Operator control is allowed to eliminate unwanted objects. If careful adherence to calibration and procedure is followed, systematic error can be avoided, apart from that due to fixation and accompanying shrinkage. Data on large numbers of fibres can be reliably and easily generated. This article describes the necessary software and hardware, macros and sample results using automated nerve biopsy analysis, as well as the theoretical principles by which the data is acquired, processed, analysed and presented.

2. Material and methods

2.1. Step 1: hardware and software set-up 2.1.1. Hardware (See Appendix 1 for suppliers.) (1) Microcomputer, 80486 CPU required, hard disk drive, V G A monitor. (2) Serial Mouse or Bus Mouse. (3) "Frame Grabber" Board, Targa Plus TrueVision. (4) Image Monitor, e.g., Sony PVM-1342Q. (5) Video camera: black and white, e.g., Sony AVC-D5; colour (optional), e.g., Sony XC711. (6) Light microscope, with C-mount adaptor for video-camera, Plan Apochromat 100 X oil immersion objective lens, with numerical aperture of > 1.30. (7) Cables: BNC cable, for connecting camera to monitor; 15-pin D connector to red, green, blue and Synch BNC plugs, for connecting computer to monitor. BNC connector to 9-pin, for connecting monitor to computer. (8) Calibration slide, Improved Neubauer. For general use of the image analysis system with macroscopic material (both opaque and transparent), a light box and photostand is desirable. 2.1.2. Software (See Appendix 1 for suppliers.) (1) Jandel video analysis software JAVA, version: > 1.40 (Jandel Scientific). (2) Lotus 1-2-3 version > 3.1 (Lotus Developments). (3) Lotus Freelance Plus, version: > 4.0 (Lotus Developments). 2.1.3. Custom files (Available from author.) (1) N E R V E - BX.MAC; a JAVA macro file containing image analysis macros. (2) N E R V E - BX.XFM; a JAVA transform file to calculate nerve fibre and axonal diameters. (3) N E R V E BX.WK3; a Lotus 1-2-3 worksheet containing macro for importing graphing, printing of data (see Appendix 3). (4) N E R V E - BD.DRW and N E R V E - BM.DRW Lotus Freelance files for automatically creating colour slides of the distribution and myelin data. 2.1.4. Set-up The hardware connections must first be made (Fig. 1). If the video signal is run from the camera through the video monitor en route to the computer, as well as connecting the video monitor to the computer, original camera image and the computer video board output can be compared. This arrangement allows direct and instantaneous comparison of the original and the processed image on the video monitor by switching from line input A (the original image) to RGB input to the monitor (the computer image at some stage of processing). The three software packages (see Appendix 1) are all "generic" (i.e., not dedicated to nerve biopsy analysis) and are suited to other uses. For example, the J A V A program is easily adapted to the quantification of infarct sizes in ischemia research (Hamilton et al., 1994).


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2.2. Step 2: set-up calibration Because the distances and magnifications of the microscope should remain constant over time, it should only be necessary to perform calibration once. However, without accurate initial calibration, all subsequent measurements will be inaccurate. Under oil immersion, the innermost tiny squares of the improved Neubauer slide, 200 /~m on a side, are used. Only two squares will fit into the screen. Calibrate for (1) x and y location, (2) distance and (3) area. The x and y coordinates will be used to eliminate the fibres at the periphery of the screen which may be cut off and hence unmeasurable in their entirety. Distance (total object perimeter) will be used together with area of the myelin sheath in cross-section to calculate the diameter of the axon and the nerve fibre (see Appendix 2). The absolute values of x and y points is unimportant and arbitrary; peripherally located fibres will be eliminated not by the absolute values of x and y, but by their values relative to the

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fiber if Xmin+b < X< 9

if Ymin +b < Y < Ymax-b

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Fig. 2. Elimination of fibres from the peripheral field. Fibres having the centroids closer than one radius from the border must be eliminated, since the larger of these will be incompletely measured due to their overlapping the edge (lower right). Smaller fibres in the peripheral border (left) must also be eliminated, in order to avoid overcounting of small fibres relative to large ones. The screen coordinates Xmin, Xmax, Ymin and Ymax allow the spreadsheet to eliminate fibres having centres within a distance b from the edge of the screen. minimum and maximum, i.e., the distance from the screen perimeter (Fig. 2).

2.3. Step 3: image and data acquisition

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I

Fig. 1. Overview of procedure and hardware modules. Image acquisition is from a toluidine blue-stained slide placed under oil immersion with a 100x objective (1), using the JAVA software (2). Images are generally not recorded to disk, due to their large size (200 kb). Artifacts are eliminated by observation of the image on the monitor (upper left) and clicking the mouse on the undesired object during a

pause in the macro. Raw data containing the total (inner and outer) circumference of each fibre the area of the myelin sheaths and the X and Y coordinates are exported to a Lotus 1-2-3 spreadsheet (3). A macro eliminates the peripheral fibres near the edge of the screen (see Fig. 2), which cannot be measured in their entirety. The data are processed to yield fibre diameter, axon diameter, myelin sheath thickness and myelin sheath variability (standard deviation of myelin sheath thickness), both for the entire specimen as a whole and also in bins by fibre size. Hardcopy printout is possible (4) and the direct generation of color slides using a film recorder (5) is possible by linking the spreadsheet graph to a graphics program (e.g., Lotus Freelance).

Turn on all components of the image analysis system and start JAVA. Go to the Object Count Menu. Select freeze IF2] to go live on the Video Monitor. Place a plastic-embedded, toluidine blue-stained, transversely sectioned nerve on the microscope stage. A d d immersion oil, rotate the 100 × objective into place and focus. Freeze the frame [F2]. Select freeze [F2] to sample the next field. Freeze [F2] acts as a toggle switching from alive to a frozen image. Load the N E R V E _ B X . M A C macros into memory, as well as N E R V E _ B X . X F M transforms and the N E R V E _ BX.ASC area of interest. Begin the macro [sF1]. See Appendix 2 for explanation of the macro structure. If fibres are touching, use [Ctrl-F2] paint to draw a white line between them when the macros pauses to allow you to do this. This will ensure subsequent separation of contiguous fibres.

2.3.1. Light intensity The macro will first analyse your image for grey scale intensity, which can range from 0 (black) on the left to 255 (white) on the right. The curve on the computer monitor appears as a somewhat bell-shaped histogram, with a hump near the middle. No pixels should appear at either the black or white end of the spectrum. If this is not the case, the light intensity should be adjusted.

2.3.2. Dynamic threshold setting After contrast enhancement, the macro will pause to allow threshold adjustment. It is through the selection of a window of grey scales that the dark myelin rings are selected for counting. Selection of a window of

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black pixels for the final digitized image enables elimination of all but the black objects for counting. In this way, the endoneurium and all but the myelinated fibres are eliminated. No black pixels should ever be eliminated, to avoid spuriously thin measurements of myelin sheath thickness. Hold the cursor button down near the triangle at the lower right of the histogram and, with the cursor button still depressed, drag it to the left. Watch the effect on the video monitor image as you do this. Move the mouse to the left and eliminate most of the endoneurium. Judge the degree of pixel elimination by simultaneously observing the image monitor (Fig. 1). The objects to be counted, the myelin rings, will appear red with the cursor (left) button of the mouse depressed. Everything else will be ignored and will appear black. Release the cursor button at any time to see the original image on the monitor. The blackest objects next to myelin will be the chromatin condensations at the periphery of Schwann cell and pericyte nuclei, directly under the nuclear membranes. Because these Schwann cell and pericyte nuclei tend not to stain as dark as myelin, they will generally be fragmented at this stage by virtue of having their nuclear membranes and subnuclear chromatin condensations broken up due to the elimination of many component pixels which are lighter than myelin. If any doubt exists as to the nature of the original object being eliminated (e.g., Schwann cell nucleus vs. small myelinated fibre), the input of the monitor can at any time be switched to the original image still on the microscope by selecting the line input on the video monitor. The microscope image itself can also be checked. In this way, quality control can be maintained over the image processing as it proceeds. Setting the threshold too far to the left will cause myelin rings to become open or C-shaped, leading to erroneous measurements. Such undesirable effects can be seen on the monitor as they are generated, when the mouse is moved in the process of threshold setting. When the cut-off threshold has finally been set, press Enter to resume the macro. During the initial break-in period during introduction of the procedure quantitating nerve biopsy and from time to time thereafter, it is mandatory that threshold setting be performed by, or at minimum be supervised by, the neuropathologist responsible for the nerve biopsy interpretation, or the researcher, to ensure that only myelin sheaths are actually measured. Responsibility for the accuracy of the procedure rests with the user.

2.3.3. Elimination of extraneous objects Since the goal is to count the hollow objects, elimination of extraneous objects such as Schwann cell nuclear fragments, is best done by criteria of total perimeter rather than area. Objects such as one-half a

pericyte nucleus, will be much smaller in total perimeter (inner + outer circumference) than the smallest myelinated nerve fibre, although areas might be comparable. Thus, all objects not having a total perimeter criteria between 10 and 150/zm are eliminated by the [sF5] macro. These limits can be changed by editing the [sF5] macro (see Appendix 2). Manual elimination of any further objects can be done when the macro pauses at this stage. For each object, press [F4], place the cursor on the object to eliminate and then press the cursor button on the mouse. When through eliminating objects manually, press [Enter] to resume the macro. Note that fibres near the screen periphery do not require attention, since they will be eliminated in the subsequent spreadsheet processing by the Lotus 1-2-3 macro, based on the X, Y location of the fibres. Possible objects needing manual elimination at this stage include: (1) large Schwann cell nuclei which were not previously fragmented; (2) dust particles appearing in the image; and (3) stain crystals in the section. All three of these are easily avoided and it then becomes unnecessary to manually manipulate many image components, speeding the processing of frames considerably. Schwann cell nuclei can be fragmented at the [Ctrl F2] paint stage (see above), causing the macro to eliminate them by size criteria. Alternatively, they can be manually eliminated at this point.

2.3.4. Sampling Repeat Freeze [F2] and [sF5] for each microscopic field sampled. Beginning at the top, sample the biopsy systematically through sequential horizontal fields overlapping at the edges. When the perineurium is reached, drop down one field and continue horizontally in the other direction. Ideally, the whole biopsy is thus sampled systematically. There is no substitute for a medium power scan of the biopsy to determine the inhomogeneity of any pathologic changes. Sampling is the responsibility of the operator. The system can only quantily the chosen microscopic fields. 2.4. Step 4: data calculation and presentation 2.4.1. Graphing, printing biopsy data Printing of the numerical data on the biopsy and graphing (fibre diameter, myelin sheath thickness for each fibre size) is performed by a spreadsheet macro which imports the data generated and saved by J A V A in a .PRN file. Here, only a description of how to use the macro is given. The macro structure and the underlying theory, is given in Appendix 3. Retrieve the worksheet file NERVE_BX.WK3. The macro will begin automatically once the worksheet is retrieved. The menus offer the opportunity to specify the .PRN file name to be imported, including its location (drive and path). Opportunity to change to the


name of your institution, place, patient name, surgical number, etc., is provided. The macro is self-explanatory and should be explored. The user-changeable parameters are highlighted on the spreadsheet in green. The existing settings are visible on the monitor. The file will be imported and processed, with the fibre size distribution histogram appearing on the screen as the first graph. The second graph to appear on the screen displays the myelin thickness and its variability. The macro can be rerun if the border width (determining how far from the border fibres are eliminated) needs to be changed. The border width should be set to one-half the diameter of the largest fibres in the biopsy. Options allow printout of numerical data and graphs for archival storage purposes, or for the patient's chart. A typical worksheet containing data on 1000 fibres in the biopsy will occupy 120 kb of disk space. It is not necessary or desirable to store each dataset in its own worksheet. Storage of each raw dataset i n . P R N files allows loading into N E R V E _ BX.WK3 for future re-examination and analysis if desired.

3. Results The primary measurement of myelin area and total object perimeter allows secondary calculation of axonal and nerve fibre diameters (Fig. 4). See Appendix 2 for derivation of the formulae. All shapes are converted into equivalent circles for the axon and nerve fibre by the procedure (Fig. 3). The method results in the ability to measure even fibres which are distorted into figure-of-eight shapes (Fig. 3). Use of the technique on oblique sections results in oversizing and undercounting of nerve fibres by a factor of cos 0 where 0 is the angle by which the section deviates from true transverse section. Fibres of all sizes are eliminated peripherally if their centroids lie in the border of specified width, even though small fibres could potentially be measured accurately (Fig. 2). Removal of this feature results in inaccurate measurement of fibres truncated at the screen edge. If only these large truncated fibres are eliminated in the periphery, leaving the small fibres to be counted, a spuriously high density of small fibres results. Two output graphs result (Fig. 5). The first corresponds to the conventional histogram, giving the number of fibres per mm 2 endoneurium, in size bins from 2 to 2 0 / z m . The second graph depicts the mean myelin and thickness and variability (standard deviation), also in size bins from 2 to 20/xm. The graphs of a normal adult female in the third decade of life are shown (Fig. 5). Appendix 4 gives the corresponding numerical data produced by the method.

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d1

d2

Fig. 3. Artefactual distortion of the shape of myelinated fibres. Myelin sheaths assume ovoid or irregular shapes after processing. Oval outlines estimated by measuring minimum diameter (d~) are undersized. The mean of minimum (d l) and maximum(d 2) diameter is also inferior to methods based on perimeter and area, since the latter can measure extremely distorted fibres (lower left) which are converted to their equivalent circles (lower right). The cross-sectional area of the myelin sheath and the total perimeter of the myelin sheath (the quantities measured directly by the image analysis system) remain relatively constant during such distortions and reconstructions. Fibres are likely near-circular in the in vivo state. Repeated analyses of the identical histologic slide by different individuals revealed an intra-observer variability of < 5%, with counts of 8913 and 8535 myelinated nerve fibres per mm 2 of endoneurium. Intra-observer variability was identical. Typically, 1000 myelinated fibres can be counted within 3 h in a total endoneurial area of 0.10-0.15 mm 2, obtained by sampiing 75-100 microscopic fields. Processing speed is Myelin A r , o Ao

C

Measured: C ° and A ° C°=C+c A°=A-a C ° =total object perimeter c = lh C o-21rA°/C ° C = 1AC° + 2~-Ao/C ° Myelin thickness M = tA(D-d)

h-.-'q

d = QhC°-2~rA°/C °)/rr D = ( I A C ° + 2 r A ° /C°)/1r

Fig. 4. Measured and derived nerve fibre parameters. The image analysis system measures the sum (C°) of the inner perimeter (c) and outer perimeter (C) of the myelinated nerve fibre. The cross-sectional area of the myelin sheath (A°) is also measured. Together, C° and A° determine a unique set of circumference, radius and diameter, of the axon (c, r and d, respectively) and of the entire nerve fibre (C, R and D, respectively). These can be determined mathematically (see Appendix 2) from the primary data C° and A° measured for each object by the image analysis system.


234

highly dependent on the speed of the computer's central processing unit (CPU). Comparison with manually generated histograms from historical archive material and with the literature, revealed a consistently greater size measurement of fibres using the present method. This resulted in the entire histogram being shifted to the right by roughly 2 /zm, compared with manual counting and sizing methods using the least diameter. This can be easily seen by examination of Fig. 5 (upper), where the frequency nadir seen between small and large fibres is shifted from the usual 7/xm size range to 10 p.m. The presently described method has recently proven useful in the quantitative morphometric study of the development of the vagus nerve of the sheep (Hasan et al., 1994). The application of the present method has resulted not only in a reduction in tedium. A time-related cost reduction has also been realized, since an entire sural nerve biopsy can now be quantitated in less than 3 h. Previously, this would have required several days, working with manual methods. 4. Discussion Peripheral nerve morphometry has proven useful in analysing peripheral nerves in numerous clinical disease situations, including amyotrophic lateral sclerosis (Atsumi and Miyatake, 1987), metachromatic leukodystrophy (Bardosi et al., 1987), aging (Tohgi et al., 1977; Vital et al., 1990), arsenic intoxication (Goebel et al.,

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1990), diabetes (Llewelyn et al., 1991), vitamin intoxication (Schaumburg et al., 1983; Windebank et al., 1985; Xu et al., 1989), vascular disease (Vital et al., 1986), scapuloperoneal myopathy (Yee et al., 1988), as well as in experimental studies of reactions to injury (Carlson et al., 1979) and even descriptions of normal anatomy (Low and Dyck, 1978) and development (Gutrecht and Dyck, 1970; Ferriere et at., 1985; Ouvrier et al., 1987). It is thus not surprising that numerous methods have been employed in an attempt to gain accurate quantitative data of peripheral nerves. Opto-mechanical devices have been used (Espir and Harding, 1961). More recently, methods based on digitizing tablets (Cavallari et al., 1989; Ewart et al., 1989) have been developed. All these methods, however, require manual attention to individual nerve fibres. Dyck and colleagues developed the first system based on computerized image analysis (Zimmerman et al., 1980). They cautioned against placing the entire procedure under complete automation without user interaction, due to either missed small fibres (if grey-scale threshold is set too low), or the detection of spurious profiles in the tissue (if grey-scale threshold is set too high) during the critical stage of dynamic thresholding and image digitization. Totally automated methods give rise to data which are vary by up to 9%, compared to semi-automated methods (Usson et al., 1991; Vita et al., 1992). A semi-automated method allowing operator interaction to pre-emptively eliminate errors would thus seem to be the ideal compromise between entirely manual and automatic methods. The fibre shapes are inevitably distorted from a circular outline in processed tissue, leaving a wide choice of primary measurements on which to base the calculation of equivalent circles. Dyck and colleagues compared six methods of measurement (Karnes et al., 1977). Diameters computed from cross-sectional areas showed the highest precision, greatest accuracy and least bias (Karnes et al., 1977). Transverse area of nerve fibres has been shown to be sensitive to fixative osmolarity while perimeter is unchanged (Dyck et al., 1980a). The present method utilizes both cross-sectional myelin area and total myelin perimeter to derive all other parameters of the equivalent circular profiles. The literature indicates such an approach is superior to that utilizing a mean diameter method (Karnes et al., 1977). Utilizing only minimum diameter (minor axis) is in error (Karnes et al., 1977) due to undersizing of fibres and may explain why measurement using the present method yields larger fibre sizes than previous methods not based on myelin area and perimeter.

Fm~ [ ] MEAN

10 11 12 13 14 15 16 17 18 19 2 0 + DIAMETER ~ m )

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Fig. 5. Two output graphs are generated, the upper one depicting the frequency distribution of the myelinated fibres by size. The lower graph shows the mean myelin thickness for each fibre size. Variability of myelin sheath thickness is seen as the standard deviation for each fibre size (mean, as a bar, standard deviation as a second bar stacked on top of the mean). Data for a normal human adult sural nerve is shown. Numerical data is shown in Appendix 4.

5. Acknowledgement Supported by the Medical Research Council of Canada (MT-9935).


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Appendix 1 Suppliers Jandel Scientific 2591 Kerner Bivd San Rafael, CA 949201, USA Toll-free: (800) 874-1888 USA, except California Tel.: (415) 453-6700 California or outside USA FAX: (415) 453-7769

(Jandel Video Analysis or J A V A Software version 1.41 or later)

Truevision Inc. 7340 Shadeland Station, Suite 100 Indianapolis, IN 46256, USA Toll-free: (800) 858-8783

(Targa plus frame grabber board)

Lotus Development Corporation 55 Cambridge Parkway Cambridge Parkway USA Tel.: (617) 253-9150

(Lotus 1-2-3 spreadsheet program, version 3.1 or later and Lotus Freelance Plus Drawing and graphics program, version 3.01 or later)

Appendix 2 Image analysis macros, formula derivation Image analysis macros

Three macros are used in JAVA: [sF1], [sF5] and [sF9]. The first, [sF1], sets up the data worksheet. The second, [sF5], gathers the data on one "frozen" microscopic field. The third, [sF9], calculates the nerve fibre and axonal diameters and saves the data. Thus, the [sFS] macro is run to process every microscopic field, whereas [sF1] and [sF9] are run only once for each specimen examination, at the beginning and end of the procedure, respectively. Details of the macro structure and operation are available on request from the author. Mathematical

c a l c u l a t i o n o f n e r v e fibre a n d a x o n a l d i a m e t e r s

The [sF9] macro invokes several transforms that calculate the nerve fibre diameter, axonal diameter and record the number of microscopic fields examined, the maximum and minimum X and Y coordinates. The calculation of nerve fibre and axonal diameter from the total object perimeter and object area will now be derived. The entire perimeter of an object is measured by JAVA. For hollow objects such as myelinated nerve fibres, this is comprised of the sum of the nerve fibre circumference (C) plus the circumference of the axon (c). Call this length C °, directly measured by JAVA. Note that C ° = C + c, the nerve fibre circumference C = C ° - c and that the axonal circumference c = C ° - C. The cross-sectional area of the object is also measured by JAVA. Since myelinated nerve fibres are hollow, this area corresponds to the difference between the area of the entire nerve fibre ( A ) and the area of the axon (a) and is actually the cross-sectional area of the myelin sheath itself. Call this area J A V A directly measures A ° = A - a. It is possible to calculate the nerve fibre diameter (D) and the axonal diameter (d) from these two measured quantities C ° and A °. The area of a circle is equal to its circumference squared, divided by 4rr. We substitute into A ° = A - a and obtain: A ° = C2//4"rr - c2//47r

(1)

We can use Eqn. 1 to express the desired quantity C in terms of the known (directly measured) quantities C ° and A °. We first eliminate c by substituting it with C ° - C. Thus: A ° = C2/4rr - (C ° - C)2/4~" 4~rA ° = C 2 - (C ° - C ) 2

(2) multiplying by 47r

4~rA ° = C 2 - ( C °2 - 2C ° + C 2) expanding the squared term 2C°C = C °2 + 4~-A ° Isolating C C = C ° / 2 + 2~rA°/C ° Dividing by ~" to get diameter D = (C°/2 + 2zrA°/C°)/rr yields nerve fibre diameter We can also use Eqn. 1 to express the desired quantity c in terms of the directly measured quantities C ° and A °. We eliminate C by substituting with C ° - c in Eqn. 1. Thus:

(3) (4)

A o = ( C ° - c)2//47r - C2/4./T Ao =

( C °2 -

2cC ° + c2)/4"rr - c2/4.1r

2cC ° = C °2 - 4~'A ° Isolating c (5) c = C ° / 2 - 2zrA°/C ° (6) Note that Eqn. 3 resembles Eqn. 6, except for the sign of the adduct 2zrA°/C°: i.e., the nerve fibre circumference is equal to C °2 plus 2rrA°/C °, whereas the axonal circumference is equal to C °2 minus 2rrA°/C °. As we did for the nerve fibre circumference, we divide Eqn. 6, the axonal circumference by 7r, yielding the axonal diameter d = ( C ° / 2 - 2zrA°/C°)/zr Axonal diameter (7) Eqns. 4 and 7 express the nerve fibre and axonal diameters, respectively, in terms of the known quantities C ° and A °, the quantities directly measured by the image analysis system.

R.N. Auer / Journal of Neuroscience Methods 51 (1994) 229-238

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(For technical reasons Appendix 3 can be found on the next page) Appendix 4 Sample print-out of numerical data

Nerve biopsy data (myelinated nerve fibres) Institution Location Nerve biopsied Name Age Surgical n u m b e r Electron microscopy n u m b e r Raw data in file D r i v e / p a t h for import Date Cut-off between small and large fibres (/~m) Area per counting field (izm 2) N u m b e r of fields examined Eliminated border strip width ( ~ m ) Total endoneurial area examined (mm 2) Total myelinated fibres counted

Foothills Hospital Calgary, Canada Sural Mrs. M.V.A. 22 years CME-3001-93 RE-6-1 CTR22-93.PRN D : \ 123 \ 123 \ N E R V E - B X 22-Jun-93 9.0 1503 59 7 0.089 645

Total density (myelinated fibres / mmZ: 7274) < 9.0/~m (small) f i b r e s / m m 2 > 9.0/~m (large) f i b r e s / p e r m m 2 Fibre diameter (tzm) mean 5: SD Axon diameter (/zm) m e a n ± SD Myelin thickness ( ~ m ) m e a n 5: SD Fibre area (/zm 2 m e a n + SD Axon area (p.m 2) m e a n 5: SD

4 759 2515 8.0 5 : 3 . 9 5.9 5 : 2 . 7 1.0 5 : 0 . 7 62.1 5:57.4 33.4 5:29.6 Myelin thickness and variability

Fibre density Fibre size (tzm)

N

E n d o n e u r i u m ( N / m m 2)

Fibre size (tzm)

Myelin thickness (/~m)

SD

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 +

0 19 64 106 90 77 42 24 12 20 34 49 50 28 18 10 2 0 0

0 214 722 1 195 1015 868 474 271 135 226 383 553 564 316 203 113 23 0 0

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 +

ERR a 0.2 0.4 0.5 0.6 0.7 0.8 1.0 1.3 1.4 1.8 1.9 2.0 2.1 2.1 2.0 2.3 ERR ERR

ERR 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.3 0.4 0.3 0.3 0.3 0.3 0.2 0.5 0.0 ERR ERR

a E R R indicates no calculation of either the m e a n or the standard deviation of the myelin sheath thickness could be carried out, since no fibers were present in that size bin.


237

Appendix 3 Spreadsheet macro structure The macro in NERVE_BX.WK3 starts automatically when the spreadsheet is loaded. File importation from the specified path is followed by elimination of the border fibres. The border width to eliminate is set by the user and should be half the diameter of the largest fibre in the biopsy, since, if that fibre happened to lie with its centroid one radius from the edge, its outline would be truncated. Although it is unlikely that the largest fibre would lie so close to the edge of the screen, this is done for absolute safety, since even the largest fibre should be accurately measured no matter where it lies within the field. However, the width of the border strip need never be greater than the radius of the largest fibre in the biopsy, or useful counting area will be eliminated. The macro deletes peripheral fibres by deleting data on all fibres not having centroid coordinates Xmin + B < X < Xmax -- B and Ymin+ B < Y < Ymax- B where B is the border width in micrometers. Calculation of the myelin sheath thickness is next performed by subtracting the nerve fibre radii from the axonal radii. The distribution of fibre diameters over the range of 1-20/~m is then determined, and the mean and standard deviation of the myelin sheath thickness for each fibre size in bins from 1 to 20 ~ m is calculated. Dividing the number of fibres found in each size bin by the total endoneurial area examined gives the fibre density by fibre size, on which the histogram is based. Dividing the total number of fibres counted by the total endoneurial area examined gives the total fibre density. The cut-off between small and large fibres (Appendix 4) is arbitrary and is chosen by the user. If a lower threshold is chosen, more fibres will be listed as "small" and fewer as "large" but the sum total will always remain the number of myelinated fibres counted over all size ranges in the sample.

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