automated measurement of peripheral nerve fibres in transverse section

AUTOMATED NERVE FIBRES

MEASUREMENT OF PERIPHERAL IN TRANSVERSE SECTION

T. J. Ellis, D. Rosen and J. 6. Cavanagh

ABSTRACT Transverse sections of rat tibial nerve were scanned with on automated flying-spot microscope and the pictures examined in a one bit Iblack-and-whitel term. Computer

ro rams have been developed, and are described LW ne y, to solote individual nerve fibres in the field of view, and to measure axon area and myelin area,from which it is trivial to calculate average axon diameterand average myelin thickness if the axon is assumed to be circular in

cross-section. At the magnification used, it was possible to measure 40-50 fibres per field’and the time required to do this was 5-7 minutes. For each s ecimen, 7-8 fields were measured, providing data on 30 8 -400 fibres. Measurements, made on nerves from rats between 3 and 38 weeks of age, show the rate at which nerve fibres grow and also show that the ratio between axon diameter and fibre diameter remains constant, within experimental error, over this period and is close to the predicted value.

INTRODUCTION

The work reported in this paper is concerned with the application of image processing techniques to the measurement of stained cross-sections of peripheral nerve fibres. The aim of the project has been to develop fully automatie methods of analysis, which allow a suitably stained section to be presen- ted to the system and determinations of myelin area (or thickness) and axon area (or diameter) to be the output, possibly in the form of histograms or scattergrams. We describe here the algorithms which extract the relevant values from the image field, and give the data resulting from applying the methods to a number of nerve sections from the sciatic nerve of normal rats of different ages. The measurements are used to assess the performance of the algorithms and the image processing system so that a comparison can be made with the results of manually measured data and the value of the automated method can be judged. Measurements of axon diameter and myelin sheath thickness are widely used for classifying and assessing the condition of peripheral nerve fibres (Fraher, 1978; Schröder and Bohl, 1978). Measurement of a statistically sufficient number of individual fibres from a single nerve bundle enables normal and ab- normal distributions of fibres to be found for a particular nerve. This information can be particu- larly useful in assessing damage or changes in the fibre distribution caused by degenerative neuropathies induced in experimental animals in drug or disease modelling, or in human biopsy or autopsy material (Sharma and Thomas, 1974; Potolicchio, Cervós-Navarro, Adhami and Stoltenburg, 1975; Stanmore, Bradbury and Wedde& 1978). In addition, theoretical models have been developed (FitzHugh, 1969) to describe the conduction pro- perties of myelinated nerve fibres, and their relation to the physical structure of the peripheral nerve. Rushton (195 1) has derived a direct cor-

Department of Biophysics and Bioengineering, Chelsea College, London S.W.3. and The Institute of Neurology, Queens Square, Londen W.C. 1.

0141-5425/80/040272-09 $02.00 0 1980 IPC Business Press

272 J. Biomed. Engng. 1980, Vol. 2, October

relation between axon diameter, myelin sheath thickness, intemode distance and nerve impulse velocity, using the method of dimensional analysis. Such predictions can be tested by direct obser- vation, and Friede and Samorajski (1967) and others (Williams and Wendell-Smith, 197 1) have shown that these relationships are in good agree- ment with experimental data. However, the ease with which one may measure the fïrst two para- meters, from transverse sections, singles them out for measurement in experimental and other situations. Manual methods for evaluating these morphometric quantities are normally performed on electron micrographs or light photomicrographs using planimetry, map meters or ruled grids (Sharma and Thomas, 1974;Mathews, 1968). An alternative and very precise method of measurement of the myelin thickness is to count the number of myelin lamellae in electron micrographs (Friede and Samorajski, 1968). H owever, these manual methods of measurements are time-consuming and laborious, and the subsequent data must be entered into and processed by a computer or calculator, or the results arranged by hand.

Image processing techniques and opto-electronic equipment have been used by a variety of workers. For example, projected equivalent circles formed the basis of a piece of equipment built by Espier and Harding (1961), though this approach wil1 necessarily introduce errors into the measurement of non-circular tibres. Schröder (1975) details several problems encountered in using a Quantimet 720 for performing measurements directly from the microscope. One of these problems, commonly found in image processing when dealing with bio- medical material, arises from the high packing density of fibres within the nerve bundle. Limitations on resolution imposed by the digital acquisition system tend to join individual fibres together into clumps, typically containing 10 - 20 fibres(Fi,pures 4 and 7). These clumped objects must tïrst be seg-

mented into single fibres before individual measurements may be made. On machines such as the Quantimet, segmentation is normally accomplished using a light-pen or tracker ball system and this arrangement necessarily requires an operator to evaluate and segment the field. An analytic approach has been adopted in the present work to overcome this important problem, and is described later in this paper. It may be noted that Adhami, Sawatzky and Homung (1976) and Potolicchio et al. (1975), have attempted to overcome this by making measurements on electron micrographs; but while such an approach allows images of higher magnifïcation to be dealt with, many more separate fïelds must be processed, and the electron micrographs must be produced.

The present work was performed on the Chelsea College Automated Microscope (Eccles, McCarthy, Proffitt and Rosen, 1976), which consists of a flying-spot scanner controlled by a special purpose, microprogrammable, preprocessor, interfaced to a PDP-8E minicomputer. The preprocessor contains a single-bit picture store consisting of 256 x 256 picture points (pixels) into which a binary or thresholded picture may be entered and operations (e.g. boundary following) may be performed on this picture by microprogmms loaded into the preprocessor by the computer. Results from these operations are transferred to the computer for further processing. A monitor screen is provided to display the store contents or various other pictures. All programs are written in FORTRAN, except the microprograms, which are in the processor’s own language, and are used as subroutine calls from the main FORTRAN program, retuming values as appropriate.

METHOD Histology Under deep ether anaesthesia, rats were perfused via the left ventricle at a pressure of 150 mm Hg, with 4% gluteraldehyde in 0.1 M phosphate buffer (pH 7.2). The posterior tibial nerve was removed from the animal and osmicated in a 1% osmium

Nerve fibre measurement: T.J. Ellis et al.

tetroxide solution for 2 h, then rinsed in buffer and passed through an alcohol series and propylene oxide before being finally embedded in araldite. Semi-thin sections (0.5 I.trn and 1.0 Pm) were treated by the method of Singh (1971) which stains the myelin sheath dark brown, and other tissue a golden colour, providing a high contrast image for the flying-spot scanner (Figure ia). For use with the automated microscope, this method was found to be far superior to the toluidine blue or thionin-acridine orange stains in more general use.

Picture acquisition In the present system, the slide must first be manually mounted within the microscope, and the fibre bundle located at low magnification. A high powered objective (x 63) is then selected, and a density (video) histogram of the complete field as viewed by the scanner is displayed on the monitor screen (Figure Ib) to allow selection of an appropriate threshold, such that the darkly-stained myelin sheath wil1 be isolated. A binary, or clipped picture of the field is then loaded into the store, using this threshold value (Figure 1~). At this point, the’ scene analysis program takes control from the operator and proceeds to perform the complete analysis of the image field. Nevertheless, an inter- active facility has been built into the program to allow manual control of any part of the automatie processing, necessary for initial program development and useful for aiding segmentation of very difficult fields. Re-entry into the program at the appropriate point is also provided.

Structure of the scene analysis program Three distinct operations may be identified in the scene analysis, that is, in the analysis of the field of view containing the nerve fibres. These operations are: (a) segmentation (b) recognition and (c) measurement. Although the program cannot be divided into sections dealing with these operations separately, it is informative to recognise their use in the flow of the program. A flow diagram of the program is given in Figure 2.

Figurc 1 (a) Video picture of a field of nerve fibres as seen on the monitor screen of the automated microscope. (b) Histogram, displayed on the monitor screen, showing number ofpicture points (given by height of columns) of given brightness, with brightness maximum on the left and decreasing linearly to the right; ihe position of the trough in the centre of the histogram is taken as the threshold brightness for analysing the picture and the bright-up in the left part of the histogram display shows exactly the leve1 of the threshold. (c) The thresholded picture (with light intensity inverted with respect to (a))

J. Biomed. Engng. 1980, Vol. 2, October 273


L

StC-0 area in

tablm

t ’

Figure 2 Flow diagram of the computer program

When an ‘object’ has been located in the field of view, the first stage of recognition is to determine whether it is a single fibre, a group of fibres touching each other (i.e. a conjugated object), or some- thing else (e.g. dirt). This is done by tracking round the boundary of the object, measuring the area of the object and also computing at each point the average curvature. Regions of high negative curvature identify indentation or “nodes” on the object boundary. If such nodes are found, and if certain other conditions are met (see below), the object can be segmented. Tests are applied to the final segmented objects and if the objects are then classed as single fibres they are measured.

SogmonPation. The segmentation procedure, a development of the algorithms discussed by Eccles, McQueen and Rosen (1977), is divided into two parts. The first is used to deal with simple conjugated objects, as in Figure 3, which contains no inter-fibre holes: the second deals with those objects which do contain inter-fibre holes, as in Figure 7~. Curvature, on which the whole procedure is based, is obtained at each point as the differente between the direction of the boundary element arriving at the point and that leaving it (Figure 5a), and is then averaged by a convolution procedure analysed in detail by Eccles et al. (1977). The precise location of a node is determined by finding the corresponding turning point in the curvature plot (Figure 4) and the numerical features of the node stored are its x,y co-ordinates, its

significante (delivered from the value of the curvature at the node, see Eccles et al. (1977)) and the direction in which the node appears to point (Figure 5b). If two or more nodes are detected, they are examined in pairs in a search for matches leading to segmentations. The program forces a decision on whether or not two nodes match, based on the distance between them, their degree of anti-parallelism, the degree to which they are aligned, and their significante. Figure 5b shows some of the possibilities appearing in a conjugated object with five nodes. Each node is assigned a direction, the bisector of the angle formed by the vectors going from the nodal point to positions a specified number of points distant along the boundary. For a pair of nodes to match, their directions and the direction of the line joining them must all lie within certain limits. In the object of Figure 5b, the node pairs (1,4) and (2, 3) match but (1,3) and (2,4) do not, and node 5 is left unmatched. Tuble 1 gives the limits for an acceptable match. When two nodes are accepted as a matching pair, a line of background points is constructed bet-

Figure 3 A simple conjugated object, containing no inter-fibre holes, from the field of Fagure 1, with its boundary displayed by the boundary-fellow su b-rou tine

Figure 4 A simple conjugated object and a graph of its curvature after the latter has been smoothed by a convolution procedure (window width 6, number of convolutions 2, see Eccles et al., 1977). Cor- respondingpoints are marked on thc object and on the graph which is also displayed, with limited resolution, on the monitor screen


b

l A A

a 2 + 0 2J-L 3 -1

3

DlWCtblS CtiveS

Figure 5 (a) The direction and curvature codes used. (6) Illustration of the method of determining the direction in which a node points and of the matching of nodes. When a node has been located, vectors are drawn between the nodaIQoint and points 5 steps forwards and 5 steps backwards round the object boundary. The bisector of the angle formed by these two vectors is taken as the direction of the node. Table 1 in the text gives the limits for an acceptable match

ween them, in the picture store, in order to segment the object, and this can be seen in Figure 6. When the segmentations have been made between al1 matched pairs of nodes, a check is made to see if any unmatched nodes are left. If there are, the program continues to the second stage. Otherwise the program jumps to the recognition section (fibre acceptance tests).

If a conjugated object contains intemal inter-fïbre holes, distinct from the axon areas, then it is necessary to break into these areas in order to segment the object. Figure 7 shows an object with such intemal holes (as wel1 as axon holes), high-lighted by the boundary-follow subroutine. It can be seen that for inter-fibre holes, the required nodes are in fact projections on the hole boundary. On simple objects, these would correspond to regions of high positive curvature. However, the boundary-follow subroutine tracks around the hole boundaries in the opposite sense to object boundaries (anti-clockwise for objects, clockwise for holes). Hence the nodes to be identified on the holes wil1 still be indicated as negative curvature regions ; tbey are found using exactly the same algorithm as for objects, and can be directly matched with object nodes. This comes about from the definition of curvature used here (Figure 5a).

There remains, however, the problem of distinguish- ing inter-fibre holes from intra-fibre holes, i.e. from axon areas appearing as holes within a myelin ring. If a node were detected on an axon hole, a match with another node would result in a segmentation line drawn through the myelin sheath. (But such a fibre would be rejected by the fourth recognition test discussed below.) If one examines the boundaries of the holes in Figure 7b, it can be seen that the

Nerve fibre meosurement: T.J. Ellis et al.

true inter-fibre holes are distinctly different in shape from the intra-fibre (axon) holes. The intra-fibre holes tend to be very much more circular, whereas the inter-fïbre holes have sharp corners on their boundaries, as one would expect for spaces between tightly packed objects. A good test of the circular- ity of an object is to examine the value of P2/A where P is the leng-& of the perimeter of the object and A is the area enclosed by the perimeter. The minimum value of P2/A is 4n when the object is a circle and rises to higher values for other shapes. To obtain a value of P, the boundary has been smoothed by one of the standard methods (Ellis, Proffitt, Rosen and Rutkowski, 1979), namely the m-step polygon method, taking m = 5.

Referring to Figure 7a and Table 2, we can see that P2/A values for inter-fibre holes and axon holes are effectively partitioned by a threshold in the

Table 1 AcceQtance criteria for a pair of nodes to be matched and for a line of segmentation to be drawn between them

1. Significante of nodes

2. Anti parallelism of node directions

3. Separation of nodes

4. Alignment of nodes

Sum of curvatures of the two nodes s; - 0.4

Where the nodes are inclined at 0, @ to the x-axis, 8 + @ < 40”

Distance between nodes less than 25 grid units but if distance is less man 6 grid units the match is absolute irrespective of angle criteria

If the line joining the nodes is inclined at an angle rl, to the x-axis, then J, - 13 < 25”, J, -$J< 25”

Table 2 Analysis of the ratio of perimeter squared to area (P’/A) for holes within a complex conjugated object shown in Figure 7

Hole

1

2

3

4

5

6

7

8

9

10

11

12

P=/A Classification

15.1 axon

20.3 interstitial

14.8 axon

25.7 interstitial

14.0 axon

46.7 interstitial

14.2 axon

14.2 axon

15.4 axon

18.2 interstitial

14.3 axon

15.2 axon



Figure 6 (a)-(d) h s ow a sequence of segmentations. In (a) the left- most part of the object of Figure 3 has been removed. Single fibres are removed in going to frames (b) and (c) and the process continues until only one fibre is left, in (d)

range 16-17.5 and after consideration of a larger Recognition (and fibre acceptance tests). Four data set, a fmal value of 17.0 was chosen. Hence, if only those holes with a P2/A value > 17.0 are

criteria are used to decide that an object is a single

selected, it is possible to detect the nodes of the measurable fibre. These are: (i) that no part of the object’s boundary lies on the edge of the digitized

inter-fibre holes, and then use these to segment the conjugated object into single fibres.

When these segmentation procedures have been applied to objects with nodes detected on their boundaries, the program proceeds to the second recognition stage, to test whether the resulting. objects are accëptable single nerve fïbres. ”

field; (ii) that the area of the object lies within the expected range; (iii) that a hole (i.e. a region with the same light intensity as background) exists at the centre of the object; and (iv) that the boundary of the object is complete.

Referrincr to the examoles in Fieure 8. it would obviously be very diff&t to m>asureJ object A

Figure 7 (a) A complex conjugated object containing inter-fibre holes. (b) The holes in the object of(a) picked out by the bounday-fellow subroutine. (This view, not normally displayed by the program, was specially generated for the present illustration, but at the expense of most of the background.) (c) The new bounohy of the object in (a) after the program has made a break between one of the inter-fibre holes and the original bounday. Some segmentation can now be made as in Figure 6


Nerve fibre meosurement: T.I. Ellis et al.

without some elaborate but stil1 arbitrary error correction technique and though object B would be very much easier to measure, the decision is made to reject al1 objects which touch at the edge. However, it should be noted that attempts are made to segment all objects before rejecting them, so object C would first be segmented and the resulting segments are then separately tested. The second test is used to reject objects with abnormally large areas. For instance, an object for which the segmentation procedure has failed would be rejected. The test also rejects smal1 specks of dirt, etc. The third test is applied to ensure that the object is a single fïbre. This is achieved by calculating the centroid of the object under consideration (e.g. object D, in Figure 8) and examining whether the point is stored as above threshold in the picture store. If the point is found to be part of a hole, then the internal (axon) area is measured and stored within the computer together with the extemal (myelin plus axon) area. Objects which do not have a central hole, and have passed tests (i) and (ii) wil1 normally be dirt, staining artefact Figure SE), or

I unusually shaped fibres (Figure SF , such as those found near the nodes of Ranvier, where the myelin sheath becomes heavily crenated. Finally, the fourth test compares the internal (axon) area with the total or external area of the object. If the in-

Figure 8 Objects to illustrate the acceptance CW teria for single fibres. A and B both touch the edge of the field and are rejected. Cis first segmented; the right-hand part is then accepted and the left-hand part rejected. D is an acceptable object since it is of the appropriate size and the centroid of its outer boundary lies in the hole con tained within that boundary, E is rejected on account of its smal1 size. F is rejected since the centroid of the outer boundary does not lie within a hole. G is rejected since the myelin sheath is incomplete. The cen- troids of objects D and F are marked X

Figure 9 A successfully measured field, with a marker point placed in the middle of each measured .fìbre

ternal area is not smaller than the external area, then the object has a break in its boundary (Figure SG) and is rejected. Objects which pass al1 the tests outlined above are recognized as single nerve fibres, and are accepted into the fibre acceptance table for that particular nerve.

MO88UnmOnt. Only two simple measurements are taken from each fibre, external (fibre) area and internal (axon) area. Radii, etc. are then calculated assuming that the areas are circular (Kames et al. 1977). The area program is written in preprocessor machine code, and called as a subroutine by the main FORTRAN routine, retuming a value of the area for the object under consideration. The two areas measured from each fibre are initially written into a buffer store in the computer. When the analysis program has dealt with al1 the objects on the field, this buffer is written onto permanent disc file with a filename corresponding to the animal section under study. Figure 9 shows a field of nerve fïbres with a marker point in each fibre successfully measured. Subsequent analysis of the data by the data analysis program can then access this information for presentation. If further fields are to be examined for the same nerve, the data generated by these fields is added to the file before it is finally closed; in this way it can be ensured that the file wil1 contain a statistically representative sample of the fibre population of that nerve.

A typical rat tibial nerve contains between 2000 and 3000 nerve fibres, from which it was considered that 300-400 would provide an adequate sample. A typical digitized field in our conditions, contains 60-70 fibres, of which usually, 40-50 can be successfully measured, though this number is highly dependent on the quality of the slide material. On optimal material, the majority of the rejected fibres wil1 be ones touching the edge of the field, but sometimes a group of fïbres may be damaged in the course of the preparative procedure or may be inadequately stained so that the number of acceptable fibres is reduced. In a good specimen, therefore, it was necessary to analyse only 7-8 fields in order to have measurements on 300-400 fibres; but in a few less good specimens more fïelds were


Nerve fibre meosurement: T.J. Ellis et al.

a b 7”

(pm)*

Figure 10 Histograms showing distribution of external (fibre) area and internal (axon) area within, in each case, a sin.cle tibial nerve section fiom rats of(a) 3 WAS, 293 fìbres; (6) 6 wks, 452 jìbres; (c) 9 wks, 371 jìbr&; (dr.26 wks; 361 fibres _

examined. It should be mentioned that the illustra- tions in this paper showing nerve fibres on the monitor screen are, for the sake of clarity, at a hio-r;r magnification than that at which we normally

.

RESULTS

A total of 14 rats was used and the right and left tibial nerves of each was*examined, giving rise to the measurement of about 10 000 individual fibres. The rats were al1 from the same litter and were aged 3, 6,9, 26 and 38 weeks. A set of histograms showing the distribution of extemal (myelin plus axon) area and internal (axon) area is shown in Figure 10 for typical animals from the various age groups; a large standard deviation about the mean is evident on inspection. A similarly broad distribution is found in the scattergram of Figure 11 in which axon area is plotted against myelin sheath area for the first hundred fibres measured in the nerve of a 6 week old rat. For the points in Figure 11 the correlation coefficient is so low (p = 0.53) that not much reliance can be placed on further analysis of them; they give, nevertheless, a regression coefficient of 0.69 and an intercept on the ordinate of 2.2 (Pm*) so that, for this age of rat and assuming nerve fibres of circular cross-section, myelination in the tibial nerve begins when, on average, the axon has a diameter of about 1.7 Pm.

In these studies the primary measurement is of area and area measurement is a particular feature of automated image analysis systems (Stanmore, Bradbury and Weddell, 1978) in contrast to the linear measurements usuahy made in matma


analyses (e.g. Mathews, 1968). However, Kames et al. (1977) state “that the circle approximation is the most suitable for use in computerized image recognition systems for nerve morphometry”. Accepting this argument, it is a simple matter then to calculate fibre and axon diameters and so arrive at a value of myelin sheath thickness. The average of this value for each age of rat, as wel1 as the area averages, are given in Table 3.

. .

.

0

Figure 11 Axon (inncr) arc’a plottcd against myelìn area for the first hundred fibres measured from the nerve of a nine-week-old rat

Table 3 Averagedpooled data from at least 1500 rat tibial nerve fibres in each case

Age of Extemal Intemal Myelin Myelin rat fibre area (axon) area area (weeks) (w’) (Pm’ )

3 11.68 * 1.52

6 23.23 f 4.57

9 34.52 * 7.46

26 46.33 f 4.87

38 43.84 ? 1.15

3.98 f 0.76

9.08 + 2.77

13.20 + 2.06

20.80 i 3.64

15.48 f 0.79

7.72 f 0.79 + 0.58 0.79 0.02

13.76 + 0.99 f 0.62 2.03 0.07

21.00 + 1.23 * 0.62 4.66 0.16

25.04 f 1.23 f 0.67 1.29 0.03

27.96 f 1.48 r 0.59 0.98 0.04

DISCUSSION The first purpose of the present work was to develop and validate a method of automated analysis of nerve fibres. The analytical procedure has been described briefly above. From the measurements we have made we estimate the analytical failure rate to be about 5%; that is, about 5% of fibres were lost by failure correctly to segment conjugated objects. NO cases were observed of objects which were not single fibres being classified as if they were. In the case of blood capillaries appearing in the field of view, the walls were so thin in al1 cases, that they never appeared to provide a complete boundary. A much larger percentage (zriz. about 45%) was lost for non-analytic reasons as noted above, mostly (- 40%) because they touched the edge of the field, but occasionally (the remaining 5%) because they were insufficiently stained or because the threshold in the analysis program had been set too high. (The difficulty can be readily understood by imagining a field of 100 fibres arranged as a 10 x 10 square array; then 36 fibres wil1 be lying on the edge of the square.) The percentage of lost fibres varied, however, with age of the animal; in nerves from young animals there were more fibres in a field than in nerves from old animals, and so a smaller proportion touching the edge ; in addition the fibres were less crowded than in the case of the old animals; but also, the myelin sheaths were thinner and more liable to appear broken. The relative number of lost fibres does not diminish the accuracy of the measurements made on the fïbres which were recognized by the program but the calculated averages would be biassed if the lost fibres were not a random selection. The fibres lost because they touched the edge of the field may be taken to be a random selection of the fibres present. However, fibres lost for the other reasons mentioned were more likely to be smal1 than large. The overall number of these is not great (i.e. as indicated, not more than about 10% of the total, not all of which are smal1 fibres) hut averaged values may be a few percent (3-5%) high. However, this possible error is significantly less than the average standard error of 12% shown

Nerve fibre measurement: T.J. Ellis et ai.

in Table 3 and so may be considered acceptable.

A few comparisons are possible between the data we have obtained and data obtained manually by other workers. Figure 12 shows average myelin sheath thickness as a function of age and in addition includes values derived from the work of Friede and Samorajski (1968) ; the values come from their published numbers of myelin lamellae found in the rat sciatic nervtz, multiplied by their suggested thickness of 120 A per lamella. Agree- ment with the present data is seen to be very close. It is also of interest that the last column of Table 3, which gives the ratio of internal (axon) diameter, a, to extemal (fibre) diameter, f, shows that this quantity remains about constant for at least the period between 3 and 38 weeks of age during the rats’ development and maturation and is close to the value expected from the analysis made by Rushton (1951). Rushton argues that evolution towards most efficient nerve conduction would lead to a ratio of axon diameter to fibre diameter given by:

a ---ze -* = 0.61 f

This compares with an average of 0.62 for the five values given in Table 3.

Probit analysis of the results, shown as histograms in Figure 10, indicates that for 26 week old rats, the distribution of nerve fibre areas is reasonably wel1 described by a Gaussian (normal) distribution, but for the 3-week old animals the distribution is log-normal and for the intermediately-aged animals the distributions are between these types. Stanmore et al. (1978) f ound a logarithmic distribution of the cross-sectional areas of fibres in the sciatic nerve, but their studies were with mice rather than rats. The extrapolation of the regression line to the data of Figure 11 gives a value of 1.7 E.cm for the average diameter of fibres before the start of myelination. This is somewhat smaller than the value proposed by Friede and Samorajski (1967), who give 2.32 Pm for fibres from the sciatic nerves of mice; both values, however, come from data with large standard deviations, and may not be incompatible.

o- io 8 Age (weeks)

0

Figure 12 Myelin sheath thickness as a function of age: experimental points and full line are the present data; the broken line is derived from the data of Friede and Samorajski (1969) (see text)



The analytical procedure we use yields measured values which are self-consistent and in accord with expectations. Typical times for the analysis are 5-7 min per field, depending on the quality of the material, enabling a single specimen to be analysed in approximately one hour. (This will include time for the operator to select new fields, and if necessary to re-focus and select a new threshold). Further automation, an automated microscope stage and automated focussing, would substantially reduce this time, as also would the use of a larger and faster computer.

The program we have developed is reliable although some problems remain in connection with fibres which are rejected. One appears in preliminary measurements of material containing very young peripheral nerves or bundles with regenerating fíbres after the application of a demyelinating agent. Because of the thinness of the myelin sheath where the myelin is recently formed and may be only 1-5 lamellae thick, the sheath may appear incomplete (c.f. Fipre 8G). This difficulty could be dealt with by using, as a method of detecting myelin, a procedure more elaborate than the simple thresholding we have employed and severaf possible methods are listed by Rosenfeld and Kac (1976). However, it would probably be simpler to deal with the matter histochemically, by intensifying the myelin stain. Another problem can arise if the fibres are packed so close together that they appear continuous over the field and segmentation is beyond the power of the program. One solution to this problem is to increase the magnification of the microscope in order to improve the resolution (though even this wil1 be unsuccessful if the fibres are actually touching). However, if the magnifícation is increased then the number of fibres on the digitized field is reduced. Also and more significantly, a large frac- tion of these fibres wil1 be then touching the edge of the field, requiring relatively more fields to be analysed to attain the requisite number of measured fibres. Hence it can be seen that a reasonable trade- off point exists, such that we may maximise the number of measurable fïbres per field, though stilf retaining suffïcient resolution of the objects.

ACKNOWLEDGEMENT

Data storage and processing in the work reported here was greatly helped by acquisition of a floppy disc unit purchased with the aid of a grant from the University of London Central Research Fund. T.J. Ellis was supported by a research studentship from the Medical Research Council.

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automated measurement of peripheral nerve fibres in transverse section

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