Spatial Pattern of Nerve Fiber A norma lity Indicativeof Pathologic Mechanisms

PETER JAMES DYCK, MD, JEANNINE KARNES, MSc,PETER O'BRIEN, PhD, HITOSHI NUKADA, MD,

ALFRED LAIS, and PHILLIP LOW, MD

Estimates of the number, density, and size distributionofmyelinated fibers at selected levels ofroots, spinal tracts,and sampled levels of peripheral nerves may be used inthe detection and characterization of alterations of mo-tor, sensory, and autonomic neurons and their axons withdevelopment, aging and disease. Use of imaging tech-niques, now available, increases the reliability, versatil-ity, and speed of such analysis. In this study, the authorsevaluated the spatial pattern offibers in sampled framesand contour areas of transverse sections of nerve fasci-cles, utilizing, the coefficient of variation and index ofdispersion (ID), the latter extensively employed by plantecologists. The ID was used for recognization of in-creased, normal, or decreased variability ofdensity withinfascicles, between fascicles, and between nerves in health

EARLY ATTEMPTS to enumerate and size myelinatedfibers (MF) in nerves and tracts produced quite varia-ble results. A notable exception was the work of Er-langer and Gasser,1 who related peaks of diameter histo-grams of fibers to components of the compound actionpotential, demonstrating that there were functional andmorphologic classes and that conduction velocity couldbe related to diameter. With the introduction of im-proved fixatives, thinner sections, electron microscopy,improved sampling, and statistical approaches and com-puter techniques and imaging, it has become possibleto determine the number, size, and shape of fibers (F)and of their subcellular components and organelles intransverse sections of peripheral nerves or fiber tractswith greatly improved precision and reliability.2-4

Morphometric approaches have also beeni extensivelyemployed in the study of pathologic abnormalities ofnerve.5 In a typical experiment, the morphometricresults, as derived from a sampled level of nerve froma group of animals (or of man) with a similar condi-tion, are statistically compared with those from con-trol sections. The summated areas of fascicles (trans-verse fascicular area, TFA) may be used in the detection

From the Peripheral Nerve Laboratory, Mayo Medical School andFoundation, Rochester, Minnesota

and in various experimental neuropathies. In addition,various morphometric measurements were made in trans-verse sections at defined levels along the hind limb nervesof rats in acute and chronic ischemia, after rhizotomyand in galactose neuropathy. These stereomorphometricstudies, emphasizing the number, size, shape, and spa-tial pattern of fibers, revealed differences among ex-perimental neuropathies and may be found to be helpfulin the characaterization and prediction of pathologicmechanisms in neuropathies of unknown cause. Spe-cifically, these approaches could be used for study ofwhether fiber loss in human diabetic neuropathy is mul-tifocal and determination ofthe levels ofsuch losses. (AmJ Pathol 1984, 117:225-238)

of congenital maldevelopment,6 hypertrophy,' oredema.8'9 The number of fibers (MF or UF) per nerve,or F/sq mm, may be increased (as from sprouting) ordecreased (as from degeneration). Diameter histograms,drawn to reflect numbers of F/nerve or F/sq mm mayindicate congenital absence, acquired decrease or in-crease; absence, decrease, or increase of a subclass, andhypertrophy or atrophy of fibers. Such hypertrophy oratrophy may be suggested by an alteration in the range,the median diameter, and the position of the peaks inthe diameter histogram. Regression lines relating ax-onal area to myelin area, myelin thickness, or myelinspiral length may provide evidence of hypertrophy oratrophy of axons. An altered shape of F profiles canbe evaluated by determining percentages of certain fiber

Supported in part by a Peripheral Neuropathy Clinical Cen-ter Grant from NINCDS (NS14304), a Center Grant fromMDA, and Mayo, Borchard, Upton and Herrick Funds.

Accepted for publication June 12, 1984.Address reprint requests to Peter James Dyck, MD, Periph-

eral Nerve Laboratory, Mayo Medical School and Founda-tion, Rochester, MN 55905.

225

226 DYCK ET AL

shapes or by calculating the index of circularity (IC =

TrD/P; where D = diameter and P = perimeter). Anincrease or decrease of axonal organelles may be stud-ied by expressing their number per square micron ofaxon area or preferably per fiber. The size of the fibermay be expressed as area or as the diameter of a circleof equivalent area. When testing for atrophy, the num-ber of organelles, eg, neurofilaments per fiber, may beregressed on myelin spiral length, if one assumes thelatter measurement to be the best measurement of thefibers' former size. In health, the number and diameterhistogram of fibers in a transverse section may be rep-resentative of a considerable distance of the nerve. Indisease, however, single transverse sections may not berepresentative of pathologic alterations along the lengthof nerves. Three-dimensional morphologic reconstruc-tion of peripheral motor, sensory, or autonomic neu-rons by serial section is generally not possible in mam-mals mainly because cells are too long and ramify tooextensively. Reconstruction for short distances, how-ever, is possible and can be performed on serial or skipsemithin and thin sections. In simpler organisms, com-puter reconstruction of individual neurons and assem-blies of neurons in serial sections has made it possibleto study the size and shape of the soma and the branch-ing pattern and size relationships of dendrites. 10,11 Asa second approach, longitudinal sections may be usedfor recognition of alterations along the length of nervefibers. For technical reasons, however, the study of aseries of consecutive internodes of the same fiber is notpossible. In the third approach, the examination ofteased fibers, prepared in glycerin, may be used for as-sessment of many consecutive internodes of the samefiber. Such preparations have been used for recognitionof alterations of internode diameter and length, my-elin thickness, the presence and frequency of myelinwrinkling, segmental demyelination, remyelination, my-elin reduplication, axonal degeneration and regenera-tion, and sprouting.5 A modification of this approach,in which teased fibers are embedded into epoxy, allowsfor examination of transverse sections at defined pointsunder light and electron microscopy.12,13

Because all of these approaches (serial reconstruc-tion, longitudinal sections, and teased fibers) only evalu-ate morphologic changes for short distances (a cm ortwo), and because peripheral neurons are very long (ap-proaching 1-2 m in man), sampling at specified levelsis necessary for delineation of three-dimensional patho-logic alterations.'4

In this study, we have morphometrically evaluatedsampled levels along the nerves of the hind limb of ratswith experimental neuropathies to recognize stereomor-phometric patterns which could be helpful in predict-ing pathologic mechanisms in human neuropathic dis-

eases of unknown cause. The models differed in respectto whether fiber loss occurred and to the level and dis-tribution of such loss. The objective was first to assessvariability of MF density among sampled frames andbetween outer and inner contour areas in transverse sec-tions of nerve with the use of the coefficient of varia-tion (CV) and the index of dispersion (ID). Addition-ally, it is then possible to evaluate variability, with theseapproaches, among various levels along the length ofnerves and among nerves with various conditions ofdevelopment and disease. The study illustrates the useof these approaches and the advantages and limitationsof the CV and the ID for these purposes. Models ofneuropathy revealed different spatial patterns of fiberpattern, loss, and regeneration.

Materials and Methods

Models of Neuropathy

Lewis rats, weighing approximately 250 g, were used.The sciatic nerve, with attached tibial and peronealnerves to the level of the knee, was removed after per-fusion (rhizotomy) or after in situ (acute and chronicischemia, lead, galactose, and control) fixation with 40Voglutaraldehyde in 0.025 M cacodylate buffer for approx-imately 15 minutes. The nerves were then immersed in2.50Wo glutaraldehyde in 0.025 M cacodylate buffer foranother 8 hours. After washing, nerve collars were cutat the levels shown in Figure 1, dehydrated, infiltrated,and embedded in epoxy. Transverse 0.75 pA semithin sec-tions were cut and stained with paraphenylenediamine.

RhizotomyUnder sodium pentobarbital anesthesia, a laminec-

tomy was performed and the L5, L6, and L7 ventral(VSR) and dorsal roots (DSR) were cut. This causes de-generation of peripheral nerve axons derived from VSRbut not, in 30 days, of axons derived from spinalganglion.

Acute Ischemia

Polystyrene microspheres, 5.6 x 106, 15 ,p in diameter,were injected into the vascular supply of the sciatic,tibial, and perineal nerves for selective occlusion ofcapillaries. This procedure reproducibly producedregions of ischemic damage, beginning in the centralfascicular regions of the sciatic nerve in the thigh andextending more diffusely into the tibial and perinealnerves. 15

Chronic IschemiaNerves damaged by microsphere embolization, as de-

scribed above, were examined 6 weeks later. At this time

AJP * November 1984

SPATIAL PATTERN OF NERVE FIBER ABNORMALITY

A

B

Figure 1 -The levels of sciatic (A, B, and C), tibial (C and D) andperoneal (E) nerves morphometrically evaluated.

the central fascicular regions contained many smallregenerating fibers.

Lead Neuropathy

Four percent lead carbonate was mixed into theirpellets and fed to the rats for 6 months.

Galactose NeuropathyForty percent galactose was mixed into the pellets and

fed to the animals for 8 months.

Morphometric Approaches

Semithin (0.75 ,), carefully orientated, transversenerve sections were stained with paraphenylenediamineand evaluated with the use of our Imaging System forNerve Morphometry (ISNM). At low magnification andusing a digitizing tablet, we traced the inner edge ofthe perineurium of each fascicle. The areas of fascicleswere summated to provide the transverse fascicular area(TFA). At a high magnification (eg, x 2000), fascicu-lar areas were sequentially traversed, in an x andy direc-tion, under an ocular frame. The area examined cor-responded to the frame digitized and displayed on video.The numbering of the frames began on the left-handside of the upper horizontal row of frames of a fasci-cle. Systematic sampling of frames was achieved asshown in Figure 2. The first frame to be analyzed waschosen at random. Imaging was used to identify MFin the sampled frames, to border the inside of myelin,and to measure perimeter and average thickness of my-elin. From these measurements we derived the follow-ing for each fiber: for axons, area, perimeter, diameter(of a circle of equivalent area), and index of circularity(IC = TD/P); for myelin, inner and outer perimeters,area and thickness; and for MF, area and diameter (ofa circle of equivalent area). The ratio of iD to P is ameasure of circularity which will equal unity for a cir-cle and less than unity for a noncircular profile such

as an ellipse and will converge to 0 as the minor axisfor the ellipse converges to 0. We stored this informa-tion for each MF by frame, by nerve, by rat, and byexperimental model on a computer disk. From thesestored values, we determined for MF the number of MFper frame, the number of MF per fascicle, the numberof MF per square millimeter and the number of MFper nerve, and the CV and ID as described below. Histo-grams of axons (area or diameter), myelin (area or thick-ness), and MF (area or diameter of equivalent area)for fascicles per square millimeter or per nerve werethen plotted. Using healthy nerve, we were able to iden-tify the diameter position of troughs between peaks andto determine the number of large (LMF) and small(SMF) MF.

Morphometric and Statistical Approaches Usedto Assess Fiber Pattern

Measurements which might be used in an assessmentof fiber distribution or pattern would include the dis-tance to the nearest fiber (FD), the shortest distance tothe perineurium (SPD) or to another structure, the num-

Figure 2-Diagrammatic representation of systematically sampledframes (1 in 3) in an x and y traverse of the fascicular area of a nervebeneath the ocular frame of a microscope. The frames which weremorphometrically assessed are indicated by an asterisk.

227Vol. 117 * No. 2

228 DYCK ET AL

ber of MF per frame or MF per square millimeter, andthe density of fibers in outer to inner contour areas offascicles. An outline, equidistant to the inner edge ofthe perineurium, was generated by computer programso that 507o of the fascicular area lay outside and 50Wolay inside of it.To recognize focal or multifocal fiber density de-

creases or increases, systematic sampling of frames wasperformed. We assumed frame size to be an importantvariable in this type of study. If frames are too large,multiple fields of a fascicle cannot be surveyed andvariability of density within fascicles cannot be esti-mated. If too small, and an extreme example, a framewould have one or no fibers. For most nerves, the useof an x63 objective and a final magnification of ap-proximately x 2000 appeared to be suitable for the pur-poses of determining the number, size, shape, and spa-tial pattern of MF.

Statistical Indices

Let xi represent the fiber density in the ith frame(i = 1, . .. , number of frames). The index of disper-sion is defined by ID = AHS2/X, where x and s are themean and standard deviation of the densities, respec-tively, and AH is the harmonic mean of the frameareas.

where Ai (i= 1, . . . , n) is the area of the ith frame andn the number of frames. If fibers are distributed ran-domly over the entire area, AHS2 will equal x on aver-age and the ID will tend to be near 1. Conversely, theID will tend to be greater than 1 if fibers are clusteredand less than 1 if they are arranged in a uniform, sys-tematic pattern. This method for identifying and meas-uring clustering generalizes the conventional ID (usedextensively in plant ecology) and has been shown byPerry and Mead16 to have good sensitivity in detectinga wide range of clustering patterns.

Despite the ability of the ID to detect and measurenonrandom patterns, there are reasons why other meas-ures should be considered as well. For example, in com-paring two nonrandom patterns, the criteria for judg-ing which shows more clustering might be based onfactors other than departures from randomness (eg,departure from the type of pattern expected in health).Thus, the usefulness of any measure must be verifiedempirically. For this reason, we have considered thecoefficient of variation (s/x) as an alternative measure.The differences between the ID and CV are illustrated

with some idealized hypothetical examples in whichframe areas all equal 1 and nerves and number of frames

are very large, so that observed values of x and s maybe taken to be the true values in the nerve. First, wesuppose that fibers are randomly distributed in the nervewith x = 4 and s = 2. In ths case the CV = 0.5 andthe ID = 1.

Next, suppose that fibers are randomly distributedin a nerve of equal size, but the density of fibers is in-creased 100-fold, so that x = 400. (Note that this is notthe same as multiplying the number of fibers in eachframe by 100, because this would introduce a clustered,nonrandom arrangement.) To visualize this, consideragain the extreme case where, although fibers are dis-tributed randomly, frame sizes are so small (or fibersso sparse) that each frame contains either 0 or 1 fiber.If the number of fibers in each frame is then multipliedby a very large number, a clear pattern of clusteringemerges. Because the ID must equal 1, s2 = 400 andthe CV 20/400 = 0.05. Although the fibers are dis-tributed randomly in both cases, the CV would indi-cate a marked reduction in clustering. Similarly, whendensity is decreased, the CV will indicate increasedclustering.At first glance, these examples would suggest that the

CV should not be used to measure clustering. However,despite the limitations within the context of randomdistributions, the CV may retain some usefulness forcomparative purposes when fiber distribution is knownto be nonrandom. To illustrate, suppose that in healthfibers tended to be distributed in such a way that s =.x. In this case, the CV = s/x may be a more meaning-ful measure of clustering. Because for many phenomenathe standard deviation is directly proportional to themean, we have computed both the ID and the CV inour evaluations.We observe that if the underlying distribution of

fibers is random, both the ID and the CV are unaffectedby changes in area observed, number of frames ob-served, or the magnification used. In terms of the firstexample, the ID and the CV will still equal 1 and 0.5,respectively. In practice, of course, the ID and CV aresubject to random fluctuation. This random variationmay be reduced for both indices by increasing the num-ber of frames sampled.

If one still assumes a random distribution, increas-ing the area will also reduce the random fluctuationsin the CV but not the ID. On the other hand, if thedistributions are nonrandom, increasing the area willcause the ID to increase (enhancing our ability to de-tect any departure from randomness), while the CV willbe unchanged, providing frames are sampled fromhomogeneous regions, ie, providing that the areas donot become too large for detection of clustering, as dis-cussed previously. This phenomenon may also be illus-trated in terms of the first example. Suppose that the

AJP * November 1984

SPATIAL PATTERN OF NERVE FIBER ABNORMALITY 229

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230 DYCK ET AL

area sampled in each frame were multiplied by 4 andthe density held constant, thus introducing clustering.To visualize this, consider again the extreme exampleof two frames of equal area in which the first contains1 fiber and the second contains none, providing no evi-dence of clustering. If both areas are enlarged 1000-fold and density is held constant, we will now have 1000fibers in one frame and none in the other -clear evi-dence of clustering. Since the density of each frame isunchanged, the CV will still equal 0.5, but the ID isnow equal to 4.

Results

Acute Ischemia

In Table 1 we give morphometric values which werederived from transverse sections of upper sciatic nerve(A), lower sciatic nerve (C), the tibial division of C, andthe tibial nerve below the knee (D) as diagramaticallyshown in Figure 1.

Considering morphometric results among differentnerves of healthy rats, differences were found, as ex-pected, for TFA, number of MF per nerve, number ofLMF per nerve, number of SMF per nerve and persquare millimeter, median MF diameter, and MF rangeof diameters. Most of these differences were statisticallysignificant.

Statistically significant differences in the variabilityof MF densities between frames, as measured by theCV and ID, were found between some of the nerves.Without exception, the CV and ID were always highestfor SMF and lowest for LMF. Using the ID, the varia-bility of frame densities for large fibers varied between

0.48 and 1.32, whereas for small fibers it varied between2.21 and 3.03. These results indicate that in healthy ratnerves, large fibers approach a random distribution,with some differences between levels, while small fiberstend to be clustered.

If acute ischemic nerves are now considered, strik-ing differences are found (Table 1). At level A, no statisti-cally significant differences in morphometric parameterswere encountered between ischemic and normal nerves.At level C, striking morphometric differences werefound between the whole and the tibial division. Con-sidering the whole nerve, statistically significant in-creases in transverse fascicular area (TFA) but not inthe number of MF per nerve were obtained. The in-crease in TFA was relatively greater for the tibial nervethan for the whole nerve. A highly significant decreaseof MF per nerve (both large and small MF) was foundwhen the tibial nerve was considered alone.Considering the variability ofMF densities between

frames, both the CV and the ID were greatly increasedfor both the whole nerve and for the tibial nerve alone.For the tibial nerve, the CV was 3.1, 3.4, and 2.2 andthe ID was 5.3, 4.4, and 3.6 times greater in disease thanin control nerves for MF, LMF, and SMF, respectively.For the whole distal sciatic nerve and for the tibial nerve,the greatest increase in the CV and the ID was for LMF,followed by MF and then by SMF.At level D, the number of MF per nerve (both large

and small MF) was significantly decreased from nor-mal. The CV was 4.2, 4.8, and 1.7 and the ID was 8.0,10.7, and 1.3 times greater than for controls for MF,LMF, and SMF, respectively. In order to display thesechanges graphically, we computed the mean value foreach measured characteristic at each site on the diseased

Acute Ischemia

NS TFANS MFN LMF

.02<p<.025 'TFANS MFNS LMF

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Figure 3-The morphometric andMF density variation in upper sciatic(A), distal sciatic (C), tibial at C andtibial at D nerves of a rat with acuteischemia, as described in the text.TFA, transfascicular area; MF (mye-linated fiber), MF number per squaremillimeter; LMF, LMF number persquare millimeter; med dm, mediandiameter of MF; MF ID, MF index ofdispersion; LMF ID, large MF ID.

MF ID // 798% 1.01<p<.02LMF ID 1073% .02<p<.025

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AJP * November 1984

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nerves, then expressed this as a percentage of the meanobserved in the controls. The results for acute ischemiaare shown in Figure 3. To illustrate, the mean TFA ofdisease nerves at level A was slightly greater than (ie,greater than lOOWo of) the mean value observed in con-trols. Similarly, the means of all measured characteris-tics were nearly equal to the control means at level A.By comparison, the ID was many times larger in dis-ease nerves at level D.The stereomorphometric abnormalities observed in

acute ischemia are graphed in Figure 3. A significantincrease in TFA occurred in the distal sciatic nerve. Asimilar, but not significant, increase was also observedin the tibial division. The number ofMF per nerve wasdecreased to statistically significant levels only for thetibial division of the distal sciatic nerve and the tibialnerve below the knee. The median MF diameter wasnot decreased at any level.

Consideration of Table 2 indicates that a compari-son of morphometric results between the 50Wo outerand inner contour areas of fascicles at selected levelsof nerve provides additional information regarding thefiber pattern. A striking reduction in density of MF andLMF, but not of SMF, for the tibial division of the dis-tal sciatic nerve was found for the inner, as comparedwith the outer, contour area. A statistically significantreduction of MF was also found when we comparedouter contour areas of ischemia nerves with those ofcontrol nerves. No statistically significant difference inthe CV or the ID could be shown between outer andinner contour areas.

Chronic Ischemia

Neuropathologic examination of nerves harvested 6weeks after microsphere embolization revealed that thecentral fascicular cores, which at 1 week had shown adecreased number of degenerating fibers, now containedmany small-diameter MF. The morphometric values arepresented in Table 3 and Figure 4. The only statisticallysignificant abnormalities observed were a decrease inthe median diameter of MF at levels A and D and anincrease in the number of SMF per nerve and smallerand larger MF at level C. Whereas the CV and ID forMF and LMF, in particular, were increased in the moredistal disease nerves, the levels did not reach statisticalsignificance because the number of nerves evaluated wassmall.

Rhizotomy

We chose the rhizotomy model to produce degener-ation of ventral root MF in peripheral nerve, hopingto simulate the effect of fiber degeneration in motor neu-

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SPATIAL PATTERN OF NERVE FIBER ABNORMALITY 233

Chronic Ischemia

NS LTFAA NS MF

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Figure 4-The morphometric and MF den-sity variation in nerves of rat in chronicischemia, as described in the text. For ab-breviations, see Figure 3.

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ron disease. The results are given in Table 4 and Figure5. The TFA was significantly increased at levels C andD. The number of MF and LMF per nerve was

significantly decreased at level A. The CV of MF andLMF densities was significantly elevated at levels C andD. The ID values were significantly elevated at level Cbut did not reach significance at level D.

Galactose

The galactose model was chosen because it is knownto produce nerve edema, an increase of TFA, and a lowrate of fiber degeneration. Only peroneal nerves were

studied (Table 5). The TFA was significantly increased,but the number of MF per nerve was unaffected. Thenumber of SMF was significantly increased and was

reflected in an alteration of the fiber spectrum: the me-dian diameter was smaller. The CV for LMF was

significantly raised. Although the ID was slightly in-creased for both MF and LMF, statistical significancewas not attained.

In some sections, the edema appeared to have affectedthe outer more than the inner contour area. The higheraverage values of the CV and ID may reflect this varia-bility in density.

Lead

Lead was chosen because it produces a demyelinat-ing neuropathy with nerve edema and little or no fiberloss. Nerve level A was used for the controls and levelB for lead. Differences may therefore be attributed ei-ther to the level of the nerve evaluated and/or to dis-

ease. The statistical decrease in TFA at level B mustreflect a difference in sampling level, because it is knownthat more distal nerves are smaller and that lead causes

nerve swelling and not shrinkage (Table 6 and Figure7). There are significantly less MF and LMF per nerve

in disease (B) than in controls (A). Both the CV andthe ID for MF, LMF, and SMF densities are respectivelyless for disease than for controls. Assuming it to be dueto disease, and in contrast to earlier examples, this wouldimply a more regularly arranged pattern than incontrols.

Discussion

Morphometric studies of nerves or fiber tracts havebeen shown to be of value for the study of neuropatho-logic abnormalities. It is possible to recognize 1) alter-ations in nerve bundle size due to maldevelopment,edema or infiltration; 2) increase (eg, sprouting) or de-crease (failure of development or degeneration) in thenumber of fibers; 3) failure of development or preferen-tial degeneration of classes of neurons (axons); 4) al-teration in size and shape; 5) increase or decrease innumber of size and/or alteration in the proportion ofclasses of nuclei; 6) autoradiographic abnormalities;and 7) ultrastructural abnormalities.The use of morphometric approaches in neuropatho-

logic study of the peripheral nervous system has recentlybeen reviewed."7 Selective absence or degeneration ofpopulations of neurons (axons) could be related tospecific clinical deficits and to a selective decrease or

absence of a peak(s) of the compound action potentialof nerve."8-'9

NS

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SPATIAL PATTERN OF NERVE FIBER ABNORMALITY 235

Rhizotomy

A

Figure 5- The morphometric andMF density variation in nerves of arat after rhizotomy, as described inthe text. For abbreviations, seeFigure 3.

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Morphometric studies of sampled levels along thelength of peripheral nerves in disease and in controlsallow the observer to make extrapolations about thedistribution of pathologic abnormality in the thirddimension."4 To reconstruct abnormalities of motorneurons, the number and size of the soma in motor neu-ron columns of spinal cord segments and of MF in aventral root and a distal muscle nerve were determined.Striking deficits of alpha and gamma motor neuronscould be demonstrated in motor neuron disease (alpha)and in dysautonomia (gamma). For peripheral sensoryneurons, the sampled sites included various levels offasciculus gracilis, dorsal root, spinal ganglia, and suralnerve. Characteristic abnormalities of classes of axonswere found in various hereditary sensory neuropathies,amyloidosis, and Fabray's disease. For sympathetic neu-rons, the interomediolateral nucleus, ventral spinal root,gray and white rami, and paravertebral sympathetic gan-glia were assessed. Abnormalities were documented forfamilial dysautonomia and Shy-Drager syndrome. Useof these approaches in patients with neuropathic dis-ease has revealed the class and proximal to distal levelof involvement of neurons.

In this study, we extended these morphometric studiesto a consideration of spatial pattern of fibers in trans-verse sections of nerve. Focal loss of fibers is encoun-tered in ischemic neuropathy, sarcoidosis, leprosy, andprimary nerve tumors. In many metabolic and inheritedneuropathies, focal fiber loss has not been recognized,but they have not been studied by the approaches in-troduced here. The idea that fiber loss is focal or mul-

tifocal in some neuropathies, while in others it is not,was the basis for this research. The approaches usedhere could be extended to a study of the fascicular nervevessels, nuclei, or other structures.We have used the idea of spatial pattern to describe

the distribution of fibers within and between fasciclesof nerves as plant ecologists use the term to describethe distribution of plants within quadrats.'6 We havealso made use of their ID to test for the presence ofa pattern or of random distribution. Similarly, we em-ploy data based on counts from sampled quadrats(frames) and have extended their idea to the use of outerand inner contour areas of the fascicle. Usually, ecolo-gists use quadrats of the same size. This cannot be donewith nerves. Some of the frames we sampled contained

Galactose

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200 100

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* CV = .001<p<.005

100 200

Percent of NormalFigure 6-The morphometric and MF density variation in nerves ofrat in galactose neuropathy as described in the text. For abbrevia-tions, see Figure 3.

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Vol. 117 * No. 2

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Vol. 117 * No. 2 SPATIAL PATTERN OF NERVE FIBER ABNORMALITY 237

Lead

.025<p<.05 TFA med dm .001 <p<.005B .025<p<.05 MF MF ID NS

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Percent of Normal (level A)

Figure 7-The morphometric and MF density variation in nerves ofa rat with lead neuropathy as described in the text. For abbreviations,see Figure 3.

less than a full frame of fascicular area. The harmonicmean of frame size was used in calculating the ID.

Three-dimensional patterns of fiber degeneration orloss emerge from these studies. In acute ischemic neu-ropathy from microsphere embolization, no abnormal-ity was demonstrated in proximal sciatic nerve, whereasat more distal levels of the same nerve, loss of fibersand excessive variability of MF densities (indicated bya markedly elevated CV and ID) have been demon-strated. At proximal levels of ischemic injury, the den-sity of MF (also of LMF) was higher in outer than ininner contour areas of fascicles. In chronic ischemia(the same lesion as in the acute variety but tissue taken6 weeks after embolization), similar but less severechanges were demonstrated. One difference between theacute and chronic variety was that proximal MF of thechronic variety exhibited a lower median diameter. Al-though this could reflect a biologic difference unrelatedto the model, it is likely to be a real atrophy of prox-imal stump fibers after disease transection. Such atro-phy takes weeks to develop and therefore is found onlyin chronic ischemia. Such atrophy of stump fibers withconcomitant reduction of maximum nerve conductionhas previously been reported.7,202' When rhizotomyis used as a model of ventral root MF loss, importantdifferences between this pattern and that of ischemiacan be shown. The principal difference was that thenumber of MF per nerve was reduced even at the up-per sciatic nerve level in rhizotomy. The tibial nerve be-low the knee did not show a decrease in MF, however,probably because the sacral roots were not cut. The IDwas not as high as in ischemia, but at certain levels itwas elevated. Although not tested, one might expecta different pattern of fiber loss in outer and inner con-tour areas in ischemia as compared with rhizotomy.Central fascicular degeneration has been reported indiabetic cranial third nerve palsy,22 in necrotizing an-giopathic neuropathy,23 and in experimental ischemicneuropathy. 24,25

No fiber loss was demonstrated in galactose neuropa-thy, differing from acute and chronic ischemia and rhi-zotomy. Similar to them, however, it showed an increasein the CV and ID, but not as large an increase. Inmarked contrast to what is found in ischemia, densityis decreased in outer, as compared with inner, contourareas. 15

Finally, no increase in the variability of fiber densitywas demonstrated in lead neuropathy.

References

1. Erlanger J, Gasser HS: Electrical Signs of Nervous Ac-tivity. Philadelphia, University of Pennsylvania Press,1933

2. Dyck PJ, Karnes J: Computer imaging for morphome-try of neuron columns and fiber tracts in neurobiologyand pathology. Trends in Neurosciences 1981, 4:138-141

3. Zimmerman IR, Karnes JL, O'Brien PC, Dyck PJ: Im-aging system for nerve and fiber tract morphometry:Components, approaches, performance and results. JNeuropathol Exp Neurol 1980, 39:409-419

4. Tuczinski H, Friede RL: Internodal length in ventral rootsof bovine spinal nerves vary independently of fiber calibre.J Anat (In press)

5. Dyck PJ, Karnes J, Lais A, Lofgren EP, Stevens JC:Pathologic alterations of the peripheral nervous sytemof humans, Peripheral Neuropathy. 2nd edition. Editedby PJ Dyck, PK Thomas, EH Lambert, R Bunge.Philadelphia, W. B. Saunders, 1984, pp 760-870

6. Ohta M, Ellefson RD, Lambert EH, Dyck PJ: Heredi-tary sensory neuropathy, type II: Clinical electrophysio-logic, histologic and biochemical studies of a Quebec kin-ship. Arch Neurol 1973, 29:23-27

7. Dyck PJ, Beahrs OH, Miller RH: Peripheral nerves inhereditary neural atrophies: Number and diameters ofmyelinated fibers. Presented at the 6th International Con-gress of Electroencephalography and Clinical Neu-rophysiology, Vienna, Austria, September 5-10, 1965

8. Nichols PC, Dyck PJ, Miller DR: Experimental hyper-trophic neuropathy: Change in fascicular area and fiberspectrum after acute crush injury. Mayo Clin Proc 1968,43:297-305

9. Ohnishi A, Schilling K, Brimijoin WS, Lambert EH, Fair-banks VF, Dyck PJ: Lead neuropathy: 1. Morphometry,nerve conduction and choline acetyltransferase transport:New findings of endoneurial edema associated with seg-mental demyelination. J Neuropathol Exp Neurol 1977,36:499-518

10. Macagno ER, Levinthal C, Sobel I: Three-dimensionalcomputer reconstruction of neurons and neuron assem-blies. Ann Rev Biophys Bioeng 1979, 8:323-351

11. Boyle PJR, Whitlock DG: Computer Analysis of Neu-ronal Structures. Edited by RD Lindsay. New York, Ple-num, 1977, pp 133-148

12. Spencer PS, Thomas PK: The examination of isolatednerve fibers by light and electron microscopy with obser-vation on demyelination proximal to neuromas. Acta Neu-ropathol (Berl) 1970, 16:177

13. Dyck PJ, Lais A: Electron microscopy of teased nervefibers: Method permitting examination of repeating struc-tures of same fiber. Brain Res 1970, 23:418-424

14. Dyck PJ, Jedrzejowska H, Karnes J, Kawamura Y, LowPA, O'Brien PC, Offord K, Ohnishi A, Ohta M, PollockM, Stevens JC: Reconstruction of motor, sensory and au-tonomic neurons based on morphometric study of sam-pled levels. Muscle Nerve 1979, 2:399-405

238 DYCK ET AL AJP * Novenmber 1984

15. Nukada H, Dyck PJ: Microsphere embolization of nervecapillaries and fiber degeneration. Am J Pathol (In press)

16. Perry JN, Mead R: On the power of the index of disper-sion test to detect spatial pattern. Biometrics 1979,35:613-622

17. Dyck PJ, Nukada H, Lais AC, Karnes JL: Permanentaxotomy: A model of chronic neuronal degenerationpreceded by axonal atrophy, myelin remodeling and de-generation,5 pp 760-870

18. Dyck PJ, Lambert EH, Nichols PC: Quantitative meas-urement of sensation related to compound action poten-tial and number and sizes of myelinated and unmyeli-nated fibers in sural nerves in health, Friedreich's ataxia,hereditary sensory neuropathy, and tabes dorsalis, Hand-book of Electroencephalography and Clinical Neu-rophysiology. Vol 9. Edited by WA Cobb. Amsterdam,Elsevier Publishing Co., 1971, pp 83-118

19. Dyck PJ, Lambert EH: Compound action potentials ofsural nerve in vitro in peripheral neuropathy,5 p 427-441

20. Gutmann E, Sanders FK: Recovery of fiber numbers anddiameters in the regeneration of peripheral nerves. J Phys-iol (Lond) 1942-43, 101:489

21. Cragg GB, Thomas PK: Changes in conduction velocityand fibre size proximal to peripheral nerve lesions. J Phys-iol (Lond) 1961, 157:315

22. Dreyfus PM, Hakim S, Adams RD: Diabeticophthalmoplegia: Report of case, with postmortem studyand comments on vascular supply of human oculomo-tor nerve. Arch Neurol Psychiatr 1957, 77:337

23. Dyck PJ, Conn DL, Okazaki H: Necrotizing angiopathicneuropathy: Three-dimensional morphology of fiber de-generation, related to sites of occluded vessels. Mayo ClinProc 1972, 47:461-475

24. Korthals JK, Wisniewski HM: Peripheral nerve ischemia:Part 1. Experimental model. J Neurol Sci 1975, 24:65

25. Korthals JK, Korthals MA, Wisniewski HM: Peripheralnerve ischemia: Part 2. Accumulation of organelles. AnnNeurol 1978, 4:487