Distribution of different fibre types in human skeletal muscles

Journal of the Neurological Sciences, 1984, 65:353-365 Elsevier

353

Distribution of Different Fibre Types in Human Skeletal Muscles A Statistical and Computational Study of the Fibre Type Arrangement in M. Vastus Lateralis of Young, Healthy Males Jan Lexell x,2, David D o w n h a m 3 and Michael SjOstrOm2 Departments of lAnatomy and 2Neurology. University of Umett (Sweden) and 3Department of Statistics and Computational Mathematics, Universityof Liverpool (Great Britain) (Received 6 December, 1983) (Revised, received 11 May, 1984) (Accepted 11 May, 1984)

SUMMARY To test whether the arrangement of fibre types in the human muscle (m. vastus lateralis) from clinically healthy and young males can be regarded as random, fascicles at different parts of the muscle and with different fibre type proportions were studied. The randomness of the arrangement of fibre types was assessed by the number of enclosed fibres in a fascicle and, on the basis of a model, tested by simulating muscle cross-sections using a microcomputer. The fibre type proportion was found to vary within a fascicle, so the original model for the test of randomness was modified to allow for different fibre type proportions on the border of the fascicle and internally. The effect of different sizes of the fibre types was also considered. The various aspects considered had only a marginal effect on the original model. For this muscle (m. vastus lateralis) the arrangement of fibre types was therefore considered random. Thus, a sample from this muscle, taken from individuals of the same sex and age group, can be tested for non-randomness, as an ~adication of a successive denervation and reinnervation process.

Correspondence to: Dr. Jan Lexell, Department of Anatomy,University of Ume~t, S-901 87 Ume~t, Sweden. This work was supported by grants from Gun and Bertil Stohne Foundation, Hans and Loo Osterman Foundation, Swedish MS Foundation, K, O. Hansson Foundation, The Research Council of the Swedish Sports Federation and The Swedish Medical Research Council. 0022-510X/84/$03.00 © 1984 Elsevier Science Publishers B.V.

354

Key words: D i a g n o s i s , c o m p u t e r a s s i s t e d - H i s t o c y t o c h e m i s t r y - M i c r o c o m p u t e r s - M u s c l e denervation

-

Muscles

-

Needle

biopsy -

Nerve

degeneration

-

Nerve

regeneration

INTRODUCTION

The human skeletal muscle is composed of fibres of two main types, type 1 (ST) and type 2 (FT), which in a cross-section of a normal muscle form a mosaic pattern (Fig. la). A change in this mosaic pattern, with the formation of large groups of one histochemical type ("fibre type grouping") (Fig. lb), is commonly regarded as evidence of a neuropathological process, possibly caused by the reinnervation of denervated individual muscle fibres. Lexell et al. (1983a) defined fibre type grouping on the basis of randomness in terms of the numbers of enclosed fibres (Jennekens et al. 1971), used a model based upon hexagonal-shaped fibres (Johnson et al. 1973) to study the statistical properties of these numbers, and described a test that simulates muscle cross-sections on a microcomputer, to distinguish muscles with fibre type grouping from those with random arrangements of fibre types. In this paper, the overall aim is to test whether the arrangement of fibre types in m . vastus lateralis, from clinically healty, young men can be regarded as random. If so, non-randomness could be indicative of a muscle exhibiting a successive denervation and reinnervation process. The ability to recognise this, particularly in the early stages, could then be of great benefit for clinical diagnosis and in the study of processes affecting the fibre type arrangement. As the proportion of fibre types varies systematically within a muscle (m. v a s t u s lateralis) (Lexell et al. 1983b), the fibre type arrangement in one part of the muscle may differ from that in another part. This could lead to error in the conclusions if only one small muscle sample is analysed. With living muscles the sections would be obtained

Fig. 1. a: micrograph from a cross-section of a whole human m. vastus lateralis with the two different fibre types, type I (lightly stained) and type 2 (heavily stained), forming a mosaic pattern, b: micrograph from a cross-section of a whole human m. vastus lateralis showing excessive grouping of both fibre types.

355 by one of the two principal biopsy techniques, the~needle technique or the open surgical technique. In this study, thin cross-sections of whole autopsied muscles, prepared by a recently described technique (Henriksson-Larsrn et al. 1983; Lexell et al. 1983b) are used. From these cross-sections, sample areas at different sites, and with different fibre type proportions, are selected. Data from each of these areas are then tested for randomness. Muscle fibres belonging to one motor unit are of the same type and likely to be located within the same fascicle. Each fascicle is, therefore, treated separately. The proportions of type 1 and type 2 fibres are calculated for each fascicle and used to test the fibre type arrangement for randomness (Lexell et al. 1983a). In the same study, a difference in the proportions of the fibre types on the border of the fascicles and internally is reported. The method of analysis is modified to allow for such a difference. The effect of different sizes of the fibre types is also considered. MATERIALS AND METHODS

Materials M. vastus lateralis from the right leg of 5 previously physically healthy males (mean age 30 years, age range 26-35) who had suffered a sudden accidental death, were extirpated less than 3 days post-mortem (storage + 6 °C). None of the individuals had a history of neuromuscular disease and there was no evidence of pathological abnormalities either at the postmortem examination or the extirpation of the muscles. Preparative procedure A slice about 10 mm thick, was cut from each muscle, at a distance of approximately 200 mm from the origin of the muscle. Each slice was then cut across the middle giving two halves of the slice. Each half of the slice was further treated using the technique for the preparation of large sections, previously described by HenrikssonLarsrn et al. (1983) and Lexell et al. (1983b). Cross-sections, of approximately 15 #m, were stained for myofibrillar adenosine triphosphatase (mATPase) at pH 10.4 to visualize type 1 (lightly stained) and type 2 (heavily stained) fibres (Fig. la). Measurement of total number of fibres and relative occurrence of the two fibre types In every 48th square millimetre of the cross-section, the numbers of type 1 and type 2 fibres were counted. Estimates of the total number of fibres and of the proportion of type 1 fibres of the whole cross-section are then readily available from these counts. Sampling procedure In every whole muscle cross-section, 5 areas were chosen, each containing several fascicles. The average number of fibres for the areas is 1308 with a range of 599-2979. Three of these five areas were chosen, one superficially, another from the middle and the third from the deep parts of the cross-section of the muscle. The other two areas were selected so that one had a high proportion of type 1 fibres and the other a high proportion of type 2 fibres.

356 All parts of each area were photographed in the microscope and an image of the whole area was formed. All fibre counts were then obtained from these photographs.

Analysis of fibre type arrangements Each area comprised several fascicles which were easily identified. The fibres on the border of a fascicle are here called "boundary fibres"; all remaining fibres are called "internal fibres". For each fascicle, the number of boundary fibres was counted and the proportion of type 1 boundary fibres was calculated; the equivalent quantities for type 1 internal fibres were similarly determined. The number of fibres and the proportion of type 1 fibres were calculated in turn for each whole fascicle. An "enclosed fibre" is a fibre that is surrounded entirely by fibres of the same histochemical type (Jennekens et al. 1971; Lexell et al. 1983a). In each fascicle the number of enclosed fibres of each type was counted. Simulation For the computer simulations, a standard ABC 800 (Luxor AB, Sweden) was used. Where the proportion of type 1 fibres is assumed to be constant throughout a fascicle, the model formulated by Johnson et al. (1973) and the simulation method described by Lexell et al. (1983a) are appropriate for the study of the number of enclosed fibres. To allow the proportion for the boundary fibres to differ from that for the internal fibres, the model and simulation program must be modified in an obvious way. The observed data were analysed for both models using both simulation programmes. For convenience the original and the modified models are called A and B, respectively. RESULTS

General morphology Muscle fibres were tightly packed forming a mosaic pattern. The fascicles were well preserved. Cracks apparent at macroscopic level usually ran between individual fascicles, and, even when they were formed inside fascicles, they did not interfere with the analysis. With very few exceptions, the shape and size of the fibres appeared normal. Total number of fibres and relative occurrence of the two fibre types The number of squares examined per whole muscle cross-section, the mean number of fibres per square millimetre, the estimated number of fibres in each muscle cross-section, and the proportion and range of type 1 fibres are presented in Table 1. These results are all consistent with results observed elsewhere (Lexell et al. 1983b). Total number of fibres and fibre type proportions in fascicles The numbers of fibres and the proportions of type 1 fibres for both the boundary and the internal fibres of each fascicle of the cross-sections are given for subjects D and E in Table 2, which also includes the equivalent quantities for each of the whole fascicles. The different areas are referred to as "S" (superficial), " M " (middle), "D"

357 TABLE 1 TOTAL NUMBER OF FIBRES AND RELATIVEOCCURRENCEIN CROSS-SECTIONSOF WHOLE M. VASTUS LATERALIS OF 5 MALE INDIVIDUALS Subject and age (years)

Area examined a (mm2)

Mean number of fibres/mm2

A26 B 34 C 30 D27 E 35

81 91 71 86 74

97 127 134 104 120

Mean ( + SD) for all 5 individuals 30 + 4 81 + 8 116 + 16

Total number of fibresb

Proportion oftype 1fibres ~o ± SD

Range

377000 555000 457000 429000 426000

46 53 53 46 45

27-69 21-84 23-76 26-67 23-84

449000 + 66000

48.5 + 4

± ± ± ± ±

9 13 11 9 11

a Corresponds approximatelyto 1/48 of the total cross-sectional area of the muscle. b Calculated by multiplying(a) by the mean number of fibres/mm2 and by a factor of 48 (cf. a).

(deep), "1" (high proportion of type 1 fibres) and "2" (high proportion of type 2 fibres). For the 5 subjects, the range of fascicle sizes is 36-1529 fibres and the range of the proportions of type 1 fibres for the fascicles is 23Yo-80~o. If the numbers of boundary and internal fibres in a fascicle are N s and N~ respectively, then the total number of fibres, NT, is given by N T = N B + N r If the proportions of type 1 fibres amongst the boundary and internal fibres are PB and P~ respectively, then the proportion of type 1 fibres in a fascicle, PT say, is given by PT = (NBPB + NIPI)/NT. The proportion of type 1 fibres on the boundary is less than the proportion for internal fibres (PB < PI) for 87 of the 105 fascicles, virtually the same in 6 and greater in the remaining 12. Because the number of boundary fibres is usually considerably less than the number of internal fibres, the proportion of type 1 internal fibres differs in most fascicles only marginally from the proportion for the whole fascicle.

Number of enclosed fibres The observed number of enclosed fibres of each type for each fascicle is given for subjects D and E in Table 2. The expected number of enclosed fibres depends upon the underlying model. The two models considered here, and summarized below, have the common assumption that each fibre is a regular hexagon lying in a beehive design. (a) Constant proportion of type I fibres. For this model, a fibre is type 1 with a probability PT and type 2 with probability (1 - PT) where PT is constant throughout the fascicle. The expected number of enclosed fibres is N~P7. To obtain the significance level, 100 configurations with N I internal fibres were simulated and the number of enclosed fibres computed for each configuration. Rough 5 ~o and 1 Yo significance limits were then available. Where the significance level of the observed number of enclosed

S

D

D

M

Area

Subject

a b c d e a b c d a b c d a b a b c d e f

Fascicle

155 165 197 221 95 350 376 214 489 250 134 315 259 360 102 948 260 122 507 267 521

32 41 26 35 51 48 51 57 47 50 63 58 57 66 75 38 33 21 33 25 34

62 71 77 76 55 81 79 68 103 71 51 64 66 82 52 150 150 50 117 69 118

26 32 19 37 27 35 71 47 48 51 49 44 53 50 64 29 29 28 21 25 49

(%)

(n)

(n)

(90)

Boundary

Internal

The data for subjects A, B and C are available on request.

217 236 274 297 150 431 455 282 592 321 185 379 325 442 154 1098 410 172 624 336 639

(n)

Whole

30 39 24 35 42 45 54 54 47 50 59 56 56 63 71 37 32 23 31 25 37

(%)

0 0 0 0 1 0 3 0 0 1 3 2 3 14 14 0 0 0 0 0 1

7 5 25 7 2 1 3 0 3 0 0 1 0 1 0 21 9 8 27 30 24

0.03 0.23 0.01 0.14 0.22 1.31 5.03 2.87 2.48 1.95 3.33 5.44 4.47 14.18 9.28 0.90 0.09 0.00 0.14 0.02 0.49

1

2

Type

1

Model A

Observed

Number of enclosed fibres

12.76 5.19 28.85 10.83 2.10 5.33 1.64 0.93 5.74 1.95 0.26 1.01 0.83 0.34 0.02 37.34 17.48 19.58 37.75 35.64 20.52

2

0.05 0.27 0.02 0.15 0.50 1.83 4.04 3.76 2.50 1.98 4.48 6.36 4.89 17.73 11.73 1.01 0.10 0.00 0.19 0.02 0.34

1

Model B

11.18 4.69 25.79 10.61 1.10 4.07 2.20 0.68 5.70 1.93 0.17 0.84 0.74 0.24 0.01 35.03 16.88 21.80 33.50 35.64 25.83

2

TOTAL NUMBER OF FIBRES AND PROPORTIONS (TYPE 1 FIBRES) INTERNALLY A N D ON THE BOUNDARY FOR EACH FASCICLE A N D IN WHOLE FASCICLES FOR EACH AREA, OBSERVED A N D EXPECTED NUMBER OF E N C L O S E D FIBRES A N D T H E S I G N I F I C A N C E LEVELS FOR BOTH METHODS

TABLE 2

oo

M

144 116 40 121 202 80 55 19 72 134 602 230 361 567 215 63 45 48 34 32 402 357 294 500 414

65 63 50 66 46 45 6O 74 39 47 38 47 45 63 58 68 62 44 53 59 54 60 60 36 40

60 38 32 49 74 37 47 17 39 68 111 71 74 109 68 36 27 34 26 32 86 89 64 100 77

40 60 25 59 39 41 55 71 26 37 30 38 34 38 50 42 37 39 39 31 45 46 53 31 34

204 154 72 170 276 117 102 36 111 202 713 301 435 676 283 99 72 82 60 64 488 446 358 600 491

57 62 39 64 44 43 58 72 34 43 37 45 43 59 56 59 53 41 47 45 52 57 59 35 39

7 4 1 16 10 7 5 6 1 0 0 0 0 10 4 1 0 0 0 0 1 4 5 0 0

1 1 2 2 12 12 1 0 8 9 !0 3 4 0 0 0 0 0 0 0 1 0 3 16 13

2.82 4.09 0.05+ 5.32* 0.64* 0.22* 1.21 1.91 0.04 0.36 0.57 0.86 0.98 14.11 3.71 1.57 0.53 0.09 0.17 0.12 4.13 6.98 7.32 0.32 0.57 0.39 0.13 1.26 0.09 + 3.49* 1.56" 0.13 0.00 3.93 2.62 23.71 3.50 7.06 1.10 0.69 0.12 0.23 1.19 0.40 0.49 2.36 0.97 0.57+ 24.51 13.01

5.23 4.43 0.08 6.06 + 0.75* 0.27* 1.33 2.14 0.07 0.55 0.64 1.04 1.23 19.60 4.36 2.74 0.97 0.13 0.26 0.22 5.03 8.97 7.84 0.37 0.64

0.17 0.12 0.63 0.08* 2.98* 1.30" 0.11 0.00 2.84 2.23 22.27 3.01 5.99 0.73 0.56 0.05 O.ll 0.94 0.26 0.18 1.91 0.70 0.52 + 22.70 12.04

360 fibres was less than 10~o, a further 500 simulated configurations permitted refinement of the limit. The computer program is the same as that used previously (Lexell et al. 1983a). The expected numbers of type 1 and type 2 enclosed fibres are given in Table 2 for each of the 46 fascicles. Significance at the 1 ~o level is indicated by "*" and at the 5 ~o level by °' + ", but no indication is given of non-significance as the vast majority of fascicles are in this category. As fibre type grouping causes more enclosed fibres than might be expected in a random arrangement of fibre types, one-tailed significance tests are used. (b) Differentproportions of type 1fibre. For model B, a boundary fibre is type 1 with probability PB and type 2 with probability (1 - PB), and an internal fibre is type 1 with probability P~ and type 2 with probability (1 - PI). By assuming different shapes of fascicles, the expected number of enclosed fibres was seen to be approximately NI P7 - NBPIS(P~ - P~) - - this particular algebraic form has an immediate physical (and plausible) explanation. To obtain the significance levels, 100 configurations with N~ internal fibres and approximately N R boundary fibres were simulated. Where the significance level of the observed number of the enclosed fibres was less than 10~o, a further 500 simulated configurations permitted refinement of the limit. The computer program required minor modification to accommodate the different probabilities. The results for model B are presented in the same manner as for model A: the expected numbers of enclosed fibres, and an indication of significance, if any, are given for each of the fascicles in Table 2. Again one-tailed significance tests are used. (c) Salientfeatures. For each fascicle, the distribution and the mean of the numbers of enclosed fibres were noted for the simulated configurations. In addition, we observed when the number of enclosed fibres was "significantly too few". As the results are not central to the argument, they are omitted from Table 2 but reference is made to them in the ensuing paragraphs. For both models, the observed numbers of enclosed fibres are more frequently less than their calculated values rather than greater. This is consistent with a distribution skewed to the left: the mode and median are less than the mean. In the simulation study, the distributions of the number of enclosed fibres of both types usually showed this property. For 87 of the 105 fascicles, the expected number of type 1 enclosed fibres in model B is greater than that for model A, reflecting the fact that the proportion of type 1 fibres is greater internally than on the boundary. The means calculated from the simulated configurations also showed the same property, albeit less strongly. The frequency of significant results at the 5 ~o level is consistent with a set of fascicles for which the fibre types have been randomly assigned. A similar consistency is shown in the frequency of significantly too few enclosed fibres. When the fibre type grouping is significant, both models usually give significant results, indicating that the two models do not yield materially different conclusions. For two fascicles the numbers of neither type 1 nor type 2 enclosed fibres were significant separately, but their total numbers were significant with levels just less than 5 ~o.

361 TABLE 3 NUMBERS OF NEIGHBOURS OF FIBRES IN ONE CROSS-SECTION OF A WHOLE

M. VASTUS LATERALIS Area

Fascicle

Type 1 Number of internal fibres

Type 2 Number of neighbours Mean

Variance

Number of internal fibres

Number of neighbours Mean

Variance

a b c d e

50 68 51 77 48

5.78 5.82 5.71 6.03 5.73

0.50 0.89 0.81 0.60 0.33

105 97 146 144 47

6.13 5.97 5.86 5.92 6.04

0.64 0.38 0.63 0.61 0.48

M

~i b c d

168 192 122 230

5.87 5.76 5.79 5.77

0.76 0.63 0.43 0.50

182 184 92 259

5.84 5.79 5.79 5.87

0.45 0.69 0.52 0.60

D

a b c d

125 84 183 I48

5.73 5.67 5.82 5.78

0.36 1.00 0.69 0.69

125 50 132 111

5.91 6.00 5.86 5.96

0.76 0.625 0.63 0.71

a b

238 77

5.73 5.94

0.63 0.61

122 25

5.89 5.84

0.55 0.56

a b c d e f

360 86 26 167 67 177

5.88 5.81 5.85 5.87 5.96 5.73

0.61 0.55 0.46 0.71 0.77 0.70

588 174 96 340 200 344

5.88 5.89 5.82 5.89 5.89 5.95

0.56 0.63 0.59 0.56 0.45 0.56

Effects of varying fibre sizes If fibres of one type are consistently smaller than fibres of the other type, then the implicit a s s u m p t i o n that the two fibre types have on average the same n u m b e r of neighbours becomes untenable a n d the method of analysis for both models could become invalid. Thus, for the 21 fascicles of the muscle from subject D, for which results are given in Table 2, the n u m b e r of neighbours of each fibre were counted. The m e a n and variance of the n u m b e r of neighbours for both types of fibres in each fascicle are given in Table 3. F o r 14 fascicles the m e a n n u m b e r of neighbours of type 1 fibres is less than that for type 2 fibres, the same for 2 fascicles, a n d greater for 5 fascicles. Although there is an indication of a systematic difference, its size is so small that it does not influence the results.

Test of the models T o illustrate that the method identifies fibre type grouping, a whole cross-section from m. vastus lateralis of an 82-year-old male was prepared and three fascicles sampled

289 141 290

47 34 66

84 69 92

31 38 48

(~o)

(n)

(n)

(~o)

Boundary

Internal

373 210 382

(n)

Whole

43 35 62

(~o)

a The observed number of enclosed fibres is significantly large at the 1 ~o level.

a b c

Fascicle

Percentage values represent proportions of type 1 fibres.

Type

1 1 12

1

Observcd

7 22 6

2

0.79 0.09 10.21

1

Model A

Expected

Number of enclosed fibres

DATA AND RESULTS FOR 3 FASCICLES FROM M. VASTUS L A T E R A L I S OF AN 82-YEAR-OLD MAN

TABLE 4

5.65 6.91" 0.33*

2

1.22 0.08 13.46

1

Model B

4.08 7.25 a 0.22 a

2

k.o ix9

363 in the same way as for the muscles from the five young men. The results of analysing these three fascicles are given in Table 4. The grouping of type 2 fibres is very strong in two of the three fascicles.

DISCUSSION The recognition of, and the efforts to quantify, fibre type grouping in biopsied muscle samples are unsatisfactory, since no reliable method of testing has been available. In the In'st paper in this series (Lexell et ai. 1983a), fibre type grouping is defined on the basis of randomness, and a statistical test is described. Before the model and the methods of analysis can be widely used, the range of applicability must be ascertained. If the proportion of a fibre type is high, then large groups are likely to occur, but this might not be fibre type grouping. This term is used here when for an observed proportion the arrangement of fibre types is non-random at a given significance level. The occurrence of a high fibre type proportion could itself be the result of a successive denervation and reinnervation process, but it could also be due to a natural adaptive response in the muscle. High proportions of each fibre type and a systematic fibre type distribution can both be found in a muscle (m. vastus lateralis) from healthy young individuals (Lexell et ai. 1983a). Therefore, we wanted to study whether the arrangement of fibre types is random in different areas of the muscles, and assess the extent to which high fibre type proportions and fibre type grouping appear together in this muscle. Several fascicles contain a high proportion of one fibre type and consequently many enclosed fibres of this type. The numbers of enclosed fibres are non-significant for all of these fascicles. No systematic effects on the fibre type arrangement as assessed by statistical significance could be found when sample areas at different sites in the muscle cross-sections were compared. If the fibre type proportions vary systematically within, a fascicle, the model could be invalid with consequent errors in the conclusions. In the analysis of each fascicle, a majority of them showed a non-negligible difference between the proportions of fibre types on the boundary and internally. (To the best of our knowledge this fmding has not been reported previously for human muscles and we intend to discuss this elsewhere.) The model is easily modified to accommodate such a difference. Unfortunately, only an approximation of the expected numbers of enclosed fibres can be derived, but the arrangements can still be tested using simulated configurations. Although the results are different in detail, there are no noteworthy differences between the two analyses for each fascicle. To apply these methods of testing, whole fascicles should be analysed, but few conclusions can be made from the analysis of a single fascicle. If the fibre types are randomly arranged in a muscle, then the observed numbers of enclosed fibres are likely to be less than their expected values more frequently than greater, because the distribution appears to be skewed to the left. The numbers of enclosed fibres display these properties for most of the fascicles. In only one muscle

364 (subject B, age 34 years) were the observed numbers of enclosed fibres more frequently greater than their expected numbers rather than less. If fibre types within the f a s c i c l e s of a muscle are randomly assigned, then from the definition of significance the arrangements of roughly 5 ~o of the fascicles should be significant at the 5 ~o level. Indeed, this is what happens for the fascicles of the five muscles in this study. However, 5 of the 6 fascicles which show a significant non-random arrangement are found in the same muscle, which is from the oldest man, 35 years old. Whether these two occurrences are true signs of denervation and reinnervation, e.g. the onset of ageing, cannot be inferred since the range of ages and sample size are insufficient. The modified model increases the expected number of enclosed fibres for 87 of the 105 fascicles. Since consistently smaller type 1 fibres might also increase the expectations, there is the possibility of a cumulative effect. The numbers of neighbours for each fibre were counted to assess the possible effect of size differences between the fibre types. As seen in Table 3, the differences between the mean number of neighbours are small for each fascicle. To assess the cumulative effect, model B must be extended with additional assumptions, the choice of which obviously affects the validity of the conclusions. Although we have undertaken such an exercise, the basis of the argument is not sufficiently substantial for publication. Nevertheless, the evidence in Tables 2 and 3 indicates that a cumulative effect (if any) is influencing model B minimally. In summary, the results of testing the fibre type arrangement using the original model, taking differences in fibre type proportions within various areas and the different fibre type proportions within a fascicle into account, and considering the effects of varying fibre sizes, all point towards two main conclusions. (i) The simplest model with the significance test, as described in the first paper (Lexell et al. 1983a), is robust enough to yield useful results. (ii) For this particular muscle and this particular age group and sex, the fibre type arrangement is, irrespective of the sampling site and fibre type proportions in various areas, and the fibre type proportion within fascicles and the size of the fibres, random as assessed by the number of enclosed fibres. Thus, it is possible to study an unknown sample from this muscle, taken from clinically healthy male individuals in this age group, and test for non-randomness as an indication of a denervation and reinnervation process. REFERENCES Henriksson-Lars6n, K., J. Lexell and M. SjOstrOm(1983) Distribution of different fibre types in human skeletal muscles, Part 1 (Method for preparation and analysis of cross-sections of whole m. tibialis anterior), Histochem. J., 15: 167-178. Jennekens, F. G..I., B.E. Tomlinson and J. N. Walton (1971) Data on the distribution of fibre types in five human limb muscles - An autopsy study, J. Neurol. Sci., 14: 259-276. Johnson, M.A., J. Polgar, D. Weightman and D. Appleton (1973) Data on the distribution of fibre types in thirty-six human muscles - An autopsy study, J. NeuroL Sci., 18:111-129. Jolesz, F. and F. A. Sreter (1981)Development,innervation and activityinduced changesin skeletal muscle, Ann. Rev. Physiol., 43: 531-552. Lexell, J., D. Downham and M. SjOstrOm(1983a) Distribution of different fibre types in human skeletal muscles - A statistical and computationalmodelfor the studyoffibre typegroupingand earlydiagnosis

365 of skeletal muscle fibre denervation and reinnervation, J. Neurol. Sci., 61: 301-314. Lexell, J., K. Henriksson-Lars6n and M. SjtistrSm (1983b) Distribution of different fibre types in human skeletal muscles, Part 2 (A study of cross-sections of whole m. vastus lateralis), Acta Physiol. Scand., 117: 115-122. Lexell, J., K. Henriksson-Lars6n, B. Winblad and M. Sj~)str6m (1983c) Distribution of different fibre types in human skeletal muscles - Effects of aging studied in whole muscle cross sections, Muscle and Nerve, 6: 588-595.