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Relations between axon length and axon caliber
Journal of the Neurological Sciences, 1984, 63:369-380
369
Elsevier
R E L A T I O N S B E T W E E N AXON L E N G T H AND AXON CALIBER "Is Maximum Conduction Velocity the Factor Controlling the Evolution of Nerve Structure?"
REINHARD L. FRIEDE, MANFRED BENDA, ACHIM DEWITZ and PETER STOLL Department of Neuropathology, University of G6ttingen, Robert-Koch-Str. 40, D-3400 G6ttingen (F.R.G.)
(Received 14 August, 1983) (Revised, received 29 November, 1983) (Accepted 5 December, 1983)
SUMMARY A search was made for any existent relationship between the length of a nerve fiber and the caliber of its axon. This was done in the hope of defining morphological parameters useful for assessing conduction time. Four fiber populations were examined: (1) phrenic fibers in rat and rabbit during different phases of body growth; (2) phrenic fibers of mature animals of greatly different body size including mouse and cow; (3) rat intercostal nerves which vary in length by a factor exceeding 5 due to the funnel-shape of the thorax; and (4) ventral root fibers of the cow. In all of these fiber populations, there was no evidence for a direct relationship between the length of a fiber and its caliber. Rather, a tendency was noted for fiber caliber to approach certain ceilings independent of length. These data, seen in conjunction with other information on fiber structure, cast serious doubt on the widely accepted concept that maximum conduction velocity is the factor controlling nerve structure. A much more likely factor controlling the structure of myelinated nerve fibers is the capacity to modulate information by frequency coding of impulses.
Key words: A x o n - Intercostal nerve fibers - M a x i m u m conduction velocity - Nerve fiber - Phrenic nervefibers - Ventral rootfibers
These studies were financiallysupported by the Deutsche Forschungsgemeinschaft(Fr. 609/1-1). Address for reprint requests: Reinhard L. Friede, M.D. (address above). 0022-510X/84/$03.00 © 1984 Elsevier SciencePublishers B.V.
370 INTRODUCTION An elementary aspect of the structure of peripheral nerves is their composition of myelinated fibers with very different calibers. Bearing in mind the basic nature of this phenomenon, there is surprisingly little information concerning the factors which control the caliber of a myelinated fiber as explored by Fernand and Young (1951). Conduction velocity is known to increase with fiber caliber. Accordingly, neurobiologists have always been ready to accept the conclusion that the acquisition of myelin sheaths, with the corresponding increase in axon caliber, is a phylogenetic advancement which has the purpose to increase conduction velocity. However, if conduction velocity is maximized, why isn't it maximized in all fibers? Moreover, if there is a biological tendency to increase conduction velocity, its efficiency should be measured by assessing conduction time, since an increase in velocity is only meaningful in reference to the distance over which the impulse is to be carded. If these premises are considered, there is also very little information on the relations between axon caliber and axon length in vertebrates, and only a few studies have been made on invertebrates. The present investigation was specifically designed to search for any existent relationship between the caliber and the length of an axon, with the aim of providing anatomical data useful for assessing conduction time. The relation between length and caliber may help to understand how axon caliber is controlled. Such data are also important for understanding the configuration of internodes and the related problem of the myelin sheath's dimensions. MATERIALAND METHODS For the developmental and adult studies of phrenic nerves, the left nerve was dissected and measured from the point of entrance into the diaphragm to the origin of its C4 root from the spinal cord, keeping tension as uniform as possible. As the segmental origin of the phrenic nerve in different species is somewhat controversial, it may be stated that for all of the species studied here, the main roots of origin were at C3 to C5 (Goshgarian and Rafols 1981). A segment of the midthoracic portion of the left nerve, sufficiently remote from the diaphragm to avoid terminal branching, was taken after preliminary fixation in situ with glutaraldehyde, then postfixed, osmicated and embedded in Araldite. Semithin sections were prepared and fiber calibers were determined by tracing the inner circumference of the myelin sheath with a Kontron videoplan, measuring 100 fibers per specimen. All values were expressed as the diameters of fibers having circular profiles. The degree of shrinkages or non-circularity, usually of 0.8, was thus eliminated from comparisons. If the data shown here are to be compared with data from native non-embedded fibers, they should be corrected by a factor of 0.70, which accounts for the shrinkage during dehydration and embedding. The fresh weight of the diaphragm was determined after its dissection from the rib cage and viscera; no efforts were made to separate its tendinous portions. Rat intercostal nerves are readily discernable underneath the pleura, where they may be prefixed in situ by filling the thoracic cavity with glutaraldehyde. The funnel-
371 shaped rat thorax accounts for a stepwise increase in length from one intercostal nerve to the next. The length of the nerves was measured from their exit at the cord to the osteochondral line of the ribs, and to the midline, respectively. Specimens were selected at the nerve's entrance into the subpleural tissue and at midlevel between this point and the most distal discernable fascicles of the nerve at the sternum. All intercostal nerves were sampled for two adult, male Sprague-Dawley rats, weighing 310 and 320 g. Bovine ventral roots from two cows were obtained from the slaughter house of the Institut far Tierzucht of the University of GOttingen. The cows were 8.3 and 8 years old, respectively, weighing 438 and 473 kg. Tissues were dissected within about 30 min of slaughtering; every other ventral root was harvested and fixed in glutaraldehyde. Processing of specimens of rat and bovine tissue was carried out as described above. Ninety fibers were measured for each given root. RESULTS
The phrenic nerve is a suitable model for studying the relations between fiber caliber and length; fiber caliber is readily determined for the predominant populations of thick fibers, and fiber length may be measured from the exit of the spinal roots to TABLE 1 P A R A M E T E R S O F R A T P H R E N I C NERVE S T R U C T U R E D U R I N G G R O W T H Age (days)
Weight (g)
Number of myelinated fibers
Fiber length (mm)
Axon diameter (circular profile) (#m)
Volume of axoplasm (106 #m 3)
Weight of diaphragm (g)
21
30
387 427 426
27 28 27
1.9 + 0.4 1.9 _+ 0.4 1.9 + 0.4
0.076 0.079 0.076
0.12 0.14 0.11
26
65
398 426 421
32 34 32
2.6 _+ 0.6 2.6 + 0.9 2.7 + 0.6
0.17 0.18 0.18
0.14 0.17 0.18
38
115
498 456 395
39 40 40
3.3 + 0.8 3.3 + 0.7 3.0 + 0.5
0.33 0.34 0.34
0.40 0.53 0.43
60
195
471 437 439
55 53 55
3.6 + 0.5 3.6 + 0.5 3.6 + 0.5
0.56 0.54 0.56
0.67 0.69 0.65
76
220
444 356 455
58 56 60
3.9 + 0.5 3.8 _+ 0.5 4.2 _+ 0.7
0.69 0.64 0.83
0.74 0.70 0.76
360
280
380 387 404
62 60 61
4.4 _+ 0.9 4.4 + 0.9 4.7 + 1.0
0.94 0.91 1.05
1.42 1.18 1.49
372
the entrance of the nerve into the diaphragm. The terminal portion of the fibers within the diaphragm represents a constant factor, as the motor endplates are arranged in a narrow zone which, for instance in the rat, is located approximately 2 mm from the nerve entrance (Nickel and Waser 1968). Developmental changes in the phrenic nerve The average number of myelinated nerve fibers in the phrenic nerve of the rabbit was 662, in the rat 425; the latter value agrees reasonably well with the 365 fibers stated by Lubifiska (1977) or the 404 + 48 fibres found by Langford and Schmidt (1983). The number of myelinated fibers did not change during the growth of the animals (Tables 1 and 2). Fiber length increased with body size. The increase in fiber length in the rat and rabbit was accompanied by a marked increase in axon caliber during initial postnatal growth. The rate of increase in caliber subsequently diminished, resulting in a parabolic curve, where particularly for the rabbit a 58 ~o increase in phrenic nerve length towards adult age was accompanied by only 12~o increase in caliber between the days 76 and TABLE 2 PARAMETERS OF RABBIT PHRENIC NERVE STRUCTURE D U R I N G GROWTH
Age
Weight
(days)
(g)
Number of myelinated fibers
Fiber length
Axon diameter (circular profile)
Volume of axoplasm
Weight of diaphragm
(mm)
(#m)
(10 6 #m 3)
(g)
42
763 646 704
38 35 38
2.4 ± 0.5 2.4 + 0.4 2.4 + 0.4
0.17 0.16 0.17
0.22 0.20 0.20
8
145
752 680 645
50 49 48
3.0 ± 0.5 3.4 ± 0.5 3.0 ± 0.5
0.35 0.44 0.34
0.61 0.68 0.70
14
260
675 627 554
56 54 54
3.5 ± 0.7 3.5 ± 0.6 3.6 __+0.6
0.54 0.52 0.55
1.17 1.33 1.20
26
500
642 734 731
68 70 67
3.9 + 0.6 3.9 ± 0.5 4.1 ± 0.5
0.81 0.84 0.88
1.99 1.82 1.92
42
1000
639 620 669
83 84 87
4.5 + 0.6 4.8 ± 0.8 4.7 ± 0.9
1.32 1.52 1.51
2.12 2.18 2.01
55
1550
585 604 782
97 99 96
5.2 ± 0.8 5.2 ± l.l 4.6 ± 0.9
2.06 2.10 1.60
5.50 5.70 5.50
210
4200
697 751 756
150 156 154
5.5 __+ 1.0 5.1 ± 0.8 5.3 ± 1.0
3.56 3.19 3.40
11.60 12.40 11.80
373
Rat
lb
c
o
3'o
i
I i
4o
so
6b
i
ro
Rabb
E 10
20
4321-
Lengh t
of phrenic nerve
(mm)
Fig. 1. Changes in the length of phrenic fibers during postnatal growth are compared with changes in the axon's caliber (expressed in #m for fibers having a circular profile). The corresponding ages are given in Tables 1 and 2.
360 (Fig. 1). There were substantial increases in the total volume of the axoplasm, by a factor of 13 in the rat and of 20 in the rabbit, for the periods studied. There were also corresponding increases in the weight of the diaphragm. Differences in phrenic nerve structure in species of different body size When comparing species of small body size with large ones, the number of phrenic fibers increased with body size, e. g. by a factor exceeding 10 between the mouse and the cow (Table 3). Fiber numbers for the dog were similar to those of Landau et al. (1962). There were corresponding increases in the weight of the diaphragm. A straight line relationship was found on plotting the cubic root of the diaphragm's weight against the number of myelinated phrenic fibers in the various species, indicating a consistency in the size of motor units, or, respectively, of axonal terminal branching (Fig. 2). The axons ofmyelinated phrenic fibers had essentially the same caliber in cat, dog, pig and cow, in spite of considerable differences in fiber length; the difference between cat and cow amounted to a factor of 4 (Fig. 3). Distinctly thinner axons were found in the mouse, rat and rabbit. Axons of large species contained considerably larger volumes of axoplasm than did those of small species, giving a factor of 71 for the mouse and the cow (Table 3). Rat intercostal nerves The intercostal nerves of the rat may be, on the whole, considered as constituting a functionally homogeneous fiber population having synchronized motor activity, but
374
TABLE 3 P A R A M E T E R S OF P H R E N I C NERVE S T R U C T U R E IN 7 SPECIES Number of myelinated fibers
Fiber length (mm)
Axon diameter (circular profile) (#m)
Volume of axoplasm (10 6 #m 3)
Weight of diaphragm
Cow
4616 3426 5 140
697 692 688
6.9 + 1.1 7.3 _+ 1.6 7.9 + 0.1
26.06 28.96 33.72
2345 2410 2250
Pig
2454 2403 1889
390 415 402
7.7 + 1.6 7.2 + 1.7 7.4 + 1.1
18.16 16.90 17.29
565 550 500
Dog
1524 1677 1784
350 375 385
6.2 + 1.2 6.8 + 1.1 6.4 + 1.0
10.57 13.62 12.39
80 87.5 90
Cat
887 923 1044
166 172 165
7.1 _+ 2.0 6.6 _+ 1.9 7.2 _+ 1.9
6.57 5.88 6.72
16.9 20.4 17.8
Rabbit
697 751 756
150 156 154
5.5 + 1.0 5.1 +0.8 5.3 + 1.0
3.56 3.19 3.40
11.6 12.4 11.8
Rat
404 380 387
61 60 60
4.7 _+ 1.0 4.7 + 0.9 4.4 + 0.9
1.05 0.94 0.91
1.49 1.42 1.18
Mouse
266 258 248
24 24 22
4.02 + 1.0 5.2 _+ 1.3 4.5 _+ 0.9
0.30 0.51 0.35
0.16 0.12 0.12
Species
.•
(g)
Cow
70oo-
32 ~" 5000
P~
i
~6
z
"
Dog
3000-
• Cat P---O Rabbit ~ 4 Rat Mouse . . . .
,
.
.
.
.
•
.
.
.
.
Weight o f d i a p h r a g m (g I
Fig. 2. The number of myelinated fibers in the phrenic nerve of different species is in a straight-line relationship to the cubic root of the weight of the diaphragm.
375
0 m0
%
4
"0
2
<[
10
20
30
40
50
60
70
Length of phrenic nerve ( c m )
Fig. 3. There is no direct relationship between the caliber of phrenic fibers (in #m, circular profiles) and the length of the phrenic nerve in species of different body size. Phrenic axons of the cat have nearly the same caliber as those of the cow, even though the latter are about 4 times longer.
':!
~lO-
I I
E i-
2
< I
I
I
I
I
I
! 10
! 12
e~ e* IF e*
e~
8
I 2
| 4
I 6
I 8
Intercostal nerves
Fig. 4. Rat intercostal nerves differ greatly in length due to the funnel-shaped rat thorax. The lower diagram shows the length of intercostal nerves measured from the exit of their roots at the cord to the osteochondral border (lower curve) and to the midline (upper curve) for each intercostal nerve in two rats. The upper diagram shows the means and standard deviations of the axon calibers in the same nerves,
individual nerves differ greatly in length. The distance from the root exit to the osteochondral border varied irregularly, but the total maximum length of the intercostal nerves from the cord to the most distal extensions varied by a factor of more than 5 from the 1st tot the 12th nerve, with fairly uniform increases in length for the nerves in between. When either the mean of axon calibers or the calibers of the thickest fibers were plotted for these intercostal nerves, there were clearly no changes of caliber that would correspond to a 5-fold increase in length (Fig 4).
376
=.. g
"o
1°t C
T
L
S
Spinal segments Fig. 5 Mean axon calibers for the thick myelinated fibers in 16 ventral spinal roots of the cow are pooled (two animals each) and compared with the mean and standard deviation for all ventral roots pooled. There is no significant segmental variation in fiber caliber.
Bovine ventral roots
Exact determinations of fiber length are not practical for the fibers in bovine ventral roots. Yet the fibers supplying the neck, trunk and extremities obviously differ greatly in length. The absence of data on length is compensated, to some extent, by the regular bimodal fiber spectra, which are favorable to exact determinations of axon caliber. The thick fibers form well-distinguished populations, having a definite Gaussian distribution. The populations of thin fibers may be neglected as they innervate the muscle spindles and also give origin to the substantial cervico-thoraco-sacral outflow of autonomic fibers The mean axon diameter of the thick ventral root fibers are shown in Fig. 5 per segment, and they are compared with the mean diameter of the entire pooled population of root fibers. There is no pattern corresponding to the length of the respective fiber populations, and means for individual roots were all within the narrow standard deviation of the pooled roots. DISCUSSION
It is known that certain axons effect spatial-temporal impulse synchronisation. In loligo, for instance, fibers vary in caliber and in conduction velocity to effect near synchronous contraction of the muscles (Pumphrey and Young 1938). In the teleost electromotor system, caliber and conduction properties of preterminal axon branches compensate for the differences in path length, synchronizing the discharge of the electric organ (Bennett 1968, 1971). Temporo-spatial impulse synchronisation may also be achieved by variation in fiber caliber and in internode length in preterminal axon arbors in the CNS (Waxman 1971, 1975; Waxman and Melker 1971; Desch6nes and Landry 1980). Generalized, these observations could bring the conclusion that human thoracic ventral roots have thinner axons than lumbar roots because their fibers are shorter
377 (Kawamura and Dyck 1977). Also, a parallel increase of fiber length and of conduction velocities in the kitten would render conduction time independent of nerve length (Ridge 1967). It would be justifiable to search for correlations between conduction velocity and body height (Campbell et al. 1981; Soudmand et al. 1982). However, all data obtained in the present study were in contradiction with this concept. The findings for rat intercostal nerves and for bovine ventral roots require no further comment, as both populations showed no relation whatsoever between fiber length and fiber caliber. Phrenic axons in species of very different body size differed in caliber by a factor of 1.55 in the adult mouse and the adult cat, but there were no further differences in axonal caliber in the cat and the cow, even though bovine fibers are four times as long. No convincing explanation was found for the differences in small and large species. Among the large species, there was no increase in fiber caliber when the fiber doubled or tripled in length, consistent with the classic observations of H~iggqvist (1948). The most complex situation was found for the developmental changes in the rat and rabbit phrenic nerves. A curvilinear relation was found between caliber and length, implying an early growth phase when both caliber and length increased, and a later maturation phase when growth in length continued, while growth in caliber subsided. The resultant parabolic curve is remarkably similar to that found by P.K. Thomas (1955) for nerve fibers in fishes of different body size. These latter observations are consistent with a biphasic pattern of caliber growth evident from Cottrell (1940) or from the electron-microscopic measurements of Schr0der et al. (1978), even though these studies did not include fiber length. In SchrOder's data, the thick fiber population of sural nerve had reached maximum diameter by the age of 5 years, long before the limb has reached its definitive length, with a slight decrease in fiber caliber thereafter. There is a corresponding rapid increase in conduction velocity during early growth (J.E. Thomas and Lambert 1960; Gamstorp 1963), followed by a slight decrease towards adulthood (Hakamada et al. 1982). In the kitten triceps surae neurons, a rapid increase in axon diameter before day 44 is followed by smaller increases towards adult values (Cullheim and Ulfhake 1979). In the rat's dorsal tail nerve, the conduction velocity levels off at 15 weeks, before definitive body size is reached (Oldfors and Ullman 1980). In the giant axon of the lobster, fiber caliber increased proportionally with fiber length, up to a given age, and conduction time remained constant (Govind and Lang 1976). Further increases in length were not accompanied by increases in caliber, with a consequent lengthening of conduction time. Funch et al. (1981) found a parabolic relation between body length and axon caliber in the giant axon of the goldfish, where axon caliber and conduction velocity actually decrease in fishes larger than 9.5 cm. A factor not considered so far is the extent of axon branching, which commences several centimeters before the nerve reaches the muscle (Eccles and Sherrington 1930). Axon caliber may accordingly vary with the size of the motor unit (Henneman and Olson 1965; Bagust 1974). The extent of branching of phrenic nerve fibers, however, appears to be rather constant, since the number of fibers in different species were in linear relation to the cubic root of the weight of the diaphragm (Fig. 2). Moreover, the
378 concept that axon caliber is controlled by the extent of terminal branching leads to gross inconsistencies when applied to sensory fiber populations. If one summons up the evidence reviewed so far, there is clearly no interdependence between the fiber length and the fiber caliber in mammalian nerves; instead, maximum fiber calibers tend to level off at certain ceilings, which are alike for populations of different length, or for species of different body size. The same conclusion could be made by studying the fiber population innervating a given skeletal muscle receiving fibers of greatly different caliber (Rexed and Therman 1948; Hgtgbarth and Wohlfart 1952; Richmond et al. 1976), although their length must be similar. It is appropriate, therefore, to examine the assumption that fiber caliber increased in order to accelerate conduction, Since Rushton's (1951) calculations in particular, there has been a strong trend to assume that "the attainment of maximum conduction velocity has been the controlling factor in the evolution of nerve structure". Velocity, however, is merely one among many parameters changing with fiber caliber, including also refractory periods, or the maximum frequency of impulses, respectively (Paintal 1966, 1967, 1973, 1978; Waxman and Bennett 1972). There is also an inverse relationship between the axon's diameter and the length of the afterhyperpolarisation of their cells (Eccles et al. 1958). Increased transmission velocity, therefore, could be only an epiphenomenon of the fiber's greater capacity to use frequency codes. With this change in the point of view, neural systems may be found in which caliber spectra are more in harmony with frequency coding than with controlling conduction time. In skeletal muscle, for instance, tonic and twitch fibers are known to receive nerve fibers having different conduction velocities (Eccles et al. 1958), but this difference may relate to the frequency of stimulation which is known to affect muscle fiber typing (Salmons and Vrbov~t 1969; Pette et al. 1973; Salmons and Srrter 1976; Hudlicka and Tyler 1980). The caliber of fibers innervating the tendon organs and the muscle spindles of a given muscle also corresponds to their characteristic impulse frequencies rather than to conduction times. For all these reasons, the widely accepted opinion that myelination primarily serves the purpose of increasing conduction velocity must be erroneous; a much more likely parameter determining fiber caliber is the capacity for transmitting higher impulse frequencies or frequency coding. Academic as this may seem, it is none the less crucial for the understanding of the relation between fiber structure and fiber function in health and disease.
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380 Ridge, R. M. A.P. (1967)The differentiation of conduction velocities of slow twitch and fast twitch muscle motor innervations in kittens and cats, Quart. J. Exp. Physiol., 52: 293-304. Rushton, W.A.H. (1951) A theory of the effects of fibre size in medullated nerve, J. Physiol. (Lond.), 115: 101-122. Salmons, S. and F.A. Sr6ter (1976) Significance of impulse activity in the transformation of skeletal muscle type, Nature (Lond.), 263: 30-34. Salmons, S. and G. Vrbovfi (1969) The influence of activity on some contractile characteristics of mammalian fast and slow muscles, J Physiol. (Lond.), 201: 535-549. SchrOder, J.M., J. Bohl and K. Brodda (1978) Changes of the ratio between myelin thickness and axon diameter in the human developing sural nerve, Acta Neuropath. (Berl.), 43: 169-178. Soudmand, R., L.C. Ward and T.R. Swift (1982) Effect of height on nerve conduction velocity, Neurology (Minneap.), 32: 407-410. Thomas, J.E. and E.H. Lambert (1960) Ulnar nerve conduction velocity and H-reflex in infants and children, J. Appl. Physiol., 15: 1-9. Thomas, P.K. (1955) Growth changes in the myelin sheath of peripheral nerve fibres in fishes, Proc. Roy. Soc. Lond. (Biol.), 143: 380-391. Waxman, S.G. (1971 ) An ultrastructural study of the pattern of myelination of preterminal fibers in teleost oculomotor nuclei, electromotor nuclei, and spinal cord, Brain Res., 27:189-201. Waxman, S.G. (1975) Integrative properties and design principles of axons, Int. Rev. NeurobioL, 18: 1-40. Waxman, S.G. and M.V.L. Bennett (1972) Relative conduction velocities of small myelinated and nonmyelinated fibres in the central nervous system, Nature (Lond.), 238: 217-219. Waxman, S.G. and R.J. Melker (1971) Closely spaced nodes of Ranvier in mammalian brain, Brain Res., 32: 445-448.
369
Elsevier
R E L A T I O N S B E T W E E N AXON L E N G T H AND AXON CALIBER "Is Maximum Conduction Velocity the Factor Controlling the Evolution of Nerve Structure?"
REINHARD L. FRIEDE, MANFRED BENDA, ACHIM DEWITZ and PETER STOLL Department of Neuropathology, University of G6ttingen, Robert-Koch-Str. 40, D-3400 G6ttingen (F.R.G.)
(Received 14 August, 1983) (Revised, received 29 November, 1983) (Accepted 5 December, 1983)
SUMMARY A search was made for any existent relationship between the length of a nerve fiber and the caliber of its axon. This was done in the hope of defining morphological parameters useful for assessing conduction time. Four fiber populations were examined: (1) phrenic fibers in rat and rabbit during different phases of body growth; (2) phrenic fibers of mature animals of greatly different body size including mouse and cow; (3) rat intercostal nerves which vary in length by a factor exceeding 5 due to the funnel-shape of the thorax; and (4) ventral root fibers of the cow. In all of these fiber populations, there was no evidence for a direct relationship between the length of a fiber and its caliber. Rather, a tendency was noted for fiber caliber to approach certain ceilings independent of length. These data, seen in conjunction with other information on fiber structure, cast serious doubt on the widely accepted concept that maximum conduction velocity is the factor controlling nerve structure. A much more likely factor controlling the structure of myelinated nerve fibers is the capacity to modulate information by frequency coding of impulses.
Key words: A x o n - Intercostal nerve fibers - M a x i m u m conduction velocity - Nerve fiber - Phrenic nervefibers - Ventral rootfibers
These studies were financiallysupported by the Deutsche Forschungsgemeinschaft(Fr. 609/1-1). Address for reprint requests: Reinhard L. Friede, M.D. (address above). 0022-510X/84/$03.00 © 1984 Elsevier SciencePublishers B.V.
370 INTRODUCTION An elementary aspect of the structure of peripheral nerves is their composition of myelinated fibers with very different calibers. Bearing in mind the basic nature of this phenomenon, there is surprisingly little information concerning the factors which control the caliber of a myelinated fiber as explored by Fernand and Young (1951). Conduction velocity is known to increase with fiber caliber. Accordingly, neurobiologists have always been ready to accept the conclusion that the acquisition of myelin sheaths, with the corresponding increase in axon caliber, is a phylogenetic advancement which has the purpose to increase conduction velocity. However, if conduction velocity is maximized, why isn't it maximized in all fibers? Moreover, if there is a biological tendency to increase conduction velocity, its efficiency should be measured by assessing conduction time, since an increase in velocity is only meaningful in reference to the distance over which the impulse is to be carded. If these premises are considered, there is also very little information on the relations between axon caliber and axon length in vertebrates, and only a few studies have been made on invertebrates. The present investigation was specifically designed to search for any existent relationship between the caliber and the length of an axon, with the aim of providing anatomical data useful for assessing conduction time. The relation between length and caliber may help to understand how axon caliber is controlled. Such data are also important for understanding the configuration of internodes and the related problem of the myelin sheath's dimensions. MATERIALAND METHODS For the developmental and adult studies of phrenic nerves, the left nerve was dissected and measured from the point of entrance into the diaphragm to the origin of its C4 root from the spinal cord, keeping tension as uniform as possible. As the segmental origin of the phrenic nerve in different species is somewhat controversial, it may be stated that for all of the species studied here, the main roots of origin were at C3 to C5 (Goshgarian and Rafols 1981). A segment of the midthoracic portion of the left nerve, sufficiently remote from the diaphragm to avoid terminal branching, was taken after preliminary fixation in situ with glutaraldehyde, then postfixed, osmicated and embedded in Araldite. Semithin sections were prepared and fiber calibers were determined by tracing the inner circumference of the myelin sheath with a Kontron videoplan, measuring 100 fibers per specimen. All values were expressed as the diameters of fibers having circular profiles. The degree of shrinkages or non-circularity, usually of 0.8, was thus eliminated from comparisons. If the data shown here are to be compared with data from native non-embedded fibers, they should be corrected by a factor of 0.70, which accounts for the shrinkage during dehydration and embedding. The fresh weight of the diaphragm was determined after its dissection from the rib cage and viscera; no efforts were made to separate its tendinous portions. Rat intercostal nerves are readily discernable underneath the pleura, where they may be prefixed in situ by filling the thoracic cavity with glutaraldehyde. The funnel-
371 shaped rat thorax accounts for a stepwise increase in length from one intercostal nerve to the next. The length of the nerves was measured from their exit at the cord to the osteochondral line of the ribs, and to the midline, respectively. Specimens were selected at the nerve's entrance into the subpleural tissue and at midlevel between this point and the most distal discernable fascicles of the nerve at the sternum. All intercostal nerves were sampled for two adult, male Sprague-Dawley rats, weighing 310 and 320 g. Bovine ventral roots from two cows were obtained from the slaughter house of the Institut far Tierzucht of the University of GOttingen. The cows were 8.3 and 8 years old, respectively, weighing 438 and 473 kg. Tissues were dissected within about 30 min of slaughtering; every other ventral root was harvested and fixed in glutaraldehyde. Processing of specimens of rat and bovine tissue was carried out as described above. Ninety fibers were measured for each given root. RESULTS
The phrenic nerve is a suitable model for studying the relations between fiber caliber and length; fiber caliber is readily determined for the predominant populations of thick fibers, and fiber length may be measured from the exit of the spinal roots to TABLE 1 P A R A M E T E R S O F R A T P H R E N I C NERVE S T R U C T U R E D U R I N G G R O W T H Age (days)
Weight (g)
Number of myelinated fibers
Fiber length (mm)
Axon diameter (circular profile) (#m)
Volume of axoplasm (106 #m 3)
Weight of diaphragm (g)
21
30
387 427 426
27 28 27
1.9 + 0.4 1.9 _+ 0.4 1.9 + 0.4
0.076 0.079 0.076
0.12 0.14 0.11
26
65
398 426 421
32 34 32
2.6 _+ 0.6 2.6 + 0.9 2.7 + 0.6
0.17 0.18 0.18
0.14 0.17 0.18
38
115
498 456 395
39 40 40
3.3 + 0.8 3.3 + 0.7 3.0 + 0.5
0.33 0.34 0.34
0.40 0.53 0.43
60
195
471 437 439
55 53 55
3.6 + 0.5 3.6 + 0.5 3.6 + 0.5
0.56 0.54 0.56
0.67 0.69 0.65
76
220
444 356 455
58 56 60
3.9 + 0.5 3.8 _+ 0.5 4.2 _+ 0.7
0.69 0.64 0.83
0.74 0.70 0.76
360
280
380 387 404
62 60 61
4.4 _+ 0.9 4.4 + 0.9 4.7 + 1.0
0.94 0.91 1.05
1.42 1.18 1.49
372
the entrance of the nerve into the diaphragm. The terminal portion of the fibers within the diaphragm represents a constant factor, as the motor endplates are arranged in a narrow zone which, for instance in the rat, is located approximately 2 mm from the nerve entrance (Nickel and Waser 1968). Developmental changes in the phrenic nerve The average number of myelinated nerve fibers in the phrenic nerve of the rabbit was 662, in the rat 425; the latter value agrees reasonably well with the 365 fibers stated by Lubifiska (1977) or the 404 + 48 fibres found by Langford and Schmidt (1983). The number of myelinated fibers did not change during the growth of the animals (Tables 1 and 2). Fiber length increased with body size. The increase in fiber length in the rat and rabbit was accompanied by a marked increase in axon caliber during initial postnatal growth. The rate of increase in caliber subsequently diminished, resulting in a parabolic curve, where particularly for the rabbit a 58 ~o increase in phrenic nerve length towards adult age was accompanied by only 12~o increase in caliber between the days 76 and TABLE 2 PARAMETERS OF RABBIT PHRENIC NERVE STRUCTURE D U R I N G GROWTH
Age
Weight
(days)
(g)
Number of myelinated fibers
Fiber length
Axon diameter (circular profile)
Volume of axoplasm
Weight of diaphragm
(mm)
(#m)
(10 6 #m 3)
(g)
42
763 646 704
38 35 38
2.4 ± 0.5 2.4 + 0.4 2.4 + 0.4
0.17 0.16 0.17
0.22 0.20 0.20
8
145
752 680 645
50 49 48
3.0 ± 0.5 3.4 ± 0.5 3.0 ± 0.5
0.35 0.44 0.34
0.61 0.68 0.70
14
260
675 627 554
56 54 54
3.5 ± 0.7 3.5 ± 0.6 3.6 __+0.6
0.54 0.52 0.55
1.17 1.33 1.20
26
500
642 734 731
68 70 67
3.9 + 0.6 3.9 ± 0.5 4.1 ± 0.5
0.81 0.84 0.88
1.99 1.82 1.92
42
1000
639 620 669
83 84 87
4.5 + 0.6 4.8 ± 0.8 4.7 ± 0.9
1.32 1.52 1.51
2.12 2.18 2.01
55
1550
585 604 782
97 99 96
5.2 ± 0.8 5.2 ± l.l 4.6 ± 0.9
2.06 2.10 1.60
5.50 5.70 5.50
210
4200
697 751 756
150 156 154
5.5 __+ 1.0 5.1 ± 0.8 5.3 ± 1.0
3.56 3.19 3.40
11.60 12.40 11.80
373
Rat
lb
c
o
3'o
i
I i
4o
so
6b
i
ro
Rabb
E 10
20
4321-
Lengh t
of phrenic nerve
(mm)
Fig. 1. Changes in the length of phrenic fibers during postnatal growth are compared with changes in the axon's caliber (expressed in #m for fibers having a circular profile). The corresponding ages are given in Tables 1 and 2.
360 (Fig. 1). There were substantial increases in the total volume of the axoplasm, by a factor of 13 in the rat and of 20 in the rabbit, for the periods studied. There were also corresponding increases in the weight of the diaphragm. Differences in phrenic nerve structure in species of different body size When comparing species of small body size with large ones, the number of phrenic fibers increased with body size, e. g. by a factor exceeding 10 between the mouse and the cow (Table 3). Fiber numbers for the dog were similar to those of Landau et al. (1962). There were corresponding increases in the weight of the diaphragm. A straight line relationship was found on plotting the cubic root of the diaphragm's weight against the number of myelinated phrenic fibers in the various species, indicating a consistency in the size of motor units, or, respectively, of axonal terminal branching (Fig. 2). The axons ofmyelinated phrenic fibers had essentially the same caliber in cat, dog, pig and cow, in spite of considerable differences in fiber length; the difference between cat and cow amounted to a factor of 4 (Fig. 3). Distinctly thinner axons were found in the mouse, rat and rabbit. Axons of large species contained considerably larger volumes of axoplasm than did those of small species, giving a factor of 71 for the mouse and the cow (Table 3). Rat intercostal nerves The intercostal nerves of the rat may be, on the whole, considered as constituting a functionally homogeneous fiber population having synchronized motor activity, but
374
TABLE 3 P A R A M E T E R S OF P H R E N I C NERVE S T R U C T U R E IN 7 SPECIES Number of myelinated fibers
Fiber length (mm)
Axon diameter (circular profile) (#m)
Volume of axoplasm (10 6 #m 3)
Weight of diaphragm
Cow
4616 3426 5 140
697 692 688
6.9 + 1.1 7.3 _+ 1.6 7.9 + 0.1
26.06 28.96 33.72
2345 2410 2250
Pig
2454 2403 1889
390 415 402
7.7 + 1.6 7.2 + 1.7 7.4 + 1.1
18.16 16.90 17.29
565 550 500
Dog
1524 1677 1784
350 375 385
6.2 + 1.2 6.8 + 1.1 6.4 + 1.0
10.57 13.62 12.39
80 87.5 90
Cat
887 923 1044
166 172 165
7.1 _+ 2.0 6.6 _+ 1.9 7.2 _+ 1.9
6.57 5.88 6.72
16.9 20.4 17.8
Rabbit
697 751 756
150 156 154
5.5 + 1.0 5.1 +0.8 5.3 + 1.0
3.56 3.19 3.40
11.6 12.4 11.8
Rat
404 380 387
61 60 60
4.7 _+ 1.0 4.7 + 0.9 4.4 + 0.9
1.05 0.94 0.91
1.49 1.42 1.18
Mouse
266 258 248
24 24 22
4.02 + 1.0 5.2 _+ 1.3 4.5 _+ 0.9
0.30 0.51 0.35
0.16 0.12 0.12
Species
.•
(g)
Cow
70oo-
32 ~" 5000
P~
i
~6
z
"
Dog
3000-
• Cat P---O Rabbit ~ 4 Rat Mouse . . . .
,
.
.
.
.
•
.
.
.
.
Weight o f d i a p h r a g m (g I
Fig. 2. The number of myelinated fibers in the phrenic nerve of different species is in a straight-line relationship to the cubic root of the weight of the diaphragm.
375
0 m0
%
4
"0
2
<[
10
20
30
40
50
60
70
Length of phrenic nerve ( c m )
Fig. 3. There is no direct relationship between the caliber of phrenic fibers (in #m, circular profiles) and the length of the phrenic nerve in species of different body size. Phrenic axons of the cat have nearly the same caliber as those of the cow, even though the latter are about 4 times longer.
':!
~lO-
I I
E i-
2
< I
I
I
I
I
I
! 10
! 12
e~ e* IF e*
e~
8
I 2
| 4
I 6
I 8
Intercostal nerves
Fig. 4. Rat intercostal nerves differ greatly in length due to the funnel-shaped rat thorax. The lower diagram shows the length of intercostal nerves measured from the exit of their roots at the cord to the osteochondral border (lower curve) and to the midline (upper curve) for each intercostal nerve in two rats. The upper diagram shows the means and standard deviations of the axon calibers in the same nerves,
individual nerves differ greatly in length. The distance from the root exit to the osteochondral border varied irregularly, but the total maximum length of the intercostal nerves from the cord to the most distal extensions varied by a factor of more than 5 from the 1st tot the 12th nerve, with fairly uniform increases in length for the nerves in between. When either the mean of axon calibers or the calibers of the thickest fibers were plotted for these intercostal nerves, there were clearly no changes of caliber that would correspond to a 5-fold increase in length (Fig 4).
376
=.. g
"o
1°t C
T
L
S
Spinal segments Fig. 5 Mean axon calibers for the thick myelinated fibers in 16 ventral spinal roots of the cow are pooled (two animals each) and compared with the mean and standard deviation for all ventral roots pooled. There is no significant segmental variation in fiber caliber.
Bovine ventral roots
Exact determinations of fiber length are not practical for the fibers in bovine ventral roots. Yet the fibers supplying the neck, trunk and extremities obviously differ greatly in length. The absence of data on length is compensated, to some extent, by the regular bimodal fiber spectra, which are favorable to exact determinations of axon caliber. The thick fibers form well-distinguished populations, having a definite Gaussian distribution. The populations of thin fibers may be neglected as they innervate the muscle spindles and also give origin to the substantial cervico-thoraco-sacral outflow of autonomic fibers The mean axon diameter of the thick ventral root fibers are shown in Fig. 5 per segment, and they are compared with the mean diameter of the entire pooled population of root fibers. There is no pattern corresponding to the length of the respective fiber populations, and means for individual roots were all within the narrow standard deviation of the pooled roots. DISCUSSION
It is known that certain axons effect spatial-temporal impulse synchronisation. In loligo, for instance, fibers vary in caliber and in conduction velocity to effect near synchronous contraction of the muscles (Pumphrey and Young 1938). In the teleost electromotor system, caliber and conduction properties of preterminal axon branches compensate for the differences in path length, synchronizing the discharge of the electric organ (Bennett 1968, 1971). Temporo-spatial impulse synchronisation may also be achieved by variation in fiber caliber and in internode length in preterminal axon arbors in the CNS (Waxman 1971, 1975; Waxman and Melker 1971; Desch6nes and Landry 1980). Generalized, these observations could bring the conclusion that human thoracic ventral roots have thinner axons than lumbar roots because their fibers are shorter
377 (Kawamura and Dyck 1977). Also, a parallel increase of fiber length and of conduction velocities in the kitten would render conduction time independent of nerve length (Ridge 1967). It would be justifiable to search for correlations between conduction velocity and body height (Campbell et al. 1981; Soudmand et al. 1982). However, all data obtained in the present study were in contradiction with this concept. The findings for rat intercostal nerves and for bovine ventral roots require no further comment, as both populations showed no relation whatsoever between fiber length and fiber caliber. Phrenic axons in species of very different body size differed in caliber by a factor of 1.55 in the adult mouse and the adult cat, but there were no further differences in axonal caliber in the cat and the cow, even though bovine fibers are four times as long. No convincing explanation was found for the differences in small and large species. Among the large species, there was no increase in fiber caliber when the fiber doubled or tripled in length, consistent with the classic observations of H~iggqvist (1948). The most complex situation was found for the developmental changes in the rat and rabbit phrenic nerves. A curvilinear relation was found between caliber and length, implying an early growth phase when both caliber and length increased, and a later maturation phase when growth in length continued, while growth in caliber subsided. The resultant parabolic curve is remarkably similar to that found by P.K. Thomas (1955) for nerve fibers in fishes of different body size. These latter observations are consistent with a biphasic pattern of caliber growth evident from Cottrell (1940) or from the electron-microscopic measurements of Schr0der et al. (1978), even though these studies did not include fiber length. In SchrOder's data, the thick fiber population of sural nerve had reached maximum diameter by the age of 5 years, long before the limb has reached its definitive length, with a slight decrease in fiber caliber thereafter. There is a corresponding rapid increase in conduction velocity during early growth (J.E. Thomas and Lambert 1960; Gamstorp 1963), followed by a slight decrease towards adulthood (Hakamada et al. 1982). In the kitten triceps surae neurons, a rapid increase in axon diameter before day 44 is followed by smaller increases towards adult values (Cullheim and Ulfhake 1979). In the rat's dorsal tail nerve, the conduction velocity levels off at 15 weeks, before definitive body size is reached (Oldfors and Ullman 1980). In the giant axon of the lobster, fiber caliber increased proportionally with fiber length, up to a given age, and conduction time remained constant (Govind and Lang 1976). Further increases in length were not accompanied by increases in caliber, with a consequent lengthening of conduction time. Funch et al. (1981) found a parabolic relation between body length and axon caliber in the giant axon of the goldfish, where axon caliber and conduction velocity actually decrease in fishes larger than 9.5 cm. A factor not considered so far is the extent of axon branching, which commences several centimeters before the nerve reaches the muscle (Eccles and Sherrington 1930). Axon caliber may accordingly vary with the size of the motor unit (Henneman and Olson 1965; Bagust 1974). The extent of branching of phrenic nerve fibers, however, appears to be rather constant, since the number of fibers in different species were in linear relation to the cubic root of the weight of the diaphragm (Fig. 2). Moreover, the
378 concept that axon caliber is controlled by the extent of terminal branching leads to gross inconsistencies when applied to sensory fiber populations. If one summons up the evidence reviewed so far, there is clearly no interdependence between the fiber length and the fiber caliber in mammalian nerves; instead, maximum fiber calibers tend to level off at certain ceilings, which are alike for populations of different length, or for species of different body size. The same conclusion could be made by studying the fiber population innervating a given skeletal muscle receiving fibers of greatly different caliber (Rexed and Therman 1948; Hgtgbarth and Wohlfart 1952; Richmond et al. 1976), although their length must be similar. It is appropriate, therefore, to examine the assumption that fiber caliber increased in order to accelerate conduction, Since Rushton's (1951) calculations in particular, there has been a strong trend to assume that "the attainment of maximum conduction velocity has been the controlling factor in the evolution of nerve structure". Velocity, however, is merely one among many parameters changing with fiber caliber, including also refractory periods, or the maximum frequency of impulses, respectively (Paintal 1966, 1967, 1973, 1978; Waxman and Bennett 1972). There is also an inverse relationship between the axon's diameter and the length of the afterhyperpolarisation of their cells (Eccles et al. 1958). Increased transmission velocity, therefore, could be only an epiphenomenon of the fiber's greater capacity to use frequency codes. With this change in the point of view, neural systems may be found in which caliber spectra are more in harmony with frequency coding than with controlling conduction time. In skeletal muscle, for instance, tonic and twitch fibers are known to receive nerve fibers having different conduction velocities (Eccles et al. 1958), but this difference may relate to the frequency of stimulation which is known to affect muscle fiber typing (Salmons and Vrbov~t 1969; Pette et al. 1973; Salmons and Srrter 1976; Hudlicka and Tyler 1980). The caliber of fibers innervating the tendon organs and the muscle spindles of a given muscle also corresponds to their characteristic impulse frequencies rather than to conduction times. For all these reasons, the widely accepted opinion that myelination primarily serves the purpose of increasing conduction velocity must be erroneous; a much more likely parameter determining fiber caliber is the capacity for transmitting higher impulse frequencies or frequency coding. Academic as this may seem, it is none the less crucial for the understanding of the relation between fiber structure and fiber function in health and disease.
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379 Cottrell, L. (1940) Histologic variations with age in apparently normal peripheral nerve trunks, Arch. Neurol. Psychiat. (Chic.), 43: 1138-1150. Cullheim, S. and B. Ulfhake (1979) Relations between cell body size, axon diameter and axon conduction velocity of triceps surae alpha motoneurons during the postnatal development in the cat, J. Comp, Neurol., 188: 679-686. Desch~nes, M. and P. Landry (1980) Axonal branch diameter and spacing of nodes in the terminal arborization of identified thalamic and cortical neurons, Brain Res., 191: 538-544. Eccles, J. C. and C. S. Sherrington (1930)Numbers and contraction-values of individual motor-units examined in some muscles of the limb, Prec. Roy. Soc. Lend. (Biol.), 106: 326-356. Eccles, J.C., R.M. Eccles and A. Lundberg (1958) The action potentials of the alpha motoneurones supplying fast and slow muscles, J. Physiol. (Lend.), 142: 275-291. Fernand, V. S.V. and J. Z. Young (1951 ) The sizes of the nerve fibres of muscle nerves, Prec. Roy. Soc. Lend. (Biol.), 139: 38-58. Funch, P.G., S.L. Kinsman, D. S. Faher, E. Koenig and S.J. Zottoli (1981) Mauthner axon diameter and impulse conduction velocity decrease with growth of goldfish, Neurosci. Lett., 27: 159-164. Gamstorp, I. (1963) Normal conduction velocity of ulnar, median and peroneal nerves in infancy, childhood and adolescence, Acta Paediat. Scand., (Suppl.), 146: 68-76. Goshgarian, H.G. and J.A. Rafols (1981) The phrenic nucleus of the albino rat - - A correlative HRP and Golgi study, J. Comp. Neurol,, 201: 441-456. H~tgbarth, K.-E. and G. Wohlfart (1952) The number of muscle-spindles in certain muscles in cat in relation to the composition of the muscle nerves, Acta Anat. (BaseO, 15: 85-104. H~ggqvist, G. (1984) Nervenfaserkaliber bei Tieren verschiedener Grtisse, Anat. Anz., 96: 398-412. Hakamada, S., T. Kumagai, K. Watanabe, Y. Koike, K. Hara and S. Miyazaki (1982) The conduction velocity of slower and the fastest fibres in infancy and childhood, J. Neurol. Neurosurg. Psychiat., 45: 851-853. Henneman, E. and C.B. Olson (1965) Relations between structure and function in the design of skeletal muscles, J. Neurophysiol., 28: 581-598. Hudlicka, O. and K.R. Tyler (1980) Importance of different patterns of frequency in the development of contractile properties and histochemical characteristics of fast skeletal muscle, J. Physiol. (Lend.), 301:10P-11P. Kawamura, Y. and P.J. Dyck (1977) The morphometric myelinated fiber composition of D11 as compared to L3, LA and L5 ventral spinal roots of man, J. Neuropath. Exp. Neurol., 36: 846-852. Landau, B.R., K. Akert and T. S. Roberts (1962) Studies on the innervation of the diaphragm, J. Comp. Neurol., 119: 1-10. Langford, L.A. and R.F. Schmidt (1983) An electron microscopic analysis of the left phrenic nerve in the rat, Anat. Rec., 205: 207-213. Lubifiska, L. (1977) Early course of Wallerian degeneration in myelinated fibres of the rat phrenic nerve, Brain Res., 130: 47-63. Nickel, E. and P.G. Waser (1968) Elektronenmikroskopische Untersuchungen am Diaphragma der Maus nach einseitiger Phrenikotomie, Teil 1 (Die degenerierende motorische Endplatte), Z. Zellforsch., 88: 278-296. Oldfors, A. and M. Ullman (1980) Motor nerve conduction velocity and nerve fibre diameter in experimental protein deprivation - Studies on rat peripheral nerve during development, Acta Neuropath. (Berl.), 51: 215-221. Paintal, A. S. (1966) The influence of diameter of meduUated nerve fibres of cats on the rising and falling phases of the spike and its recovery, J. Physiol. (Lend.), 184:791-811. Paintal, A. S. (1973) Conduction in mammalian nerve fibres. In: J. E. Desmedt (Ed.), New Developments in Electromyography and Clinical Neurophysiology, Vol. 2, Karger, Basel, pp. 19-41. Paintal, A.S. (1978) Conduction properties of normal peripheral mammalian axons. In: S. G. Waxman (Ed.), Physiology and Pathobiology of Axons, Raven Press, New York, pp. 131-144. Pette, D., M.E. Smith, H.W. Staudte and G. Vrbovfi (1973) Effects of long-term electrical stimulation on some contractile and metabolic characteristics of fast rabbit muscles, Pfliigers Arch. Ges. Physiol., 338: 257-272. Pumphrey, R.J. and J.Z. Young (1938) The rates of conduction of nerve fibres of various diameters in cephalopods, J. Exp. Biol., 15: 453-466. Rexed, B. and P.-O. Therman (1984) Calibre spectra of motor and sensory nerve fibres to flexor and extensor muscles, J. Neurophysiol., 11: 133-140. Richmond, F.J.R., G.C.B. Anstee, E.A. Sherwin and V. C. Abrahams (1976) Motor and sensory fibres of neck muscle nerves in the cat, Canad. J. Physiol. Pharmacol., 54: 294-304.
380 Ridge, R. M. A.P. (1967)The differentiation of conduction velocities of slow twitch and fast twitch muscle motor innervations in kittens and cats, Quart. J. Exp. Physiol., 52: 293-304. Rushton, W.A.H. (1951) A theory of the effects of fibre size in medullated nerve, J. Physiol. (Lond.), 115: 101-122. Salmons, S. and F.A. Sr6ter (1976) Significance of impulse activity in the transformation of skeletal muscle type, Nature (Lond.), 263: 30-34. Salmons, S. and G. Vrbovfi (1969) The influence of activity on some contractile characteristics of mammalian fast and slow muscles, J Physiol. (Lond.), 201: 535-549. SchrOder, J.M., J. Bohl and K. Brodda (1978) Changes of the ratio between myelin thickness and axon diameter in the human developing sural nerve, Acta Neuropath. (Berl.), 43: 169-178. Soudmand, R., L.C. Ward and T.R. Swift (1982) Effect of height on nerve conduction velocity, Neurology (Minneap.), 32: 407-410. Thomas, J.E. and E.H. Lambert (1960) Ulnar nerve conduction velocity and H-reflex in infants and children, J. Appl. Physiol., 15: 1-9. Thomas, P.K. (1955) Growth changes in the myelin sheath of peripheral nerve fibres in fishes, Proc. Roy. Soc. Lond. (Biol.), 143: 380-391. Waxman, S.G. (1971 ) An ultrastructural study of the pattern of myelination of preterminal fibers in teleost oculomotor nuclei, electromotor nuclei, and spinal cord, Brain Res., 27:189-201. Waxman, S.G. (1975) Integrative properties and design principles of axons, Int. Rev. NeurobioL, 18: 1-40. Waxman, S.G. and M.V.L. Bennett (1972) Relative conduction velocities of small myelinated and nonmyelinated fibres in the central nervous system, Nature (Lond.), 238: 217-219. Waxman, S.G. and R.J. Melker (1971) Closely spaced nodes of Ranvier in mammalian brain, Brain Res., 32: 445-448.