~~
The spatial distribution of muscle fibers belonging to a motor unit was studied in the soleus (SOL) and tibialis anterior (TA) of adult cats to provide a detailed description of the spatial patterns which exist within the territory of a motor unit. Glycogen depletion of the motor unit was achieved through repetitive stimulation of either the intracellularly identified motoneuron or the functionally isolated motor axon. Muscle fibers belonging to the stimulated unit were identified in serial cross-sections, and in the cross-section which contained the most depleted fibers the centroid of each depleted fiber was determined. Subsequently, three spatial analyses, ie, a quadrat analysis, a point-to nearest neighbor analysis and an interfiber distance analysis, were used to determine if motor unit fibers were distributed randomly throughout the territory of the unit. Motor unit fibers tended to be localized within the muscle cross-section and were not evenly or homogeneously distributed throughout the territory. In general, the analyses suggested that motor unit fibers may be arranged in clusters or subgroups of varying size. The data demonstrate three different quantitative analyses for studying the organization of muscle fibers of normal motor units, which can be used for objective assessment and diagnosis of neuromuscular diseases. Key words: Monte Carlo simulations glycogen depletion soleus tibialis anterior spatial statistics MUSCLE & NERVE 13:1133-1145 1990
.
SPATIAL DISTRIBUTION OF MUSCLE FIBERS WITHIN THE TERRITORY OF A MOTOR UNIT SUE BODINE-FOWLER, PhD, ALAN GARFINKEL, PhD, ROLAND R. ROY, PhD, and V. REGGIE EDGERTON, PhD
Motoncuroris located in specific regions of the lateral motor column of the spinal cord innervate specific musclcs of the hiiidlinih with remarkable acc~racy.".'~Moreover, motor axoris belonging to a specific muscle nerve appear to selectively innervate specific rcgions of a muscle fxom thc initial stages of the innervation proccss, ie, prior to synapse elimination, and establish what are conimonly referred t.o as muscle compartments prior to the period of synapse elimination.2'4"4'20'""The From the Department of Kinesiology (Drs Bodine-Fowler, Garfinkel, and Edgerton) and Brain Research Institute (Drs Roy and Edgerton), University of California at Los Angeles. Los Angeles. CA. Acknowledgments: This work was supported by National Institute of Neurological and Communicative Disorders and Stroke Grant NS-16333 We thank Drs. Tim C. Cope and John A Hodgson lor their contributions to the collection of this data. We also thank Dr Donald Walter for his assistance in writing the analysis programs Address correspondence and reprint requests to Sue Bodine-Fowler. PhD. Division of Orthopaedics. Unlversity of California, San Diego, V A. Medical Center, V-151, 3350 La Jolla Village Drive, San Diego, CA 92161. Accepted for publication December 13. 1989. CCC 0148-639X/90101201133-013 $04.00 0 1990 John Wiley & Sons, IIIC.
Spatial Pattern of Motor Unit Fibers
degree to which a motoneurori selectively innervatcs muscle fibers within the whole muscle or muscle compartments, however, is relatively tinknown. 'l'he distribution pattern of muscle libers belonging to a motor unit should reHect the net rcsult of thc control cxerled by thosc mechanisms which influence the Iorination and elimination of synapses. Mammalian muscle fibers are multiply innervated a t birth, however, during the first few weeks of postnatal development all but one of' the synapses is eliminated." Synapse elimination could have some role in determining the spatial arrangenierit of muscle fibers belonging to a single niotor unit. By studying Lhe spatial distribution of' muscle fibers belonging to a single motor unit, pallerns may emerge which lend insight into the mechanisirrs which govern the formation and/or elirnination of rriusclc libers during development and reiiincrvalion. Further, a detailed description 01' the pat.terns which exist in normal motor units should aid in the interpretation 01. single-fiber EMG data and provide a quantitative measure of assessing aiid diagnosing the involvcment o f de-
MUSCLE & NERVE
December 1990
1133
A'
FIGURE 1. Distribution of depleted motor unit fibers within the defined territorial boundaries of the unit (A). For the quadrat analysis, the maximum x and y distances within the motor unit were calculated and a square with sides equal to the longer of the two distances was drawn to enclose all the fibers belonging to the unit. This sample area (B) was divided into smaller squares or quadrats and the number of fibers in each quadrat was counted. Only those quadrats located within the territorial boundaries of the motor unit (quadrats with triangles) were used in the calculation of the index of dispersion
generation and reinncrvation in neurogenic muscle diseases. The fibers belonging to a motor unit can he visualized using glycogen depletion techniques. Quantification of the distribution patterns of the muscle fibers belonging to identified motor units is liniited to a few Brandstater and Lanibert" reported that the nunibcr of adjacencies among rriotor unit fibers was not different from random, while Willisoii"2 clairried t o fitid eviderice
''
supporting nonrandom innervation, in that fewer adjacericies were found among motor unit fibers than would be expected t'rom a random distribution. I n a recent we found that the incidence of fibers of the samc unit being adjacent to one another was riot difTerent from random, ie, there appeared to be 110 processes that tended to prevent or ericourage riiotor unit fibers LO be adjacent to one another. I n general, previous descriptions of the distri-
((7)
c BQ
/"..,
WM MU
==
40 mm2 53
,-_
WM MU
53 mm2 23 mmz
. , '
\
. .. . . _ . ? :. :. 'I.
.
I
_ ... ..
'
.
FIGURE 2. Location of motor unit territory within the whole muscle cross-section and distribution of depleted motor unit fibers within the territory for soleus (SOL) units 1 (A), 2 (B), and 3 (C). The area of the whole muscle cross-section (WM) and motor unit territory (MU) are given for each unit.
1134
Spatial Pattern of Motor Unit Fibers
MUSCLE & NERVE
December 1990
hution of motor unit fibci-s has been based on visual interpr-etations lrom rlycogen depleted units. nrandstater and Lambert desc.ribed the distribution o f motor unit fibers i n 23 T A units of the rat as being “diffusely scattered throughi>ut the motor unit territory, with little or no tendency for grouping.” Phrases such as “randomly scattered,” “irregularly spaced,” and “uni Iormly dispersed” have also been used to describe the spatial patterns of motor unit fibers.”.”’.‘’ The purpose of the present study was to evaluate the spatial distribution of motor unit fibers by analyzing the palterns which exist over the cnt.ir-e motor unit territory using several density and distance rrieasurements. ‘I’he nicasures used in this study were designed to tcst the hypothesis that. the muscle fibers innervated by a single motoncuron are ranclorrrly distributed throughout t.heit- territory in the rnuscle cross-section. To achieve t.his, actual distributions of the spatial arrangements of‘ nio~or unit fibers were calculated arid compared to what would be expected from a purely random process based on Monte Carlo simulation tct:h~iiques.‘~ Preliminary results have been reported cIsewhere.”
b
slimuldtion of the muscle fibers, using a stirridus paradigm that optimized glycogeii utilization and minimi7ecl neuromuscular junction tailure.’ Upon cessation of stimulation, the muscle was excised, weighed, cut into blocks, arid rapidly lrozen in isopentane cooled to - 160°C with liquid nitrogen. Histological Mapping of Motor Unit. Muscle fibers belonging to a stimulated motor unit (MU) were identified by their low level of glycogen. It was assumed that all depleted fibcrs belonged to thc siirnulated unit and that the stimulation regime used, depleted all and only those fibers belonging to the unil. ‘1’0assess the glycogen count of fibers, cross-sections (20 km) were cut from the experimental muscle and stained using the periodic acidSchiff Only those cross-sections in which a perpendicular section containing no oblique fibcrs was obtained, were used in the spatial analyses. The level of glycogen staining was determined using an image-processing computer system which calculated an optical density of glycogen staining lor each fiber that was o u t l i ~ i e d . ~ ” ~ ~
TA 1
MATERIALS AND METHODS
T h e muscle Iibers innervated by a single motoneuron were identified using glycogen depletion techniques in 3 soleus (SOL) Zind 4 tibialis antct-ior ( T A ) units in 7 adult (6 nionths or older) cats. Experiments were performed under pentobarbital anesthesia, 35 rrigikg, IP, supplemented intravenously as needed to keep withdrawl and eye-blink responses supp~essecl. The spinal cord was exposed from level L5 to SI arid the rnusclcs ol‘ the tail, hip, thigh, arid lower leg were tienervated with the excepliori of the ‘ I A o r SOL, which were isolated f’~.orn surrc.)unding tissues will1 care taken to preserve tlic tdood supply t o each muscle. I n each TA muscle, one rriotor unit was characterizcd physiologically and glycogen depleted by stimulating its func:tionally isolated axon. Criteria for functional isolation were elicitation of ( 1) an all-or-none twitch response following lilanicnt stiniulat,ion at voltages ranging f.rorn threshold to X10 threshold, (2) a corresponding all-or-norie EMG recorded from the niusclc demonstrating a consistent waveform, and (3) an all-or-none action potential in the ventral root filament following graded stimulation of the muscle nerve. Soleus motor units were isolated arid stimulated using itit.racellular tecliriiques as descrilied by Cope et. Glycogen (1epIetion of the iiiotor unit was achieved through repetitive Motor Unit Identification.
Spatial Pattern of Motor Unit Fibers
WM
= 200 mm2
MU =
16
mm2
(r.< 1;7 : ;’:i : i; .:
A 7 ;. .’._.
. . .. . ..... _ ... ._ . . . . . . . . . .__
D-
TA 4 200 mmz M U = 24 mm2 WM
I
FIGURE 3. Location of motor unit territory within the whole muscle cross-section and distribution of depleted motor unit fibers within the territory for tibialis anterior (TA) units 1 (A), 2 (B), 3 (C) and 4 (0).The area of the whole muscle cross-section (WM) and motor unit territory (MU) are given for each unit.
MUSCLE & NERVE
December 1990
1135
80
-
0
> 0 E
60
k U
cew I-= -e
~
.
0
40-
.
UI
?; F
20 -
3YI
W
W
W
U
0,
50
I
0
r
U
?!
40
-
[E-
E "E
Fg
30-
h pi
20-
W W
9 10
!
50
I
150
250
350
NUMBER OF FIBERS FIGURE 4. Relationship between the number of motor unit fibers and (A) the relative territory size and (B) the absolute territory size for the 3 soleus (SOL, a) and 4 tibialis anterior (TA, m) units analyzed. These data were taken from that cross-section with the largest number of depleted motor unit fibers.
The position of glycogen-depleted muscle fibers was mapped on serial cross-sections taken along the length of the muscle. From that cross-section which contained the greatest number of depleted muscle fibers, ie, motor unit fibers, the x, y coordinate of the centroid of each fiber was determined and saved in a computer file. The territory of the motor unit, ie, the region of the muscle occupied by the fibers innervated by a single motoneuron, was estimated by connecting outlying fibers by straight lines to form the smallest convex area containing all of the motor unit fibers. The term motor unitfiber will be used to refer to those muscle fibers innervated by a single motoneuron. Spatial Analyses
Qu,adrat Analysis. The territory of each motor unit was divided into small subregions to assess the variability of fiber density. For each MU, a square was drawn to enclose all the fibers belonging to the unit (Fig. 1A). The dimensions of the square were determined by calculating the maxi-
1136
Spatial Pattern of Motor Unit Fibers
tances between MU fibers. The dimensions of the square were set at the longer of the two distances. This area then was divided into square subregions or quadrats (Fig. IR), and the number of MU fikers in each quadrat was counted arid used to calculate the index of' dispersion. Note t.hat this area was often larger than the convex area representing the MU territory. However, only those quadrats residing within the territory defined by the convex area were included in the calculation of
dispersion, a sensitive measure for detecting a lack of homogeneity in a dist.ribution of points,31 was calculated as follows. I f the observed counts in n quadrats are denoted by x l , x2, xS . . ., x n , then these counts have a nieaii x = xz/n and a variance s p = x i - ? l ' / ( ~ ~ - I )where , the summat.ions are ovathe values of i from 1 to Y ~ L 'l'he index of dispersiori can be calculated using the equation: [ ( n - l ) ~ % ] . For " ~ a random distribution, the index of' dispersion should have a chi-square distribution, provided tliat the number- of' quadrats is greater Lhan six arid tlic i r i c x i is greatcr than one.3 I These criteria were met for each of the 7 units studied. Distribution of Interfiber Distances. 'I'he distances between each m&r unit fiber and all other motor unit fibers were calculated to provide information regarding the spacing of M U fibers within the territory. For each unit, a polygonal subregion of the MU territory was chosen which maximized the number of MU fibers included for analysis yet cxclutied those areas witliiri the territory which did not contain M U fibers. Inclusion of a large area which did not contain MU fibers would tend to bias the analysis towards finding a clustering pattern. Consequently, we selected an area within the defined territory which excluded large areas devoid of MU fibers, thercby biasing the analysis in the direction of not. finding clustering. Within each subregion, the interfiber distances between motor unit fibtrs were calculated. For each fiber in the sample area, the distance bctween it and every other niotor unit fiber was calculated as the distance between the (x, y) coordinates of the centroids of each fiber. For n motor unit fibers, a total of (n' - n)/2 distances were computed for those pairs i, j ( 1 5 i < j 5 11,). A histogram of the distances derived from the motor unit was compared to histograms derived from Monk Carlo simulations in order to deter-
MUSCLE & NERVE
December 1990
mine whether thc actual distriburion of distances was significantly different from random. For each unit, a Monte Carlo simulation was carried o u t by choosing n (x, y) locations (where n equaled the number of MU fibers) randomly and independently within the sample area. To account for the fact that fibers have finite sizes, the minimum distance between randomly chosen points was restricted to the shortest distance found between M U fibers in the actual sample. Interfiber distances were calculated and entered into a histogram with the same bin sizes as the actual distribution. A total of 100 simulations were performed for each unit and a confidence interval was generated. The confidence interval was defined as follows: for each bin, the I00 simulations were sorted from high to low and the third highest and third lowest of the values were chosen as the upper and lower 3% confidence limits (P < 0.06). Kundom, Points to Nearest M U Fiber. T h e distribution of distanccs from randomly chosen points within the sample area to the nearest MU fiber was determined to test the hypothesis that there are holes, ie, areas containing no MU fibers, in the distribution of M U fibers. In each M U , a rectangular subregion of the territory was chosen for analysis. This subregion was riot the same as the one used [or the interfiber distance analysis because the program required a rectangular region for analysis. The reason for this limitation is that this measure is scnsitive to edge effects, and therefbre edge corrections must be used, the best of which is the toroidal method in which opposite edges are identified. In order to do that, a rectang d a r legion is ne~essary.'~ It should be noted that the number of rectangles that could be drawn within each M U territory was limited by the shape ancl size of the territories. Consequently, areas were chosen which maximized the number of points to be analyzed given the restraints of the software. The rectangular sample area was dividcd into approximately lOn square boxes (where r i equals the nurnber of fibers in the sample area) and a point was chosen at random in each box. 'l'he distance from each raiidomly chosen point to the nearest. MU fiber was calculated. The distribution of point-to-nearest ncighbor distances was plotted and compared to a distribution generated b y Monte (;ado simulations. 'I'he Monte Carlo procedures were similar to those described for the interfiber distance measuremerit. For each unit, n points wcre chosen at random within the sample area. 'The sample area was divided as described above and the point-to-
Spatial Pattern of Motor Unit Fibers
nearest neighbor distances were calculated. The simulations were repeated 100 times for each unit, and the high and low 3% probabilities ( P < 0.06) were derived. RESULTS
The spatial distribution of motor unit fibers over the muscle cross-section was investigated in 7 units: 3 slow SOL units; 1 slow T A unit; 2 fast, fatigue-resistant T A units; and 1 fast, fatigue-interA 121
SOL 1
B
14
0
FIGURE 5. A 3-dimensional representation of the distribution of motor unit fibers within the defined MU territory for soieus units 1 (A), 2 (B), and 3 (C). The z-axis represents the density of motor unit fibers within each quadrat. The number given on the z-axis represents the maximum density per quadrat.
MUSCLE & NERVE
December 1990
1137
Table 1. Physiological properties of motor units in the cat soleus and tibialis anterior muscles ~~~
Motor unit
SOL1 SOL2 SOL3 TA1 TA2 TA3 TA4
Type
CT (rns)
Po (9)
S S S
107
112 156 137 52 96 12 7 29.0
S FR FR FI
65 63 39 39 33 23
IR
Myosin staining
135
Light Light Light Light Dark Dark Dark
278
169 132 188 243 311
Abbrevmons CT coritraction time, Po maximum isometric tetanic tension, IR, innervation rabo of that muscle cross section with the greatest number of depleted motor unit fibers Motor units were classified into types based on the mechanfcal characteristics of the muscle unit S, slow, FR, fast fatigue-resistant and Fl. fast fabgue-intermediate Muscie fibers were ciassified as eithef hghl (siow) or dark (fast) based on thev reactions to staining for myosin ATPase, alkaline preincubation
mediatc TA unit. The niaxiniuni tetariic tensions of the 3 SOL units were 11.2, 13.7 and 15.6 g (Table l), tensions that are within the population range (3.2 to 40.2 g) for adult cat soleus units."'"" The T A units had maximum tetanic tensions be-
tween 5.2 and 29.0 g, also witliiii thci prcvioiisly repor-ted population range 01. I .O to 40.0 g for the cat I.A.'' 'I'he riuiriber hf fibers per unit ranged from 132 to 3 I I fi t n - s for t tie 7 units. I t slwuld tx noted that previous studies in ttic cat7 and rat" show a strong positive (:orrelation between maxir n u m tetanic tension and the iiumber of' fibers inriervaled by a single motoriwron. Moreover, it has been s h o w n that ariiong innervation ratio, mean fiber cross-sectional area mid spccific tension, ie, variahlcs wtiich influence maxirnuni tetanic tension, innervation ratio is the priniiii-y determinant of thc niaxirrium tetanic tension of ;1 motor unit.7
The location of the M U territory within that cr-oss-section which contained the largest number of depleted fibers ancl the distribution of the depleted motor unit fibers arc shown for cach of tlic SOL arid '1.A units in Figures 2 ancl 3, respectively. The territory of' eac-l-i unit, as illustrated in E'igurcs 2 arid 3, was defined as thc srriallest convex area containing all motor Motor Unit Territory Size.
B A
51 10
0
TA 1
C
TA 2
D 71
TA 3 TA 4 FIGURE 6. A 3-dimensional representation of the distribution of motor unit fibers within the defined MU territory for tibialis anterior units 1 (A), 2 (B), 3 (C), and 4 (D). The z-axis represents the density of motor unit fibers within each quadrat. The number given on the z-axis represents the maximum density per quadrat.
1138
Spatial Pattern of Motor Unit Fibers
MUSCLE & NERVE
December 1990
SOLEUS
unit l-iibers. I n general, the fibers belonging t o a unit were riot distributed across tlie entire riiirsc:le cross-scction, hut were localized to a particular region of the muscle. Moreover, the territory was generally more elliptical than circular in shape. 'Ihc relative territory size of c:ich unit, calculatccl as a percentage of the whole muscle cross-section, ranged from 8% to 76% (Fig. 4A). *l'ticSOL units extended over a larger pr.rce11tage of t.he muscle cross-section (41$% to 76%) iliari the T A units (8% to 22%). Calculation 01' the absolute size of' each of the motor uriit territories revcaled that the torritories of the SOL arid ?'A units were similar in sizr:, ranging f'roin I ( j t o 47 iiirii' (Fig. 413). 'Tilc cIiITorerice iri the relative a r i d absolutc s i x s of' SOL a i d T A units was related to differences in wholc muscle cross-sectional areas, ie, the ci-oss-sectional area of the T A i s 4 tirrles that of thc SOI. (see Figs. 2 and 3 ) .
A
To investigate how motor unit fibers were distributed througho u t their territory, a quadrat analysis was pcrformecl on each of the units. For each unit, a sumniary of ttic number of quadrats with fiber cknsitics ranging from 0 to 14 fibers is givcti in Tablc 2. Within ~tlieterritory dehried by Llie convex area, sevei-al of the units had a large number of quadrats which coiit;iined no motor unit fibers. 'These quadrats were iricluded in the analysis since they resided within the territorial boundaries of the unit. The index of dispersion, a nieasure used t.o detect a lack of horiiogeneity in a point was calculated for each unit using the quadrat density data given in Table '2. As showri in Table 3, 6 0 1 the 7 units tiad significant index of dispersion values, indicating that the disiribution of MU fibcrs deviated lrom a randorn distribution. In general, tlie 6 units with significant index of' clispersion values had large ranges in their quadrat densities which resultecl in relatively large variances (Taklc 3). A large variance :iiieaii raiio suggests the presence of clustci-s within the clistribu tion. Figures 5 and 6 illustrate, in 3-ditrierisioiis, how t.he motor unil fi1)ers were clistributecl throughout their territory fi)r each of' the SOI. and T A units. 'I'liese plots i1lustrat.e that M U {ibers were not evenly distributcd throughout tlie M U territory. Notice that regions of high arid low fiber densities were scatterecl throughout the unit, as opposed t o being located in ihe center of the M U territory. Moreover, tticrc iippearecl to be regions with no motor unit fibers, ie, "holes," within the territory of the unit. Distribution of Motor Unit Fibers.
0
200
400
600
BOO
C 1000 -
750
-
500 -
250
-
O i
DISTANCE (pm) FIGURE 7. Distribution of nearest neighbor distances calculated from the point-to-nearest neighbor analysis. For soleus units 1 (A), 2 (B) and 3 (C), nearest neighbor distances were calculated and plotted in histograms with bin widths of 55, 59, and 50 km, respectively. The actual distribution is represented by the bold lines and the 95% confidence interval, determined from the simulations, by the narrow lines. The arrows denote areas where the actual distribution significantly deviates from a random distribution.
Spatial Pattern of Motor Unit Fibers
MUSCLE & NERVE
December 1990
1139
Table 2. Quadrat analysis SOL1
SOL2
TA2
TA3
TA4
16 10
2 0 0
10 31 24 13 1 2 0 0 0
12 13 11 11 10 11 6
1 1
18 19 24 17 10 1 5 1 0 0 0 0 0
SOL3
TA1
Number of quadrats
Number of fibers per quadrat
6
2 4 1
7
3
a
0
9 10 11 12 13
0
15 17 18 18 10 7 2 0 2 2
0
0
0
0
0
1
0
1
1 1
0 0 0
1
0
0
0 1 2 3 4 5
46
25 10
7
0 0
14
35 27 25 15 4 1
0
0 0 0
11
11 6 4 4 4 1
0 0
0 0
0 0
4 3 2 1 0
2 0 0
~
The number of quadrats containing 1 , 2,
14 fibers was determined for each of the soleus (SOL) and tibialis anterior (TA) motor units
T o test for the existence of “holes” within the motor unit territory, a point-to-nearest neighbor analysis was performed. Figures 7 arid 8 show that in 5 of the 7 units, the actual dist.ribution of nearest neighbor distances deviated from the confidence interval derived for a random distribution using Monte Carlo simulations. The excess of points with large distances to the nearest motor unit fiber suggests the existcnce of “holes” and lends further support to the possibility that motor unit fibers may be organized into subgroups of varying sizes. The calculation of the distances between motor unit fibers gives additional information regarding the distribution patterns of fibers within a single motor unit. Figures 9 and 10 show the areas analyzed wit.hin each of the SOL and T A units and
Table 3. Calculation of the index of dispersion MU
Mean
Variance
ID
df
P value
4.16 8.13 1 .a7
304 261 142 58 155 124 192
9a 94 108 a0
0
SOL1
1.34
SOL2
2.93
SOL3 TA 1 TA2 TA3 TA4
1.42 1.63 2.72 2.10 3.50
1.18 6.20
2.77 7.97
68 94
a5
0 .02 .97 0 .02 0
For each soleus (SOL) and tibialis anterior (TA) motor unit the index of dispersion (ID) was calculated using the equation described in the “Materials and Methods section A P-value was determined from a chi square distribution table with a degrees of freedom ( d f ) equal to n - I . where n equals the number of quadrats Significance was set at P < 0 05
1140
Spatial Pattern of Motor Unit Fibers
the distributions of the actual distances and the confidence intervals generated from the Monte Carlo simulations. I n all of the SOL units (Fig. 9), the actual distribution of interfiber distances neviated from the upper limits of the confidence interval at distances less than 1000 pm. In SOL 1 arid 2, the actual distribution also deviated from random at the larger interfiber distances, having fewer interfiber distances than expected. ‘I‘he large distances, ie, up to 15,000 pm, calculated in SOL 2 reflect the large sample area (-90% of the MU territory) analyzed in this unit. Of the 4 T A units studied? 2 units ( T A I and T A 2) had distributions of interfiber distances that were not. significantly different from that expected from a random distribution of motor unit fibers (Figs. 10A and 13). Further, note that in the point-to-nearest neighbor analysis (Fig. 8 ) , TA 1 and TA 2 were not significantly different from random. In TA 3 (Fig. 10C), there was a significant excess of distances with values less than 600 pm than was predicted from a random distribulion. T A 4 had significantly more interfiber distances less t.han 1600 pm and significantly fewer interfiber distances greater than 1800 p m (Fig. 10D). This unit appeared to be densely packed, having 31 I motor unit fibers distributed over an area equal to only 24 mm‘. In general, the calculation of interfiber distances revealed a tendency for the motor unit to have a pretiomince of short, ie, opraphic;tl i n a p in developing rat gastrocriemius m u ~ l cduririg synapse elimiriation. J P h p u l (Land) 1988;306:47 1-496. 5. Uodine S(:, C.arfiiikc1 A, Koy R R , Edgctton VK: Spatial distrihiiiion of iiiotor uriit libcrs in the cat soleus and tibialis ;tntcrior ~iiuscles: lorn1 interactions. .J N r u t o . , t i I 988;8:2 142- 2152. 6. Bodirie SC, (.;ai-hnkcl A, Koy RK, Edgcrton VK: AII m a l y sis of the spatial distribution of muscle fibers within the territory n t a motor unit. Bioirtec.llcttiir.\.I 98!) (io press). 7. Bodiire SC:, Roy RR, Elrli.cd E, Edgerroil VR: Maxirnal force as a function of aiiatorriic.al features of inotor units 1!+X7;57: 1730in rhr cat tibialis ariteriot. J h’~?rn,ip/zy.s~~~/ 1745. 8. Brandstater ME, Larnbcrt EH: Motor unit :tnarorrly. in Dcsmedt, JS (ed): )V~70L)rvr/u/mwrttt itr PMC rrrtd Clinical h’uurophy.riology. Baael, Karger. 1973, pp 14-22. 9. Buchrhal I;, Guld (:, Rosenfalck P: Multi~lecirodcstudy o f the territory of a motor unit. Artu Physid Sraiid 1 957 ;38 :3 3 I - 354. 10. Burke RE: Motor units: matoiriy. physiology ;ind IMKtional orgmizatioti. in Haridbook o/ Pliyriology. 7%o Nerv0.1~5 S y ~ k r n , Motor Control. Rcthesda, MD; AIL Physiol. Soc. 1981, vol. 2, part I , sect. I , pp 345-422.
1144
Spatial Pattern of Motor Unit Fibers
I 1 Chamhetlain S , Lewis UM: Contractile characteristics and intiervation ratio of rat soleus motor units. ,J Phyriol (Lond) I
1989; 412:1-12. 12. Chheri MH, Lester J M , A r a d l c y W(i, Brenner JF, Hirsrh RP, Silbcr DI, Ziegelrniller D: A cornputer triode1 of dmcrvation- reirinervation in skeletal inuscle. 12/li~sc,le N r n i e 1987; 10:826-836. 13. Cope ‘I.
The spatial distribution of muscle fibers belonging to a motor unit was studied in the soleus (SOL) and tibialis anterior (TA) of adult cats to provide a detailed description of the spatial patterns which exist within the territory of a motor unit. Glycogen depletion of the motor unit was achieved through repetitive stimulation of either the intracellularly identified motoneuron or the functionally isolated motor axon. Muscle fibers belonging to the stimulated unit were identified in serial cross-sections, and in the cross-section which contained the most depleted fibers the centroid of each depleted fiber was determined. Subsequently, three spatial analyses, ie, a quadrat analysis, a point-to nearest neighbor analysis and an interfiber distance analysis, were used to determine if motor unit fibers were distributed randomly throughout the territory of the unit. Motor unit fibers tended to be localized within the muscle cross-section and were not evenly or homogeneously distributed throughout the territory. In general, the analyses suggested that motor unit fibers may be arranged in clusters or subgroups of varying size. The data demonstrate three different quantitative analyses for studying the organization of muscle fibers of normal motor units, which can be used for objective assessment and diagnosis of neuromuscular diseases. Key words: Monte Carlo simulations glycogen depletion soleus tibialis anterior spatial statistics MUSCLE & NERVE 13:1133-1145 1990
.
SPATIAL DISTRIBUTION OF MUSCLE FIBERS WITHIN THE TERRITORY OF A MOTOR UNIT SUE BODINE-FOWLER, PhD, ALAN GARFINKEL, PhD, ROLAND R. ROY, PhD, and V. REGGIE EDGERTON, PhD
Motoncuroris located in specific regions of the lateral motor column of the spinal cord innervate specific musclcs of the hiiidlinih with remarkable acc~racy.".'~Moreover, motor axoris belonging to a specific muscle nerve appear to selectively innervate specific rcgions of a muscle fxom thc initial stages of the innervation proccss, ie, prior to synapse elimination, and establish what are conimonly referred t.o as muscle compartments prior to the period of synapse elimination.2'4"4'20'""The From the Department of Kinesiology (Drs Bodine-Fowler, Garfinkel, and Edgerton) and Brain Research Institute (Drs Roy and Edgerton), University of California at Los Angeles. Los Angeles. CA. Acknowledgments: This work was supported by National Institute of Neurological and Communicative Disorders and Stroke Grant NS-16333 We thank Drs. Tim C. Cope and John A Hodgson lor their contributions to the collection of this data. We also thank Dr Donald Walter for his assistance in writing the analysis programs Address correspondence and reprint requests to Sue Bodine-Fowler. PhD. Division of Orthopaedics. Unlversity of California, San Diego, V A. Medical Center, V-151, 3350 La Jolla Village Drive, San Diego, CA 92161. Accepted for publication December 13. 1989. CCC 0148-639X/90101201133-013 $04.00 0 1990 John Wiley & Sons, IIIC.
Spatial Pattern of Motor Unit Fibers
degree to which a motoneurori selectively innervatcs muscle fibers within the whole muscle or muscle compartments, however, is relatively tinknown. 'l'he distribution pattern of muscle libers belonging to a motor unit should reHect the net rcsult of thc control cxerled by thosc mechanisms which influence the Iorination and elimination of synapses. Mammalian muscle fibers are multiply innervated a t birth, however, during the first few weeks of postnatal development all but one of' the synapses is eliminated." Synapse elimination could have some role in determining the spatial arrangenierit of muscle fibers belonging to a single niotor unit. By studying Lhe spatial distribution of' muscle fibers belonging to a single motor unit, pallerns may emerge which lend insight into the mechanisirrs which govern the formation and/or elirnination of rriusclc libers during development and reiiincrvalion. Further, a detailed description 01' the pat.terns which exist in normal motor units should aid in the interpretation 01. single-fiber EMG data and provide a quantitative measure of assessing aiid diagnosing the involvcment o f de-
MUSCLE & NERVE
December 1990
1133
A'
FIGURE 1. Distribution of depleted motor unit fibers within the defined territorial boundaries of the unit (A). For the quadrat analysis, the maximum x and y distances within the motor unit were calculated and a square with sides equal to the longer of the two distances was drawn to enclose all the fibers belonging to the unit. This sample area (B) was divided into smaller squares or quadrats and the number of fibers in each quadrat was counted. Only those quadrats located within the territorial boundaries of the motor unit (quadrats with triangles) were used in the calculation of the index of dispersion
generation and reinncrvation in neurogenic muscle diseases. The fibers belonging to a motor unit can he visualized using glycogen depletion techniques. Quantification of the distribution patterns of the muscle fibers belonging to identified motor units is liniited to a few Brandstater and Lanibert" reported that the nunibcr of adjacencies among rriotor unit fibers was not different from random, while Willisoii"2 clairried t o fitid eviderice
''
supporting nonrandom innervation, in that fewer adjacericies were found among motor unit fibers than would be expected t'rom a random distribution. I n a recent we found that the incidence of fibers of the samc unit being adjacent to one another was riot difTerent from random, ie, there appeared to be 110 processes that tended to prevent or ericourage riiotor unit fibers LO be adjacent to one another. I n general, previous descriptions of the distri-
((7)
c BQ
/"..,
WM MU
==
40 mm2 53
,-_
WM MU
53 mm2 23 mmz
. , '
\
. .. . . _ . ? :. :. 'I.
.
I
_ ... ..
'
.
FIGURE 2. Location of motor unit territory within the whole muscle cross-section and distribution of depleted motor unit fibers within the territory for soleus (SOL) units 1 (A), 2 (B), and 3 (C). The area of the whole muscle cross-section (WM) and motor unit territory (MU) are given for each unit.
1134
Spatial Pattern of Motor Unit Fibers
MUSCLE & NERVE
December 1990
hution of motor unit fibci-s has been based on visual interpr-etations lrom rlycogen depleted units. nrandstater and Lambert desc.ribed the distribution o f motor unit fibers i n 23 T A units of the rat as being “diffusely scattered throughi>ut the motor unit territory, with little or no tendency for grouping.” Phrases such as “randomly scattered,” “irregularly spaced,” and “uni Iormly dispersed” have also been used to describe the spatial patterns of motor unit fibers.”.”’.‘’ The purpose of the present study was to evaluate the spatial distribution of motor unit fibers by analyzing the palterns which exist over the cnt.ir-e motor unit territory using several density and distance rrieasurements. ‘I’he nicasures used in this study were designed to tcst the hypothesis that. the muscle fibers innervated by a single motoncuron are ranclorrrly distributed throughout t.heit- territory in the rnuscle cross-section. To achieve t.his, actual distributions of the spatial arrangements of‘ nio~or unit fibers were calculated arid compared to what would be expected from a purely random process based on Monte Carlo simulation tct:h~iiques.‘~ Preliminary results have been reported cIsewhere.”
b
slimuldtion of the muscle fibers, using a stirridus paradigm that optimized glycogeii utilization and minimi7ecl neuromuscular junction tailure.’ Upon cessation of stimulation, the muscle was excised, weighed, cut into blocks, arid rapidly lrozen in isopentane cooled to - 160°C with liquid nitrogen. Histological Mapping of Motor Unit. Muscle fibers belonging to a stimulated motor unit (MU) were identified by their low level of glycogen. It was assumed that all depleted fibcrs belonged to thc siirnulated unit and that the stimulation regime used, depleted all and only those fibers belonging to the unil. ‘1’0assess the glycogen count of fibers, cross-sections (20 km) were cut from the experimental muscle and stained using the periodic acidSchiff Only those cross-sections in which a perpendicular section containing no oblique fibcrs was obtained, were used in the spatial analyses. The level of glycogen staining was determined using an image-processing computer system which calculated an optical density of glycogen staining lor each fiber that was o u t l i ~ i e d . ~ ” ~ ~
TA 1
MATERIALS AND METHODS
T h e muscle Iibers innervated by a single motoneuron were identified using glycogen depletion techniques in 3 soleus (SOL) Zind 4 tibialis antct-ior ( T A ) units in 7 adult (6 nionths or older) cats. Experiments were performed under pentobarbital anesthesia, 35 rrigikg, IP, supplemented intravenously as needed to keep withdrawl and eye-blink responses supp~essecl. The spinal cord was exposed from level L5 to SI arid the rnusclcs ol‘ the tail, hip, thigh, arid lower leg were tienervated with the excepliori of the ‘ I A o r SOL, which were isolated f’~.orn surrc.)unding tissues will1 care taken to preserve tlic tdood supply t o each muscle. I n each TA muscle, one rriotor unit was characterizcd physiologically and glycogen depleted by stimulating its func:tionally isolated axon. Criteria for functional isolation were elicitation of ( 1) an all-or-none twitch response following lilanicnt stiniulat,ion at voltages ranging f.rorn threshold to X10 threshold, (2) a corresponding all-or-norie EMG recorded from the niusclc demonstrating a consistent waveform, and (3) an all-or-none action potential in the ventral root filament following graded stimulation of the muscle nerve. Soleus motor units were isolated arid stimulated using itit.racellular tecliriiques as descrilied by Cope et. Glycogen (1epIetion of the iiiotor unit was achieved through repetitive Motor Unit Identification.
Spatial Pattern of Motor Unit Fibers
WM
= 200 mm2
MU =
16
mm2
(r.< 1;7 : ;’:i : i; .:
A 7 ;. .’._.
. . .. . ..... _ ... ._ . . . . . . . . . .__
D-
TA 4 200 mmz M U = 24 mm2 WM
I
FIGURE 3. Location of motor unit territory within the whole muscle cross-section and distribution of depleted motor unit fibers within the territory for tibialis anterior (TA) units 1 (A), 2 (B), 3 (C) and 4 (0).The area of the whole muscle cross-section (WM) and motor unit territory (MU) are given for each unit.
MUSCLE & NERVE
December 1990
1135
80
-
0
> 0 E
60
k U
cew I-= -e
~
.
0
40-
.
UI
?; F
20 -
3YI
W
W
W
U
0,
50
I
0
r
U
?!
40
-
[E-
E "E
Fg
30-
h pi
20-
W W
9 10
!
50
I
150
250
350
NUMBER OF FIBERS FIGURE 4. Relationship between the number of motor unit fibers and (A) the relative territory size and (B) the absolute territory size for the 3 soleus (SOL, a) and 4 tibialis anterior (TA, m) units analyzed. These data were taken from that cross-section with the largest number of depleted motor unit fibers.
The position of glycogen-depleted muscle fibers was mapped on serial cross-sections taken along the length of the muscle. From that cross-section which contained the greatest number of depleted muscle fibers, ie, motor unit fibers, the x, y coordinate of the centroid of each fiber was determined and saved in a computer file. The territory of the motor unit, ie, the region of the muscle occupied by the fibers innervated by a single motoneuron, was estimated by connecting outlying fibers by straight lines to form the smallest convex area containing all of the motor unit fibers. The term motor unitfiber will be used to refer to those muscle fibers innervated by a single motoneuron. Spatial Analyses
Qu,adrat Analysis. The territory of each motor unit was divided into small subregions to assess the variability of fiber density. For each MU, a square was drawn to enclose all the fibers belonging to the unit (Fig. 1A). The dimensions of the square were determined by calculating the maxi-
1136
Spatial Pattern of Motor Unit Fibers
tances between MU fibers. The dimensions of the square were set at the longer of the two distances. This area then was divided into square subregions or quadrats (Fig. IR), and the number of MU fikers in each quadrat was counted arid used to calculate the index of' dispersion. Note t.hat this area was often larger than the convex area representing the MU territory. However, only those quadrats residing within the territory defined by the convex area were included in the calculation of
dispersion, a sensitive measure for detecting a lack of homogeneity in a dist.ribution of points,31 was calculated as follows. I f the observed counts in n quadrats are denoted by x l , x2, xS . . ., x n , then these counts have a nieaii x = xz/n and a variance s p = x i - ? l ' / ( ~ ~ - I )where , the summat.ions are ovathe values of i from 1 to Y ~ L 'l'he index of dispersiori can be calculated using the equation: [ ( n - l ) ~ % ] . For " ~ a random distribution, the index of' dispersion should have a chi-square distribution, provided tliat the number- of' quadrats is greater Lhan six arid tlic i r i c x i is greatcr than one.3 I These criteria were met for each of the 7 units studied. Distribution of Interfiber Distances. 'I'he distances between each m&r unit fiber and all other motor unit fibers were calculated to provide information regarding the spacing of M U fibers within the territory. For each unit, a polygonal subregion of the MU territory was chosen which maximized the number of MU fibers included for analysis yet cxclutied those areas witliiri the territory which did not contain M U fibers. Inclusion of a large area which did not contain MU fibers would tend to bias the analysis towards finding a clustering pattern. Consequently, we selected an area within the defined territory which excluded large areas devoid of MU fibers, thercby biasing the analysis in the direction of not. finding clustering. Within each subregion, the interfiber distances between motor unit fibtrs were calculated. For each fiber in the sample area, the distance bctween it and every other niotor unit fiber was calculated as the distance between the (x, y) coordinates of the centroids of each fiber. For n motor unit fibers, a total of (n' - n)/2 distances were computed for those pairs i, j ( 1 5 i < j 5 11,). A histogram of the distances derived from the motor unit was compared to histograms derived from Monk Carlo simulations in order to deter-
MUSCLE & NERVE
December 1990
mine whether thc actual distriburion of distances was significantly different from random. For each unit, a Monte Carlo simulation was carried o u t by choosing n (x, y) locations (where n equaled the number of MU fibers) randomly and independently within the sample area. To account for the fact that fibers have finite sizes, the minimum distance between randomly chosen points was restricted to the shortest distance found between M U fibers in the actual sample. Interfiber distances were calculated and entered into a histogram with the same bin sizes as the actual distribution. A total of 100 simulations were performed for each unit and a confidence interval was generated. The confidence interval was defined as follows: for each bin, the I00 simulations were sorted from high to low and the third highest and third lowest of the values were chosen as the upper and lower 3% confidence limits (P < 0.06). Kundom, Points to Nearest M U Fiber. T h e distribution of distanccs from randomly chosen points within the sample area to the nearest MU fiber was determined to test the hypothesis that there are holes, ie, areas containing no MU fibers, in the distribution of M U fibers. In each M U , a rectangular subregion of the territory was chosen for analysis. This subregion was riot the same as the one used [or the interfiber distance analysis because the program required a rectangular region for analysis. The reason for this limitation is that this measure is scnsitive to edge effects, and therefbre edge corrections must be used, the best of which is the toroidal method in which opposite edges are identified. In order to do that, a rectang d a r legion is ne~essary.'~ It should be noted that the number of rectangles that could be drawn within each M U territory was limited by the shape ancl size of the territories. Consequently, areas were chosen which maximized the number of points to be analyzed given the restraints of the software. The rectangular sample area was dividcd into approximately lOn square boxes (where r i equals the nurnber of fibers in the sample area) and a point was chosen at random in each box. 'l'he distance from each raiidomly chosen point to the nearest. MU fiber was calculated. The distribution of point-to-nearest ncighbor distances was plotted and compared to a distribution generated b y Monte (;ado simulations. 'I'he Monte Carlo procedures were similar to those described for the interfiber distance measuremerit. For each unit, n points wcre chosen at random within the sample area. 'The sample area was divided as described above and the point-to-
Spatial Pattern of Motor Unit Fibers
nearest neighbor distances were calculated. The simulations were repeated 100 times for each unit, and the high and low 3% probabilities ( P < 0.06) were derived. RESULTS
The spatial distribution of motor unit fibers over the muscle cross-section was investigated in 7 units: 3 slow SOL units; 1 slow T A unit; 2 fast, fatigue-resistant T A units; and 1 fast, fatigue-interA 121
SOL 1
B
14
0
FIGURE 5. A 3-dimensional representation of the distribution of motor unit fibers within the defined MU territory for soieus units 1 (A), 2 (B), and 3 (C). The z-axis represents the density of motor unit fibers within each quadrat. The number given on the z-axis represents the maximum density per quadrat.
MUSCLE & NERVE
December 1990
1137
Table 1. Physiological properties of motor units in the cat soleus and tibialis anterior muscles ~~~
Motor unit
SOL1 SOL2 SOL3 TA1 TA2 TA3 TA4
Type
CT (rns)
Po (9)
S S S
107
112 156 137 52 96 12 7 29.0
S FR FR FI
65 63 39 39 33 23
IR
Myosin staining
135
Light Light Light Light Dark Dark Dark
278
169 132 188 243 311
Abbrevmons CT coritraction time, Po maximum isometric tetanic tension, IR, innervation rabo of that muscle cross section with the greatest number of depleted motor unit fibers Motor units were classified into types based on the mechanfcal characteristics of the muscle unit S, slow, FR, fast fatigue-resistant and Fl. fast fabgue-intermediate Muscie fibers were ciassified as eithef hghl (siow) or dark (fast) based on thev reactions to staining for myosin ATPase, alkaline preincubation
mediatc TA unit. The niaxiniuni tetariic tensions of the 3 SOL units were 11.2, 13.7 and 15.6 g (Table l), tensions that are within the population range (3.2 to 40.2 g) for adult cat soleus units."'"" The T A units had maximum tetanic tensions be-
tween 5.2 and 29.0 g, also witliiii thci prcvioiisly repor-ted population range 01. I .O to 40.0 g for the cat I.A.'' 'I'he riuiriber hf fibers per unit ranged from 132 to 3 I I fi t n - s for t tie 7 units. I t slwuld tx noted that previous studies in ttic cat7 and rat" show a strong positive (:orrelation between maxir n u m tetanic tension and the iiumber of' fibers inriervaled by a single motoriwron. Moreover, it has been s h o w n that ariiong innervation ratio, mean fiber cross-sectional area mid spccific tension, ie, variahlcs wtiich influence maxirnuni tetanic tension, innervation ratio is the priniiii-y determinant of thc niaxirrium tetanic tension of ;1 motor unit.7
The location of the M U territory within that cr-oss-section which contained the largest number of depleted fibers ancl the distribution of the depleted motor unit fibers arc shown for cach of tlic SOL arid '1.A units in Figures 2 ancl 3, respectively. The territory of' eac-l-i unit, as illustrated in E'igurcs 2 arid 3, was defined as thc srriallest convex area containing all motor Motor Unit Territory Size.
B A
51 10
0
TA 1
C
TA 2
D 71
TA 3 TA 4 FIGURE 6. A 3-dimensional representation of the distribution of motor unit fibers within the defined MU territory for tibialis anterior units 1 (A), 2 (B), 3 (C), and 4 (D). The z-axis represents the density of motor unit fibers within each quadrat. The number given on the z-axis represents the maximum density per quadrat.
1138
Spatial Pattern of Motor Unit Fibers
MUSCLE & NERVE
December 1990
SOLEUS
unit l-iibers. I n general, the fibers belonging t o a unit were riot distributed across tlie entire riiirsc:le cross-scction, hut were localized to a particular region of the muscle. Moreover, the territory was generally more elliptical than circular in shape. 'Ihc relative territory size of c:ich unit, calculatccl as a percentage of the whole muscle cross-section, ranged from 8% to 76% (Fig. 4A). *l'ticSOL units extended over a larger pr.rce11tage of t.he muscle cross-section (41$% to 76%) iliari the T A units (8% to 22%). Calculation 01' the absolute size of' each of the motor uriit territories revcaled that the torritories of the SOL arid ?'A units were similar in sizr:, ranging f'roin I ( j t o 47 iiirii' (Fig. 413). 'Tilc cIiITorerice iri the relative a r i d absolutc s i x s of' SOL a i d T A units was related to differences in wholc muscle cross-sectional areas, ie, the ci-oss-sectional area of the T A i s 4 tirrles that of thc SOI. (see Figs. 2 and 3 ) .
A
To investigate how motor unit fibers were distributed througho u t their territory, a quadrat analysis was pcrformecl on each of the units. For each unit, a sumniary of ttic number of quadrats with fiber cknsitics ranging from 0 to 14 fibers is givcti in Tablc 2. Within ~tlieterritory dehried by Llie convex area, sevei-al of the units had a large number of quadrats which coiit;iined no motor unit fibers. 'These quadrats were iricluded in the analysis since they resided within the territorial boundaries of the unit. The index of dispersion, a nieasure used t.o detect a lack of horiiogeneity in a point was calculated for each unit using the quadrat density data given in Table '2. As showri in Table 3, 6 0 1 the 7 units tiad significant index of dispersion values, indicating that the disiribution of MU fibcrs deviated lrom a randorn distribution. In general, tlie 6 units with significant index of' clispersion values had large ranges in their quadrat densities which resultecl in relatively large variances (Taklc 3). A large variance :iiieaii raiio suggests the presence of clustci-s within the clistribu tion. Figures 5 and 6 illustrate, in 3-ditrierisioiis, how t.he motor unil fi1)ers were clistributecl throughout their territory fi)r each of' the SOI. and T A units. 'I'liese plots i1lustrat.e that M U {ibers were not evenly distributcd throughout tlie M U territory. Notice that regions of high arid low fiber densities were scatterecl throughout the unit, as opposed t o being located in ihe center of the M U territory. Moreover, tticrc iippearecl to be regions with no motor unit fibers, ie, "holes," within the territory of the unit. Distribution of Motor Unit Fibers.
0
200
400
600
BOO
C 1000 -
750
-
500 -
250
-
O i
DISTANCE (pm) FIGURE 7. Distribution of nearest neighbor distances calculated from the point-to-nearest neighbor analysis. For soleus units 1 (A), 2 (B) and 3 (C), nearest neighbor distances were calculated and plotted in histograms with bin widths of 55, 59, and 50 km, respectively. The actual distribution is represented by the bold lines and the 95% confidence interval, determined from the simulations, by the narrow lines. The arrows denote areas where the actual distribution significantly deviates from a random distribution.
Spatial Pattern of Motor Unit Fibers
MUSCLE & NERVE
December 1990
1139
Table 2. Quadrat analysis SOL1
SOL2
TA2
TA3
TA4
16 10
2 0 0
10 31 24 13 1 2 0 0 0
12 13 11 11 10 11 6
1 1
18 19 24 17 10 1 5 1 0 0 0 0 0
SOL3
TA1
Number of quadrats
Number of fibers per quadrat
6
2 4 1
7
3
a
0
9 10 11 12 13
0
15 17 18 18 10 7 2 0 2 2
0
0
0
0
0
1
0
1
1 1
0 0 0
1
0
0
0 1 2 3 4 5
46
25 10
7
0 0
14
35 27 25 15 4 1
0
0 0 0
11
11 6 4 4 4 1
0 0
0 0
0 0
4 3 2 1 0
2 0 0
~
The number of quadrats containing 1 , 2,
14 fibers was determined for each of the soleus (SOL) and tibialis anterior (TA) motor units
T o test for the existence of “holes” within the motor unit territory, a point-to-nearest neighbor analysis was performed. Figures 7 arid 8 show that in 5 of the 7 units, the actual dist.ribution of nearest neighbor distances deviated from the confidence interval derived for a random distribution using Monte Carlo simulations. The excess of points with large distances to the nearest motor unit fiber suggests the existcnce of “holes” and lends further support to the possibility that motor unit fibers may be organized into subgroups of varying sizes. The calculation of the distances between motor unit fibers gives additional information regarding the distribution patterns of fibers within a single motor unit. Figures 9 and 10 show the areas analyzed wit.hin each of the SOL and T A units and
Table 3. Calculation of the index of dispersion MU
Mean
Variance
ID
df
P value
4.16 8.13 1 .a7
304 261 142 58 155 124 192
9a 94 108 a0
0
SOL1
1.34
SOL2
2.93
SOL3 TA 1 TA2 TA3 TA4
1.42 1.63 2.72 2.10 3.50
1.18 6.20
2.77 7.97
68 94
a5
0 .02 .97 0 .02 0
For each soleus (SOL) and tibialis anterior (TA) motor unit the index of dispersion (ID) was calculated using the equation described in the “Materials and Methods section A P-value was determined from a chi square distribution table with a degrees of freedom ( d f ) equal to n - I . where n equals the number of quadrats Significance was set at P < 0 05
1140
Spatial Pattern of Motor Unit Fibers
the distributions of the actual distances and the confidence intervals generated from the Monte Carlo simulations. I n all of the SOL units (Fig. 9), the actual distribution of interfiber distances neviated from the upper limits of the confidence interval at distances less than 1000 pm. In SOL 1 arid 2, the actual distribution also deviated from random at the larger interfiber distances, having fewer interfiber distances than expected. ‘I‘he large distances, ie, up to 15,000 pm, calculated in SOL 2 reflect the large sample area (-90% of the MU territory) analyzed in this unit. Of the 4 T A units studied? 2 units ( T A I and T A 2) had distributions of interfiber distances that were not. significantly different from that expected from a random distribution of motor unit fibers (Figs. 10A and 13). Further, note that in the point-to-nearest neighbor analysis (Fig. 8 ) , TA 1 and TA 2 were not significantly different from random. In TA 3 (Fig. 10C), there was a significant excess of distances with values less than 600 pm than was predicted from a random distribulion. T A 4 had significantly more interfiber distances less t.han 1600 pm and significantly fewer interfiber distances greater than 1800 p m (Fig. 10D). This unit appeared to be densely packed, having 31 I motor unit fibers distributed over an area equal to only 24 mm‘. In general, the calculation of interfiber distances revealed a tendency for the motor unit to have a pretiomince of short, ie, opraphic;tl i n a p in developing rat gastrocriemius m u ~ l cduririg synapse elimiriation. J P h p u l (Land) 1988;306:47 1-496. 5. Uodine S(:, C.arfiiikc1 A, Koy R R , Edgctton VK: Spatial distrihiiiion of iiiotor uriit libcrs in the cat soleus and tibialis ;tntcrior ~iiuscles: lorn1 interactions. .J N r u t o . , t i I 988;8:2 142- 2152. 6. Bodirie SC, (.;ai-hnkcl A, Koy RK, Edgcrton VK: AII m a l y sis of the spatial distribution of muscle fibers within the territory n t a motor unit. Bioirtec.llcttiir.\.I 98!) (io press). 7. Bodiire SC:, Roy RR, Elrli.cd E, Edgerroil VR: Maxirnal force as a function of aiiatorriic.al features of inotor units 1!+X7;57: 1730in rhr cat tibialis ariteriot. J h’~?rn,ip/zy.s~~~/ 1745. 8. Brandstater ME, Larnbcrt EH: Motor unit :tnarorrly. in Dcsmedt, JS (ed): )V~70L)rvr/u/mwrttt itr PMC rrrtd Clinical h’uurophy.riology. Baael, Karger. 1973, pp 14-22. 9. Buchrhal I;, Guld (:, Rosenfalck P: Multi~lecirodcstudy o f the territory of a motor unit. Artu Physid Sraiid 1 957 ;38 :3 3 I - 354. 10. Burke RE: Motor units: matoiriy. physiology ;ind IMKtional orgmizatioti. in Haridbook o/ Pliyriology. 7%o Nerv0.1~5 S y ~ k r n , Motor Control. Rcthesda, MD; AIL Physiol. Soc. 1981, vol. 2, part I , sect. I , pp 345-422.
1144
Spatial Pattern of Motor Unit Fibers
I 1 Chamhetlain S , Lewis UM: Contractile characteristics and intiervation ratio of rat soleus motor units. ,J Phyriol (Lond) I
1989; 412:1-12. 12. Chheri MH, Lester J M , A r a d l c y W(i, Brenner JF, Hirsrh RP, Silbcr DI, Ziegelrniller D: A cornputer triode1 of dmcrvation- reirinervation in skeletal inuscle. 12/li~sc,le N r n i e 1987; 10:826-836. 13. Cope ‘I.
