soleus motoneurone excitability in man: an indirect ... · of medicine (neurology), mcmaster...

Journal ofNeurology, Neurosurgery, and Psychiatry, 1979, 42, 1091-1099

Soleus motoneurone excitability in man: an indirectapproach for obtaining quantitative dataA. J. McCOMAS, M. MIRSKY, F. VELHO, AND A. STRUPPLER

From the Neurologische Klinik der Technischen Universittat Munchen, Munchen, West Germany

S U MM A R Y Using combinations of H and T reflexes, spatial summation has been studied in thehuman soleus motoneurone pool. With certain assumptions, mathematical treatment of theresults yielded estimates of the thresholds of motoneurones to monosynaptic activation by Ianerve fibres. It was found that, on average, about 62 EPSPs were required to discharge a moto-neurone and that a single Ia fibre supplied about 139 neurones.

Using intracellular recording the responses ofmotoneurones to monosynaptic inputs from primaryendings of muscle spindles have been investigated invarious species and in the cat in particular (see Eccles,1957, and Discussion). These studies have enabledthe excitatory postsynaptic potentials (EPSPs) evokedby single impulses in Ia nerve fibres to be measured.In addition, estimates have been made of the degreeof branching, or divergence, of la fibres within themotoneurone pool. For obvious reasons it has notbeen possible to apply the same experimental tech-niques to man, and consequently quantitative dataconcerning the synaptic connections between primaryafferent nerve fibres and motoneurones have beenlargely lacking. The purpose of this paper is todemonstrate that the problem ofsynaptic connectivityin man can be approached indirectly, provided certainmajor assumptions are permitted. A preliminaryreport has appeared elsewhere (McComas et al.,1979).The method to be described makes use of the twin

phenomena of subliminal fringes and spatial summa-tion described by Sherrington (1929). The term"subliminal fringe" was applied to those cells situatedaround a zone of discharging neurones, whichreceived some excitation themselves but insufficient toinitiate impulses. Sherrington recognised that if twogroups of afferent fibres were stimulated simul-taneously, parts of the subliminal fringes couldoverlap and some of the cells would then gathersufficient excitation to discharge impulses. This was"spatial summation." Because of this extra fraction

Address for reprint requests: Professor A. J. McComas, Departmentof Medicine (Neurology), McMaster University Medical Centre,1200 Main Street West, Hamilton, Ontario, Canada L85 4J9.

1

2

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Fig. 1 Extents of fublim-nal fringes (concentric ring,)arcund two neuronvs (innermost stippled circles)requiring one, two, or five EPSPs respectively forimpulse initiation. When two simultaneous stimuli arepresented the additional number of neurones that willdischarge as a resu!t of spatial summation is identifiedby extra stippling. Numbers in circles refer to EPSPsreceived by cells in different parts of motoneuronepool as a result of spatial summation. See text.

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A. J. McComas, M. Mirsky, F. Velho, and A. Struppler

of discharging cells, the response to two simultaneousstimuli would exceed the sum of the responses to thesame stimuli delivered separately. It is evident thatthe subliminal fringe will be increased for cells withrelatively high thresholds, that is, for cells requiringlarger numbers of EPSPs for impulse initiation.Figure 1 shows that the opportunity for spatialsummation must also be greater for these cells. Thisrelationship would suggest that if the degree ofspatial summation could be measured it might then bepossible to determine thresholds of the cells, providedthat the EPSPs sum in a linear manner (Burke, 1967).We will now show that, subject to certain assumptions,mathematical treatment of the situation is indeedpossible.Suppose that a single la fibre branches to make

excitatory synaptic connections with d cells within apool ofM motoneurones. After one impulse in thisfibre d neurones will receive one EPSP while M- dcells will remain unaffected. The chance of any onecell receiving an EPSP will be dIM.

If on the next occasion an additional la fibre isactivated and also fires a single impulse, there willbe 2d EPSPs distributed throughout themotoneuronepool. Under these conditions the chance of any onecell gathering two EPSPs-that is, one from each ofthe la fibres-will be (diM)2. The number of neuronesin this state will be d. (d/M). The number of neuronesreceiving only one EPSP will now be 2d- (2d2/M) =2d[J - (d/M)].

Similarly, if a third Ia fibre is activated, the numberofcells gaining three EPSPs will bed3/M2. The numberof cells with two EPSPs will be equal to the cellspreviously receiving two EPSPs (d2/M, see above),minus those cells which have acquired a third EPSP(d2/M. dIM), plus a new population of cells, formerlyreceiving one EPSP, which have now gathered asecond (2d [1-(dIM)] . dIM):

d+d.2d(I .=3d (1_d)

The number of cells having only one EPSP will be3d, the total number of EPSPs delivered, minus twicethe number of cells receiving two EPSPs and threetimes the number of cells gathering three EPSPs.That is, the total number of cells with one EPSP willbe:

3d2r3d(J d 3d3 6d2 M3d3Md-M2IJ M2 M M2

Thus, if there are 1000 cells in the motoneurone pooland three la fibres are activated, each of which dividesto supply 100 motoneurones randomly, then therewill be:

1OO3=one cell with three EPSPs

3100021 101000 VI-ooo) =27 cells with two EPSPs

and

300- 6 x100 + 3X100 =243 cells with three EPSPs

The same approach can be used to calculate thenumbers of motoneurones receiving different excit-atory inputs when larger numbers of Ta fibres areactivated.The next aspect to consider is the result of applying

two volleys, in different populations of Ia fibres, to thesame motoneurone pool simultaneously. For sim-plicity, imagine that each volley involves only threeIa fibres and that, as in the example above, each fibrefires a single impulse into its 100 branches. Supposealso that the motoneurone pool comprises 1000 cellsand that only three EPSPs are needed to initiate animpulse (that is, y =3).Under these circumstances each volley, if delivered

separately, would have been expected to excite onecell with three EPSPs, thereby causing it to discharge.When the two volleys are given together, however,there will be partial overlap of the two subliminalfringes. Thus, some of the cells receiving two EPSPsfrom one volley will receive one or two EPSPs fromthe other volley and consequently discharge.

In the present example such an occurrence wouldinvolve:

(27+ 243)27 x = 7.3 cells1000

Finally, some cells receiving one EPSP from onevolley will gather two EPSPs from the other. Sum-mation of this kind would involve:

27243 x l =6.6 cells1000

Since only three EPSPs are needed to cause amotoneurone to discharge there will now be a total of2+7.3 + 6.6= 15.9 cells responding when the twovolleys are given together.

Recalling that each volley by itself would have onlyfired a single motoneurone, the facilitation, F,produced by the two volleys togethermay be expressedas:

15.9

In summary, if 1000 motoneurones have similarthresholds (see Discussion) and iftwo weak excitatoryvolleys are presented, each of which fires a single cellby itself but which together cause 16 cells to discharge,it can be deduced that the excitatory threshold for themotoneurone is three EPSPs and that each volleyinvolves only three Ia fibres.

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Soleus motoneurone excitability in man

5.m. obtained first, by applying weak electrical stimuli to/ No. the tibial nerve behind the knee so as to elicit H reflexes

neurones (Hoffmann, 1918), and second, by lightly percussing.2) the Achilles tendon, thereby evoking T (tendon)

reflexes.The amount of facilitation, F, will then be equal to

HT/(H+ T), where H and T are the neurones dis-charging in the H and tendon reflexes respectively,

/51 and HT represents the combined response to pairedelectrical and mechanical stimulation.

4. It is well established that weak electrical stimulationof the tibial nerve preferentially activates muscleafferent fibres capable of evoking monosynapticresponses in homonymous motoneurones (Hoffmann,

No. EPSPs 1918; Magladery et al., 1951) and, by analogy with-(10) extensive studies in animals, there is little doubt that

the sensory fibres involved are of the Ia moiety.- *///-.520) Similarly, it has been shown in animals that the

20 * - / @2- primary endings of the muscle spindles have thel I lowest thresholds to rapid stretch, such as that50 100 1502i 250 300 350 produced by a tendon tap (Lundberg and Winsbury,

DIVERGENCE (d) 1960; Matthews, 1972), and are connected to Iafibres. There are no a priori grounds, however, for

Amount of facilitation (F) to be expected for supposing that the two types of stimulation employedatioons of motoneurones with different thresholds in this study would have selectively activated theipulse initiation (ie different critical numbers ofPs(y)) and four different degrees of axonal same Ia fibres. Further, given the small sizes of thehing. The critical numbers of EPSPs are stimuli, it is unlikely that any of the Ia fibres would beited by values at left of curves and are assumed activated by both types of stimuli by chance (see*respond to the numbers o.f Ia fibres activated Discussion).ext). Numbers at right in parentheses show It should be noted that it is not actually necessary'ations of motoneurones reflexly excited by single to know M, the population of motoneurones in the

i5 pool, to find either the number of EPSPs required todischarge a cell, y, or d, the extent of axonal diver-

Iure 2 shows the facilitation to be expected when gence (branching). Provided the reflexly-dischargingring thresholds of motoneurones, the degrees of cells amount to 0. 1, 0.2, 0.5, 1, or 2% respectively ofhing (divergence) ofIa fibres, and the sizes ofthe the total population, the five curves in Figure 2 willdischarges (to one volley alone) are altered. For be applicable to the results. Experimentally, thecurve it is assumed that the two impulse volleys percentage of motor units, and hence of moto-insible for spatial summation are ofequal size. In neurones, participating in an H or T reflex may bement with Fig. 1 it can be seen that facilitation is determined by comparing the amplitude of thatest when the firing thresholds of the cells are response to the muscle M wave evoked by maximal1. Facilitation is also larger when relatively a-motor nerve fibre stimulation. In practice it isLexcitatory inputs are employed. Figure 2 also difficult to obtain small H and T reflexes of equals that, if the sizes of the initial reflex responses amplitude and instead the average size of the twothe amount of facilitation are measured, it is responses can be used for comparison with the Mble to determine the average number of EPSPs wave. The resulting percentage of the motoneuronered for impulse initiation together with the pool can then be interpolated between two of thee of axonal divergence. In plotting Fig. 2 curves in Fig. 2 for the determination of y and d.

it has beenassumed that thenumber ofEPSPs requiredfor impulse initiation also corresponds to the numberof axons stimulated. It can be shown mathematicallythat, since most experiments in this study involvedreflexes with fewer than 10 motoneurones partici-pating, this assumption is valid.

In the experiments to be described the impulsevolleys in separate populations of Ia fibres were

Methods

Experiments were conducted on 18 legs of 15 healthyyoung adults (four men and 11 women) free ofneurological disease. All subjects volunteered for theexperiments and were paid for their services. Subjectslay prone on a couch and were encouraged to relax.

40r

30r

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20r

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Fig. 2populfor inEPSP.brancindicato cor(see tpopulvolley

Figthe filbrancreflexeach (respoagree:great(raisecsmallshowand tpossilrequi]degre

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The ankle of the leg under investigation was fixed in necessary, the Dia holder at a right angle. Ethical problems were stimuli were deli'discussed and resolved at the Neurological Clinic random sequencebefore the experiments started. three types of st

intervals betweenSTIMULATING AND RECORDING ARRANGEMENT mately 10 secondsThe recording electrodes were a pair of metal discs paired, the latter v12 mm in diameter (Beckmann Ltd), coated with by 4.0-8.5 ms, theelectrode jelly. The stigmatic electrode of the pair gave the greateswas placed in the midline over the soleus muscle considered equiv,while the reference electrode was attached to the skin transmission of tof the heel. The earth (ground) electrode was a strap muscle spindles,which was soaked in saline and fastened around the annulospiral endileg below the knee. The signals were fed into a tibial nerve Ia fibTektronix oscilloscope (type 5103) amplifier; they stimulus intensitie:were also entered into an averaging device (Nicolet that is, supraliminmodel 1072). end of a sequence

Electrical stimuli were applied to the tibial nerve in lus strength wasthe popliteal fossa through a pair of pad electrodes, maximum H refle7 mm in diameter, soaked in saline. The stimuli were of the maximumrectangular current pulses, 0.5 ms in duration, using a tendon hzdelivered from a Disa Multistim. with that of the r(

Mechanical stimuli were delivered to the Achilles stimuli. Four trialtendon by a spring loaded hammer, which enabled averaged. Finallythe force to be adjusted. The contact of the hammer response (M wavwith the skin triggered the averager and, when tibial nerve wasm

RELAXED WEAK Cl

(a) (b)

T-

HT HTmA

eisa stimulator. The two types ofvered separately or together in auntil eight responses to each of thetimulus had been averaged. Thesuccessive stimuli were approxi-

s. When the H and T stimuli werewas arranged to precede the formerc selected interval being that whicht facilitation. This interval wasralent to the time occupied bythe force from the tendon to thethe initiation of impulses in theings, and impulse conduction inbres to the level of the knee. Thes selected werejust above threshold,ial, for the T and H reflexes. At theof 24 stimuli (see above) the stimu-raised and the amplitude of thex was determined. The amplitudetendon reflex was next obtainedammer held in the hand, togetheresponse to the combined H and TIs of each type of stimulation werey, the maximum evoked musclere) after strong stimulation of theeasured.

,ONTRACTION

(c)

W-'

I0oo.LV

_L,4

1400,uV

I 1OmV

lOmsFig. 3 Facilitation produced by a combination of H and T st-muli when the subject was relaxed (a) andmaking a weak voluntary contraction of the calf muscles (b and c). In (b) the stimulus strength was the sameas that in (a), while in (c) it was reduced so as to evoke H and T responses similar in size to those in (a). Themaximum evoked muscle response (M wave) is shown at the bottom. Note different amplitude calibrations.

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Results

A total of 41 trials were conducted on 15 subjects inthe relaxed condition; in three of these subjectsmeasurements were made on both legs. The observedamount of facilitation, F, varied markedly from oneindividual to another and also in the same subjectdepending on the level of arousal (see below). Thegreatest facilitation observed in any of the 41 trialswas 17.6 and the mean value for the series was 4.26±3.78. When the values for the same leg were averagedthe degree of facilitation ranged from 1.0 to 10.3 indifferent subjects. The experiment yielding the mostfacilitation in the resting state is shown in Fig. 3. Therelatively small numbers of motoneurones partici-pating in the supraliminal H and T reflexes can begauged by comparison of these responses with that ofthe maximum evoked muscle response (M wave) atthe bottom of Fig. 3.

It was possible to demonstrate two experimentalfactors which influenced the degree of facilitation.These were the strength of the testing stimuli andthe level of voluntary activation of the motoneuronepool.

STIMULUS STRENGTHThe effect of three stimulus intensities on the amountof facilitation is shown in Fig. 4. The intensities weresupraliminal, maximal, and intermediate in relationto the sizes of the T and H reflexes. It can be seen thatas the stimulus intensities increased, the single T andH reflexes enlarged but the facilitation became less.When the facilitation was unity, the extra moto-neurones recruited through spatial summation wereexactly offset by those subjected to occlusion-thatis, some neurones would have discharged to both theT and H reflex stimuli when the latter were presentedseparately. Inspection of Fig. 4 suggests that thiscondition would have been reached when the stimulusintensity was between the intermediate and maximalvalues. For occlusion to be total, the T and H reflexesmust be equal in amplitude and no further incrementin response should occur when the stimuli werepresented together. The corresponding value for Fwould be 0.5. In the 15 experiments in which maximalstimuli were presented at rest full occlusion wasachieved on only two occasions. In the remaining 13experiments the maximum T reflex was smaller thanthe maximum H reflex (Fig. 5). Interestingly, theresponses to combined H and T stimulation (HTresponses) were significantly larger than the maximumH reflex on only one occasion and were at least I0O%smaller than the latter in eight of 15 experiments.Possible reasons are given later (see Discussion).When the results were pooled (Fig. 4) the meanfacilitation calculated for maximal stimulation was

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Q51supraliminal intermediate

STIMUWS

H T HTmaximal

Fig. 4 Top. Facilitation (F) produced in relaxedsubjects by stimulus intensities which weresuprathreshold, intermediate, and maximal forcorresponding tendon and H reflexes. Mean values±SD given at right of each group of results. Notelogarithmic scale. Bottom. Mean (+SD) reflexresponse amplitude to same three stimulus intensitiesdescribed above. Results expressed on log scale aspercentage of motoneurone pool discharging (usingM wave as index of motoneurone pool size).

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70 f

601-

o- 50U)wz 400

w 30z0

O- 20

101-

O0

Fig. 5 Maximal H and Treflexes (filled and open circlesrespectively) in 12 subjects (15legs), arranged in ranking order.The responses to paired H andT stimuli (HT) are shown byhorizontal bars. Resultsexpressed as percentage ofmotoneurone pool discharg.ng(using M wave as index ofmotoneurone pool size).

0.6, ignoring those occasions when the HT responsewas less than the H reflex.

VOLUNTARY ACTIVATIONThe second experimental factor which could beshown to influence the amount of facilitation wasvoluntary activation of the motoneurone pool. If thesupraliminal H and T stimuli were kept constant,the transition from rest to weak contraction of thecalf muscles potentiated both reflexes in accord withprevious observations (see, for example, Fig. 4 ofUpton et al., 1971). The degree of facilitation,however, declined in all 14 pairs of observations. Itcould be argued that this reduction was simply areflection of greater occlusion due to the increasedpopulations of motoneurones involved in the H andT reflexes, in keeping with the observations on theeffects of increased stimulus strength (above). To testthis possibility, further experiments were undertakenin which the stimulus intensity was reduced so that,during voluntary activity, the H and T reflexes wereapproximately of the same amplitude as thoserecorded at rest for slightly stronger stimuli. Even

Table Reflex responses and degrees of facilitation (F)after stimulation during relaxation and weakcontraction of calf muscles. The stimulus wassuprathreshold at rest, was unchanged duringcontraction (middle column of results), and thenreduced to be just above threshold again (right-handcolumn). The response amplitudes have beenexpressed as percentages of the maximum M wave.Abbreviations as given in text

Stimulus Rest Weak contraction

Suprathreshold (a) As for (a) Reduced

H 0.71 ±0.76 1.75±1.60 0.91 ±0.96T 0.99±0.82 2.54±1.54 1.18±0.69HT 4.97±4.39 6.12 ±3.79 3.58 ±2.22F 4.3 ±3.8 1.62±0.70 1.85 ±+0.84Number 41 14 19

under these circumstances it was found that the degreeof facilitation was substantially smaller than thatobserved at rest (Table).

CRITICAL NUMBER OF EPSPSUsing the curves in Fig. 2, an attempt was made todetermine the critical numbers of EPSPs (y) requiredto discharge soleus motoneurones innervating 18legs of 15 subjects studied at rest. In three subjects(four legs) the calculated degree of facilitation wasless than 2 and fell beyond the lower limits of thecurves plotted in Fig. 2. The interpretation of theseresults was that the critical number of EPSPs in suchsubjects ranged from one to two. Unfortunately themathematical analysis described in the introductioncannot be applied to such a situation and theseexperiments were, therefore, omitted from furtherconsideration. For the remaining 12 subjects (28experiments on 14 legs) the mean value for thecritical number of EPSPs was 2.61 ±0.69, the highestindividual value being 4.4. As discussed below, theseresults are only applicable to the most excitable cellsin each of the motoneurone pools and a specialtreatment is necessary to derive mean values for thefull populations of cells.

DIVERGENCE FACTORThe number of motoneurones supplied by a single Iafibre was termed the divergence factor, d (see Intro-duction). This factor was derived from Fig. 2 usingthe curve(s) appropriate to the sizes of the reflexresponses and the observed degree of facilitation, F.In the 28 experiments which were suitable for thisanalysis (see above) the divergence values rangedfrom 64 to 304, the mean value being 139±62.3.

Discussion

Although there have been other studies of synapticresponses resulting from inputs in two different Ia

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afferent nerve fibre populations, these have beenconcerned with the time course of changes in synapticexcitability (for example, Katz et al., 1977). Thepresent study appears to be the first to give a detailedanalysis of the phenomena of subliminal fringes andspatial summation. It has been possible to show thatthe degree of facilitation resulting from spatialsummation varies several-fold among individuals andit also does so in any one subject on different occasions.Thus, the largest facilitation observed was 17.6 but intwo subjects virtually none could be seen. In any oneindividual the change in facilitation with stimulusstrength was that to be expected on the basis ofSherrington's classical studies (Sherrington, 1929).Thus, as the H and T stimuli became larger there wasan increasing likelihood that some Ia fibres would beexcited by both stimuli. This in turn would cause thesame motoneurones to respond to the two types ofstimulus. Under these circumstances the combined(HT) response would be less than the sum oftheH andT reflexes. This type of behaviour was termed"occlusion" by Sherrington. As shown in the Resultssection, H and T stimulus intensities can be chosen sothat the facilitation due to spatial summation isbalanced by the diminution of response caused byocclusion. An additional finding was that the maxi-mum tendon reflex potential was usually considerablysmaller than that of the maximum H reflex. It ispossible, though unlikely, that strong percussion ofthe Achilles tendon failed to excite all the spindleprimary endings in the muscle. Some of the relativediminution of the T reflex may have been caused bydispersion in the arrival of impulses in Ta fibres atthe cord. This asynchrony would be caused by thedifferent times taken for the percussion wave to reachthe muscle spindles and by the different lengths of Tafibres. Both factors would, of course, depend on thepositions of the muscle spindles within the musclebelly. A third factor causing a reduction in the size ofT reflex relative to the H reflex could have beeninhibition produced by the T stimulus. This wouldaccount for the often smaller size of the HTresponsecompared with the H reflex. There was insufficienttime between the T and H impulse volleys for thisinhibition to be of the presynaptic type. A betterexplanation would be that the strong mechanicalpercussion had excited Golgi tendon afferent nervefibres which would, in turn, cause disynaptic inhibi-tion of homonymous motoneurones (Eccles et al.,1957).The degree of facilitation was also found to depend

on the background excitability of the motoneuronepool, being greater when the subject was relaxed thanwhen a weak contraction was performed. This resultwas in keeping with theoretical predictions, for thethreshold for reflex discharge would be less if the

motoneurone excitability was raised-that is, sinceless motoneurone depolarisation would be requiredfor impulse initiation, fewer EPSPs would be needed.In the introduction, it was shown that as y, the criticalnumber of EPSPs, fell the subliminal fringe becamesmaller and the opportunity for spatial summation,and hence for facilitation, became less.The critical number of EPSPs, y, required for

impulse initiation ranged from less than 2 to 4.4.However, this calculation depends on the assumptionthat all the cells in the motoneurone pool had similarthresholds, as depicted in Fig. 6 (left). This assumptionis obviously false, for even with maximal stimulationof Ta fibres only about half the motoneurones res-ponded with a reflex discharge (Fig. 5). The y valueshould instead be regarded as an approximate meanvalue for the subgroup ofneurones contributing to thesupraliminal H and T reflexes (less than 2% of thetotal cell population). This subgroup is indicated bythe lower arrow on the ordinate of Fig. 6 (right).In the latter graph the thresholds for the entiremotoneurone pool are assumed to have a normaldistribution about the mean so as to yield a cumula-tive frequency curve with a characteristic S shape.The distance between the two arrows on the ordinateof Fig. 6 (right) represents the extra number ofneurones recruited through spatial summation. It canbe seen that the thresholds for these additionalneurones will be higher than those for the cells givingthe supraliminal H and T reflexes. Clearly, the mostmeaningful expression of motoneurone excitabilitywould be the number ofEPSPs required to excite cells

H+T)M

dxn maxM

Fig. 6 Cumulative frequency plots of motoneuronethresholds, assuming that these are either identical(left) or distributed normally about the mean (right).The arrows on each ordinate indicate the neuronesresponding to the suprathreshold H and T stimuligiven separately (lower arrow) or together (upperarrow). The top horizontal line intersecting the curveat right represents the cells responding to maximalreflex stimulation (see text).

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in the 50th percentile for a given individual. Com-putation of the S curve for such an individual woulddepend on having a second pair of co-ordinates tocomplement the pair already used for the low thres-hold segment of the curve. Provided two furtherassumptions are made, the second pair ofco-ordinatescan be determined by estimating the number ofmotoneurones discharging when all the la fibres havebeen excited. It is reasonable to assume that thiscondition is met when the maximum H reflex hasbeen elicited. Certainly, adding a mechanical stimulusexcites no additional motoneurones and therefore,presumably, no extra Ia fibres (see Results). The totalnumber ofEPSPs generated in the motoneurone poolafter such maximal stimulation would be equal to theproduct of the total number of Ta fibres to the muscleand the divergence factor, d. The average number ofEPSPs received by single motoneurones can be foundby dividing this product by the number of cells in themotoneurone pool. Although the mean number ofsoleus motoneurones has been estimated in normalsubjects as 957 ±254 (McComas, 1977),there is nocorresponding figure for the Ia fibres, or alternativelyfor the number of spindles, since each of the latter hasa single Ia nerve fibre (Matthews 1972; Kennedyet al., 1975). Some guidance on this point may,however, be obtained from the anatomical study byCooper (1966) and the review by Matthews (1972)in both of which numbers of a-motor fibres werecompared with spindle populations for variousmammalian muscles. Although the human soleuswas not one of the muscles examined it is probablethat the a-motor: spindle ratio would be about halfthat for the medial gastrocnemius, in keeping withobservations in the cat and rat. Since the ratio for themedial gastrocnemius is about 5.5:1 in man (see Fig. 2ofCooper, 1966), a reasonable estimate for the soleusmight be 3: 1, similar to the value for this muscle in thecat. If the 3:1 ratio is correct, the human soleuswould have about 320 spindles, the same number asin the biceps brachii (see Table 1.1 of Matthews, 1972).

Using the estimated divergence value of 139motoneurones per Ia nerve fibre (see Results) and ana-motor: spindle ratio of 3: 1, the average number ofEPSPs received by a single motoneurone aftermaximal Ia activation would be 139 x 1/3 =46. Thisdegree of convergence was capable of exciting17-71 % of the motoneurone pools in the subjectsstudied at rest. The corresponding thresholds for the50th percentile ranged from 38 to 103 EPSPs, themean value being 62 ±20.The assumption that approximately 320 la fibres

arise from muscle spindles in the soleus also permitscalculation of the likelihood of any one fibre beinginvolved in both the weak excitatory volleys employedto elicit the H and T reflexes respectively. Since the

Ia: a-MOTONEURONE SYNAPSE (HUMAN SOLEUS)41 experiments on 18 legs

la fibre (n=M x '/3)

Convergence46 ± 21 branches

Pivergence (d)139 ± 62 branches

Threshold (y) 0 0 OoC) nroepool(M_

Mean =62i20EPSPs"Lowest" =2.6EPSPs

Fig. 7 Summary of mean e;tima!es for thre-hold±,convergence, and divergence (see text).

facilitation obtained in this investigation can beaccounted for on the basis of volleys comprisingnot more than five Ta fibres (Fig. 2), the chance of anyof five fibres activated by the H stimulus also beingexcited by the T stimulus (or vice versa) will be5 x 5/320=0.08 (fibre), and therefore extremelyunlikely.How well do the present values, summarised in

Fig. 7, compare with those obtained by direct measure-ment in animal experiments ? In relation to divergenceMendell and Henneman (1971) found that a single Iafibre would supply nearly all (93 %) of the 300 moto-neurones in the medial gastrocnemius pool. In thecat semitendinosus Nelson and Mendell (1978) founda projection frequency of 820% for homonymous lafibres, the motoneurone population being 255 cells(Boyd and Davey, 1968). The present estimate ofdivergence, about 139 soleus motoneurones per Tafibre, is rather lower than the cat values in absoluteterms and, because of the larger motoneurone pool inman, it corresponds to a much smaller fraction of thelatter. The excitability values are also somewhatsmaller than those derived from animal experiments.Thus, a depolarisation of some 10 mV is required tobring a motoneurone to the firing level (Eccles,1957).The amplitude of a homonymous EPSP is about100 pV, the most reliable values being derived fromspike-triggered averaging and comprising 67 /zV(Watt etal., 1976), 91 ,.V (Nelson and Mendell, 1978),102 /.zV (Mendell and Henneman, 1971), and less than137 i±V (Mendell and Weiner, 1976). If the EPSPsafter Ta activation were synchronous, approximately100 would be needed to effect the 10 mV depolaris-ation required to bring the motoneurone to the firinglevel. Although our present estimate of 62 EPSPs isconsiderably smaller than the above value it would notbe surprising if the level of motoneurone excitability

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was appreciably lower in the animal experiments as aconsequence ofthe anaesthesia and surgery employed.Alternatively, part of the discrepancy could be theresult of underestimation of the extents of the sub-liminal fringes in the present experiments, because ofinhomogeneity of thresholds even within the verysmall populations of neurones sampled. Despite theassumptions inherent in the present study, the methodemployed appears to offer a valid approach to theexamination of motoneurone excitability in man.Increasing experience of the method, the introductionof technical refinements, and the acquisition offurther information concerning the properties of thereflex loop, may all be expected to improve thereliability of the estimates in the future.

We are indebted to Dr Jean Delbeke for reviewing themanuscript and for correcting the mathematicaltreatment of the results. Dr Alan J. McComasreceived financial support from the Nuffield Founda-tion, Medical Research Council of Canada and theMuscular Dystrophy Association of Canada. Hewas on leave from the Department of Medicine(Neurology), McMaster University, Hamilton,Ontario, Canada during the course of the study.Dr Michael Mirsky's work was sponsored by theAlexander von Humboldt Foundation (Germany),and he was on leave from the Department of Neuro-logy, Hadassah University Hospital, Jerusalem.

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