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Some Properties of Motor Unit Action Potential Trains Recorded
during Constant Force Isometric Contractions in Man
Carlo J. De Luca and William J. Forrest Anatomy Department. Queen's University. Kingston. Ontario. Canada
Received: December 3. 1972
Abstract
A specially designed needle electrode was used to record motor unit action potentials for the complete time duration of constant force isometric contractions varying in discrete steps from minimum to maximum force levels. A total of 70 motor unit action potential trains were recorded and analyzed Several properties of the motor unit action potentials were observed The inter-pulse intervals between adjacent motor unit action potentials of a particular motor unit action potential train were measured and subsequently analyzed as a real continuous random variable. The distribution of the values of the inter-pulse intervals was described by the Weibull probability distribution function with time and force dependent parameters. Furthermore' the Survivor function and the Hazard function of the Weibull probability distribution function described certain characteristics of the motor unit firing intervals. Most important of all. it became possible to derive an equation that would generate a real continu ous random variable whose properties would be identical to those of the inter-pulse intervals.
Introduction
A muscle contraction is the result of concurrent contractions of several motor units. A motor unit consists of a group of muscle fibers and their inner vating terminal branches of one nerve fiber whose cell body is located in the anterior horn of the spinal gray matter. When a motor unit is stimulated, an extra-cellularly placed electrode will record the current distribution in the territory of the motor unit. The recorded pulse is called the motor unit action potential. A sequence of motor unit action potentials is known as a motor unit action potential train (MUAPT); the time interval between adjacent pulses will be referred to as the inter-pulse intercal (lPI). MUAPT's from human skeletal muscles have been analyzed under various conditions by numerous investigators (Bigland and Lippold. 1954; Buchthal et al.. 1954: Clamann, 1967; Gilson and Mills, 1941; Gurfinkel et al.; 1970: Kaiser and Petersen, 1965;
Larsson et al.. 1965; Masland et al.. 1969: Person and Kudina, 19'7~) This paper will deal with the properties of MU A PT's recorded at various levels of constant force isometric contraction for the complete time duration of a human skeletal muscle contraction.
Materials and Methods
The following equipment arrangement was used to record the MUAPT's. A sturdy wooden chair with a high back was modified as follows. Two adjustable Velcro straps were fastened to both sides of the back of the chair. A force gauge capable of measuring 50 kg of force with a displacement of 0.1 mm was secured to the chair. A cuff consisting of an adjustable band of cotton webbing 5 ern in width and two pieces of Velcro was connected to the force gauge by a flexible steel cable. The output of the force gauge was attached to one channel of a dual-beam oscilloscope (oscilloscope I). The differential preamplifier was cascaded with a single-ended amplifier. The output of the amplifier was connected to a separate oscilloscope. The outputs of the amplifier and the force gauge
were fed to an FM tape recorder. An audio amplifier and a
speaker were cascaded to the differential preamplifier. Acoustic representation of motor unit action potentials assisted significantly in detecting the presence of different MUAPT's. A block diagram for the equipment arrangement is presented in Fig 1.
Tape
Force Recorde^ r
Gauge
i
~
Fig. I. Block diagram of the equipment arrangement of the
experiment
,
161
C. J. De Luca and W. J. Forrest: Properties of Motor Unit Action Potential Trains
Four right-handed male subjects volunteered for the experiment. Their ages varied from 22-32 years. with an average of 25.3 years. \ II -ubjccts denied past injury to the right shoulder region. A ,,,hlect was seated in the chair and the two Velcro straps were t.i-tcncd over his shoulders. The straps kept the torso of the subject in a fixed position with respect to the force gauge and prevented shrugging of the shoulder by restricting the elevation of the scapula. but did not impede the rotation of the scapula. The cuff was secured snugly about the distal part of the right arm just proximal to the elbow joint The maximum force output of the isometric abduction of each subject was measured. A specially designed quadri-filar electrode (De Luca and Forrest. 1972) was inserted into the central area of the middle fibers of the deltoid muscle. The r electrode was capable of recording distinct MUAPTs from a muscle contracting at any force level (including maximal force). The tip of the electrode penetrated to the middle of the depth of the deltoid muscle. Clamann (1967) pointed out that this region of a muscle contains motor units having a gradation of thresholds from low to high. The electrode was connected to the input of the differential preamplifier. The
:1 dB points of the bandwidth of the preamplifier were set at 100 and
IAOO Hz. The gain of the preamplifier and amplifier was regulated (\ give the largest possible signal output that could be stored on Ill.lgnetic tape. thereby optimizing the signal-to-noise ratio.
The trace of the isolated second channel of oscilloscope I
w"s placed at the equivalent voltage representation of 5 kg above
the trace of the other channel which displayed the output of the force gauge. Each subject was instructed to abduct the upper limb in the coronal plane with the arm medialIy rotated and the forearm pronated. Then he was asked to superimpose the two
traces on oscilloscope I as quickly as possible with a minimal
amount of overshoot. When the desired level of isometric abduction was achieved. the subject was requested to maintain the force out put constant until he was no longer capable of doing so. At the end of the contraction. the electrode was removed from the muscle. Each subject had a minimal rest period of two hours between successive contractions. Prior to each contraction, the electrode was reinserted into the deltoid muscle. Hence. different MUAPTs were recorded for each contraction. MUAPTs were obtained for contractions with monitored force outputs of 5, 10, 15, 20 and 25 kg. The recorded MUA PTs were photographed on a 35 mm film moving at a speed of 250 mm/sec. A 50 Hz square-wave calibration Signal was photographed to check the true speed of the camera. A l(\t,,1 of 70 MUAPT's were recorded from the four subjects. Two persons independently interpreted the records, thus reducing the probability of allocating a motor unit action potential to the \rong MUAPT. The IPl's of all the MUAPTs were measured. The accuracy of the measurement was ± 0.1 msec.
Analysis of Data A recent study (De Luca, 1972) showed that the relative force contribution of the anterior. middle and posterior fibers of the deltoid muscle and that of the supraspinatus muscle remains constant during isometric abduction. The force contribution of the middle fibers of the deltoid muscle during isometric abduction was calculated from the values of the measured force of abduction by employing a special technique described by De Luca (1972). The force output of the middle fibers of the deltoid muscle was found I,) he linearly proportional to the measured force of abduction.
The IPI's of a MUAPT were analvzed as a random variable. The following terminology will he used to describe the various tests:
X = a real continuous random variable representing the I PI.
x = the range of all possible values (outcomes) which can be
assumed by X.
x, = a specific outcome of X: the value of a specific I PI.
Xi array = a complete series of outcomes of X: hence. it represents
all the IPI's of one M UAPT.
Stationarit v
The mean value and the standard deviation of the l Pl's for
every 5 sec interval of a MUAPT were calculated. These values were calculated for all 70 MUAPTs. The mean values were plotted against the corresponding time. In addition. for each MUAPT. the mean values were plotted against the corresponding standard deviations. and a polynomial least-square regression was perfor med on all the values for each MUAPT. All the MUAPT's were fitted with a Znd, 3rd or 4th degree polynomial. The degree of the polynomial which provided the best fit for the values of a parti cular MUAPT was determined by calculating the residual sum-of squares between two successive degrees of the polynomial. This procedure has been described by Ostle (1954). The accepted degree was obtained when the values of the residuals was less than
5 x 10- 6.
The histograms of the l Pl's for each of the 70 MUAPTs
were plotted by a computer program. The mean, standard devia tion, skewness, minimum value, maximum value and total number of IPI's were calculated for each MUAPT. Histograms were also plotted for sections of the MUAPT's. Each MUAPT was divided into 10 equal time-sections; 700 histograms were formed.
Probability Distribution Function The following three probability distribution functions (PDF's) were fitted to the histograms of the [PI's of each MUAPT:
Lognormal fx(x) = 1 , exp { [In ( x; a )f} (x - a) (2rrK)· - .. 2K
Gamma fx(x) = _f! )U<S [x;a. r- I exp [ _Ix;_a_l] ~-- -~--- ..)~~ ~l""\ 'l::
Weibull fx(x) = 4 _[x;a r- ., [- (X;~)l
The PDF's are described by three parameters K. {3 and x; where
K = shape parameter. {3 = scale parameter and x = location param
eter. The parameter K has no units, {3 and a have the units of the
IPI's (msec). The parameter a was evaluated by finding the minimum value of Xi' The «best" estimates of K and fJ were obtained by the Maximum Likelihood method which maximized the function
In L(K. {3) = I In ftx, I K. f3) i = 1 The goodness-of-fit of the three PDF's with the «best" estimates of the parameters was measured by the Kolmogorov-Smirnov test. The three PDF's were also fitted to the IPI's of sections of a MUAPT. Each MUAPT was divided into consecutive time sections each containing at least 1501Prs; this is the minimum number of I PI's that should be used to obtain a meaningful test of the goodness-of-fit of a PDF (Pearson and Hartley. 19541. A total of 225 sections was formed.
I.' Hd.Hel/3,1'l73 c. I. De Luca and W. J. Forrest: Properties of Motor Unit Action Poienual Trains (^) 16-'
Vl
o ~ 6 ~ I.
E
z" 2 o~'""""''''':':-4''+---.c.,,",,+,c..:.LJ.'+L'''~':'':'':;'L.....l.+..LL.qf--.L.:L
Percentage change In time duration
lIt' ~ Percentage change in the time duration of the motor unit
act 1'111 potentials measured at the beginning and end of the
constant force isometric contractions
180 D
+_ .... -+--+
c c; 2 60 ~
o 5 :e 15 20 25 30 35
I.rne In sec
J·It'..' Time dependence of the mean value of the inter-pulse
uuervals: the force output of the recorded muscle was 45.3 kg
LT
(L -1.
~"6 I
D"' D
D^ o
if-.
Mean of IPI
lit' -+ Rclallon,hlp of the mean and standard deviation of the
mter-pulsc interval, of It> motor unit acuon potential trains
recorded from one subtect. contraction force varied from minimum
to rnaxrrnum The ab,el"a and ordinate are scaled in milliseconds
the time duration is plotted in Fig. 2. The time duration increased for 40 motor unit action potentials. decreased for 23 and remained unchanged for 7. The group that increased in time duration had a change of (39.4 ± 33.1) '.Jo and the group that decreased in time duration had a change of (- I g..+ ± 13.2) "0. Collectively. the time duration of the 70 M UA PTs increased by (16.7 ± 28.0) "0.
SIal ionaritv
Fig. 3 shows the mean value of the I Pls of three simultaneously recorded MUAPTs. The mean value increases with time. This trend was observed for all 70 MUAPTs and agrees with the findings of Person and K udina (1972). Fig. 4 contains curves for the mean and corresponding standard deviation of the I PI's of 16 MUAPTs recorded from one subject. Another three such plots were formed for the other subjects. The MLJAPTs in Fig. 4 were obtained from contractions which ranged from low to maxi mum force. The mean and standard deviation values vary simultaneously. irrespective of time and force. A linear least square regression was performed on the mean values against the standard deviation values of the IPI's for every 5 sec interval in all 70 MUAPT's simultaneously; the slope (coefficient of variation) was found to be 0.69 and the correlation coefficient was 0.83. The linear regression intercepted the mean value axis at 16.3 msec. Fig. 5 shows a typical histogram of all the J PI's of a MUAPT. In 52 histograms. the mean was larger than the standard deviation: in 3. the mean and the standard deviation were approximately equal: and in the remaining IS. the standard deviation was slightly larger than the mean. The em elopes of all the M U A PT's clearly demonstrated a positive skew ness. The time dependence of the mean and standard deviation of the I PI's indicate that the histograms of the I PI's should vary throughout the M LA PT. Fig. 6 shows the histograms of a typical. sectioned MUAPT. The following observations can be made: (a) the positive skewness persists in a II sections. (b) the mean and standard deviation values in crease with time. These observations were confirmed in the remain ing 690 h ist ograms of t he sect i oned M LA PT s. The shape and time dependence of the histograms in Figs. 5 and 6 are compatible with the histograms of MUAPTs that Lippold /'1 al. (1960) recorded from the human triceps muscle and the histograms that Person and Kudina (19 72)^ obtained for 10\ -level constant-force isometric contractions from the human
80
10
1M C J De Luca and Vi J Forrest: Properties of Motor Unit Action Potential Trains
rectus femoris muscle. Person and Kudina ( maintained that for motor unit firing rates greater than 10-13 pulses per sec. the I PI histograms were
symmetrical. Clamann (1967). recording from the
human biceps brachii muscle. found that the IPI histograms had a Gaussian distribution. No evidence of symmetry was detected in the IPI histograms
obtained in this study. It is interesting to note that
IPI"s of neural motor activity in the central nervous
70 MEAN 138·9 MS STO OEV 115·3 MS (^60) SKEW 1· VMIN 5·3 MS _ 50 VMAX^ 866·9^ MS a. NO OF VALUES^756 ::, 40 C( W <II ::; 30 ~
z 20
75 150 225 3X 3?S 450 525 fIX 675 750 825 T MEl N MS
FIg. 5. Histogram of the inter-pulse intervals of a motor unit action potential train which was recorded during an isometric contraction. The contraction was sustained until the pre-set constant force could no longer be maintained. The force from the monitored muscle was 26 kg
,11-11946 p-1l6.94 (^20)
20 50- 8639 20 5. D.- 89.
6
,LL-19l
5
100 300 500 7JO
9
system of mammals have histograms with large positive skewness and a shape similar to the histo grams of Figs. 5 and 6. Martin and Branch (1958) obtained histograms of spontaneous activity from single Betz cells in the motor cortex of anesthetized cats with midbrain lesions. Evarts (1964) recorded action potentials from pyramidal tract neurons in the precentral gyrus of intact. unanesthetized mon keys at rest and during movements. The time dependence of the mean. standard deviation and shape of the histograms of the IPI's strongly indicate that the l Pl's of a MUAPT are nonstationary. This result agrees with that of Masland et al. ( 1969).
Probability Distribution Function
The results of the goodness-of-fit of the three PDF's to the IPl's of the complete MUAPT arc listed in Table 2. A large Kolrnogorov-Srnirnov probability level indicates a good fit. The Gamma PDF provides by far the worst fit for the IPl"s of the complete MUAPT's: 83 00 of the MUAPT's had a p ~ 0.05. The results for the Log normal and Weibull PDF's are quite similar with the Weibull PDF providing a slightly better fit than the Lognormal. Even in the best case. 39') of the MUAPT's have a p~0.05 which indicates that none of the three PDF's provides an acceptable fit for the IPI's of the complete MUAPT's. This is not a sur
p-12571 p-137 07
100 30e (^500) IDe 300 500 3 25 ,lL-122 (^00) " p- ~~L5'0'Cl01'76^ 50'107^78
10 5 o 10C: 300 5C:: (^) 10C 3:10 500 25 7 B 20 ' 10
~lJwIJLLI 'L.-~LL...l--U'---.L .1,1" "' IJJ 30J :: 10
Fig. 6. Histograms of len cqu.i] and consecutive time-sections of a motor unit action potential train that was recorded during an isometric contract Inn. The contraction was sustained until the pre-set constant force could no longer be maintained. The abscissa is scaled in milli seconds
lot> C .J De Luca and W.J Forrcst : Properties of Motor L'nu Action Potential Trains
The average time and force dependence of %and Ii
can be expressed by the following equations:
KlI.cPl= 1.16-0.19T+OI8cP (^) O<T<I for (l(I. cP) = expl-+.60 - 0,67 T - 1.16~IJI msec (^) O<cP<
where r = normalized time duration of the MUAPT,
cP = normalized constant force.
The above equations are general expressions valid for
all ML'APTs, rand cP were found to be independent
with no significant interaction term. The average value of the parameter. 1.. calculated for the complete
\1LAPT's \as found to be 389± 2,82msec.
Stociiastic Properties of' Motor l'llir Acrioll Potential Trains
Some properties of the Weibull PDF yield useful inforrna tion about the M L'APT. The following proper
ties are valid for all MLAPT's recorded during a voluntary constant force isometric contraction from
t he deltoid muscle
The mean value of the time and force dependent Wcibull PDF is given by:
! 1) p(I.cP)=IJ(I.cPlr!1 +------ +1.
- K(r.cP)
where F = the Gamma function
{J(I. cP) time and force dependent parameters of the %II.cPl= V,'eibul1 PDF 'J. = minimum value of the I PI's. The qeneralized t"'illg rate may be expressed as the inverse of the mean
1000 q( T. cP) =. pulses per sec.
. (3IT. cP) r( 1 + -K 1 -hI + 'J. , (I. '1')
The qcneraiizrd firing rare represents the expected dependence of the firing rate of a typical motor unit with respect to time during a constant force isometric contraction. The family of curves for the qeneralized [iritu; ratt' is plotted in Fig. 7. Near the end of a very weak contraction T~ 1 and </>::::.0. then %(I.</»::::.I and Il(T.cP)::::. 195 msec. At these parameter values the Weibull PDF approaches the Exponential PDF and the scale parameter {J(I.</>l becomes the mean value of the IPI. Hence the lowest firing rate of a typical motor unit is approximately 5 pulses per sec. This result corresponds with ob servations made by Bigland and Lippold (1954) and Person and Kudina (19721.
o o 2 D.• 0.6 (^) 0.8 '. 0 Normalized contraction -t.rne
Fig. 7. Generalized firing rate of motor unit action potenuals as a function of normalized contraction-time at various normalized
constant-force levels. The force was normalized with re-peci to the
maximum isometric contraction
The Survivor function of the time and force de pendent Weibull PDF is
30
r I I r
~ I
This function gives the probability that a motor unit has not fired up to time 17 measured from the time of the previous firing. The equation indicates that the probability of a motor unit not having fired after a previous firing decreases exponentially with respect to the amount of time that elapses. The negative derivative with respect io n of the logarithm of the Survivor function describes another useful function known as the Hazard function that can be expressed as
K(r, </>1 ( '7 - 'J. ')"lr.4>'" J 0H(II, T, </» = --~. --_. {J(T, </>l {J(I. </>l
This function gives the probability per unit time of an immediate firing when no firing has occurred for 17 time. The quantity 0H(Il, T, </»:1'1 is the probability that a motor unit will fire during the small time interval :1'7, given that the motor unit has not fired for '7 lime.
. .~. L
('. J. Ik Luca and W. J. Forrest : Properties of Motor Unit Action Potential Trains \
lor K(r. (/»> I. which is usually the case for the IPI's of the M LJAPT's. there is positive "aging" with ()IIIII. c. (M varying from zero to infinity as 'I increases. TI"" Indicates that the longer the elapsed time since the previous motor unit firing. the greater the pro bability that the motor unit will fire. This is known as the "wear effect". Near the end of a very weak contraction. Kti, ¢) ~ 1 and the wear effect will dis a ppear The Hazard function attains the constant value of (195 msec) - I. The Cumulative probability distribution function of the WeibuJl PDF is x - IX )KlT.4>lj Fx(x.r.¢)=I-exp - (^) ( filr.¢). j I
where X represents Ihe I PL In the above equation, replace the term I _1_ tv, r. ¢) by a real continuous random variable.. l). whose values have a Uniform PDF between (\ .unl I: take the logarithm of both sides and h\ rc.uranging the equation it follows that
This equal ion is completely defined and can be used 10 generate a real continuous random variable which will behave similarly to the IPI's of a MUA.PT. The values of D can be obtained from random number generator such as a digital computer or specialized instrumentation.
Dependence
The scatter diagram of the IPI's of a complete MUAPT revealed a grouping of points along the diagonal of the scatter diagram. This result was ex pected because the I PI values at the beginning of the M U A PT's are smaller than those at the end. Hence the relatively smaller I PI's at the beginning of the , I (^) MUAPT's will be followed by other smaller IPI's;
near the end of the MUAPT, the relatively larger IL (^) I PI's will be followed by larger I PI's. Such a trend
is evident in Fig. 3. The test for dependence of the I PI's performed on the sections of MUAPT's greatly reduced the effect of nonstationarity. Ideally, if the [Pi's were independent, the l test statistic should have a / distribution; this means that approxima tely 5 % of the sections should have a probability level of p~O.os: 1O%~0.10: etc. Table 5 lists the number In and^ percentages of sections which have the^ indicated probability level. A / test with nine degrees of free 'I lal dom^ was^ performed^ to^ test the^ uniformity of^ the^ re
al^ sults.^ It^ was only necessary to^ consider^ the displace
ic. merit^ parameters^ d^ =^ 1,^ J^ For^ d^ =^ 1,^ the^ probability
Table 5. Number and percentage of motor unit action potential (rain sections at ten levels of .; probability for two values of the displacement parameter
Probability Displacement parameter
level d=1 <1=.
0.1-0.2 15 6.7~o 21 9.4^ ~l() 0.2-0.3 26 11.6l% 1 .10 13.4^ ~,; 0.3-04 19 8.5()~ 24 10.7% 04-0.5 12 9.8 ~b 26 11.6 .;" 0.5-0.6 22 9.8~" 24 10.7% 0.6-0.7 26 11.6% 20 8.9 ",~ 0.7-0.8 28 t2.5% 20 8.9~n 0.8-0.9 18 8.0^ fy,^ t7 7.6""
0.9-1.0 19 8.5% 20 8.l}<>o
Total number of sections = 224.
significance level was p = 0.45 and for d = 3: P = 0.77. These probability significance levels imply that the IPI's of a section of the MUAPTs can be considered to be locally independent within the limitations of the test A contingency table (Kendall and Stuart, 1967) was set up to measure the similarity between the results of d = 1, 3. The probability significance level of the contingency table was p = 0.79. This value provided strong evidence that there is no significant difference between the results for d = 1, 3. Previous reports in the literature contain conflict ing statements about the statistical dependence of the I PI's recorded during voluntary isometric constant force contractions. The results of Clamann (1967) agreed with those of this study. He demonstrated that IPI's are statistically independent Masland et at. (1969) stated that the majority of MUAPTs which they recorded contained IPI's which by their criteria were statistically independent; however, all the MUAPTs had some IPI's which were dependent at some time during their recording. Person and Kudina (1972) found no correlation between adjacent IPI's for motor units firing below 10 pulses per sec. At firing rates above 10-13 pulses per sec, they found a negative correlation between adjacent I PI's. The observed and derived properties that have been presented are only valid for MUAPTs recorded from the middle fibers of the deltoid muscle. It remains to be proven that these properties are valid for MUAPTs recorded from other muscles.
Conclusion
Motor unit action potential trains (MUAPTs) were recorded from the middle fibers of the deltoid muscle for the complete time duration and force
