JOURNALOF NEUROPHYSIOLOGY Vol. 68, No. 2, August 1992. Printed
in U.S.A.
Neural Compensation for Fatigue-Induced Changes in Muscle Stiffness During Perturbations of Elbow Angle in Human R. F. KIRSCH AND W. 2. RYMER Departments of Biomedical Engineering, Physiology, and Physical Medicine and Rehabilitation, Northwestern University and the Sensory Motor Performance Program, Rehabilitation Institute of’ Chicago, Chicago, Illinois 60611 SUMMARY
AND
CONCLUSIONS
I. The contribution to muscle force regulation provided by reflex pathways was studied in the elbow flexor muscles of seven normal human subjects, with the use of voluntary fatigue to induce a deficit in the force-generating capability of these muscles. To estimate the changes in the mechanical state of the muscle and the compensatory actions taken by reflex pathways to minimize the impact of fatigue, stochastic and “step” angular perturbations were applied to the joint, and the resulting joint stiffness and electromyographic (EMG) responses were compared before and after fatigue. 2. The magnitude of contractile fatigue, induced by repeatedly lifting a weight via a pulley system, was quantified by comparing the slope of the isometric torque-EMG relationship before and after fatigue. The exercise routine was quite effective in producing severe and long-lasting fatigue, with average percentage changes in the isometric torque-EMG slope of 2 lo-306% for biceps and 129205% for brachioradialis, depending on the point in time examined. 3. The torque response to a rapid step stretch of the elbow joint was quite similar before and after fatigue for the time interval before reflex action (~20 ms after stretch onset), suggesting that intrinsic muscle stiffness for a given mean torque level was not changed by fatigue. The steady-state torque level attained after completion of the stretch was always decreased after fatigue, indicating a decrease in the reflex component ofjoint stiffness, but this decrease was small compared with the change in the isometric torque-EMG relationship and was accompanied by a significantly larger incremental EMG response after fatigue. This increase in incremental EMG after fatigue was found to be of reflex origin, with activation-related reflex gain changes apparently playing a significant role only at low contraction levels. 4. Torque and angle responses recorded during stochastic perturbations were used to identify elbow joint compliance impulse responses. A second-order mechanical model was fit to each impulse response, and the parameters representing joint inertia, elastic stiffness, and viscous stiffness were used to summarize changes in joint mechanical properties as the mean contraction level was varied. For a perturbation with a relatively wide bandwidth (O-25 Hz), fatigue had little or no effect on the form of the compliance impulse response, apparently because the stimulus disabled reflex force generation in elbow flexor muscles, whereas a perturbation with a more restricted bandwidth (0- 10 Hz) demonstrated consistent decreases in joint stiffness after fatigue. Most (>90%) of this decrease in stiffness was attributable to a decrease in the elastic component, with only small and variable changes in viscous stiffness observed. As with step responses, the decreases in stiffness were small compared with isometric torque-EMG changes, and EMG responses elicited by stochastic perturbations of either bandwidth were significantly increased after fatigue, both in absolute magnitude and in the gain of the input-output relationship
between the perturbation angle and the resulting EMG, especially for the heavily fatigued biceps muscle. 5. The mechanical and EMG responses obtained from both step and stochastic perturbations were consistent with the actions of a force-regulating feedback mechanism. Force feedback loop gains were estimated for the low bandwidth stochastic perturbation by the use of two different techniques, each of which gave broadly similar results. Average loop gains across all seven subjects of 1.27-4.6 1 were computed, depending on the method used and the assumptions made. Loop gain estimates from step perturbations were somewhat larger, averaging 8.3 1, but still within the same range. 6. These large loop gain values indicate that force regulation significantly reduces the sensitivity of the overall neuromuscular system to fatigue (by 56-89%) and imply that force regulation may be an important component of the overall reflex control of muscle contraction during nonfatiguing conditions as well.
INTRODUCTION
Although force is the primary output variable for muscle, the prominence of the reflex connections of muscle stretch receptors, such as spindle receptors, onto homonymous motoneurons (Sherrington 1909) has led to a disproportionate emphasis on the length-regulating features of reflex action. It is now well established that Golgi tendon organs provide a very sensitive and accurate representation of instantaneous muscle force (Crag0 et al. 1982; Houk and Henneman 1967). Furthermore, these tendon organ afferents make appropriate reflex connections (Eccles et al. 1957; Granit 1950) to close a force-regulating feedback pathway, although there is also substantial evidence of convergence onto these same interneurons from a range of other receptors systems, including joint receptors (Lundberg et al. 1978) cutaneous receptors (Lundberg et al. 1977) and even muscle spindle Ia receptors (-Czarkowska et al. 198 1; Jankowska et al. 198 1; Jankowska and McCrea 1983). In spite of this wealth of electrophysiological evidence, the potency and functional role of even the simple autogenetic force feedback pathway remains unconfirmed. It has been asserted that length and force feedback pathways work in concert to regulate muscle stiffness, the ratio of force to length, rather than either length or fo-rce separately (Crag0 et al. 1976; Nichols and Houk 1976). The existence of such a stiffness regulator has been difficult to confirm, however, because previous assessments of force feedback has shown it to be fairly weak or nonexistent
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(Houk et al. 1970; Jack and Roberts 1980; Rymer and Hasan 1980). However, the aforementioned studies were performed in the decerebrate cat model, the findings from which may not be applicable to normal intact systems because interneuronal pathways mediating the tendon organ reflex loop appear to be abnormally inhibited, at least to some degree (Engberg et al. 1968). This limitation of the decerebrate preparation has led us to examine force regulation in normal human subjects. The first evidence that force-sensitive reflex pathways are functionally important in normal human subjects was presented in an earlier report from this laboratory (Kirsch and Rymer 1987a). In this earlier study we found that torque responses to a ramp extension of the elbow flexor muscles decreased only slightly after fatigue, even though the reflexively mediated torque component should have been significantly reduced due to fatigue. Electromyographic (EMG) responses evoked by the stretch were significantly increased, indicating that the compensation was neurally mediated. These results were noteworthy because they provided the first demonstration of effective force regulation in an intact system, but they were limited by the possibility of voluntary intervention and restricted to essentially static conditions. The present study also uses fatigue to investigate the regulation of force in human elbow flexor muscles, but several limitations associated with our past work have been addressed. Specifically, we employed stochastic positional perturbations in addition to a more conventional “step” stretch because such perturbations have two useful features. First, the occurrence of voluntary or triggered reactions are minimized by the random nature of stochastic perturbations, making them wholly unpredictable to the subject (Dufresne et al. 1978). Second, because of the richness of their stimulus characteristics (Bendat and Piersol 1986; Marmarelis and Marmarelis 19 7 8 ) , stochastic perturbations also permit a general and experimentally efficient characterization of the dynamic properties of the system. This approach is also computationally efficient because powerful numerical techniques for characterizing both linear and nonlinear system properties for stochastic perturbations have been developed (Bendat and Piersol 1986; Hunter and Kearney 1983a; Marmarelis and Marmarelis 1978 ) , although linear techniques have been used exclusively in the present study. A step perturbation has been used as well to allow comparisons with previous studies. In the present study the exercise routine used to generate fatigue inflicted an enormous deficit on the force-generating capacity of the flexor muscles acting at the elbow joint, yet after fatigue it was found that the stiffness of the joint was reduced by a much smaller degree. This relative preservation of joint stiffness was accompanied by a significant increase in the magnitude of the evoked EMG responses after fatigue. Estimates of force feedback loop gain indicate that this feedback system reduced the sensitivity of the output joint torque to fatigue by 55-89%, suggesting that forcesensitive reflex pathways make a significant contribution to the control of muscle contraction. Portions of this work have appeared previously in abstract form (Kirsch and Rymer 1987b, 199 1).
METHODS
Experimental
apparatus
A large torque motor configured as an angular position servo was used to apply controlled perturbations to the elbow joint of each subject. A lightweight aluminum beam was bolted to a strain gauge-based torque transducer, which in turn was rigidly attached to the motor shaft. Each subject was seated in a dental chair with his arm attached to the beam such that joint rotation was in a horizontal plane and the axis of rotation of the motor corresponded to that of the elbow. A fiberglass cast was molded to the distal half of the forearm in each experiment, and, after it had solidified, it was rigidly attached to the beam by a U-bolt. This arrangement prevented virtually all movement of the forearm relative to the beam, but was not so restrictive as to impair circulation. The initial position of the motor shaft was set to provide an elbow angle of 90” (midflexion-extension). In addition to the torque signal, a potentiometer and tachometer provided signals proportional to angular position and velocity, respectively. EMGs of several elbow muscles were recorded with the use of disposable solid gel silver / silver chloride surface electrodes, applied after appropriate skin preparation. EMG signals were recorded differentially from pairs of electrodes over the medial and lateral heads of biceps, brachioradialis, and triceps. The EMG signals were high-pass filtered (4-pole Butter-worth) at 4.5 Hz before amplification. The combination of skin preparation, flexible electrodes, and high-pass filtering resulted in negligible movement artifact in the EMG records. All mechanical and EMG signals were filtered identically by eight-pole Butterworth low-pass filters before sampling by an analog-to-digital converter. For stochastic perturbations, where a sampling frequency of 250 Hz was used, a filter cutoff frequency of 100 Hz was chosen. A 400-Hz filter cutoff was chosen for step perturbation trials, which used a sampling frequency of 1,000 Hz. For all trials, a total of 4,096 points per record were collected during each trial (i.e., 16.384 s for stochastic trials, 4.096 s for step trials). A PDP 11/73 computer was used to control the experiments and to digitally record the data. Digitized data were transferred to a Macintosh 11x computer for analysis.
Perturbation
sequence generation
STOCHASTIC PERTURBATIONS. Stimulus sequences were constructed by generating a 2,048point, normally distributed stochastic sequence (Press et al. 1986). This original sequence was digitally filtered and scaled in two ways to produce perturbations of approximately k6.0” (0- to lo-Hz bandwidth) and 24.0” (0- to 25Hz bandwidth) when applied to the actuator. Data were recorded for a l-s isometric period before perturbation onset to allow characterization of isometric torque-EMG properties. Figure 1A illustrates the quantities recorded during a typical stochastic trial ( t6” ) performed at m 25% of the prefatigue maximum voluntary contraction (MVC). Note that the EMG signals have been rectified and that triceps EMG is not shown. The large modulation of joint torque and the flexor EMGs by the imposed perturbation (top record) was subsequently used to estimate the dynamic properties of the system (see below). Figure 1 B shows the relative frequency content of the two different stochastic perturbations by overlaying the power spectra (normalized to their respective maximum values) from each of the two angle records. As described above, the 4O perturbation contained significant frequency components to -25 Hz, whereas the 6” perturbation was limited to 10 Hz. The use of perturbations with two different bandwidths was a compromise between the requirements for a frequency range suf-
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FORCE REGULATION
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FIG. 1. A : data recorded during a typical stochastic perturbation ( +6” ) trial at 25% maximum voluntary contraction for 1 subject. Joint torque and the three flexor electromyographic (EMG) signals all showed clear modulation by the perturbation. Rectified EMG records are shown in arbitrary units. B: Power spectra for the 2 stochastic perturbations, each normalized to its maximum value.
ficiently broad to fully capture the mechanical properties of the system, yet restricted enough in bandwidth to remain within the capabilities of reflex pathways acting through significant loop delays. Other investigators (Kearney and Hunter 1990; Marmarelis and Marmarelis 1978 ) have pointed out the need for a wide bandwidth to adequately identify joint dynamics, especially inertia. If the bandwidth is too restricted, the performance of the estimation procedures to be described below begins to deteriorate. An opposing consideration, however, is that the mechanical efficacy of reflex action is apparently obliterated for stochastic perturbations with bandwidths containing significant components higher than
- 15 Hz (Kirsch and Rymer 1989). Thus we chose the higher 25Hz bandwidth to ensure adequate characterization ofjoint inertia, whereas the lower lo-Hz bandwidth was chosen to be within the range of reflex action, but still unpredictable by the subject. STEP PERTURBATION. Step changes in the angular position of the elbow joint ( L.JOwith a rise time of -40-50 ms), in a direction that stretched the flexor muscles, were also imposed on the joint. This perturbation will be referred to as “step” or “stretch” in subsequent sections. A l-s isometric period preceded the stretch to allow for isometric measurements, followed by the stretch, a 2-s plateau, and finally a return to the original position. The quanti-
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60.040.0
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FIG. 2. Data records collected during the 4” “step” perturbation trial at 25% maximum voluntary contraction. The perturbation evoked clear responses in the joint torque record and the 3 flexor electromyographic signals (rectified and shown in arbitrary units).
0.0
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Time (set) tiesrecordedduring the stretch portion of a typical steptrial (25% MVC) areshownin Fig. 2. The imposedangularperturbation (top record) resultedin a largetransient changein joint torque and a poststretchmaintained value that was larger than the isometric contraction level, although the significantinertially inducedoscillations makethis difficult to see.Noninertial effectsare more easily visualized when pre- and postfatigueresponses are subtracted (see STEP RESPONSE ANALYSIS, below). The flexor EMG records (shown after rectification) show clear bursting activity after the stretch, due in part to smallposition oscillationswhile approaching the final position.
Experimental
protocol
During a given trial, the subjectwas askedto maintain a prescribed mean torque level and to “not intervene voluntarily” when the perturbation was applied. The subject received visual feedbackof low-passfiltered (7.5 Hz) torque, which gavean indication of mean torque without the large excursionsdue to joint inertia at higher frequencies.For both stochasticand stepperturbations,trials containing evidenceof voluntary intervention, such asnonstationarity in torque or EMG responses to stochasticperturbations or unusual variations in force or EMG in step responses, were excludedfrom further analysis. The MVC of eachsubjectwasdetermined,and subsequentperturbation trials were performed with background torque levels varying from 0 to 40%of this maximum. Higher contraction levels werenot tested,to minimize the potential for posttetanicpotentiation (Edwardset al. 1977;Jami et al. 1983) and becausesubjects often could not maintain higher levelsfor the entire 16.384-sstochastictrials after fatigue. For eachof the three different perturbations, a set of three trials at each of 6 or 7 initial torque levels within the O-40%torque rangewere performed for a total of 18 21 trials/perturbation. The three trials at eachmeantorque level wereperformedsequentially,and the torque levelswereincreased progressivelyfrom low to high. The k4.0” perturbation set was completedfirst, followed by the -t6.0”, and, finally, the stepperturbations. After thesethree setsof trials were completed,fatigue wasinduced in the elbow flexor muscles,and the three setswere then repeated.
Induction
offatigue
Fatigue was induced by having the subject repeatedly lift a weight with the useof the elbow flexors only. The weight chosen (S-10 kg) dependedon the subject,the criteria beingthe ability to repeatthe action 15-20 times.After a rest of - 30 s,similar setsof contractions were continued for a total of 15 min. After completion of the fatiguing exercise,a restperiod of 10min wasimposed to allow musclefiber conduction to recover from the accumulation of metabolicproductsproducedduring the contractions.This precautionis necessary becausepreviouswork (Kirsch and Rymer 1987a;Lindstrom and Petersen1983; Mortimer et al. 1971) has shownthat decreases in musclefiber conduction velocity leadto a shift in the EMG power spectrumtoward lower frequencies.Becausethe tissueintervening between the muscle fibers and the surfaceelectrodesactsasa low-passfilter (Lindstrom and Petersen 1983)) the frequency-shifted EMG would be more completely transmitted to the surface,resultingin an increasein amplitude. Furthermore, becausea portion of our resultsis basedon a comparisonof EMG responses to a positionalperturbation beforeand after fatigue, it is important to eliminate this potential sourceof distortion. Fortunately, it hasbeenfound in an earlier study with the useof a similar fatiguing protocol (Kirsch and Rymer 1987a), and elsewhere(Mortimer et al. 1971)) that EMG spectralcharacteristics after fatigue returned to normal within 10 min after the completion of fatiguing contractions. Contractile fatigue (as expressedby the slopeof the isometric torque-EMG relationship) wasfound to persistfor >2 h, however, allowing direct comparison of EMG amplitudesin fatigued and unfatigued muscle.After the IO-min rest, the perturbation protocol describedabove was repeated.
Data conditioning The recordedtorque valuescontained a component due to the inertia of the apparatususedto attach the arm to the motor. This componentwasremovedfrom eachof the torque recordsby identifying the stiffnessimpulseresponse(seebelow) for data collected with the subject’sarm, but not the cast,removedfrom the apparatus. This impulseresponsewasthen convolved with the recorded
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FORCE REGULATION
anglerecordsfrom eachtrial, yielding the torque componentthat wasindependentof the subject’sarm. This torque componentwas subtractedpoint by point from the measuredtorque to yield the estimatesof joint torque that were used for all subsequent analyses. The four EMG signalswere full-wave rectified, and the angle, torque, and bicepsand brachioradialisEMG signalsrecordedduring stochastictrials were tested for stationarity with the useof a “runs” test (Bendat and Piersol 1986). Lessthan 5% of all trials were rejected by this test. Finally, the triceps EMG signal was visually inspectedfor obviousevidenceof cocontraction. No trials were rejectedon this basis.
Data analysis To evaluatethe impact of fatigue on the elbow flexors, a number of analysisprocedureswereappliedto both the prefatigueand postfatiguedata, and the resultsfor the two casescomparedusing a statistical t test ( Walpole and Myers 1978) with a confidence level of 95%.Averagevaluesare commonly presentedwith a standard deviation in the form meant SD. AVERAGE TORQUE AND EMG VALUES DURING STOCHASTIC PERTURBATIONS. Averagesof the torque andrectified EMG rec-
ords were madeduring the l-s preperturbation isometric period and during a 13.5-speriod centeredon the perturbation. The averagesfor a rangeof isometric mean torque levelsgave rise to orderedpairsof torque-EMG points to which a line wasfit by the use of standard linear regressiontechniques (Walpole and Myers 1978). The slopesdetermined by regressionwere then used to comparethe contractile state of the musclesbefore and after fatigue. IncrementalEMG valueswerecomputedby subtractingthe isometric averagefrom the averagevalue obtained during each perturbation. ESTIMATION OFJOINTCOMPLIANCE DYNAMICS. Thedynamic mechanicalpropertiesof the elbowjoint werecharacterizedby the useof complianceimpulseresponses (CIRs), estimatedwith the useof a modified correlation-basedidentification scheme(Hunter and Kearney 1983a),with joint torque asthe input and angleas the output. For a linear system,the impulseresponseis sufficient to characterizethe dynamics of the systemand can be usedto predict the output of the systemto an arbitrary input. In general, musclemechanicalpropertiesare known to be nonlinear, but it has been shown repeatedly in the past (Dufresne et al. 1978; Hunter and Kearney 1982;Kirsch and Rymer 1989;Weisset al. 1988) that musclebehavior is remarkably linear about a given operatingpoint for stochasticperturbations. In the presentstudy, linear techniqueswill be usedto quantify systembehavior at several different operatingpoints, and the variations in the resulting parameterswith operatingpoint and experimentalcondition will be described. In the experimentalprotocol describedabove, the actual input wasjoint angle(and not joint torque), but the descriptionof system dynamicsin termsof stiffnesstendsto emphasizethe high-frequency, inertial characteristicsof the joint and to obscurethe more interestingviscoelasticbehavior of muscle.Compliance(the dynamic reciprocalof stiffness),by virtue of the integral relationship of torque to position, emphasizesthe elasticand viscousbehavior of the joint, i.e., the musclepropertiesthat can be modified by neural inputs. The compliancedescriptionwasalsoattractive becausethe identified complianceimpulseresponses have a form similar to that of a second-order,underdampedmechanicalsystem, the parametersof which (i.e., elasticstiffnessK, viscousstiffnessB, and inertia 1) can be readily estimatedby establishednonlinear fitting techniques.No closed-formexpressionexists,however, for the equivalent stiffnessimpulseresponse.Specifically,the
IN HUMAN
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equation describingthe compliance impulse responseof such a systemis given by h(t) =
1 /neySln 1T 1 -i - 412
-Bt
.
K B2 7 -St
(0
V
The Levenberg-Marquardt nonlinear parameter estimation method (Presset al. 1986)wasusedto determinethe valuesfor K, B, and I, which best fit the identified compliance impulse responses. To be certain that reversingthe order of input and output was valid, a preliminary analysiswasperformed to comparestiffness frequency responses identified directly from the recordeddata to simulatedfrequency responses generatedby the useof parameters computedfrom fits to the complianceimpulseresponse,stiffness frequency responsegain, and stiffnessfrequency responsephase. The compliancefit wasmore robust than either of the frequency domain fits, which fit either the gain or phasewell, but not both. Compliance impulseresponsefits, on the other hand, predicted both gain and phasebehavior quite accurately. ESTIMATIONOFANGLE-EMGDYNAMICS. Thedynamicrelationshipbetweenthe imposedstochasticanglerecord and the evoked EMG signalwasquantified in two different ways.The first wasthe incremental EMG value computed as describedabove. The second approachwasto quantify the dynamic input-output relationshipbetweenthe imposedperturbation and the evoked EMG. In this instancethe velocity signalwashalf-wave rectified (by setting all shortening velocity values to 0) and usedas the input to a systemwhoseoutput wasone of the rectified EMG records.The frequency responsewasthen estimatedasthe complex ratio between the input-output crossspectrum and the input autospectrum, both of which were estimatedwith the useof overlapped, windowed periodogramtechniques(Bendat and Piersol 1986). The frequency responseresultspresentedbelowwill bein the form of gain and phaseresponses, computed asthe magnitudeand argument,respectively,of the complex frequencyresponse.The adequacy of the linear frequency responsedescriptionwasevaluated by useof the squaredcoherencefunction. Briefly, squaredcoherence describesthe fraction of the output related linearly to the input asa function of frequency. Its value rangesfrom 0 (if the output at a particular frequency hasno linear relation to the input) to 1 (if the output at a particular frequency is completely describedby a linear transformation of the input). The half-wave rectification operation wasperformed on the velocity record becauseit was found in preliminary tests that, in accordancewith earlier work (Kearney and Hunter 1983)) this operationsignificantly improved the match betweenthe predicted and actual EMG responses. STEP RESPONSE ANALYSIS. To emphasizethe impact of fatigue on step responses,we calculated the point-by-point differences between torque, bicepsEMG, and brachioradialisEMG before and after fatigue for trials matchedby prestretchtorque level. The difference operation wasnot performed for angle,becauseit was identical before and after fatigue. This subtraction proceduresignificantly reduced the dominant effect of inertia on the torque record and allowed a direct evaluation of the relative impact of fatigue on both the intrinsic mechanicaland reflex propertiesof the musclesspanningthis joint. The resulting difference torque recordsweretime averagedduring three periods,eachof which is depicted in Fig. 4B: a 500-msisometric prestretch region (only the end of which is shown), a 20-ms“prereflex” period beginning with the onsetof the stretch, and a 75ms “steady-state” period beginning50 msafter stretch onset. The placementof the prereflex period waschosenbecausethe torque responsehere wasentirely free of reflex contributions and wasdue solelyto the intrinsic
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mechanicalproperties of the joint. The placement of the time window for the steady-stateperiod wasbasedon the observation that torque wasrelatively steadyduring this period and reflected the impact of reflex action. Subtractingthe isometrictorque averagefrom the steady-statetorque averagethen gavean incremental torque value, which wasdivided by the amplitude of the stretch to yield an estimateof staticjoint stiffness. The timing of relevant portions of the EMG responses to step stretchweresomewhatdifferent than for torque, sothey wereanalyzed by the useof different window placements.The first time window wasidentical to the isometric window describedabove, but the “dynamic” window began at the onset of EMG reflex activity (the end of the prereflex window for torque) and ended ~45 mslater (at the beginningof the torque steady-statewindow) when the stretch-relatedEMG burst was mostly completed. The isometricaveragewassubtractedfrom this poststretchaverageto yield incremental EMG. Note that incremental EMG wascomputed separatelybeforeand after fatigue (with the useof the time windowsshownin Fig. 4B) and wasnot calculatedfrom “difference” records.The differencetechnique tendsto reduce the prepost fatigue isometric EMG differenceson a point-by-point basis becausethe EMG time variations beforeand after fatigue are unlikely to be correlated. The stretch-evokedEMG difference responseswill likely be more representativethan isometric values becauseof synchronization to the stretch, sothe differenceEMG responses have been included (for illustrative purposesonly) for comparisonto the correspondingtorque responses.
Isometric torque (No m) 3. Isometric torque electromyographic (EMG) relationships for the biceps muscle of 1 subject before and after fatigue. The linearity of this relationship is indicated by best-fit regression lines, and the impact of fatigue is clear from the 354% change in slope. Biceps EMG is shown as a fraction of its prefatigue maximum. FIG.
performance of postfatigue testing. For the &4” perturbation trials, which were performed first after fatigue, the average shift in the slope of the biceps muscle for the seven Subject population subjects was 306% (range, 140-4 1 l%), whereas the shift Sevensubjects(5 male, 2 female) were usedin this study. All decreased to 2 10% (range, 58-403%) by the time the step werevolunteers,2 l-55 yr of age,who consentedto participate in the average the study after being informed of the protocol and the minimal trials were performed. For brachioradialis, shifts were 205% (range, 88-331%) for the t4” trials and risk involved, and were free to withdraw at any time. 129% (range, 47-233%) for the step trials. Even though the RESULTS pre-post fatigue differences tended to lessen with time, the difference between slopes before and after fatigue remained Induction of fatigue highly significant (P = 0.95) for both muscles of each subThe approach taken in this study utilized fatigue to pro- ject. Because a percentage change of 100% in the isometric duce long-lasting reductions in muscle contractile force. To torque-EMG relationship means that a given amount of begin, it is therefore important to establish that the exercise EMG produces only one-half the torque generated before protocol did indeed produce a significant loss of force. As fatigue, it is clear that the fatiguing exercise used in this described in METHODS, a sequence of repeated shortening study inflicted an enormous deficit on the neuromuscular contractions against substantial loads was used to induce system in every case. As discussed above, the 40% MVC fatigue, and the slope of the isometric torque-EMG rela- level upper contraction level was chosen because it was the tionship was then used to summarize the contractile state of maximum level that could be sustained for an entire stothe muscle before and after fatigue. The isometric torquechastic trial after fatigue, further indicating that muscle EMG relationships for the biceps muscle of one subject is force generation was severely impaired. shown in Fig. 3 over the O-40% MVC range ( ~0-3 1 Nm The relative increases in isometric EMG after fatigue for this subject) used in these experiments. This plot shows were consistently greater for biceps than for brachioradialis, that the relationship between isometric torque and EMG probably because the exercise routine (during which the was basically linear in nature; the squared coefficient of forearm was supinated) imposed a disproportionate load correlation (R2) of the linear fits averaged 0.93 across all on biceps. The position of the arm in the apparatus during seven subjects for the two muscles (biceps and brachiorathe stretch testing was also fairly supinated, forcing the fadialis) and various conditions (a total of 96 regression fits), tigued biceps to support a significant portion of the perturand the linear fit was found to be statistically significant in bation (Buchanan et al. 1989). The results described in the all cases for P = 0.95. rest of the study will therefore be drawn mostly from the Figure 3 also shows that fatigue severely impaired elbow biceps muscle, although summary statistics will also be flexor force generation. For the subject illustrated, the slope given for brachioradialis. of the isometric torque-EMG relationship shifted by >350% after fatigue. Similar slope changes were found for Eflect offatigue on step responses other subjects, although the magnitude of the shift dechange in the TORQUE RESPONSES. The fatigue-induced pended on the muscle used and the point in time examined, torque response elicited by a step stretch of the elbow joint as the magnitude of the slope change after fatigue was found to decrease somewhat with the passage of time during the is illustrated for one subject in Fig. 4A, where pre- and Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (129.186.138.035) on January 10, 2019.
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Time (set) 4. A : torque responses of 1 subject to step stretch before and after fatigue for matched 25% isometric contraction levels. Large oscillations in the torque responses due to joint inertia have been clipped to show the larger maintained mean torque level remaining when the oscillations have died out (shown by the dashed lines). B: “difference” records (except for angle) computed by subtracting postfatigue responses from prefatigue ones for a 25% maximum voluntary contraction level of 1 subject. Also shown are the various time windows used to compute time averages for the step trials. Electromyographic difference records (shown relative to prefatigue maximum) are presented for illustrative purposes only (see text). FIG.
postfatigue trials have been matched at an initial torque level of -25% of prefatigue maximum. The inertia of the forearm is responsible for the large oscillations in the torque records during the stretch, so the associated peaks of the torque record have been clipped to better present the smaller, but functionally important, contributions of muscle. Because of the inertial effects, any difference in the
torque response before and after fatigue is difficult to visualize in the first 50-60 ms after stretch onset, but after this time it is clear that the maintained postfatigue torque level is reduced compared with that before fatigue. Figure 4B presents difference records obtained by subtracting postfatigue responses from prefatigue ones for matched 25% MVC contraction levels (except for angle,
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which was identical in the 2 cases). The effect of fatigue on intrinsic mechanical properties of the joint was estimated by examining the difference torque responses during the prereflex time interval after stretch onset (20 ms), which is before reflex pathways would have had time to act. Reflex output changes were estimated by examining the torque difference record during the steady-state period, when reflex action was manifested mechanically. As shown in Fig. 423, we found that, for matched mean torque levels, there was virtually no difference in the early prereflex torque elicited pre- and postfatigue, whereas during the steady-state period, the difference torque record has a positive mean value, indicating that the prefatigue torque response was larger than the postfatigue one. For all seven subjects, the steady-state torque differences were statistically significant, whereas none of the prereflex differences were statistically significant. Figure 5A plots the averages of the torque difference signal over the two time windows for the same subject illus-
Isometric
torque (N m) l
trated in Fig. 4, over a range of initial torque levels. The prereflex torque differences were essentially zero across the whole range of background torques examined ( -O-40% of maximum), indicating that stiffness during this time period was determined solely by components insensitive to fatigue. Steady-state torque differences were found to be consistently positive, however, indicating that the reflexively evoked torque was smaller after fatigue than before. It is interesting that significant differences between pre- and postfatigue torque increments begin to arise after mean torque exceeds 15% of maximum ( -7 N m for the subject illustrated). This contraction level has been found (Bigland-Ritchie and Woods 1984) to represent a typical boundary between fatigue-resistant and fatigue-susceptible motor units in a variety of human muscles. To facilitate comparisons between subjects, the torque differences have been further processed by averaging points such as those shown in Fig. 54 across torque levels of 1540% of maximum to produce a single value for each subject. This average value was then normalized with respect to the average prefatigue incremental torque value (for the same mean torque range) to obtain the percentage change in the prereflex and steady-state torque values due to fatigue. These results are shown for all seven subjects in Fig. 5 B. The prereflex torque difference was small and varied in sign, being virtually zero for several subjects. Across all subjects, this difference averaged 1.4 t 4.1% (mean t SD) of the ultimate prefatigue steady-state torque increment, indicating that the intrinsic stiffness of active muscle is unchanged by significant fatigue, at least for matched torque levels. The steady-state torque difference was clearly positive in all subjects, however, averaging 34.7 t 13.6% of the steadystate prefatigue value. Because the intrinsic stiffness component is apparently unaffected by fatigue, this last result indicates that the mechanical contribution of reflex action to joint torque is decreased somewhat after fatigue. This is not surprising given the severe degree of muscle weakness induced (isometric torque-EMG shift of 355% for the subject shown in Fig. 5A) ; new motor units recruited by reflex action would generate less than one-fourth of their prefatigue force if the isometric torque-EMG relation is a good indicator. l
RESPONSES. The EMG response elicited by the step stretch was almost always increased in magnitude after fatigue, a finding illustrated in the pre-post fatigue difference records shown in Fig. 4B. In both muscles examined, the difference EMG signals (shown here as a fraction of prefatigue maximum) were routinely negative after the stretch, indicating that the postfatigue responses were greater than the corresponding prefatigue response. As described above, the EMG responses were averaged over a 45-ms dynamic time window starting at the onset of the stretch-evoked burst of activity. Figure 6/1 presents the behavior of the resulting incremental biceps EMG responses before and after fatigue for one subject. The biceps EMG increment increased monotonically with background torque in both cases, but the postfatigue EMG responses were much larger than the prefatigue responses across the entire range of torque examined. EMG
1'2'3'4'5'6'7
Subject FIG. 5. A : prereflex and steady-state torque “difference” time averages for 1 subject over a O-40% maximum voluntary contraction (MVC) range of prestretch contraction levels. The prereflex torque values averaged near 0, indicating that intrinsic joint stiffness was unaffected by fatigue, but the positive steady-state torque differences indicate that reflex stiffness was decreased by fatigue. B: subject summary for torque responses to step stretch. Single averages obtained for each subject by averaging responses (like those in A) for trials from 15-40% MVC, shown with error bars indicating the standard deviation of the mean. Prereflex differences were quite small across subjects ( none statistically significant ) , whereas steadystate differences were significantly larger and all were statistically significant.
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Fig. 6A were not included). The pre- and postfatigue averages (tl SD) were then expressed as a percentage of the prefatigue average for each subject; the data illustrated in A correspond to subject 1. Overall, the pre-post fatigue shift in average incremental EMG was statistically significant (P = 0.95 ) in all seven subjects, with an average shift across all subjects of 72.3%. For brachioradialis, pie-post fatigue shifts for all seven subjects averaged 5 8.5%, and all were statistically significant. OPERATING POINT CONSIDERATIONS. The effect of activation level (apart from torque level) on reflex responsiveness is evaluated in Fig. 6B by plotting the incremental EMG response as a function of isometric EMG (which presumably matches motoneuronal pool state), rather than as a function of background torque. It is seen that the prefatigue points do tend to increase with mean EMG at low contraction levels, but the EMG increment quickly approaches a saturation level and remains rather constant over the remaining range of contraction. Furthermore, the postfatigue incremental EMG values are significantly increased above the prefatigue points except at very low contraction levels.
10
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IN HUMAN
torque (N am)
Efect of fatigue on stochastic responses OFTHE CIR. CIRswereidentifiedwith the use of angle and torque records from each of the two stochastic angular perturbations ( &4”, O-25 Hz and &6”, 0- 10 Hz). Figure 7A shows a superimposed series of CIRs derived from the prefatigue responses of one subject to the t4” perturbation, over a range of initial torques. Trials collected at similar mean torque levels produced compliance impulse responses with similar characteristics, as evidenced by the grouping of the three CIRs at each mean torque level. The decrease in impulse response amplitude and duration with increases in mean torque indicates that the joint is becoming progressively stiffer. The adequacy of the compliance description was evaluated by convolving the CIR with the joint torque record to predict joint angle. The top of Fig. 7C overlays such a predicted response with the actual recorded angle, and it is clear that the correspondence is good. The goodness of fit was quantified by computing the percentage of the output variance accounted for by the CIR (percent variance accounted for or %VAF). The %VAF of 9 1.1% for the trial of Fig. 7C was slightly higher than average; for the -+4” perturbation, the average %VAF across all prefatigue trials across all seven subjects was 88.6 t 2.6%, whereas postfatigue the average dropped somewhat to 82.8 t 3.0%. For the t6” perturbation, the average %VAF values pre- and postfatigue were 88.3 t 4.7 and 85.9 t 2.3%, respectively. The residual angle not predicted by the compliance impulse response was small and, as shown in Fig. 7 D, distributed almost exclusively at frequencies
in U.S.A.
Neural Compensation for Fatigue-Induced Changes in Muscle Stiffness During Perturbations of Elbow Angle in Human R. F. KIRSCH AND W. 2. RYMER Departments of Biomedical Engineering, Physiology, and Physical Medicine and Rehabilitation, Northwestern University and the Sensory Motor Performance Program, Rehabilitation Institute of’ Chicago, Chicago, Illinois 60611 SUMMARY
AND
CONCLUSIONS
I. The contribution to muscle force regulation provided by reflex pathways was studied in the elbow flexor muscles of seven normal human subjects, with the use of voluntary fatigue to induce a deficit in the force-generating capability of these muscles. To estimate the changes in the mechanical state of the muscle and the compensatory actions taken by reflex pathways to minimize the impact of fatigue, stochastic and “step” angular perturbations were applied to the joint, and the resulting joint stiffness and electromyographic (EMG) responses were compared before and after fatigue. 2. The magnitude of contractile fatigue, induced by repeatedly lifting a weight via a pulley system, was quantified by comparing the slope of the isometric torque-EMG relationship before and after fatigue. The exercise routine was quite effective in producing severe and long-lasting fatigue, with average percentage changes in the isometric torque-EMG slope of 2 lo-306% for biceps and 129205% for brachioradialis, depending on the point in time examined. 3. The torque response to a rapid step stretch of the elbow joint was quite similar before and after fatigue for the time interval before reflex action (~20 ms after stretch onset), suggesting that intrinsic muscle stiffness for a given mean torque level was not changed by fatigue. The steady-state torque level attained after completion of the stretch was always decreased after fatigue, indicating a decrease in the reflex component ofjoint stiffness, but this decrease was small compared with the change in the isometric torque-EMG relationship and was accompanied by a significantly larger incremental EMG response after fatigue. This increase in incremental EMG after fatigue was found to be of reflex origin, with activation-related reflex gain changes apparently playing a significant role only at low contraction levels. 4. Torque and angle responses recorded during stochastic perturbations were used to identify elbow joint compliance impulse responses. A second-order mechanical model was fit to each impulse response, and the parameters representing joint inertia, elastic stiffness, and viscous stiffness were used to summarize changes in joint mechanical properties as the mean contraction level was varied. For a perturbation with a relatively wide bandwidth (O-25 Hz), fatigue had little or no effect on the form of the compliance impulse response, apparently because the stimulus disabled reflex force generation in elbow flexor muscles, whereas a perturbation with a more restricted bandwidth (0- 10 Hz) demonstrated consistent decreases in joint stiffness after fatigue. Most (>90%) of this decrease in stiffness was attributable to a decrease in the elastic component, with only small and variable changes in viscous stiffness observed. As with step responses, the decreases in stiffness were small compared with isometric torque-EMG changes, and EMG responses elicited by stochastic perturbations of either bandwidth were significantly increased after fatigue, both in absolute magnitude and in the gain of the input-output relationship
between the perturbation angle and the resulting EMG, especially for the heavily fatigued biceps muscle. 5. The mechanical and EMG responses obtained from both step and stochastic perturbations were consistent with the actions of a force-regulating feedback mechanism. Force feedback loop gains were estimated for the low bandwidth stochastic perturbation by the use of two different techniques, each of which gave broadly similar results. Average loop gains across all seven subjects of 1.27-4.6 1 were computed, depending on the method used and the assumptions made. Loop gain estimates from step perturbations were somewhat larger, averaging 8.3 1, but still within the same range. 6. These large loop gain values indicate that force regulation significantly reduces the sensitivity of the overall neuromuscular system to fatigue (by 56-89%) and imply that force regulation may be an important component of the overall reflex control of muscle contraction during nonfatiguing conditions as well.
INTRODUCTION
Although force is the primary output variable for muscle, the prominence of the reflex connections of muscle stretch receptors, such as spindle receptors, onto homonymous motoneurons (Sherrington 1909) has led to a disproportionate emphasis on the length-regulating features of reflex action. It is now well established that Golgi tendon organs provide a very sensitive and accurate representation of instantaneous muscle force (Crag0 et al. 1982; Houk and Henneman 1967). Furthermore, these tendon organ afferents make appropriate reflex connections (Eccles et al. 1957; Granit 1950) to close a force-regulating feedback pathway, although there is also substantial evidence of convergence onto these same interneurons from a range of other receptors systems, including joint receptors (Lundberg et al. 1978) cutaneous receptors (Lundberg et al. 1977) and even muscle spindle Ia receptors (-Czarkowska et al. 198 1; Jankowska et al. 198 1; Jankowska and McCrea 1983). In spite of this wealth of electrophysiological evidence, the potency and functional role of even the simple autogenetic force feedback pathway remains unconfirmed. It has been asserted that length and force feedback pathways work in concert to regulate muscle stiffness, the ratio of force to length, rather than either length or fo-rce separately (Crag0 et al. 1976; Nichols and Houk 1976). The existence of such a stiffness regulator has been difficult to confirm, however, because previous assessments of force feedback has shown it to be fairly weak or nonexistent
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(Houk et al. 1970; Jack and Roberts 1980; Rymer and Hasan 1980). However, the aforementioned studies were performed in the decerebrate cat model, the findings from which may not be applicable to normal intact systems because interneuronal pathways mediating the tendon organ reflex loop appear to be abnormally inhibited, at least to some degree (Engberg et al. 1968). This limitation of the decerebrate preparation has led us to examine force regulation in normal human subjects. The first evidence that force-sensitive reflex pathways are functionally important in normal human subjects was presented in an earlier report from this laboratory (Kirsch and Rymer 1987a). In this earlier study we found that torque responses to a ramp extension of the elbow flexor muscles decreased only slightly after fatigue, even though the reflexively mediated torque component should have been significantly reduced due to fatigue. Electromyographic (EMG) responses evoked by the stretch were significantly increased, indicating that the compensation was neurally mediated. These results were noteworthy because they provided the first demonstration of effective force regulation in an intact system, but they were limited by the possibility of voluntary intervention and restricted to essentially static conditions. The present study also uses fatigue to investigate the regulation of force in human elbow flexor muscles, but several limitations associated with our past work have been addressed. Specifically, we employed stochastic positional perturbations in addition to a more conventional “step” stretch because such perturbations have two useful features. First, the occurrence of voluntary or triggered reactions are minimized by the random nature of stochastic perturbations, making them wholly unpredictable to the subject (Dufresne et al. 1978). Second, because of the richness of their stimulus characteristics (Bendat and Piersol 1986; Marmarelis and Marmarelis 19 7 8 ) , stochastic perturbations also permit a general and experimentally efficient characterization of the dynamic properties of the system. This approach is also computationally efficient because powerful numerical techniques for characterizing both linear and nonlinear system properties for stochastic perturbations have been developed (Bendat and Piersol 1986; Hunter and Kearney 1983a; Marmarelis and Marmarelis 1978 ) , although linear techniques have been used exclusively in the present study. A step perturbation has been used as well to allow comparisons with previous studies. In the present study the exercise routine used to generate fatigue inflicted an enormous deficit on the force-generating capacity of the flexor muscles acting at the elbow joint, yet after fatigue it was found that the stiffness of the joint was reduced by a much smaller degree. This relative preservation of joint stiffness was accompanied by a significant increase in the magnitude of the evoked EMG responses after fatigue. Estimates of force feedback loop gain indicate that this feedback system reduced the sensitivity of the output joint torque to fatigue by 55-89%, suggesting that forcesensitive reflex pathways make a significant contribution to the control of muscle contraction. Portions of this work have appeared previously in abstract form (Kirsch and Rymer 1987b, 199 1).
METHODS
Experimental
apparatus
A large torque motor configured as an angular position servo was used to apply controlled perturbations to the elbow joint of each subject. A lightweight aluminum beam was bolted to a strain gauge-based torque transducer, which in turn was rigidly attached to the motor shaft. Each subject was seated in a dental chair with his arm attached to the beam such that joint rotation was in a horizontal plane and the axis of rotation of the motor corresponded to that of the elbow. A fiberglass cast was molded to the distal half of the forearm in each experiment, and, after it had solidified, it was rigidly attached to the beam by a U-bolt. This arrangement prevented virtually all movement of the forearm relative to the beam, but was not so restrictive as to impair circulation. The initial position of the motor shaft was set to provide an elbow angle of 90” (midflexion-extension). In addition to the torque signal, a potentiometer and tachometer provided signals proportional to angular position and velocity, respectively. EMGs of several elbow muscles were recorded with the use of disposable solid gel silver / silver chloride surface electrodes, applied after appropriate skin preparation. EMG signals were recorded differentially from pairs of electrodes over the medial and lateral heads of biceps, brachioradialis, and triceps. The EMG signals were high-pass filtered (4-pole Butter-worth) at 4.5 Hz before amplification. The combination of skin preparation, flexible electrodes, and high-pass filtering resulted in negligible movement artifact in the EMG records. All mechanical and EMG signals were filtered identically by eight-pole Butterworth low-pass filters before sampling by an analog-to-digital converter. For stochastic perturbations, where a sampling frequency of 250 Hz was used, a filter cutoff frequency of 100 Hz was chosen. A 400-Hz filter cutoff was chosen for step perturbation trials, which used a sampling frequency of 1,000 Hz. For all trials, a total of 4,096 points per record were collected during each trial (i.e., 16.384 s for stochastic trials, 4.096 s for step trials). A PDP 11/73 computer was used to control the experiments and to digitally record the data. Digitized data were transferred to a Macintosh 11x computer for analysis.
Perturbation
sequence generation
STOCHASTIC PERTURBATIONS. Stimulus sequences were constructed by generating a 2,048point, normally distributed stochastic sequence (Press et al. 1986). This original sequence was digitally filtered and scaled in two ways to produce perturbations of approximately k6.0” (0- to lo-Hz bandwidth) and 24.0” (0- to 25Hz bandwidth) when applied to the actuator. Data were recorded for a l-s isometric period before perturbation onset to allow characterization of isometric torque-EMG properties. Figure 1A illustrates the quantities recorded during a typical stochastic trial ( t6” ) performed at m 25% of the prefatigue maximum voluntary contraction (MVC). Note that the EMG signals have been rectified and that triceps EMG is not shown. The large modulation of joint torque and the flexor EMGs by the imposed perturbation (top record) was subsequently used to estimate the dynamic properties of the system (see below). Figure 1 B shows the relative frequency content of the two different stochastic perturbations by overlaying the power spectra (normalized to their respective maximum values) from each of the two angle records. As described above, the 4O perturbation contained significant frequency components to -25 Hz, whereas the 6” perturbation was limited to 10 Hz. The use of perturbations with two different bandwidths was a compromise between the requirements for a frequency range suf-
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FORCE REGULATION
Lateral biceps
EMG (A.U.) Brachioradialis EMG
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FIG. 1. A : data recorded during a typical stochastic perturbation ( +6” ) trial at 25% maximum voluntary contraction for 1 subject. Joint torque and the three flexor electromyographic (EMG) signals all showed clear modulation by the perturbation. Rectified EMG records are shown in arbitrary units. B: Power spectra for the 2 stochastic perturbations, each normalized to its maximum value.
ficiently broad to fully capture the mechanical properties of the system, yet restricted enough in bandwidth to remain within the capabilities of reflex pathways acting through significant loop delays. Other investigators (Kearney and Hunter 1990; Marmarelis and Marmarelis 1978 ) have pointed out the need for a wide bandwidth to adequately identify joint dynamics, especially inertia. If the bandwidth is too restricted, the performance of the estimation procedures to be described below begins to deteriorate. An opposing consideration, however, is that the mechanical efficacy of reflex action is apparently obliterated for stochastic perturbations with bandwidths containing significant components higher than
- 15 Hz (Kirsch and Rymer 1989). Thus we chose the higher 25Hz bandwidth to ensure adequate characterization ofjoint inertia, whereas the lower lo-Hz bandwidth was chosen to be within the range of reflex action, but still unpredictable by the subject. STEP PERTURBATION. Step changes in the angular position of the elbow joint ( L.JOwith a rise time of -40-50 ms), in a direction that stretched the flexor muscles, were also imposed on the joint. This perturbation will be referred to as “step” or “stretch” in subsequent sections. A l-s isometric period preceded the stretch to allow for isometric measurements, followed by the stretch, a 2-s plateau, and finally a return to the original position. The quanti-
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60.040.0
l m
Torque 2(-J& :; Pm)
00.: . m
Lateral biceps
4. o ’
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WJJ
FIG. 2. Data records collected during the 4” “step” perturbation trial at 25% maximum voluntary contraction. The perturbation evoked clear responses in the joint torque record and the 3 flexor electromyographic signals (rectified and shown in arbitrary units).
0.0
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Time (set) tiesrecordedduring the stretch portion of a typical steptrial (25% MVC) areshownin Fig. 2. The imposedangularperturbation (top record) resultedin a largetransient changein joint torque and a poststretchmaintained value that was larger than the isometric contraction level, although the significantinertially inducedoscillations makethis difficult to see.Noninertial effectsare more easily visualized when pre- and postfatigueresponses are subtracted (see STEP RESPONSE ANALYSIS, below). The flexor EMG records (shown after rectification) show clear bursting activity after the stretch, due in part to smallposition oscillationswhile approaching the final position.
Experimental
protocol
During a given trial, the subjectwas askedto maintain a prescribed mean torque level and to “not intervene voluntarily” when the perturbation was applied. The subject received visual feedbackof low-passfiltered (7.5 Hz) torque, which gavean indication of mean torque without the large excursionsdue to joint inertia at higher frequencies.For both stochasticand stepperturbations,trials containing evidenceof voluntary intervention, such asnonstationarity in torque or EMG responses to stochasticperturbations or unusual variations in force or EMG in step responses, were excludedfrom further analysis. The MVC of eachsubjectwasdetermined,and subsequentperturbation trials were performed with background torque levels varying from 0 to 40%of this maximum. Higher contraction levels werenot tested,to minimize the potential for posttetanicpotentiation (Edwardset al. 1977;Jami et al. 1983) and becausesubjects often could not maintain higher levelsfor the entire 16.384-sstochastictrials after fatigue. For eachof the three different perturbations, a set of three trials at each of 6 or 7 initial torque levels within the O-40%torque rangewere performed for a total of 18 21 trials/perturbation. The three trials at eachmeantorque level wereperformedsequentially,and the torque levelswereincreased progressivelyfrom low to high. The k4.0” perturbation set was completedfirst, followed by the -t6.0”, and, finally, the stepperturbations. After thesethree setsof trials were completed,fatigue wasinduced in the elbow flexor muscles,and the three setswere then repeated.
Induction
offatigue
Fatigue was induced by having the subject repeatedly lift a weight with the useof the elbow flexors only. The weight chosen (S-10 kg) dependedon the subject,the criteria beingthe ability to repeatthe action 15-20 times.After a rest of - 30 s,similar setsof contractions were continued for a total of 15 min. After completion of the fatiguing exercise,a restperiod of 10min wasimposed to allow musclefiber conduction to recover from the accumulation of metabolicproductsproducedduring the contractions.This precautionis necessary becausepreviouswork (Kirsch and Rymer 1987a;Lindstrom and Petersen1983; Mortimer et al. 1971) has shownthat decreases in musclefiber conduction velocity leadto a shift in the EMG power spectrumtoward lower frequencies.Becausethe tissueintervening between the muscle fibers and the surfaceelectrodesactsasa low-passfilter (Lindstrom and Petersen 1983)) the frequency-shifted EMG would be more completely transmitted to the surface,resultingin an increasein amplitude. Furthermore, becausea portion of our resultsis basedon a comparisonof EMG responses to a positionalperturbation beforeand after fatigue, it is important to eliminate this potential sourceof distortion. Fortunately, it hasbeenfound in an earlier study with the useof a similar fatiguing protocol (Kirsch and Rymer 1987a), and elsewhere(Mortimer et al. 1971)) that EMG spectralcharacteristics after fatigue returned to normal within 10 min after the completion of fatiguing contractions. Contractile fatigue (as expressedby the slopeof the isometric torque-EMG relationship) wasfound to persistfor >2 h, however, allowing direct comparison of EMG amplitudesin fatigued and unfatigued muscle.After the IO-min rest, the perturbation protocol describedabove was repeated.
Data conditioning The recordedtorque valuescontained a component due to the inertia of the apparatususedto attach the arm to the motor. This componentwasremovedfrom eachof the torque recordsby identifying the stiffnessimpulseresponse(seebelow) for data collected with the subject’sarm, but not the cast,removedfrom the apparatus. This impulseresponsewasthen convolved with the recorded
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FORCE REGULATION
anglerecordsfrom eachtrial, yielding the torque componentthat wasindependentof the subject’sarm. This torque componentwas subtractedpoint by point from the measuredtorque to yield the estimatesof joint torque that were used for all subsequent analyses. The four EMG signalswere full-wave rectified, and the angle, torque, and bicepsand brachioradialisEMG signalsrecordedduring stochastictrials were tested for stationarity with the useof a “runs” test (Bendat and Piersol 1986). Lessthan 5% of all trials were rejected by this test. Finally, the triceps EMG signal was visually inspectedfor obviousevidenceof cocontraction. No trials were rejectedon this basis.
Data analysis To evaluatethe impact of fatigue on the elbow flexors, a number of analysisprocedureswereappliedto both the prefatigueand postfatiguedata, and the resultsfor the two casescomparedusing a statistical t test ( Walpole and Myers 1978) with a confidence level of 95%.Averagevaluesare commonly presentedwith a standard deviation in the form meant SD. AVERAGE TORQUE AND EMG VALUES DURING STOCHASTIC PERTURBATIONS. Averagesof the torque andrectified EMG rec-
ords were madeduring the l-s preperturbation isometric period and during a 13.5-speriod centeredon the perturbation. The averagesfor a rangeof isometric mean torque levelsgave rise to orderedpairsof torque-EMG points to which a line wasfit by the use of standard linear regressiontechniques (Walpole and Myers 1978). The slopesdetermined by regressionwere then used to comparethe contractile state of the musclesbefore and after fatigue. IncrementalEMG valueswerecomputedby subtractingthe isometric averagefrom the averagevalue obtained during each perturbation. ESTIMATION OFJOINTCOMPLIANCE DYNAMICS. Thedynamic mechanicalpropertiesof the elbowjoint werecharacterizedby the useof complianceimpulseresponses (CIRs), estimatedwith the useof a modified correlation-basedidentification scheme(Hunter and Kearney 1983a),with joint torque asthe input and angleas the output. For a linear system,the impulseresponseis sufficient to characterizethe dynamics of the systemand can be usedto predict the output of the systemto an arbitrary input. In general, musclemechanicalpropertiesare known to be nonlinear, but it has been shown repeatedly in the past (Dufresne et al. 1978; Hunter and Kearney 1982;Kirsch and Rymer 1989;Weisset al. 1988) that musclebehavior is remarkably linear about a given operatingpoint for stochasticperturbations. In the presentstudy, linear techniqueswill be usedto quantify systembehavior at several different operatingpoints, and the variations in the resulting parameterswith operatingpoint and experimentalcondition will be described. In the experimentalprotocol describedabove, the actual input wasjoint angle(and not joint torque), but the descriptionof system dynamicsin termsof stiffnesstendsto emphasizethe high-frequency, inertial characteristicsof the joint and to obscurethe more interestingviscoelasticbehavior of muscle.Compliance(the dynamic reciprocalof stiffness),by virtue of the integral relationship of torque to position, emphasizesthe elasticand viscousbehavior of the joint, i.e., the musclepropertiesthat can be modified by neural inputs. The compliancedescriptionwasalsoattractive becausethe identified complianceimpulseresponses have a form similar to that of a second-order,underdampedmechanicalsystem, the parametersof which (i.e., elasticstiffnessK, viscousstiffnessB, and inertia 1) can be readily estimatedby establishednonlinear fitting techniques.No closed-formexpressionexists,however, for the equivalent stiffnessimpulseresponse.Specifically,the
IN HUMAN
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453
equation describingthe compliance impulse responseof such a systemis given by h(t) =
1 /neySln 1T 1 -i - 412
-Bt
.
K B2 7 -St
(0
V
The Levenberg-Marquardt nonlinear parameter estimation method (Presset al. 1986)wasusedto determinethe valuesfor K, B, and I, which best fit the identified compliance impulse responses. To be certain that reversingthe order of input and output was valid, a preliminary analysiswasperformed to comparestiffness frequency responses identified directly from the recordeddata to simulatedfrequency responses generatedby the useof parameters computedfrom fits to the complianceimpulseresponse,stiffness frequency responsegain, and stiffnessfrequency responsephase. The compliancefit wasmore robust than either of the frequency domain fits, which fit either the gain or phasewell, but not both. Compliance impulseresponsefits, on the other hand, predicted both gain and phasebehavior quite accurately. ESTIMATIONOFANGLE-EMGDYNAMICS. Thedynamicrelationshipbetweenthe imposedstochasticanglerecord and the evoked EMG signalwasquantified in two different ways.The first wasthe incremental EMG value computed as describedabove. The second approachwasto quantify the dynamic input-output relationshipbetweenthe imposedperturbation and the evoked EMG. In this instancethe velocity signalwashalf-wave rectified (by setting all shortening velocity values to 0) and usedas the input to a systemwhoseoutput wasone of the rectified EMG records.The frequency responsewasthen estimatedasthe complex ratio between the input-output crossspectrum and the input autospectrum, both of which were estimatedwith the useof overlapped, windowed periodogramtechniques(Bendat and Piersol 1986). The frequency responseresultspresentedbelowwill bein the form of gain and phaseresponses, computed asthe magnitudeand argument,respectively,of the complex frequencyresponse.The adequacy of the linear frequency responsedescriptionwasevaluated by useof the squaredcoherencefunction. Briefly, squaredcoherence describesthe fraction of the output related linearly to the input asa function of frequency. Its value rangesfrom 0 (if the output at a particular frequency hasno linear relation to the input) to 1 (if the output at a particular frequency is completely describedby a linear transformation of the input). The half-wave rectification operation wasperformed on the velocity record becauseit was found in preliminary tests that, in accordancewith earlier work (Kearney and Hunter 1983)) this operationsignificantly improved the match betweenthe predicted and actual EMG responses. STEP RESPONSE ANALYSIS. To emphasizethe impact of fatigue on step responses,we calculated the point-by-point differences between torque, bicepsEMG, and brachioradialisEMG before and after fatigue for trials matchedby prestretchtorque level. The difference operation wasnot performed for angle,becauseit was identical before and after fatigue. This subtraction proceduresignificantly reduced the dominant effect of inertia on the torque record and allowed a direct evaluation of the relative impact of fatigue on both the intrinsic mechanicaland reflex propertiesof the musclesspanningthis joint. The resulting difference torque recordsweretime averagedduring three periods,eachof which is depicted in Fig. 4B: a 500-msisometric prestretch region (only the end of which is shown), a 20-ms“prereflex” period beginning with the onsetof the stretch, and a 75ms “steady-state” period beginning50 msafter stretch onset. The placementof the prereflex period waschosenbecausethe torque responsehere wasentirely free of reflex contributions and wasdue solelyto the intrinsic
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mechanicalproperties of the joint. The placement of the time window for the steady-stateperiod wasbasedon the observation that torque wasrelatively steadyduring this period and reflected the impact of reflex action. Subtractingthe isometrictorque averagefrom the steady-statetorque averagethen gavean incremental torque value, which wasdivided by the amplitude of the stretch to yield an estimateof staticjoint stiffness. The timing of relevant portions of the EMG responses to step stretchweresomewhatdifferent than for torque, sothey wereanalyzed by the useof different window placements.The first time window wasidentical to the isometric window describedabove, but the “dynamic” window began at the onset of EMG reflex activity (the end of the prereflex window for torque) and ended ~45 mslater (at the beginningof the torque steady-statewindow) when the stretch-relatedEMG burst was mostly completed. The isometricaveragewassubtractedfrom this poststretchaverageto yield incremental EMG. Note that incremental EMG wascomputed separatelybeforeand after fatigue (with the useof the time windowsshownin Fig. 4B) and wasnot calculatedfrom “difference” records.The differencetechnique tendsto reduce the prepost fatigue isometric EMG differenceson a point-by-point basis becausethe EMG time variations beforeand after fatigue are unlikely to be correlated. The stretch-evokedEMG difference responseswill likely be more representativethan isometric values becauseof synchronization to the stretch, sothe differenceEMG responses have been included (for illustrative purposesonly) for comparisonto the correspondingtorque responses.
Isometric torque (No m) 3. Isometric torque electromyographic (EMG) relationships for the biceps muscle of 1 subject before and after fatigue. The linearity of this relationship is indicated by best-fit regression lines, and the impact of fatigue is clear from the 354% change in slope. Biceps EMG is shown as a fraction of its prefatigue maximum. FIG.
performance of postfatigue testing. For the &4” perturbation trials, which were performed first after fatigue, the average shift in the slope of the biceps muscle for the seven Subject population subjects was 306% (range, 140-4 1 l%), whereas the shift Sevensubjects(5 male, 2 female) were usedin this study. All decreased to 2 10% (range, 58-403%) by the time the step werevolunteers,2 l-55 yr of age,who consentedto participate in the average the study after being informed of the protocol and the minimal trials were performed. For brachioradialis, shifts were 205% (range, 88-331%) for the t4” trials and risk involved, and were free to withdraw at any time. 129% (range, 47-233%) for the step trials. Even though the RESULTS pre-post fatigue differences tended to lessen with time, the difference between slopes before and after fatigue remained Induction of fatigue highly significant (P = 0.95) for both muscles of each subThe approach taken in this study utilized fatigue to pro- ject. Because a percentage change of 100% in the isometric duce long-lasting reductions in muscle contractile force. To torque-EMG relationship means that a given amount of begin, it is therefore important to establish that the exercise EMG produces only one-half the torque generated before protocol did indeed produce a significant loss of force. As fatigue, it is clear that the fatiguing exercise used in this described in METHODS, a sequence of repeated shortening study inflicted an enormous deficit on the neuromuscular contractions against substantial loads was used to induce system in every case. As discussed above, the 40% MVC fatigue, and the slope of the isometric torque-EMG rela- level upper contraction level was chosen because it was the tionship was then used to summarize the contractile state of maximum level that could be sustained for an entire stothe muscle before and after fatigue. The isometric torquechastic trial after fatigue, further indicating that muscle EMG relationships for the biceps muscle of one subject is force generation was severely impaired. shown in Fig. 3 over the O-40% MVC range ( ~0-3 1 Nm The relative increases in isometric EMG after fatigue for this subject) used in these experiments. This plot shows were consistently greater for biceps than for brachioradialis, that the relationship between isometric torque and EMG probably because the exercise routine (during which the was basically linear in nature; the squared coefficient of forearm was supinated) imposed a disproportionate load correlation (R2) of the linear fits averaged 0.93 across all on biceps. The position of the arm in the apparatus during seven subjects for the two muscles (biceps and brachiorathe stretch testing was also fairly supinated, forcing the fadialis) and various conditions (a total of 96 regression fits), tigued biceps to support a significant portion of the perturand the linear fit was found to be statistically significant in bation (Buchanan et al. 1989). The results described in the all cases for P = 0.95. rest of the study will therefore be drawn mostly from the Figure 3 also shows that fatigue severely impaired elbow biceps muscle, although summary statistics will also be flexor force generation. For the subject illustrated, the slope given for brachioradialis. of the isometric torque-EMG relationship shifted by >350% after fatigue. Similar slope changes were found for Eflect offatigue on step responses other subjects, although the magnitude of the shift dechange in the TORQUE RESPONSES. The fatigue-induced pended on the muscle used and the point in time examined, torque response elicited by a step stretch of the elbow joint as the magnitude of the slope change after fatigue was found to decrease somewhat with the passage of time during the is illustrated for one subject in Fig. 4A, where pre- and Downloaded from www.physiology.org/journal/jn by ${individualUser.givenNames} ${individualUser.surname} (129.186.138.035) on January 10, 2019.
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Time (set) 4. A : torque responses of 1 subject to step stretch before and after fatigue for matched 25% isometric contraction levels. Large oscillations in the torque responses due to joint inertia have been clipped to show the larger maintained mean torque level remaining when the oscillations have died out (shown by the dashed lines). B: “difference” records (except for angle) computed by subtracting postfatigue responses from prefatigue ones for a 25% maximum voluntary contraction level of 1 subject. Also shown are the various time windows used to compute time averages for the step trials. Electromyographic difference records (shown relative to prefatigue maximum) are presented for illustrative purposes only (see text). FIG.
postfatigue trials have been matched at an initial torque level of -25% of prefatigue maximum. The inertia of the forearm is responsible for the large oscillations in the torque records during the stretch, so the associated peaks of the torque record have been clipped to better present the smaller, but functionally important, contributions of muscle. Because of the inertial effects, any difference in the
torque response before and after fatigue is difficult to visualize in the first 50-60 ms after stretch onset, but after this time it is clear that the maintained postfatigue torque level is reduced compared with that before fatigue. Figure 4B presents difference records obtained by subtracting postfatigue responses from prefatigue ones for matched 25% MVC contraction levels (except for angle,
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R. F. KIRSCH AND W. Z. RYMER
which was identical in the 2 cases). The effect of fatigue on intrinsic mechanical properties of the joint was estimated by examining the difference torque responses during the prereflex time interval after stretch onset (20 ms), which is before reflex pathways would have had time to act. Reflex output changes were estimated by examining the torque difference record during the steady-state period, when reflex action was manifested mechanically. As shown in Fig. 423, we found that, for matched mean torque levels, there was virtually no difference in the early prereflex torque elicited pre- and postfatigue, whereas during the steady-state period, the difference torque record has a positive mean value, indicating that the prefatigue torque response was larger than the postfatigue one. For all seven subjects, the steady-state torque differences were statistically significant, whereas none of the prereflex differences were statistically significant. Figure 5A plots the averages of the torque difference signal over the two time windows for the same subject illus-
Isometric
torque (N m) l
trated in Fig. 4, over a range of initial torque levels. The prereflex torque differences were essentially zero across the whole range of background torques examined ( -O-40% of maximum), indicating that stiffness during this time period was determined solely by components insensitive to fatigue. Steady-state torque differences were found to be consistently positive, however, indicating that the reflexively evoked torque was smaller after fatigue than before. It is interesting that significant differences between pre- and postfatigue torque increments begin to arise after mean torque exceeds 15% of maximum ( -7 N m for the subject illustrated). This contraction level has been found (Bigland-Ritchie and Woods 1984) to represent a typical boundary between fatigue-resistant and fatigue-susceptible motor units in a variety of human muscles. To facilitate comparisons between subjects, the torque differences have been further processed by averaging points such as those shown in Fig. 54 across torque levels of 1540% of maximum to produce a single value for each subject. This average value was then normalized with respect to the average prefatigue incremental torque value (for the same mean torque range) to obtain the percentage change in the prereflex and steady-state torque values due to fatigue. These results are shown for all seven subjects in Fig. 5 B. The prereflex torque difference was small and varied in sign, being virtually zero for several subjects. Across all subjects, this difference averaged 1.4 t 4.1% (mean t SD) of the ultimate prefatigue steady-state torque increment, indicating that the intrinsic stiffness of active muscle is unchanged by significant fatigue, at least for matched torque levels. The steady-state torque difference was clearly positive in all subjects, however, averaging 34.7 t 13.6% of the steadystate prefatigue value. Because the intrinsic stiffness component is apparently unaffected by fatigue, this last result indicates that the mechanical contribution of reflex action to joint torque is decreased somewhat after fatigue. This is not surprising given the severe degree of muscle weakness induced (isometric torque-EMG shift of 355% for the subject shown in Fig. 5A) ; new motor units recruited by reflex action would generate less than one-fourth of their prefatigue force if the isometric torque-EMG relation is a good indicator. l
RESPONSES. The EMG response elicited by the step stretch was almost always increased in magnitude after fatigue, a finding illustrated in the pre-post fatigue difference records shown in Fig. 4B. In both muscles examined, the difference EMG signals (shown here as a fraction of prefatigue maximum) were routinely negative after the stretch, indicating that the postfatigue responses were greater than the corresponding prefatigue response. As described above, the EMG responses were averaged over a 45-ms dynamic time window starting at the onset of the stretch-evoked burst of activity. Figure 6/1 presents the behavior of the resulting incremental biceps EMG responses before and after fatigue for one subject. The biceps EMG increment increased monotonically with background torque in both cases, but the postfatigue EMG responses were much larger than the prefatigue responses across the entire range of torque examined. EMG
1'2'3'4'5'6'7
Subject FIG. 5. A : prereflex and steady-state torque “difference” time averages for 1 subject over a O-40% maximum voluntary contraction (MVC) range of prestretch contraction levels. The prereflex torque values averaged near 0, indicating that intrinsic joint stiffness was unaffected by fatigue, but the positive steady-state torque differences indicate that reflex stiffness was decreased by fatigue. B: subject summary for torque responses to step stretch. Single averages obtained for each subject by averaging responses (like those in A) for trials from 15-40% MVC, shown with error bars indicating the standard deviation of the mean. Prereflex differences were quite small across subjects ( none statistically significant ) , whereas steadystate differences were significantly larger and all were statistically significant.
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FORCE REGULATION
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Fig. 6A were not included). The pre- and postfatigue averages (tl SD) were then expressed as a percentage of the prefatigue average for each subject; the data illustrated in A correspond to subject 1. Overall, the pre-post fatigue shift in average incremental EMG was statistically significant (P = 0.95 ) in all seven subjects, with an average shift across all subjects of 72.3%. For brachioradialis, pie-post fatigue shifts for all seven subjects averaged 5 8.5%, and all were statistically significant. OPERATING POINT CONSIDERATIONS. The effect of activation level (apart from torque level) on reflex responsiveness is evaluated in Fig. 6B by plotting the incremental EMG response as a function of isometric EMG (which presumably matches motoneuronal pool state), rather than as a function of background torque. It is seen that the prefatigue points do tend to increase with mean EMG at low contraction levels, but the EMG increment quickly approaches a saturation level and remains rather constant over the remaining range of contraction. Furthermore, the postfatigue incremental EMG values are significantly increased above the prefatigue points except at very low contraction levels.
10
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torque (N am)
Efect of fatigue on stochastic responses OFTHE CIR. CIRswereidentifiedwith the use of angle and torque records from each of the two stochastic angular perturbations ( &4”, O-25 Hz and &6”, 0- 10 Hz). Figure 7A shows a superimposed series of CIRs derived from the prefatigue responses of one subject to the t4” perturbation, over a range of initial torques. Trials collected at similar mean torque levels produced compliance impulse responses with similar characteristics, as evidenced by the grouping of the three CIRs at each mean torque level. The decrease in impulse response amplitude and duration with increases in mean torque indicates that the joint is becoming progressively stiffer. The adequacy of the compliance description was evaluated by convolving the CIR with the joint torque record to predict joint angle. The top of Fig. 7C overlays such a predicted response with the actual recorded angle, and it is clear that the correspondence is good. The goodness of fit was quantified by computing the percentage of the output variance accounted for by the CIR (percent variance accounted for or %VAF). The %VAF of 9 1.1% for the trial of Fig. 7C was slightly higher than average; for the -+4” perturbation, the average %VAF across all prefatigue trials across all seven subjects was 88.6 t 2.6%, whereas postfatigue the average dropped somewhat to 82.8 t 3.0%. For the t6” perturbation, the average %VAF values pre- and postfatigue were 88.3 t 4.7 and 85.9 t 2.3%, respectively. The residual angle not predicted by the compliance impulse response was small and, as shown in Fig. 7 D, distributed almost exclusively at frequencies
