EMG-Based Measures ofFatigue During a RepetitiveSquat ExerciseAssessment of Dynamic Conditions Can Provide InformationAbout Compensatory Muscle Function in ACL Patients
During the last two decades, researchershave developed [12] and applied spec-
tral electromyographic (EMG) techniquesto clinical problems [6, 40, 46] in order toassess muscle fatigue during isometricconstant-force contractions. When surfaceEMG data are recorded during such con-tractions, they may be considered as real-izations of wide-sense stationarystochastic processes [3]. Under these con-ditions, traditional techniques (i.e., the useof the spectrogram) may be adopted to esti-mate the frequency content of the EMGsignal. The median or mean frequency pa-rameters may be used to monitor the spec-tral scaling resulting from the progressionof localized muscle fatigue [22]. Unfortu-nately, the spectrogram technique may notbe utilized to process surface EMG signalsacquired during dynamic contractions. Fordynamic muscle contractions (i.e., con-tractions that are not isometric and iso-tonic) the frequency content of the EMGsignal varies rapidly over time, thus violat-ing the assumption of stationarity and mak-ing it impossible to interpret the results.
Recent developments in time-fre-quency analysis procedures have pro-vided tools to overcome the limitations oftraditional spectral techniques [1]. Basedon these developments, our group [7, 10,11, 34, 47] and others [33, 53, 54] haveproposed using time-frequency tech-niques to assess muscle fatigue during dy-namic contractions. We found CohenClass time-frequency transformations[20] to be particularly suitable to analyzesurface EMG signals recorded during dy-namic contractions. The Cohen Class con-sists of all the bilinear time-frequencyrepresentations that are time and fre-quency shift invariant [20]. This charac-teristic is of paramount importance when
the purpose is to correlate the time-fre-quency representation of a signal with theunderlying physical or physiological phe-nomena [8]. Using this class of transfor-mations, we defined a new parameter toassess muscle fatigue, referred to as theinstantaneous median frequency, which isderived by replacing the power spectraldensi ty funct ion with the EMGtime-frequency distribution in the defini-tion of the median frequency parameter[10].
The time-frequency-based approachextends the assessment of muscle fatiguefrom static conditions (i .e. , con-stant-force, isometric contractions) to dy-namic conditions, thus opening up a widerange of new applications for EMG-basedprocedures in the clinical setting. Al-though important clinical results havebeen obtained in the past by assessing fa-tigue under static conditions, fatigue as-sessments during dynamic tasks are likelymore relevant to daily function. Methodscurrently used in the clinical environmentare often limited to qualitative observa-tions or to simple mechanical measures ofstrength and major postural changes dur-ing a dynamic test. Quantitative EMG-based measures have the potential to pro-vide information that can be directly re-lated to the patient’s clinical condition,namely to compensatory mechanisms thatmay come into play because of muscleweakness, fatigue, pain, etc.
OverviewIn the past few years our group imple-
mented EMG time-frequency analysisprocedures for the assessment of muscleimpairment in patients with lower backpain. This work followed previous studies[6, 40, 46] that, although limited to static
contractions, demonstrated the relevanceof EMG-based methodologies in assess-ing muscle impairment in patients withlower back pain. Recent work led to thedevelopment of novel EMG-processingtechniques [10], the definition of proce-dures to perform the fatigue assessmentduring a test commonly utilized in theclinical setting (i.e., repetitive lifting andlowering of a weighted box) [47], theidentification of distinctive changes inEMG and mechanical parameters for con-trol subjects during this test [11], and theidentification of characteristic patterns offatigue associated with different degreesof impairment in patients with lower backpain [7].
The encouraging results obtained fromthe application of time-frequency-basedtechniques to the assessment of fatigue inpatients with lower back pain motivatedour group to pursue the development ofprocedures for application to other clini-cal problems. In this article we describethe work recently done by our researchteam to design and implement a method-ology aimed at assessing compensatorymechanisms during rehabilitation exer-cises that occur in patients with anteriorcruciate ligament (ACL) deficiency.
Disruption of the ACL of the knee isamong the most common and devastating
injuries to the high-performance athlete orperson participating in sports. The annualincidence of acute rupture of the anteriorcruciate ligament has been estimated to beone in 3000 in the U.S. population (ap-proximately 80,000 to 95,000 new inju-ries each year [26, 42]). More than 50,000knees are reconstructed annually for atorn ACL in the U.S. alone [32] with anestimated cost of almost a billion dollarsper year in managing these injuries [26].
The primary role of the ACL is to pre-vent anterior tibial displacement with re-spect to the femur [43]. Studies havedocumented that the ACL is responsiblefor 85% of the total restraining force to an-terior translation of the tibia during vari-ous activities associated with or withoutcutting [13, 28, 29, 48, 49, 56]. Disruptionof the ACL results in abnormal arthro-ki-nematics of the tibio-femoral joint and al-lows the tibia to sublux, which ismanifested clinically by episodes of giv-ing way. Repeated episodes of instabilitylead to stretching of secondary restraints,injury to the menisci, and deterioration ofjoint surfaces [31, 44, 59]. If left un-treated, injury to the ACL can lead to pro-gressive instability, degenerative changesto the joint, recurrent pain, and severelyimpaired function even during level walk-ing [27, 30]. Unresolved ACL insuffi-ciency in the young, active populationfollows a predictable course of progres-sive knee dysfunction [18], thus indicat-ing the need for ACL reconstructivesurgery and rehabilitation.
Surgical reconstruction of the ACL in-creases the stability of the knee, but it is of-ten observed that dysfunction persists.Change in neuromuscular function of thethigh muscles has frequently been cited asa major contributor to disability followingACL injury [50, 52]. Deficits in thequadriceps muscle are well described fol-lowing both ACL injury and surgery.Isokinetic strength deficits have been re-ported within two years [45, 59], five years[50], and ten years [2] following recon-struction for ACL rupture. The quadricepsfemoris muscle cross-sectional area, asmeasured by CT scan, is either decreasedor unchanged in the cruciate deficient orreconstructed knee [58]. Direct [50, 52]and indirect [2] functional deficits havebeen described in the patient with a recon-structed ACL. Following this body of evi-dence, rehabili tation after ACLreconstructive intervention has been tradi-tionally focused on exercises for strength-ening the quadriceps muscle. This
approach to ACL rehabilitation can take theform of either open or closed kinetic chainexercises. Open kinetic chain exercises aretypically nonweight-bearing, with move-ment occurring at the single joint, whereas aclosed kinetic chain exercise is weight-bearing and involves multiple joints. It isbelieved that closed kinetic chain exercisesminimize stress on the ACL by decreasingthe tibiofemoral shear forces through in-creased joint compression and muscularco-contraction [41]. Therefore, the squatexercise, a form of closed kinetic chain ex-ercise, is routinely prescribed by physicaltherapists and sports medicine physicians topatients with ACL deficiency or ACL re-construction in order to strengthen musclesand improve joint stability.
In recent years, studies have shownthat co-contraction between the quadri-ceps and the hamstring muscles acts as aform of compensation for ACL insuffic-iency or ACL reconstruction during vari-ous activities, including walking anddoing a squat exercise. More specifically,Ciccoti et al. [17] concluded from anEMG study of subjects with ACL defi-ciency or ACL reconstruction that in-creased activity of the biceps femorismuscle might indicate a protective mech-anism to prevent tibial anterior transla-tion. Hamstring co-contraction with thequadriceps is effective in reducing in-situforces in the ACL, particularly between15 and 60 degrees of knee flexion [35],and in reducing internal rotation and ante-rior translation of the tibia [38]. The effectof the hamstring muscle compensating foranterior laxity in the ACL-deficient kneeduring gait is also reported [4, 36]. De-spite the evidence from the extensivestudies on the effect of the hamstring mus-cle in compensating for anterior tibialtranslation, little is known about the influ-ence of muscle fatigue in this compensa-tory mechanism. Common effects offatigue are loss of the contractile force anddisturbance to the timing of muscle acti-vation, which may lead to joint instabilityand alterations in the biomechanics of thetask [52].
Mechanical studies were previouslyperformed to assess ligament forces dur-ing exercises commonly prescribed in pa-tients with ACL deficiency [56]. Theability to assess muscle fatigue duringthese exercises might lead to clues on theincreased likelihood of redistribution ofthe loads and decrease of muscular sup-port to the knee joint. This is a conditionthat the therapist might want to avoid, par-
134 IEEE ENGINEERING IN MEDICINE AND BIOLOGY November/December 2001
Co-contraction
between the
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acts as a form of
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ticularly in the early phases of the rehabil-itation process.
Based on these considerations, we de-veloped a method of enhancing EMG-based techniques using time-frequencyprocedures in order to assess muscle fa-tigue during a repetitive squat exercise.We improved upon the technique that wasdeveloped in previous studies using Co-hen Class transformations [20]. Spe-cifically, improvements in the stability ofthe estimation procedure were needed toapply the procedure to analyzing the re-petitive squat exercise. In order to accom-plish this objective, we relied onCohen-Posch transformations. This ad-vancement in the time-frequency analysisprocedure for EMG signals acquired dur-ing a repetitive squat exercise is describedin the following section. Details of the ex-perimental procedure are provided to-gether with an example of its applicationin a patient with ACL deficiency and acontrol subject. The results are not in-tended to make any generalized state-ments regarding how patients with a tornACL compensate for their deficiency dur-ing a fatiguing exercise, but rather as an il-lustration of how the EMG technique maybe used for investigations of this kind. Weare currently pursuing a more comprehen-sive study employing this technique to ad-dress such larger questions.
Changes in the frequency content ofthe surface EMG signal relate to physio-logical mechanisms that underlie a mus-cle contraction [3]. Traditional techniqueswere utilized in the past to derive parame-ters to assess muscle fatigue during static(i.e., isometric, constant-force) contrac-tions [22]. Time-frequency techniqueshave provided a way to perform the fa-tigue assessment during dynamic contrac-tions [8]. Our work was based on CohenClass transformations [8, 10, 34], whichdemonstrated that these time-frequencyrepresentations are capable of detectingchanges in the frequency content of thesurface EMG signals recorded during dy-namic contractions. We showed that a pa-rameter derived from the EMG time-frequency representations, the instanta-neous median frequency, may be used tomonitor changes in the EMG signal thatare associated with fatigue [9, 10, 11, 34,47]. However, our study of the estimationerrors associated with the proposed tech-nique indicated that improvements were
needed to decrease the variability of theinstantaneous median frequency esti-mates [10]. The standard deviation associ-ated with the instantaneous medianfrequency estimates ranged between 30and 40 Hz, which is not acceptable for thefatigue assessment. One solution was tosmooth the Cohen Class time-frequencyrepresentation of the EMG data over timeand across cycles of repetitive tasks [10]to increase the stability of the instanta-neous median frequency estimates. How-ever, this solut ion is not alwaysacceptable because it might require thetime-frequency representations to be inte-grated over time-intervals marked bystrong nonstationarities or average acrosscycles when the signal is not cycle-sta-tionary [10]. Methods are needed to ob-tain stable estimates without smoothingthe time-frequency representation, or atleast reducing the length of thetime-window utilized for smoothing therepresentation or the number of cycleswithin which the cycle-stationarity of the
EMG data is assumed. Herein we demon-strate how Cohen-Posch distributions[19] may provide advantages in this re-spect over Cohen Class distributions.
Cohen-Posch distributions are time-frequency representations with the follow-ing properties: 1) the distribution is posi-tive; 2) the time marginal is equal to theinstantaneous energy of the signal; and 3)the frequency marginal is equal to the en-ergy density spectrum. Both Cohen-Poschand Cohen Class distributions satisfy thetime and frequency marginal conditions[20]. However, Cohen Class representa-tions may assume locally negative values,thus introducing “oscillatory” behaviorsthat increase the variability of the instanta-neous median frequency estimates.
Based on these considerations, we de-cided to compare the performance of Co-hen Class and Cohen-Posch Classrepresentations via simulations. The in-stantaneous median frequency estimatesobtained using the Choi-Williams trans-formation [16] were compared with esti-
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1. Distance (measured via a L∞ norm) between the reconstructed trajectories after 100iterations of the algorithm used to compute the Cohen-Posch distribution of the syn-thesized EMG data and the trajectories estimated at the ith iteration. The distancewas computed for each of the 100 realizations synthesized to characterize the algo-rithm. A separate plot was obtained for each trajectory type. Herein we show the re-sults for the trajectory reported in Fig. 2(c), where the frequency content of thesurface EMG signal linearly decreases for the first half and increases for the secondhalf of the time-interval considered. The three curves plotted with different line stylesrepresent minima (dashed line), average values (dash-dotted line), and maxima (solidline) obtained at each iteration for the 100 realizations. The shaded area between 0and 15 iterations and 0 and 0.2 Hz is shown in the frame located at the upper right ofthe figure. A threshold equal to 0.1 Hz was set in order to determine the number of it-erations to be used for deriving the instantaneous median frequency.
mates derived from Cohen-Poschrepresentations, because previous workshowed that among several transforma-tions belonging to the Cohen Class, theChoi-Williams transformation is the mostsuitable for analyzing EMG data acquiredfrom dynamic contractions [7]. The Co-
hen-Posch representation was computedby using the algorithm proposed byLoughlin et al. [37]. This algorithm con-sists of an iterative procedure that adjuststime and frequency marginals until con-vergence is reached. A prior estimate toinitialize the iterative algorithm is pro-vided by taking the absolute value of a Co-hen Class distribution [9].
Cohen Class and Cohen-Posch Classtransformations were applied to synthe-sized surface EMG data obtained bybandpass filtering a white Gaussian se-ries. The bandpass filter was chosen ac-cording to previous work by Stulen andDe Luca [55], who suggested simulatingsurface EMG signals by applying a shap-ing filter to a white Gaussian series. Thetransfer function of this shaping filterwas transformed in the discrete domainby means of a bilinear transformationand the corresponding infinite impulseresponse filter was derived. Variations tothe frequency content of the simulatedsurface EMG signal were produced byincrementally adapting the filter’s coef-ficients every 16 samples. A samplingrate equal to 1024 Hz was simulated.
White Gaussian noise was generated andadded to the synthesized EMG data in or-der to simulate signal-to-noise ratios(SNRs) of 100, 50, 20, and 10 dB. Weconsidered four different trajectories ofthe instantaneous median frequency inwhich fast variations of the spectral char-acteristics were simulated. For each tra-jectory we synthesized 100 realizations.The four theoretical trajectories areshown as solid lines in Fig. 2. The synthe-sized EMG data were utilized, first to as-sess the minimum number of iterationsnecessary to compute the Cohen-Poschrepresentation needed to estimate the in-stantaneous median frequency, and sec-ond to compare the errors associated withthe estimates derived by means ofChoi-Williams and Cohen-Posch trans-formations. Time-frequency distribu-tions were smoothed over time using a16-sample window before computing theinstantaneous median frequency.
Figure 1 demonstrates that no morethan a few iterations are needed to derive aCohen-Posch distribution that provides asatisfactory estimate of the instantaneousmedian frequency. This figure shows thedistance (measured via a L∞ norm) be-tween the instantaneous median fre-quency derived from the Cohen-Poschdistribution estimate obtained after 100 it-erations and the estimates obtained at theith iteration of Loughlin’s algorithm [37].The plot differentiates the maximum, av-erage, and minimum distances obtainedfor each iteration from the 100 realiza-tions of one of the simulated instanta-neous median frequency trajectories.Similar results were derived for other tra-jectories. The frame in the upper right ofthe figure makes it apparent that after fiveiterations the improvement provided byfurther iterations is smaller than 0.1 Hz,which is a fraction of the frequency reso-lution associated with the time-frequencydistribution estimate. Based on these re-sults, we decided to compute the instanta-neous median frequency estimates fromthe Cohen-Posch distribution obtained atthe fifth iteration of the algorithm.
Figure 2 shows the four instantaneousmedian frequency trajectories corre-sponding to each of the synthesizednonstationarities. Because of the shape ofthese trajectories, we refer to them as“step” (a), “linear” (b), “triangular” (c),and “parabola” (d), respectively. Thesolid lines represent the target trajectory;i.e., the simulated values of the instanta-neous median frequency. The other two
136 IEEE ENGINEERING IN MEDICINE AND BIOLOGY November/December 2001
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2. Instantaneous median frequency trajectories (a-d) utilized to characterize the esti-mation error associated with the Choi-Williams (CW) transformation and the Co-hen-Posch (CP) distribution derived by means of the above-mentioned iterativealgorithm. Theoretical values (i.e., targets) related to the different simulated trajec-tories are shown by the continuous line. The dotted line represents the ensemble av-erage obtained from 100 realizations for each trajectory using the Choi-Williams(CW) transformation. The dashed line demonstrates the results obtained by meansof the Cohen-Posch (CP)-based approach. See text for details.
Time-frequency
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perform the fatigue
assessment during
dynamic contractions.
lines correspond to the estimates obtainedusing the Choi-Williams transformation(CW) and the Cohen-Posch representa-tion (CP). The ensemble average of the re-sults derived from the 100 synthesizedrealizations of the EMG data is shown inFig. 2. It can be observed that, except forthe “linear” trajectory, the Choi-Williamsbased estimator provides values whoseaverage is slightly closer to the target thanthe estimates obtained with the Co-hen-Posch transformation. The plots ofFig. 2 show results obtained for SNR =100 dB. Similar plots were derived forother simulated SNR values (e.g. 10, 20,and 50 dB).
Figures 3 and 4 show bias and stan-dard deviation values associated with theinstantaneous median frequency esti-mates derived by means of the Choi-Wil-liams and the Cohen-Posch transforma-tions. Figure 3 shows the estimators’ biascomputed as the mean of the absolutevalue of the bias over the 250 ms intervalof simulated EMG data. Results areshown for different SNR values. It is ap-parent that the Choi-Williams-based esti-mator has generally a slight edge (i.e., 2 or3 Hz) over the Cohen-Posch based esti-mator. This situation appears to be re-versed, however, for the linear trajectory.Figure 4 shows the estimators’ standarddeviation computed as the mean standarddeviation over the 250-ms interval ofsimulated EMG data. This figure demon-strates that the Cohen-Posch based ap-proach outperforms the Choi-Williams-based estimation technique by more than10 Hz for all the synthesized trajectories.This is an important result because it in-dicates that stable estimates may be ob-tained using the Cohen-Posch transfor-mation without relying on methods likesmoothing the time-frequency represen-tation over long time-intervals or averag-ing the results over a high number ofrepetitions of the cyclical exercise. Sta-ble estimates associated with an accept-able bias may be also derived forrelatively low SNR values (i.e., 10 dB)by introducing the instantaneous upperfrequency [21] to upper-bound theintegrals utilized to derive the instanta-neous median frequency. We demon-strated in previous work that thisproperty holds for the estimator based onCohen Class transformations [10]. Withthe results illustrated in Figs. 3 and 4 weshow that such an approach may also beapplied to the estimator based on the Co-hen Posch transformation.
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4. Standard deviation associated with different trajectories of the instantaneous me-dian frequency for the Choi-Williams (CW) transformation and the Cohen-Posch(CP) distribution. Results are shown for signal-to-noise ratios equal to 10, 20, 50, and100 dB. For 10 dB the shaded bars indicate the results derived by using the instanta-neous upper frequency to upper bound the computation of the instantaneous medianfrequency. The four panels (a-d) correspond to the trajectories shown in Fig. 2.
Cohen-Posch transformations aretherefore more suitable than Cohen Classdistributions to assess muscle fatigue dur-ing dynamic contractions. In the follow-ing section we demonstrate that the CohenPosch transformation procedure can beused to identify patterns of fatigue for thequadriceps and the hamstring musclesduring a repetitive squat exercise.
Analysis of RepetitiveSquat Movements
The EMG and kinematic data pre-sented in this section are representative
examples from an ongoing study involv-ing patients with ACL deficiency or re-construction and a control sample. Hereinwe present the results for a patient withunsuccessful ACL reconstruction demon-strated by episodes of giving way with theresults derived for a control subjectmatched for age, gender, body size, andlevel of sport activity. The study is de-signed to investigate the relationship be-tween muscle fatigue and joint mechanicsduring a repetitive squat exercise. All sub-jects were recruited from the universitycommunity and were actively involved inrecreational sport activities. Informedconsent was obtained from the subjectsprior to their enrollment in the study.
Data collection included kinematicsand surface EMG recordings. Kinematicdata were derived using a stereo-photogrammetric system with two infra-red cameras (Elite, BTS, Milan, Italy).The sampling rate was set at 100 Hz. Clus-ters of four markers were placed on thefoot, shank, thigh, and pelvis. Anatomicalplanes were defined to estimate joint an-gular displacements determined using theanatomical landmark calibration proce-dure proposed by Cappozzo et al. [5, 14,15]. This entails the location of a numberof anatomical landmarks in the technicalframes that is determined by using apointer with two markers mounted at an
adequate distance. Figure 5 illustrates theexperimental set-up and protocol. An ex-perienced physical therapist palpated thebony landmarks and then located withthe tip of a pointer each of the anatomicallandmarks. Figure 5(a) shows an exam-ple of this calibration procedure. A fewcamera frames were recorded for eachanatomical landmark. Through geomet-ric calculations and reconstruction of theposition of the tip of the pointer, the loca-tions of several anatomical landmarkswere determined. Figure 5(b) shows asubject during the test. Using the recon-structed three-dimensional (3-D) posi-tions of the anatomical landmarks, jointangular displacements were computed [5,14, 15].
A four-channel EMG system (Bagnoli,Delsys, Boston, MA) was utilized to re-cord the muscular activity. Active surfaceelectrodes (Model #DE-02, DelSys, Inc.)with a detection geometry consisting ofparallel silver bars (1 mm square × 1 cmlength) separated by 1 cm were secured tothe skin using a custom made, dou-ble-sided interface. The electrodes havean input CMRR > 80 dB, an input imped-ance 10 E+12 Ω/5 pF, and a voltage gainof 10 ± 10%. The electrodes were furtherconditioned by a custom-made isolatedpreamplifier that provided a total gain of3000, a bandwidth of 20 Hz to 450 Hz (12dB/oct roll-off), and a noise < 1.25 µV(RMS). Single differential electrodeswere placed on the vastus lateralis, rectusfemoris, vastus medialis, and bicepsfemoris muscles of the leg where we posi-tioned the clusters of markers. The sam-pling rate was set at 1024 Hz.
Figure 6 shows an example of the esti-mated angular displacement at the kneeand the surface EMG data recorded dur-ing four cycles of the squat exercise.
Subjects performed the squat exerciseusing a commercially available com-puter-interfaced dynamometer (Ariel,Trabuco Canyon, CA) specifically de-signed for implementing this exercise(Fig. 5). Subjects were instructed to do thesquat exercise for 30 repetitions at a rateof 2 s per cycle. Subjects were instructedto look straight ahead, grab the handles ofthe exercise machine, lower their body toabout 90 degrees of knee flexion, and re-turn to full knee extension keeping theirback as straight as possible. The dyna-mometer was set to provide resistanceequal to half of the subject’s body weightduring the exercise. A metronome wasused to pace the exercise and an audio
138 IEEE ENGINEERING IN MEDICINE AND BIOLOGY November/December 2001
(a) (b)
5. Pictures of the experimental setup and protocol. (a) Calibration of an anatomicallandmark on the foot according to a well-established procedure [5, 14, 15]. A pointeris used to locate the dorsal aspect of the first metatarsal head. Similarly, other ana-tomical landmarks are located (see text for details). The relative position of the clus-ters and the anatomical landmarks are derived in order to compute the position ofthe anatomical landmarks from the clusters’ position during the exercise. It followsthat angular displacement at the ankle, knee, and hip may be estimated based on thebones’ position and orientation. (b) Subject performing the squat exercise.
Common effects of
fatigue are a loss of
contractile force and a
disturbance to muscle
activation timing.
feedback based on the position of the leverarm of the exercise machine was set in or-der to let the subject know when thefull-flexed and full-extended positionswere reached.
Maxima (maximum knee flexion) andminima (maximum knee extension) ofthe knee flexion/extension angular dis-placement were identified to determinethe phases of knee extension when theexercise machine was programmed toprovide resistance. The time-frequencyrepresentations of the surface EMG datafor the extension phases of the exercisewere derived using the Cohen-Poschtransformation described in the previoussection. The instantaneous median fre-quency was then derived for each cycleof the exercise and a procedure that weproposed in previous work was appliedto determine the most suitable portion ofthe cycle for the EMG analysis [11]. Se-lecting this portion of the exercise cycleis important because the EMG data col-lected during dynamic contractions areaffected by several factors related to themechanics of the analyzed movement.Factors such as the force exerted by themuscle, the muscle fiber length, and thedisplacement between the surface elec-trode and the active muscle fibers all af-fect the frequency content of the surfaceEMG signal [23]. This modulation in fre-quency is superimposed on a slower evo-lution of the EMG frequency content thatrelates to the fatigue process. During re-petitive exercises, the above-mentionedfactors related to the mechanics of move-ment follow a periodic pattern with peri-odicity equal to the rate at which the taskis repeated. Therefore, if one considersthe same portion of the cycle over succes-sive repetitions of the task, the above-de-scribed factors affect the EMG frequencycontent in a predictable way, thereby al-lowing changes due to the fatigue pro-cess to be estimated [10]. Furthermore, ifthere is variability in the mechanics ofthe task, the portion of the exercise asso-ciated with the highest repeatability ofthe mechanics will coincide with valuesof the instantaneous median frequencywith the least variability [10, 11].
Based on these considerations, we pro-posed [11] the following procedure to per-form an EMG-based assessment ofmuscle fatigue during a dynamic exercise:1) divide the EMG data into segments cor-responding to the phases of the task to beanalyzed (in this case, the knee extensionphases); 2) compute the Cohen-Posch
representation of the surface EMGsignals and estimate the instantaneousmedian frequency; 3) determine the stan-dard deviation of the instantaneous me-dian frequency for different phases of thecycle over the entire exercise; 4) choosethe percentage of the cycle associatedwith lowest standard deviation of the in-stantaneous median frequency and derivethe instantaneous median frequency valuefor each cycle for this specific point; and5) utilize the derived time-course of theinstantaneous median frequency to assess
the progression of muscle fatigue duringthe exercise.
During a dynamic exercise, surfaceEMG data display a compression towardthe lower frequencies. The results from thedata analyzed for this report quantify thisbehavior by means of the fatigue parameter(i.e., the instantaneous median frequency).To derive an index of fatigue, we definedthe percentage drop of the instantaneousmedian frequency as the difference be-tween the average of the estimates derivedfrom the first five and the last five repeti-
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6. The upper plot shows the estimate of the flexion/extension (F/E) angular displace-ment at the knee for four cycles of the squat exercise. Flexion phases correspond toan increase in angular displacement; extension phases of the exercise correspond todecreases in the angular displacement value. The plots below the one showing theknee flexion/extension depict the raw EMG data recorded during the correspondingtime-interval. Data are shown for the vastus lateralis (VL), rectus femoris (RF),vastus medialis (VM), and biceps femoris (BF) muscles.
tions of the exercise. This definition al-lowed us to derive fatigue patterns acrossthe monitored muscles.
The possibilities for using this mea-surement procedure in clinical researchare demonstrated by the comparison ofthe results for an ACL patient and a con-trol subject (Fig. 7). The fatigue patternsare depicted using a bar plot of the per-centage decrement of instantaneous me-dian frequency (Fig. 7) for each of the
muscles being monitored (i.e., vastuslateralis—VL, rectus femoris—RF,vastus medialis—VM, and bicepsfemoris—BF). The results indicate thatthe method proposed in this article is ca-pable of identifying fatigue patterns dur-ing the repetitive squat exercise. Thegreater percentage drop in instantaneousmedian frequency observed for thequadriceps muscle in the patient withACL deficiency is in agreement withclinically observed weakness of thequadriceps muscle [2, 45, 50, 59] in thesepatients [4, 36]. When subjects arematched for body size (as is the case forthe example presented in Fig. 7) we canassume that similar loads are sustainedby the musculature acting on the kneejoint. In the presence of quadricepsweakness, the patient will have to sustaina relatively higher percentage of theirmaximum, compared to the healthy sub-ject with normal strength, and wouldtherefore be likely to fatigue at a rela-tively greater rate. Similarly, the higherrate of instantaneous median frequencydecay in the biceps femoris muscle forthe patient would also be expected basedon the hypothesis that the biceps femorismuscle acts on the knee joint to compen-sate for the ACL deficiency [4, 36]. Theactivity of the biceps femoris in the pa-tient is expected to be greater than in thecontrol subject because of the need for acompensatory mechanism.
Common effects of fatigue are a loss ofcontractile force and a disturbance to
muscle activation timing. It has been sug-gested that these factors may contribute tothe instability of the knee joint in patientswith ACL deficiency [52]. It is possible,therefore, that extending the squat exer-cise beyond a given fatigue rate mightcause undesirable rearrangements of theloads on the knee. Fatigue should there-fore be considered as a factor when de-signing rehabilitation exercises for theknee. It follows that the duration, pace,and resistance of the exercise must bespecified carefully in order to avoid ex-cessive levels of fatigue. The methodspresented in this article may provide animportant way to allow clinicians to opti-mize their rehabilitation exercise proce-dures on a subject-by-subject basis.Although our goal in this article was topresent an example of how the EMG tech-nique can be applied, the results indicat-ing a greater rate of fatigue for the bicepsfemoris muscle in the patient with ACLdeficiency suggests that the techniquemay be useful to test the controversial hy-pothesis that the hamstring muscles playan important role in compensating forACL deficiency.
ConclusionsIn this article we have demonstrated
a technique to calculate the EMG instan-taneous median frequency to assessmuscle fatigue during a dynamic exer-cise commonly prescribed in patientswith ACL deficiency. We used Co-hen-Posch time-frequency representa-tions to improve upon the variability ofthe instantaneous median frequency es-timates derived using Cohen Classtransformations. The technique was ap-plied to surface EMG data recordedfrom the quadriceps and hamstring mus-cles of a control subject and a patientwith ACL deficiency during a repetitivesquat exercise. Instantaneous medianfrequency values were derived for theknee-extension phases of the exercise.Ensemble average and standard devia-tion of the instantaneous median fre-quency were computed for the portion ofthe cycle associated with the lowestvariability of the mechanics.
The time-course of the instantaneousmedian frequency during the dynamic ex-ercise was defined as the series of esti-mates obtained for the selected part of thecycle for all the repetitions. The percent-age drop in instantaneous median fre-quency was defined by means of thedifference between the first five and the
140 IEEE ENGINEERING IN MEDICINE AND BIOLOGY November/December 2001
Fatigue Patterns
% D
rop
IMD
F
20
15
10
5
0VL RF VM BF
7. Fatigue patterns for a patient with ACL deficiency and a control subject matchedby age and body size. The percentage drop in instantaneous median frequency isshown for the vastus lateralis (VL), rectus femoris (RF), vastus medialis (VM), andbiceps femoris (BF) muscles. For each muscle, the bar on the left side is relative tothe results of the EMG analysis for the patient with ACL deficiency, and the bar onthe right side is relative to the results for the control subject. Different patterns aredemonstrated for these two subjects, thus indicating that the patient with ACL defi-ciency fatigues more than the healthy subject during the exercise.
The technique may
allow clinicians a
greater opportunity
to take into account
changes in muscle
function and
mechanics during
prolonged exercises.
last five cycles of the exercise. Fatiguepatterns were characterized as the per-centage drop of instantaneous median fre-quency for the four muscles monitored;i.e., vastus lateralis, rectus femoris, vastusmedialis, and biceps femoris. Differencesin fatigue patterns for control subjects anda patient with ACL deficiency lend sup-port to existing theories of muscle com-pensatory function in these patients. Thegreater fatigue rate for the quadricepsmuscle, as measured by the decrease in in-stantaneous median frequency, in the pa-tient with ACL deficiency compared tothe control subject is in agreement withthe clinically observed weakness of thismuscle. The greater fatigability shown forthe biceps femoris muscle supports thehypothesis that this muscle compensatesfor the instability of the knee joint result-ing from the ACL deficiency.
We see possibilities for using the tech-niques presented in this article as a meansof enhancing tools currently available toclinicians to design their rehabilitation ex-ercise procedures. The technique may al-low the clinicians a greater opportunity totake into account changes in muscle func-tion and mechanics during prolonged ex-ercises. Future clinical studies are neededto test these techniques more rigorously ina clinical setting.
Paolo Bonato receivedthe Italian Laurea de-gree in electrical engi-neering from Politec-nico di Torino, Torino,Italy, in 1989. From1990 to 1991 he was aresearch fellow with theBiophysics Research
Group of IRST, Trento, Italy where hewas active in the field of signal processingapplied to the cardiovascular system.From 1992 to 1994 he was a Ph.D. candi-date at the Dipartimento INFOCOM ofthe Università di Roma “La Sapienza,”Roma, Italy. His work addressed the anal-ysis of surface myoelectric signals re-corded during dynamic contractions.After he received the Ph.D. degree in bio-medical engineering, he gained a postdoc-toral fellowship at the Dipartimento diElettronica of Politecnico di Torino,Torino, Italy. Since 1996 he has been a re-search assistant professor at the Neuro-Muscular Research Center of BostonUniversity, Boston, MA. His principal re-search interests include signal processingapplied to the biomedical field and reha-bilitation engineering, analysis of
nonstationary signals by time-frequencyanalysis, electromyography applied tokinesiology, and biomechanics of move-ment. He is a member of the IEEE EMBSand IEEE Signal Processing societies.
Ming-Shun S. Cheng was born in Taipei,Taiwan, in 1970. He received his B.S. de-gree in physical therapy from NationalTaiwan University, Taipei, Taiwan, in1993 and his M.S. degree in orthopedicphysical therapy from MGH Institute ofHealth Professions, Boston, MA, in 1999.He is currently working toward his Sc.D.degree in movement and rehabilitationscience in the Department of PhysicalTherapy, Sargent College of Health andRehabilitation Science, Boston Univer-sity, Boston, MA. He was a leader of a pla-toon in the Taiwanese Army from 1993-1995. He worked as a clinical physicaltherapist in the Department of Physicaland Rehabilitation Medicine, TaipeiYang-Ming Municipal Hospital, Taipei,Taiwan, from 1995-1996. Currently, heconducts his research work at the Neuro-Muscular Research Center, Boston Uni-versity, Boston, MA. He also teachesmusculoskeletal physical therapy labs inthe Department of Physical Therapy atBoston University. His research interestsinclude artificial neural networks, kine-matic analysis, and surface electromyo-graphy in clinical applications.
José A. González-Cueto received theB.Eng. degree in automatic control fromthe Central University of Las Villas(UCLV), Santa Clara, VC, Cuba, in 1991,the M.ScE. degree in telecommunicationsfrom UCLV in 1996, and the Ph.D. degreein electrical and computer engineeringfrom the University of New Brunswick(UNB), Fredericton, NB, Canada, in2001. He is currently with the Neuro-Muscular Research Center at Boston Uni-versity, Boston, MA, as a researchassociate. His research interests includeprocessing techniques applied toneuromuscular signals, DSP algorithms,and real-time implementations. He hasbeen a student member of the CanadianMedical & Biological Engineering Soci-ety (CMBES) since 1997.
Alberto Leardini has been working as a re-search engineer at the Movement Analy-sis Lab of Istituti Ortopedici Rizzoli-Bologna since 1990, where he has beenresponsible for many research projects re-lated to the testing and development of
gait analysis techniques and protocols.The work on his recent D.Phil. at the Or-thopaedic Engineering Centre of OxfordUniversity concerned a new geometricand mechanical model of the intact and re-placed ankle complex.
John O’Connor is afull professor and re-search director of theOxford OrthopaedicEngineering Centre(OOEC), University ofOxford, and supervisorof more than 20 Ph.D.theses on human joint
mechanics and author of over 100 journalpublications and book chapters on the ge-ometry and mechanics of human joints. Incollaboration with surgeon John Good-fellow, he has designed and developednew forms of meniscal knee replace-ments. The Oxford Knee, implanted witha minimally invasive technique, is nowwidely used for the treatment of unicom-partimental osteoarthritis.
Serge H. Roy received aB.S. degree in physicaltherapy from New YorkUniversity (1975), anM.S. degree in physicaltherapy from BostonUniversity (1981), and aSc.D. from Boston Uni-versity in applied anat-
omy and kinesiology (1992). He iscurrently a research associate professor atthe NeuroMuscular Research Center(NMRC) and the Sargent College ofHealth and Rehabilitation Sciences atBoston University. At the NMRC, he su-pervises the Muscle Fatigue Laboratory(1984) and the Electrophysiology Labora-tory (1989). His work is directed at devel-oping surface electromyographic systemsfor the assessment of muscle impairmentsin patients with musculoskeletal disor-ders. He has also been a research associatefor the Department of Veterans Affairssince 1988. Dr. Roy is the recipient of theFounder’s Day Award for Scholarshipand the Elizabeth C. Adams Award(NYU, 1974 and 1975), and two GroupAchievement Awards from the NationalAeronautics and Space Administrationfor Spacelab Life-Science Missions (1992and 1994). He was recently awarded aFellowship to the American Institute forMedical and Biological Engineering(AIMBE) and is president of the Interna-tional Society of Electrophysiology andKinesiology (ISEK).
November/December 2001 IEEE ENGINEERING IN MEDICINE AND BIOLOGY 141
Address for Correspondence: PaoloBonato, NeuroMuscular Research Cen-ter, Boston University, 19 DeerfieldStreet, Boston MA 02215. Tel: +1 617358 0715. Fax: +1 617 353 5737.E-mai l : [email protected]. URL:http://nmrc.bu.edu/.
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