Isokinetic torque assessment of the knee extensors has been performed extensively following an anterior cruciate ligament injury1-3. Typically, evaluation of the torque-time curves involves the determination of peak1,2 or angle-specific3,4 torque; yet, associations between these conventional isokinetic measurements and physical performance tasks have ranged from low to moderate at best5. Furthermore, measurements of peak or angle-specific torque do not assess torque steadiness or irregularities throughout the test movement, and it seems plausible that the quantification of torque steadiness may elicit important information about joint function6 and, thus, offer another dimension for analysis.
In addition to the so-called natural movement frequency, which is typically low and determined by the speed of the test movement, smaller rapid fluctuations in the torque-time signals are reflected in higher-frequency content7,8 when these signals are transformed into the frequency domain with use of algorithms such as the fast Fourier transform. Using fast Fourier transform analysis, Tsepis et al.6 found, in patients with an anterior cruciate ligament deficiency, that the frequency content of knee-extensor torque was higher in the involved limb compared with the uninvolved limb. They suggested that the high frequency content indicated that the knee extensors were unable to exert a precise force (i.e., they were less steady) because of neurosensory deficits. While Tsepis et al.6 may be credited for being among the first to systematically examine the smoothness of isokinetic torque-time curves, we believe their study has limitations that raise doubts about their conclusions.
First, the notion that higher-frequency oscillations are indicative of impaired muscle or joint function in individuals with an anterior cruciate ligament deficiency can be questioned. Certainly, in these individuals, the high frequency content of the quadriceps torque-time curve may be influenced by increased hamstring (antagonist) activation—a positive neuromuscular adaptation known to enhance joint stability9,10.
Second, Tsepis et al.6 did not examine the convergent validity of their frequency data with physical performance tasks (e.g., single-limb hopping) and, thus, essentially ignored the clinical question: Is the degree of quadriceps torque smoothness associated with physical performance in individuals with anterior cruciate ligament deficiency?
Third, the use of fast Fourier transform analysis to estimate frequency content is not appropriate when analyzing isokinetic movements. Specifically, when biological (torque) signals are recorded under dynamic conditions, the frequency content of the signals continuously changes over time and is therefore nonstationary11—violating a key assumption of fast Fourier transform analysis. In contrast, deriving the instantaneous frequency content of the signal by implementing a time-frequency transform (i.e., wavelet transform) may better characterize the torque-time morphology than fast Fourier transform analysis because, unlike fast Fourier transform analysis, wavelet analysis assumes no stationarity of signals12.
Finally, Tsepis et al.6 limited their study to an anterior cruciate ligament-deficient sample and the degree of quadriceps torque smoothness in individuals with a reconstructed anterior cruciate ligament remains unknown. While an anterior cruciate ligament reconstruction may restore anterior static knee stability13-15, a return of normal quadriceps muscle function10,16,17 and hamstring antagonist behavior10 is not always achieved. Accordingly, we believe it is important to examine and compare the frequency content of isokinetic torque-time curves of individuals with an anterior cruciate ligament deficiency and those with a reconstructed anterior cruciate ligament.
Given these considerations, we initiated this study with the following aims: (1) to quantify the frequency content of extension torque-time curves generated by patients with a deficient anterior cruciate ligament and those with a reconstructed anterior cruciate ligament relative to the intact, contralateral limb and to uninjured control subjects; (2) to examine, in patients with an anterior cruciate ligament deficiency and those with anterior cruciate ligament reconstruction, the association between knee-extensor torque smoothness and hamstring antagonist electromyographic activity; and (3) to examine, in patients with an anterior cruciate ligament deficiency and those with anterior cruciate ligament reconstruction, the association of physical performance with extension torque smoothness and isokinetic peak torque. Accordingly, our hypotheses were as follows: (1) the frequency content of isokinetic extension torque-time curves would be higher in the involved limb of patients with an anterior cruciate ligament deficiency or reconstruction than in the uninjured limb and in the limb of control subjects; (2) the amount of hamstring antagonist electromyographic activity would be positively associated with potential irregularities in extension isokinetic torque-time curves of patients with an anterior cruciate ligament deficiency and those with anterior cruciate ligament reconstruction; and (3) physical performance would associate more closely with extension torque-time frequency analysis than with measures of isokinetic peak torque.
Materials and Methods
The subjects for this study were recruited from a potential pool of 113 patients with an anterior cruciate ligament deficiency or reconstruction. Following the application of the eligibility criteria, thirteen subjects with an anterior cruciate ligament deficiency (three women and ten men) together with twenty-five subjects with an anterior cruciate ligament reconstruction (eleven women and fourteen men) who had undergone reconstruction with use of a bone-patellar tendon-bone graft at a mean (and standard deviation) of 15.7 ± 5.5 months earlier were recruited to participate in this study. On clinical examination, all subjects with a reconstructed anterior cruciate ligament had regained full range of motion of the knee and the knees were stable in flexion and extension (i.e., they had negative Lachman and pivot shift tests). For the anterior cruciate ligament-deficient subjects, isolated complete rupture of the anterior cruciate ligament was confirmed by previous arthroscopy, and the initial injury had occurred at least one year (mean, 75.6 ± 72.5 months) before testing. These anterior cruciate ligament-deficient subjects were identified early after the injury as having good potential to dynamically stabilize the injured knee18 and were therefore advised by the surgeon that they were good candidates for nonoperative treatment. All anterior cruciate ligament-deficient subjects demonstrated a minimum of grade 2 (mean, 2.5 ± 0.4) on the Lachman test and grade 2 (mean, 2.4 ± 0.4) on the pivot shift test. Subjects in the groups with a deficient or a reconstructed anterior cruciate ligament also met the following eligibility criteria: (1) an age of between eighteen and thirty-five years; (2) no evidence of damage or repair of the collateral ligament or the posterior cruciate ligament at the time of arthroscopy or surgery; (3) no previous surgery on the anterior cruciate ligament or subsequent knee surgery on the involved leg; (4) no history of surgery or traumatic injury of the contralateral knee; and (5) participation in a rehabilitation program for the injured knee following knee injury or surgery.
An additional thirty-three subjects (eleven women and twenty-two men) with no history of trauma or disease in either knee and no evidence of abnormality on clinical examination were selected as control subjects. The control subjects were matched to the subjects with a deficient or reconstructed anterior cruciate ligament for age, activity level, and anthropometric characteristics. The protocol was approved by the university human ethics committee, and all subjects read and signed an approved consent document prior to participating in the study.
Surgical Procedure and Rehabilitation
All anterior cruciate ligament reconstructions were performed by the same orthopaedic surgeon with use of an arthroscopically assisted two-incision technique. The bone-patellar tendon-bone graft (10 mm wide) was constructed from the central third of the tendon of the ipsilateral knee. Along with the tendon strip, bone blocks (20 × 10 mm) were removed with the graft on either end, leaving osseous defects in the patella and tibial tuberosity. Tibial and femoral tunnels (drilled with use of a 4.5-mm drill) were fashioned with guide pins, and a notchplasty was performed as required to ensure that graft impingement did not occur in the intercondylar notch region. The graft was passed into the joint, and the bone plug was fixed on the femoral site with an interference screw. Similarly, tibial bone plug fixation was accomplished with an interference screw at 10° of knee flexion. The graft was observed under a final arthroscopic examination to determine its ability to resist anterior displacement during a Lachman test19-21.
Following surgery, all subjects who had had reconstruction of the anterior cruciate ligament participated in the same standard accelerated physical therapy rehabilitation program as originally described by Shelbourne and Nitz22 for the injured knee. On the average, subjects who had had the anterior cruciate ligament reconstructed underwent supervised rehabilitation for twelve weeks and then entered the return-to-sport phase when they gradually increased the complexity and intensity of activities. Subjects with a deficient anterior cruciate ligament were also subjected to an accelerated protocol with immediate training for range of motion and weight-bearing. Supervised rehabilitation continued for eight to ten weeks following injury and primarily consisted of quadriceps and hamstring muscle-strengthening (open and closed kinetic chain) together with agility skill training and sport-specific training in the latter part of the program.
Quadriceps Isokinetic Torque and Hamstring Electromyographic Activity
Following standard preparation to reduce cutaneous impedance below 5 kΩ (measured on an impedance meter [M-3650; Metex Instruments, Seoul, South Korea]), silver-silver chloride preamplified surface electrodes (5-mm diameter; Quantec, Brisbane, Australia) were placed over the bellies of the semitendinosus and biceps femoris muscles of the involved limb of the subjects with a deficiency of the anterior cruciate ligament and those who had had anterior cruciate ligament reconstruction in a bipolar electrode configuration (with an interelectrode distance of 20 mm, according to Daanen et al.23). A reference electrode was placed equidistant with respect to the differential electrodes24. Saline solution gel was placed between each electrode and the skin to enhance conductivity.
After a standardized warm-up (five minutes of low-resistance ergometer cycling at 60 rpm at 1 KPM and five minutes of slow static quadriceps and hamstring muscle stretching), each subject was positioned on the testing bench of the isokinetic dynamometer (Cybex, New York, NY) following the standard subject positioning protocol25. Before data collection, subjects performed five to ten submaximal and then four maximal knee extension and flexion repetitions. These trials served as a specific extension-flexion warm-up of the knee and also familiarized the subjects with the testing protocol. The warm-up phase was followed by two minutes of rest to prevent fatigue from impairing performance. Each subject then performed two sets of five maximal extension and flexion repetitions at 180°/sec. This test velocity was selected as previous researchers have established a close relationship between torque produced during knee extension and flexion at this speed and performance in functional tasks such as jumping and landing9,26,27. A standardized script of verbal encouragement was provided to all subjects in order to facilitate maximum performance.
Two minutes of rest was permitted between the two sets to prevent fatigue from impairing the performance of the quadriceps and hamstring muscles. In order to gain confidence with the strength-testing protocol, the noninvolved limb of the subjects with an anterior cruciate ligament deficiency and those with an anterior cruciate ligament reconstruction was tested before the involved limb28. For the control group, test order for the nondominant and dominant limbs was randomized. At least ten minutes of active recovery (slow walking and stretching) was permitted before the warm-up phase commenced on the contralateral limb.
Preamplified electromyographic data were relayed to an amplifier (Quantec; gain = 10,000, common mode rejection of >120 dB, input bias current of <40 pA, and input impedance of >1012 Ω). Electromyographic data from the amplifiers, together with raw isokinetic torque and knee displacement data from the Cybex isokinetic dynamometer, were recorded with use of an AMLAB signal acquisition system (Associative Measurement, Sydney, Australia). Data were relayed to the AMLAB alternating current amplifiers (gain = 10,000, common mode rejection of >120 dB, input bias current of <40 pA, and input impedance of >1012 Ω). Following amplification, the data were converted from analog to digital (12 bit, 1000 Hz) by the AMLAB system.
Subjects with a deficiency or a reconstruction of the anterior cruciate ligament were required to complete a timed-hop test for the involved limb. During each trial, the subjects were encouraged to use large forceful hopping motions, rather than a series of small steps29, to hop 3 m, turn toward the side on which they were hopping, and then return to the starting line as quickly as possible. A dual-beam timing light system (Swift Performance Equipment, Lismore, Australia) was used to measure the time taken for the timed-hop test. The timing light signal was fed into an AMLAB signal acquisition system (1000-Hz sampling rate), and the time taken to complete the task was determined in milliseconds. The timing system was triggered to start counting when the subject moved off the starting line and passed through the two beams emitted by the timing system and was triggered to stop counting when the subject moved across the starting-finishing line for the second time. Three trials were performed with a one-minute rest between trials.
Isokinetic Extension Torque
In order to ensure that the test limb was moving at the preset velocity, torque measurements were conducted between 70° and 20° of knee flexion to avoid the phases of limb acceleration and deceleration as described by Iossifidou and Baltzopoulos30. Peak extension torque was calculated as the highest torque achieved. The gravitational effects of limb mass were eliminated by adding the weight of the limb to the extension torque values.
Prior to the time-frequency analysis, signal prefiltering was performed with use of a wavelet-based denoising filter. This filter allows for the removal of extraneous random noise, while ensuring the integrity of the data31. The time-frequency outcome variable in this experiment was the mean instantaneous frequency of the isokinetic torque data. The mean instantaneous frequency is analogous to mean power frequency, which is commonly used to quantify the result of a fast Fourier transformation. To derive this variable, the analytic wavelet transform—a form of continuous wavelet transform—was chosen as it provides accurate magnitude and phase information in the time-frequency domain32-35. Following the analyses, the peak extension torque and the mean instantaneous frequency of the extension torque-time data derived from the three trials with the highest torque were averaged. The data were analyzed with use of custom-written software (LabVIEW 8.5 and the Advanced Signal Processing Toolkit; National Instruments, Austin, Texas).
Hamstring Electromyographic Activity
The raw electromyographic signals from the semitendinosus and biceps femoris muscles were filtered with use of a fourth-order zero-phase-shift Butterworth filter (high-pass cutoff frequency [fc] = 5 Hz and low-pass fc = 250 Hz, according to Winter36). To create a linear envelope (m·V), the filtered electromyographic data were full-wave rectified and then filtered again with use of a fourth-order zero-phase-shift Butterworth low-pass filter (fc = 30 Hz). To convert any negative values arising at the extreme ends, the linear envelope was again full-wave rectified.
Like the isokinetic torque analyses, electromyographic signals were examined between 70° and 20° of knee flexion. In quantifying semitendinosus and biceps femoris antagonistic muscle activity during knee extension, the average integrated electromyographic values for each muscle across this knee flexion interval of 50° were compared with the average integrated electromyographic values over the same knee angular position interval when acting as an agonist at maximal effort37-41. Such a normalization procedure eliminated the possible dependence of the electromyographic signal on the muscle length (or joint angle) and contraction rate changes during the isokinetic loading over the complete joint range of motion41-43. Normalized antagonistic activity from the semitendinosus and biceps femoris muscles across the knee flexion interval of 50° was averaged in order to provide an overall measure of hamstring antagonist electromyographic activity. Like the analysis performed on the isokinetic data, the average hamstring antagonist electromyographic activity was calculated with use of all ten trials. The data were analyzed with use of custom-written software (Visual Basic, version 5; Microsoft, Redmond, Washington).
The two fastest trials of the single-limb timed hop were averaged.
The means and standard deviations were calculated for the mean instantaneous frequency of the extension torque-time curves. Preliminary analyses of the mean instantaneous frequency data for the control group were conducted in order to determine the effect of limb dominance. The paired-samples t test revealed no significant difference between the mean instantaneous frequency of the extension torque generated by the dominant and nondominant limbs. Consequently, the control group data were pooled across test limbs, producing a so-called standardized data set for comparison with the noninvolved and the involved limbs of the groups with a deficiency or reconstruction of the anterior cruciate ligament. Repeated-measures analysis of variance was then used to compare the mean instantaneous frequency of the extension torque-time curve across test limbs (involved and noninvolved) and subject groups (deficient anterior cruciate ligament, reconstructed anterior cruciate ligament, and control). In the event of a significant main effect or interaction following the analysis-of-variance contrast, post hoc comparisons were conducted with use of the Fisher least-significant-difference test.
For the subjects with an anterior cruciate ligament deficiency and those with an anterior cruciate ligament reconstruction, Pearson correlation analysis was used to establish the relationship between the mean instantaneous frequency of the extension torque and the level of hamstring antagonist activity. Next, multiple regression analyses were applied to examine the extent to which the mean instantaneous frequency of the extension torque and the peak torque predicted the single-limb timed hop performance. The mean instantaneous frequency of the extension torque and the peak torque were entered in the same model because the two variables were weakly correlated (r = 0.150, p = 0.368) and because a multivariable approach allowed us to compare their inferential capacity in predicting hopping performance. Normality and equal variance were determined for each data set with use of the Kolmogorov-Smirnov test with the Lilliefor correction and the Levene median test, respectively. A level of significance of p < 0.05 was selected in all analyses.
Source of Funding
We did not receive any outside funding in support of this study.
Table I presents the descriptive data pertaining to the physiological characteristics, isokinetic measures, and hopping performance of the group with a deficient anterior cruciate ligament, the group with a reconstructed anterior cruciate ligament, and the control group. The three groups did not differ with regard to age, height, or body mass.
Figure 1 shows the descriptive data pertaining to the mean instantaneous frequency of the extension torque generated by the subjects who had an anterior cruciate ligament deficiency, those who had reconstruction of the anterior cruciate ligament, and the control subjects. Statistical analysis revealed a significant interaction of test limb × subject group (F = 31.197; p < 0.001). Within-subject group post hoc contrasts revealed that the mean instantaneous frequency of the extension torque was significantly higher for the involved limb of the subjects with an anterior cruciate ligament deficiency (percentage difference = 16.0; p < 0.001) and the subjects with a reconstructed anterior cruciate ligament (percentage difference = 10.8; p < 0.001) compared with the noninvolved limb. Between-subject group post hoc contrasts for the involved limb indicated that the mean instantaneous frequency of the extension torque was significantly higher for the subjects with an anterior cruciate ligament deficiency (percentage difference = 16.2; p = 0.003) and the subjects with a reconstructed anterior cruciate ligament (percentage difference = 15.40; p < 0.001) compared with the control group. In contrast, with the numbers studied, there was no significant difference between subject groups for the noninvolved limb.
As no difference was detected in the average mean instantaneous frequency of the extension torque generated by the subjects with an anterior cruciate ligament deficiency or reconstruction, the groups were considered similar and therefore were pooled for correlation analysis with hamstring antagonist activity. Pearson correlation analysis revealed a positive, moderate correlation between the mean instantaneous frequency of the extension torque and hamstring antagonist activity (r = 0.580, p < 0.001). Finally, multiple regression analysis revealed that the mean instantaneous frequency of the extension torque was significantly related to single-limb hopping performance following anterior cruciate ligament injury or reconstruction (b = −0.943, p = 0.019), while peak extension torque was not (b = −0.001, p = 0.797).
Typically, isokinetic muscle performance is assessed by measuring the peak or angle-specific torque; yet, another distinct aspect of muscle performance relates to torque steadiness—that is, the ability to control muscle force output44. In this context, Tsepis et al.6 quantified torque steadiness in anterior cruciate ligament-deficient patients and observed, as we have, bilateral differences in the frequency content of the knee-extensors torque. Moreover, our results extend their findings to a group of patients with a reconstructed anterior cruciate ligament and suggest that, while the oscillatory torque profiles were higher in the involved limbs than in the noninvolved and control limbs (as per our first hypothesis), the frequency content of the involved limbs did not differ between the anterior cruciate ligament-deficient and the reconstructed anterior cruciate ligament groups. Because a reconstructed anterior cruciate ligament is known to improve anterior knee stability13-15, our findings do not support the speculation by Tsepis et al.6 that mechanical knee instability during isokinetic testing contributes to the high-frequency aberrations observed in the torque-time curves.
This leads to the question: What neural mechanisms could account for the disparity in frequency content between the involved and uninvolved limbs of the subjects with an anterior cruciate ligament deficiency and the subjects with a reconstructed anterior cruciate ligament? To explain this, we measured the level of hamstring antagonist electromyographic activity in these subjects and found it associated inversely with torque steadiness—that is, the subjects with an anterior cruciate ligament deficiency and those with a reconstructed anterior cruciate ligament showed greater quadriceps irregularities with greater hamstring (antagonistic) activity (as per our second hypothesis). Given that precise movement depends on consistent muscle-torque production44, it seems natural to speculate, as did Tsepis et al.6, that torque irregularities are a maladaptive feature in patients with a reconstructed or a deficient anterior cruciate ligament. Yet, in such patients, we argue that the reduced torque steadiness is reportedly a function of increased hamstring activation, which in turn has the potential to reduce anterior tibial translation45. Hence, contrary to the position that torque irregularities are indicative of muscle coordination deficits or diminished functional control during high mechanical knee loadings, the results of this study indicate the reverse by suggesting that the so-called high-frequency aberrations are corollary to a protective mechanism produced by the hamstrings to enhance dynamic joint stability (as per our third hypothesis).
Furthermore, perhaps the most persuasive evidence for our argument comes from the finding that the frequency content of the knee-extensors torque is positively associated with hopping performance—that is, greater torque irregularities were associated with shorter (faster) single-limb hopping times. Mechanistically, the abrupt single-limb landing and deceleration during the hopping task may necessitate an augmented hamstring antagonist activity to provide dynamic tibial restraint, which, in turn, produces a higher oscillatory knee-extensors profile. Indeed, in situations when the anterior cruciate ligament is subjected to acute strain, a stiffer musculotendinous system is more advantageous than a compliant system46,47. Specifically, hamstring muscles that are stiff are better able to counteract deleterious forces and, thus, shield the secondary restraints within the knee—for example, the menisci, collateral ligaments, and anterior cruciate ligament tendon graft—from bearing the full responsibility of joint stability48.
Also noteworthy was that, while our wavelet-derived measure of torque steadiness correlated with hopping performance, peak knee-extensors torque—a conventional isokinetic measure—did not. Because previous studies have also failed to identify a significant association between knee-extensors peak torque and functional capacity in subjects with a deficient anterior cruciate ligament and those with a reconstructed anterior cruciate ligament49-51, we believe that wavelet-derived measures of torque steadiness can provide additional valuable information pertaining to knee function that would hitherto have eluded detection. Accordingly, we agree with the statement of Tsepis et al.6 that the quantification of isokinetic torque steadiness is clinically important for patients with knee abnormalities.
That being said, however, we acknowledge that, at present, the absence of wavelet analysis software in the current clinical setting substantially hampers the application of our proposed torque-steadiness measures. Yet, given the availability of isokinetic dynamometers in most clinical and sports medicine facilities, and given our results supporting the potential clinical utility of the torque-steadiness measures, we see no reason why commercially written software cannot be incorporated within the operating systems of current isokinetic dynamometers. In this context, our study should be viewed as a hypothesis-generating investigation intended to motivate a wider research agenda.
Although novel, our study has limitations. First, our results may not generalize to subjects with a deficient anterior cruciate ligament or those with a reconstructed anterior cruciate ligament with characteristics—namely, the duration of time since the anterior cruciate ligament deficiency or anterior cruciate ligament reconstruction and the type of anterior cruciate ligament tendon graft—that were different from those of our subjects. Second, our results may be affected by reverse causation because of their cross-sectional nature—that is, torque irregularities could adversely affect hamstring activity—and longitudinal studies are needed to establish the direction of causation. Furthermore, given that factors that alter the stress-strain distribution within the articular cartilage may, in the long term, contribute to degeneration of the articular surfaces and subchondral bone52, there is a greater need for longitudinal studies to delineate the long-term consequences of torque irregularities.
In conclusion, the morphology of extension torque-time curves generated by subjects with a deficient anterior cruciate ligament and those with a reconstructed anterior cruciate ligament were characterized by higher-frequency oscillations compared with the uninvolved limbs and with control subjects. Higher-frequency profiles reflected a positive neuromuscular adaptation by the hamstrings to enhance joint stability and, thus, wielded a greater influence on physical performance than did traditional peak torque measures. Although our findings are strictly correlational, they suggest that quantification of torque steadiness in individuals with a deficient anterior cruciate ligament and those with a reconstructed anterior cruciate ligament may be clinically indicated. Future studies should investigate the long-term relevance and consequences of extension torque-time curve morphology following anterior cruciate ligament injury and anterior cruciate ligament reconstruction.
Disclosure: The authors did not receive any outside funding or grants in support of their research for or preparation of this work. Neither they nor a member of their immediate families received payments or other benefits or a commitment or agreement to provide such benefits from a commercial entity. No commercial entity paid or directed, or agreed to pay or direct, any benefits to any research fund, foundation, division, center, clinical practice, or other charitable or nonprofit organization with which the authors, or a member of their immediate families, are affiliated or associated.
Investigation performed at the Centre for Health, Exercise and Sports Medicine, Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne, Parkville, Victoria, Australia
1. Swanik CB, Lephart SM, Swanik KA, Stone DA, Fu FH. Neuromuscular dynamic restraint in women with anterior cruciate ligament injuries. Clin Orthop Relat Res. 2004;425:189-99.
2. Lephart SM, Perrin DH, Fu FH, Gieck JH, McCue FC, Irrgang JJ. Relationship between selected physical characteristics and functional capacity in the anterior cruciate ligament-insufficient athlete. J Orthop Sports Phys Ther. 1992;16:174-81.
3. Ikeda H, Kurosawa H, Kim SG. Quadriceps torque curve pattern in patients with anterior cruciate ligament injury. Int Orthop. 2002;26:374-6.
4. Harter RA, Osternig LR, Standifer LW. Isokinetic evaluation of quadriceps and hamstring symmetry following anterior cruciate ligament reconstruction. Arch Phys Med Rehabil. 1990;71:465-8.
5. Pua YH, Bryant AL, Steele JR, Newton RU, Wrigley TV. Isokinetic dynamometry in anterior cruciate ligament injury and reconstruction. Ann Acad Med Singapore. 2008;37:330-40.
6. Tsepis E, Giakas G, Vagenas G, Georgoulis A. Frequency content asymmetry of the isokinetic curve between ACL deficient and healthy knee. J Biomech. 2004;37:857-64.
7. Giakas G, Baltzopoulos V. A comparison of automatic filtering techniques applied to biomechanical walking data. J Biomech. 1997;30:847-50.
8. Stergiou N, Giakas G, Byrne JB, Pomeroy V. Frequency domain characteristics of ground reaction forces during walking of young and elderly females. Clin Biomech (Bristol, Avon). 2002;17:615-7.
9. Wilk KE, Romaniello WT, Soscia SM, Arrigo CA, Andrews JR. The relationship between subjective knee scores, isokinetic testing, and functional testing in the ACL-reconstructed knee. J Orthop Sports Phys Ther. 1994;20:60-73.
10. Bryant AL, Creaby MW, Newton RU, Steele JR. Dynamic restraint capacity of the hamstring muscles has important functional implications after anterior cruciate ligament injury and anterior cruciate ligament reconstruction. Arch Phys Med Rehabil. 2008;89:2324-31.
11. Bonato P, Roy SH, Knaflitz M, De Luca CJ. Time-frequency parameters of the surface myoelectric signal for assessing muscle fatigue during cyclic dynamic contractions. IEEE Trans Biomed Eng. 2001;48:745-53.
12. Beck TW, Housh TJ, Johnson GO, Weir JP, Cramer JT, Coburn JW, Malek MH. Mechanomyographic and electromyographic amplitude and frequency responses during fatiguing isokinetic muscle actions of the biceps brachii. Electromyogr Clin Neurophysiol. 2004;44:431-41.
13. Woo SL, Kanamori A, Zeminski J, Yagi M, Papageorgiou C, Fu FH. The effectiveness of reconstruction of the anterior cruciate ligament with hamstrings and patellar tendon. A cadaveric study comparing anterior tibial and rotational loads. J Bone Joint Surg Am. 2002;84:907-14.
14. Frndak PA, Berasi CC. Rehabilitation concerns following anterior cruciate ligament reconstruction. Sports Medicine. 1991;12:338-46.
15. Tibone JE, Antich TJ. A biomechanical analysis of anterior cruciate ligament reconstruction with the patellar tendon. A two year followup. Am J Sports Med. 1988;16:332-5.
16. Keays SL, Bullock-Saxton J, Keays AC. Strength and function before and after anterior cruciate ligament reconstruction. Clin Orthop Relat Res. 2000;373:174-83.
17. Mattacola CG, Perrin DH, Gansneder BM, Gieck JH, Saliba EN, McCue FC 3rd. Strength, functional outcome, and postural stability after anterior cruciate ligament reconstruction. J Athl Train. 2002;37:262-8.
18. Chmielewski TL, Hurd WJ, Snyder-Mackler L. Elucidation of a potentially destabilizing control strategy in ACL deficient non-copers. J Electromyogr Kinesiol. 2005;15:83-92.
19. Buss DD, Warren RF, Wickiewicz TL, Galinat BJ, Panariello R. Arthroscopically assisted reconstruction of the anterior cruciate ligament with use of autogenous patellar-ligament grafts. Results after twenty-four to forty-two months. J Bone Joint Surg Am. 1993;75:1346-55.
20. Barber-Westin SD, Noyes FR, Andrews M. A rigorous comparison between the sexes of results and complications after anterior cruciate ligament reconstruction. Am J Sports Med. 1997;25:514-26.
21. Beynnon BD, Johnson RJ, Fleming BC, Kannus P, Kaplan M, Samani J, Renström P. Anterior cruciate ligament replacement: comparison of bone-patellar tendon-bone grafts with two-strand hamstring grafts. A prospective, randomized study. J Bone Joint Surg Am. 2002;84:1503-13.
22. Shelbourne KD, Nitz P. Accelerated rehabilitation after anterior cruciate ligament reconstruction. Am J Sports Med. 1990;18:292-9.
23. Daanen HA, Mazure M, Holewijn M, Van der Velde EA. Reproducibility of the mean power frequency of the surface electromyogram. Eur J Appl Physiol Occup Physiol. 1990;61:274-7.
24. De Luca CJ. Control properties of motor units. J Exp Biol. 1985;115:125-36.
25. Kannus P. Isokinetic evaluation of muscular performance: implications for muscle testing and rehabilitation. Int J Sports Med. 1994;15 Suppl 1:S11-8.
26. Tegner Y, Lysholm J, Lysholm M, Gillquist J. A performance test to monitor rehabilitation and evaluate anterior cruciate ligament injuries. Am J Sports Med. 1986;14:156-9.
27. Wiklander J, Lysholm J. Simple tests for surveying muscle strength and muscle stiffness in sportsmen. Int J Sports Med. 1987;8:50-4.
28. Kannus P, Järvinen M, Johnson R, Renström P, Pope M, Beynnon B, Nichols C, Kaplan M. Function of the quadriceps and hamstrings muscles in knees with chronic partial deficiency of the anterior cruciate ligament: Isometric and isokinetic evaluation. Am J Sports Med. 1992;20:162-8.
29. Barber SD, Noyes FR, Mangine RE, McCloskey JW, Hartman W. Quantitative assessment of functional limitations in normal and anterior cruciate ligament-deficient knees. Clin Orthop Relat Res. 1990;255:204-14.
30. Iossifidou AN, Baltzopoulos V. Inertial effects on the assessment of performance in isokinetic dynamometry. Int J Sports Med. 1998;19:567-73.
31. Krishnaveni V, Jayaraman S, Anitha L, Ramadoss K. Removal of ocular artifacts from EEG using adaptive thresholding of wavelet coefficients. J Neural Eng. 2006;3:338-46.
32. Zhang L, Theurer CB, Gao RX, Kazmer DO. Analytic wavelet-based ultrasonic pulse differentiation for injection mold cavity pressure measurement. J Manuf Sci Eng. 2006;128:370-4.
33. Kijewski T, Kareem A. Wavelet transforms for system identification in civil engineering. Comput Aided Civ Infrastruct Eng. 2003;18:339-55.
34. Kijewski-Correa T, Kareem A. Efficacy of Hilbert and wavelet transforms for time-frequency analysis. J Eng Mech. 2006;132:1037-49.
35. Kijewski-Correa T, Kareem A. Nonlinear signal analysis: time-frequency perspectives. J Eng Mech. 2007;133:238-45.
36. Winter DA, editor. Biomechanics and motor control of human movement. 2nd ed. New York: Wiley-Interscience; 1990. p 41-5.
37. Kellis E. Quantification of quadriceps and hamstring antagonist activity. Sports Med. 1998;25:37-62. Erratum in: Sports Med. 1998;25:211.
38. Kellis E, Baltzopoulos V. Muscle activation differences between eccentric and concentric isokinetic exercise. Med Sci Sports Exerc. 1998;30:1616-23.
39. Kellis E, Baltzopoulos V. The effects of normalization method on antagonistic activity patterns during eccentric and concentric isokinetic knee extension and flexion. J Electromyogr Kinesiol. 1996;6:235-45.
40. Kellis E. The effects of fatigue on the resultant joint moment, agonist and antagonist electromyographic activity at different angles during dynamic knee extension efforts. J Electromyogr Kinesiol. 1999;9:191-9.
41. Baratta R, Solomonow M, Zhou BH, Letson D, Chuinard R, D'Ambrosia R. Muscular coactivation. The role of the antagonist musculature in maintaining knee stability. Am J Sports Med. 1988;16:113-22.
42. Heckathorne CW, Childress DS. Relationships of the surface electromyogram to the force, length, velocity, and contraction rate of the cineplastic human biceps. Am J Phys Med. 1981;60:1-19.
43. Perry J, Bekey GA. EMG-force relationships in skeletal muscle. Crit Rev Biomed Eng. 1981;7:1-22.
44. Tracy BL, Enoka RM. Older adults are less steady during submaximal isometric contractions with the knee extensor muscles. J Appl Physiol. 2002;92:1004-12.
45. More RC, Karras BT, Neiman R, Fritschy D, Woo SL, Daniel DM. Hamstrings—an anterior cruciate ligament protagonist. An in vitro study. Am J Sports Med. 1993;21:231-7.
46. Granata KP, Padua DA, Wilson SE. Gender differences in active musculoskeletal stiffness. Part II. Quantification of leg stiffness during functional hopping tasks. J Electromyogr Kinesiol. 2002;12:127-35.
47. Eiling E, Bryant AL, Petersen W, Murphy A, Hohmann E. Effects of menstrual-cycle hormone fluctuations on musculotendinous stiffness and knee joint laxity. Knee Surg Sports Traumatol Arthrosc. 2007;15:126-32.
48. McNair PJ, Marshall RN. Landing characteristics in subjects with normal and anterior cruciate ligament deficient knee joints. Arch Phys Med Rehabil. 1994;75:584-9.
49. Harter RA, Osternig LR, Singer KM, James SL, Larson RL, Jones DC. Long-term evaluation of knee stability and function following surgical reconstruction for anterior cruciate ligament insufficiency. Am J Sports Med. 1988;16:434-43.
50. Holm I, Risberg MA, Aune AK, Tjomsland O, Steen H. Muscle strength recovery following anterior cruciate ligament reconstruction: a prospective study of 151 patients with a two-year follow-up. Isokinet Exerc Sci. 2000;8:57-63.
51. Ross MD, Irrgang JJ, Denegar CR, McCloy CM, Unangst ET. The relationship between participation restrictions and selected clinical measures following anterior cruciate ligament reconstruction. Knee Surg Sports Traumatol Arthrosc. 2002;10:10-9.
52. Herzog W, Longino D, Clark A. The role of muscles in joint adaptation and degeneration. Langenbecks Arch Surg. 2003;388:305-15.