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Effect of Knee Joint Angle on Side-to-Side Strength Ratios

Krishnan, Chandramouli1; Williams, Glenn N.2,3

Journal of Strength and Conditioning Research: October 2014 - Volume 28 - Issue 10 - p 2981–2987
doi: 10.1519/JSC.0000000000000476
Original Research
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Krishnan, C and Williams, GN. Effect of knee joint angle on side-to-side strength ratios. J Strength Cond Res 28(10): 2981–2987, 2014—Isometric knee extensor and flexor strength are typically tested at different joint angles due to the differences in length-tension relationships of the quadriceps and hamstring muscles. The efficiency of strength testing can be improved if the same angle can be used to test both the knee extensor and flexor muscle groups. The aim of this study was to determine an optimal angle for isometric knee strength testing by examining the effect of knee angle on side-to-side peak torque ratios. Eighteen active young people (9 males and 9 females) participated in this study. Knee extensor and knee flexor strength were tested on both sides at 30°, 60°, and 90° of knee flexion. The effect of knee flexion angle on side-to-side peak torque ratios, raw torque values, and side-to-side flexor-to-extensor torque ratios were assessed. Side-to-side knee extensor peak torque ratios and knee flexor-to-extensor torque ratios differed significantly by knee flexion angle (p = 0.024 and p = 0.011, respectively), but side-to-side knee flexor peak torque ratios did not differ significantly (p = 0.311). When considering both side-to-side peak torque ratios and flexor-to-extensor torque ratios, the values were more symmetrical (i.e., closer to 100%) only at 60° of knee flexion. Our results indicate that both the knee flexors and the knee extensors can be tested clinically at 60° of knee flexion. Our results also indicate that the hamstrings can be tested at any of the 3 angles if the examiner is interested in side-to-side ratios rather than raw torque values. These results may facilitate more efficient and flexible clinical knee strength testing.

1Department of Physical Medicine & Rehabilitation, University of Michigan, Ann Arbor, Michigan;

2Department of Physical Therapy & Rehabilitation Science, University of Iowa, Iowa City, Iowa; and

3University of Iowa Sports Medicine Center, Department of Orthopaedics and Rehabilitation, University of Iowa, Iowa City, Iowa

Address correspondence to Dr. Chandramouli Krishnan, mouli@umich.edu.

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Introduction

Muscle weakness has been linked to the pathogenesis of posttraumatic osteoarthritis (13,42), frailty and functional impairment in elderly individuals (4,45), disability and functional limitations in individuals with neurologic and orthopedic disorders (9,33,36,38), and various metabolic and cardiovascular disease processes (3,17,29). For example, quadriceps muscle weakness and atrophy observed after knee joint trauma (e.g., ligament injuries, osteoarthritis, and ligament reconstruction or total joint arthroplasty procedures) are strongly associated with altered biomechanics in gait and persistent disability (30,32,47,48). Similarly, data from longitudinal studies suggest that impaired muscle strength is a robust predictor of functional decline with aging and of mortality in people of all ages (3,17,35,39,41). Considering the broader impact of muscle strength on a wide variety of disease conditions, it is clear that maintaining optimal muscle strength is important to the health and well-being of an individual.

Muscle strength is also critical for optimal performance in sports and for preventing certain serious sport-related injuries (34,44,49). For example, there is a strong association of maximal squat strength with sprint performance and vertical jump height in soccer players (49). Similarly, impaired hamstring strength has been linked to the predisposition of hamstring and anterior cruciate ligament injury in elite athletes (34,44). Accordingly, it is not surprising that strength testing forms an important component of clinical intervention and rehabilitation as well as in research related to human performance and conditioning.

Knee strength testing is routine practice in many clinical and research settings based on the importance of thigh muscle strength to healthy human function (9,33,36,38). Sophisticated testing instruments such as a force/torque dynamometer are commonly used to provide objective data and display changes in strength over time. Isokinetic testing is preferred by some because it is perceived to have greater functional relevance than isometric testing. Conversely, isometric testing is considered to be safer and is more reproducible, as there is less of a learning effect than with isokinetic testing (6). Isometric strength measurements are also preferred when quantifying voluntary activation deficits (i.e., when estimating the level of neural drive to a muscle during a maximum voluntary contraction) using electrical superimposition (e.g., interpolated twitch or burst superimposition techniques) (10,11,40).

Accuracy and efficiency are important considerations when selecting a strength testing method. Clinicians and scientists interested in knee function often test knee extensor and knee flexor muscle strength during the same session. In isometric designs, the knee extensors and flexors are typically tested at different knee joint angles because the quadriceps and hamstrings muscles have different length-tension relationships (21). If the knee extensors and flexors could be tested at the same knee angle, it would improve efficiency. But, this is only possible if this approach would yield similar results irrespective of the angle in which the testing is performed. Because the quadriceps muscle group is typically more severely affected by injury than the hamstring muscle group (8,18), the most logical approach would be to test the knee flexors at the optimal angle for the knee extensors (around 60° of knee flexion) (22). In some circumstances (e.g., when assessing voluntary activation), it is favorable to test the quadriceps at 90° of knee flexion (30). Isometric knee extensor strength testing is rarely performed at angles <50° of flexion based on quadriceps muscle length-tension relationships (21). Conversely, isometric knee flexor strength testing is usually performed at about 30° of knee flexion because the hamstring group's mechanical advantage is greatest at this angle (22).

In clinical settings, it is typical to assess knee strength using a side-to-side ratio (i.e., involved side results are presented with respect to uninvolved side results). This is a practical selection as preinjury strength data are rarely available. Although the uninvolved limb generally provides an acceptable reference, evidence indicates that the uninvolved limb also experiences a decline in strength after unilateral injury (15,46), and there is some inherent variability (∼10%) in knee strength between sides even in uninjured healthy individuals (26–28,40). It is unclear whether similar variability is present in side-to-side strength ratios across knee angles. Defining the effect of knee angle on side-to-side strength ratios would be meaningful, as it would provide information on measurement error when comparing results across knee angles and guidance on whether or not it is appropriate to test knee extensor and knee flexor strength at the same joint angle. Therefore, the purpose of this study was to determine an optimal angle for isometric knee strength testing by examining the effect of knee angle on side-to-side peak torque ratios.

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Methods

Experimental Approach to the Problem

This study aimed at determining an optimal testing angle for administering both isometric knee extensor and flexor strength tests by examining the changes in peak torque ratios with changes in knee flexion angle. The side-to-side peak torque and flexor-to-extensor torque ratios were chosen as the primary dependent variables as these ratios are commonly used in clinical and research settings (1,7,19,47). We selected 30°, 60°, and 90° of knee flexion as our levels of independent variable, as these are the most commonly used joint angles for testing isometric knee extensor and flexor strength (16,26,30,47). Previous research has established sufficient reliability for isometric strength testing procedures (ICC = 0.92–0.99) (37).

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Subjects

Eighteen people (9 females and 9 males) aged between 19 and 27 years volunteered to participate in this study. All subjects were regular participants in fitness or sports activities (Tegner activity level of >4). Sixteen subjects were right leg dominant, whereas 2 were left leg dominant as determined by their preferred leg for kicking a ball. Exclusion criteria included a history of: a major knee ligament injury, knee surgery, a lower extremity fracture or thigh muscle injury within the previous year, the presence of a knee joint effusion, lower extremity nerve injury, abnormal gait pattern, or another health condition that would adversely impact the outcomes of the study. All subjects provided written informed consent before participation. The research procedures used were in accordance with the ethical standards laid down by The National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research and were approved by the University of Iowa Human Subjects Research Institutional Review Board.

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Procedures

The testing procedures began by having subjects perform a 5 minute warm-up on a cycle ergometer. Subjects were instructed to use their preferred resistance and maintain a speed of about 60 revolutions per minute while biking. After completing the warm-up, subjects were seated on a Cybex isokinetic dynamometer with a HUMAC NORM upgrade (Computer Sports Medicine, Inc., Stoughton, MA, USA) and fixed to the device in standard isometric testing fashion (Figure 1) (24,25). The order of limb testing and the beginning knee angle were randomized a priori using a computer-based random number generator to minimize effects associated with order of testing.

Figure 1

Figure 1

The knee was positioned at the first test angle (30°, 60°, or 90°) with the hip in approximately 90° of flexion. Five submaximal isometric knee extension and flexion trials were performed to familiarize subjects with the testing system and prepare their muscles for testing. A 1-minute rest period was provided between these submaximal trials and maximal testing. Subjects then performed 3 knee extensor and 3 knee flexor maximal voluntary isometric contractions (MVICs) with direction alternating (extension, flexion, extension, flexion, extension, flexion). Each MVIC was 5 seconds in duration. Repeat extension and flexion contractions were separated by 2 minutes to minimize fatigue. After completing 3 MVICs in each direction, the knee was repositioned to the second knee angle, and testing was repeated in an identical fashion. When testing was completed at the second angle, the knee was repositioned to the third knee angle, and testing was once again repeated. After completing testing at all 3 angles with the first leg, the subjects were repositioned to test the opposite leg using the same procedures.

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Data Management

Custom-written LabVIEW (version 7.0; National Instruments Corporation, Austin, TX, USA) programs were used to collect and analyze the torque data. Torque signals were sampled at 1,000 Hz, low pass filtered at 4 Hz using a third order analog Butterworth filter, and converted to torque values (N·m) using calibrated conversion factors. The torque produced by the weight of the limb was taken into account when determining peak torque values (gravity correction). Data were analyzed using mean peak torque (average of the 3 trials at each angle) and maximum peak torque (peak value in any of the 3 trials at each angle), which were compared in analysis.

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Statistical Analyses

Statistical analyses were performed using SPSS for Windows version 15.0 (SPSS, Inc., Chicago, IL, USA). Power analysis indicated that a sample size of 18 would yield 90% power to detect a mean difference of 10% in side-to-side strength ratios with an estimated SD of the differences of 12% at α = 0.05. Descriptive statistics were calculated for peak torque and flexor-to-extensor torque ratios in raw values and side-to-side strength ratios (right/left × 100). Nonparametric statistics were used based on the sample size. A Kruskal-Wallis 1-way analysis of variance (ANOVA) was performed to evaluate differences in demographics by sex. A Friedman ANOVA by Ranks was used to assess whether there were significant differences in mean and maximum peak torque side-to-side knee extensor and knee flexor strength ratios by angle. Friedman's test was also used to assess whether there were significant differences in side-to-side flexor-to-extensor torque ratios by angle. When Friedman's test was significant, post hoc analyses were performed using a Wilcoxon signed Rank-test. The Wilcoxon signed rank test was also used to assess whether there were significant differences in side-to-side peak torque ratios and side-to-side flexor-to-extensor torque ratios obtained using the mean peak torque method and the maximum peak torque method. The significance level was set at α = 0.05. Estimates of effect size were reported using Kendall's coefficient of concordance “W” and absolute(r), which was computed using the following formula:

, where “N” is the total sample size.

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Results

The demographics of the male and female subjects were not significantly different except for their height and weight (Table 1). The raw peak knee flexor and extensor torque values produced by side and angle are provided in Table 2 and Table 3.

Table 1

Table 1

Table 2

Table 2

Table 3

Table 3

There was a significant difference in peak flexor torque values by angle when assessed using the mean peak torque method and the maximum peak torque method (

= 47.722 and 50.889; df = 2; p < 0.001; Kendall's W = 0.663 and 0.707). Post hoc analyses revealed that peak flexor torque values produced at 30° and 60° of knee flexion were significantly greater than those produced at 90° of knee flexion (p < 0.001, abs(r) = 0.864 and 0.862; Table 2). Peak extensor torque values also varied significantly by angle when assessed using the mean peak torque method and the maximum peak torque method (

= 51.389; df = 2; p < 0.001; Kendall's W = 0.714). Post hoc analyses revealed that peak extensor torque values were similar in magnitude at 60° and 90° of knee flexion (p = 0.489; abs(r) = 0.115) but were significantly lower at 30° of flexion (p < 0.001; abs(r) = 0.872 and 0.869; Table 3).

The side-to-side peak torque ratios were statistically similar whether assessed using mean peak torque or maximum peak torque values (p > 0.05; abs(r) = 0.026–0.272). This was also the case for side-to-side flexor-to-extensor torque ratios (p > 0.05; abs(r) = 0.110–0.248). There was also no significant difference in side-to-side knee flexor peak torque ratios by angle when assessed using the mean peak torque method and the maximum peak torque method (

= 2.333; df = 2; p = 0.311; Kendall's W = 0.065; Figure 2A). There were, however, significant differences in the side-to-side knee extensor torque ratios by angle when assessed using the mean peak torque method and the maximum peak torque method (

= 7.444; df = 2; p = 0.024; Kendall's W = 0.207; Figure 2B). Post hoc analyses revealed that side-to-side knee extensor torque ratio at 30° of knee flexion was significantly different from the ratios obtained at 60° (97.1 vs. 105; p = 0.018; abs(r) = 0.559) and 90° of knee flexion (95.3 vs. 105; p = 0.014; abs(r) = 0.580). Side-to-side knee extensor torque ratios at 60° and 90° of knee flexion were not significantly different (97.1 vs. 95.3; p = 0.286; abs(r) = 0.251).

Figure 2

Figure 2

As expected, knee flexor-to-extensor torque ratios decreased with increases in knee flexion angle when assessed using the mean peak torque method and the maximum peak torque method (

= 64.889 and 63.389; df = 2; p < 0.001; Kendall's W = 0.901 and 0.880; Figure 3A). Post hoc analyses indicated that knee flexor-to-extensor torque ratios at all angles significantly differed from one another (p < 0.001; abs(r) = 0.809–0.872). Side-to-side knee flexor-to-extensor torque ratios were significantly different across knee angles (

= 9.0; df = 2; p = 0.011; Kendall's W = 0.250; Figure 3B). Post hoc analyses revealed that side-to-side flexor-to-extensor torque ratios were significantly higher at 90° than at 30° (111.0 vs. 95.2; p = 0.006; abs(r) = 0.642) and 60° (111.0 vs. 101.0; p = 0.008; abs(r) = 0.621) of knee flexion. This was true regardless of whether mean or maximum peak torque values were used (Figure 3B). Side-to-side peak torque ratios and flexor-to-extensor torque ratios were more symmetrical (i.e., closer to 100%) at 60° of knee flexion than at 30° or 90° of knee flexion (Figures 2 and 3B).

Figure 3

Figure 3

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Discussion

The time and related costs associated with knee strength testing have led many rehabilitation specialists to abandon strength testing in clinical practice despite strong evidence that quadriceps and hamstring muscle strength are vital to functional performance (9,32,47,48). Our results provide evidence that clinical isometric knee strength testing can be simplified by testing the knee flexors and extensors at 60° of knee flexion when the goal is to obtain side-to-side strength ratios as is typical in clinical practice. Our findings also indicate that valid isometric knee flexor strength testing can be performed at joint angles considered to be mechanically suboptimal for the hamstring muscles. Peak torque values and side-to-side torque ratios are similar when assessed using mean peak torque values and maximum peak torque values; therefore, it is appropriate to use either approach for isometric knee strength tests.

Peak isometric knee flexor torque was recorded at 30° of knee flexion, whereas peak isometric knee extensor torque was recorded at 60° of knee flexion. These findings agree with previously published data (22,31). The torque generating capacity of the knee flexor muscles at 90° of knee flexion was significantly lower than that measured at 30° and 60° of knee flexion. Conversely, the torque generating capacity of the knee extensor muscles was significantly lower at 30° of knee flexion than it was at 60° or 90° of knee flexion. These findings are also consistent with the literature and are not surprising considering the known changes in physiological (neural activation) and mechanical properties (moment-arms, length-tension relationships) of the quadriceps and hamstring muscles across the range of knee flexion (5,20). The observed similarities in knee flexor peak torque values at 30° and 60° of knee flexion and knee extensor peak torque values at 60° and 90° of knee flexion suggest that testing at either of these respective angles is defendable. The results also indicate that 60° of knee flexion seems to be an optimal angle for obtaining both peak knee extension and flexion values if testing has to be performed at the same knee angle.

Some researchers have described sharp differences in knee flexor torque values when knee position is changed from 30° to 60° of flexion and in knee extensor torque values when knee position is changed from 60° to 90° of flexion (22,31). Like Herzog et al. (12), we observed relatively small changes in peak torque across these respective knee angles. The differences in results between studies are likely related to differences in the samples studied and the methodologies used. We did not account for small changes in knee angle that occur when performing MVICs. Researchers have demonstrated that knee angle can change 10°–20° during an MVIC (2,23). Such changes can affect the shape of torque-angle curves. We intentionally chose not to precisely account for the changes in knee flexion angle during MVICs because this is not done clinically. Our primary focus was evaluating the effect of knee angle on side-to-side strength ratios to provide insight on whether the knee extensors and flexors can be tested at the same joint angle in settings where time is limited. Because side-to-side ratios are most commonly used in clinical settings, we felt that it was important to evaluate data in a manner that replicates clinical practice.

The differences in side-to-side knee flexor-to-extensor torque ratios observed with changes in knee flexion angle are interesting. Knee flexor-to-extensor torque ratios are thought to be indicators of the balance of strength among muscles spanning the knee joint (1,14). Side-to-side knee flexor-to-extensor torque ratios positively correlate with the long-term patient-based outcomes and functional performance (19). Some clinicians also use these side-to-side knee flexor-to-extensor torque ratio comparisons as a determinant of an athlete's readiness to return to sports participation (43,50). Previous reports suggest that knee flexor-to-extensor torque ratios are similar across sides (7,50). The influence of knee joint position on side-to-side knee flexor-to-extensor torque ratios has not been studied. Our results indicate that side-to-side knee flexor-to-extensor torque ratios are in fact affected by changes in knee flexion angle. Side-to-side knee flexor-to-extensor torque ratios were more symmetrical (i.e., closer to 100%, which indicates lower asymmetry between sides) at 60° than at 30° or 90° of knee flexion. This finding provides further support for testing knee strength testing at 60° of knee flexion.

There are some limitations to this study. First, we only included active “healthy” young people as our primary intention was to establish typical variability in side-to-side peak torque ratios across knee angles. However, this is a limitation as the applicability in injured populations is not clear from this study, although a recent report suggests that our results are generalizable to individuals with ligament injuries (16). Second, the relatively small sample size of this study could have resulted in a type II statistical error. Therefore, some of the nonsignificant findings should be interpreted with caution. We recommend that the readers make their judgment based on the estimates of effect size reported for these nonsignificant observations. Finally, we assumed that more symmetrical values at 60° of knee flexion indicate that this angle is optimal for testing. However, it is possible that more symmetrical values could have been observed because this angle was less sensitive to detecting asymmetries.

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Practical Applications

Isometric strength testing of the knee flexors can be performed at the same angle as the knee extensors because side-to-side knee flexor peak torque ratios are not significantly different at 30°, 60°, and 90° of knee flexion. Our results indicate that 60° of knee flexion is the most appropriate angle to use when testing both muscle groups at the same angle. Similar results were obtained when side-to-side peak torque ratios were assessed using mean and maximum peak torque values. Either of these methods is appropriate when analyzing strength test results and comparisons of results from studies using mean vs. maximum peak torque values are valid.

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Acknowledgments

The authors acknowledge Wade Soenksen, Mindy Bormann, and Kellie Pierce for their assistance with data collection and article preparation. The authors also thank Dr. Mark Peterson for his insightful comments on an earlier version of this article. None of the authors declare any conflict of interest, and the results of this study do not constitute an endorsement of the product by the authors or the National Strength and Conditioning Association. Experiment was conducted at the Musculoskeletal Biomechanics & Sports Medicine Research Laboratory, University of Iowa College of Medicine, Iowa City, IA, USA.

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References

1. Aagaard P, Simonsen EB, Trolle M, Bangsbo J, Klausen K. Isokinetic hamstring/quadriceps strength ratio: Influence from joint angular velocity, gravity correction and contraction mode. Acta Physiol Scand 154: 421–427, 1995.
2. Arampatzis A, Karamanidis K, De Monte G, Stafilidis S, Morey-Klapsing G, Bruggemann GP. Differences between measured and resultant joint moments during voluntary and artificially elicited isometric knee extension contractions. Clin Biomech (Bristol, Avon) 19: 277–283, 2004.
3. Artero EG, Lee DC, Ruiz JR, Sui X, Ortega FB, Church TS, Lavie CJ, Castillo MJ, Blair SN. A prospective study of muscular strength and all-cause mortality in men with hypertension. J Am Coll Cardiol 57: 1831–1837, 2011.
4. Barbat-Artigas S, Rolland Y, Cesari M, Abellan van Kan G, Vellas B, Aubertin-Leheudre M. Clinical relevance of different muscle strength indexes and functional impairment in women aged 75 years and older. J Gerontol A Biol Sci Med Sci 68: 811–819, 2013.
5. Becker R, Awiszus F. Physiological alterations of maximal voluntary quadriceps activation by changes of knee joint angle. Muscle Nerve 24: 667–672, 2001.
6. Callaghan MJ, McCarthy CJ, Al-Omar A, Oldham JA. The reproducibility of multi-joint isokinetic and isometric assessments in a healthy and patient population. Clin Biomech (Bristol, Avon) 15: 678–683, 2000.
7. Calmels PM, Nellen M, van der Borne I, Jourdin P, Minaire P. Concentric and eccentric isokinetic assessment of flexor-extensor torque ratios at the hip, knee, and ankle in a sample population of healthy subjects. Arch Phys Med Rehabil 78: 1224–1230, 1997.
8. Campbell DE, Glenn W. Rehabilitation of knee flexor and knee extensor muscle strength in patients with meniscectomies, ligamentous repairs, and chondromalacia. Phys Ther 62: 10–15, 1982.
9. Ericsson YB, Roos EM, Dahlberg L. Muscle strength, functional performance, and self-reported outcomes four years after arthroscopic partial meniscectomy in middle-aged patients. Arthritis Rheum 55: 946–952, 2006.
10. Grindstaff TL, Hertel J, Beazell JR, Magrum EM, Kerrigan DC, Fan X, Ingersoll CD. Lumbopelvic joint manipulation and quadriceps activation of people with patellofemoral pain syndrome. J Athl Train 47: 24–31, 2012.
11. Grindstaff TL, Threlkeld AJ. Optimal Stimulation Parameters to detect deficits in quadriceps voluntary activation. J Strength Cond Res 28: 381–389, 2014.
12. Herzog W, Hasler E, Abrahamse SK. A comparison of knee extensor strength curves obtained theoretically and experimentally. Med Sci Sports Exerc 23: 108–114, 1991.
13. Herzog W, Longino D, Clark A. The role of muscles in joint adaptation and degeneration. Langenbecks Arch Surg 388: 305–315, 2003.
14. Hiemstra LA, Webber S, MacDonald PB, Kriellaars DJ. Hamstring and quadriceps strength balance in normal and hamstring anterior cruciate ligament-reconstructed subjects. Clin J Sport Med 14: 274–280, 2004.
15. Hiemstra LA, Webber S, MacDonald PB, Kriellaars DJ. Contralateral limb strength deficits after anterior cruciate ligament reconstruction using a hamstring tendon graft. Clin Biomech (Bristol, Avon) 22: 543–550, 2007.
16. Hsiao SF, Chou PH, Hsu HC, Lue YJ. Changes of muscle mechanics associated with anterior cruciate ligament deficiency and reconstruction. J Strength Cond Res 28: 390–400, 2014.
17. Izawa KP, Watanabe S, Osada N, Kasahara Y, Yokoyama H, Hiraki K, Morio Y, Yoshioka S, Oka K, Omiya K. Handgrip strength as a predictor of prognosis in Japanese patients with congestive heart failure. Eur J Cardiovasc Prev Rehabil 16: 21–27, 2009.
18. Kannus P. Ratio of hamstring to quadriceps femoris muscles' strength in the anterior cruciate ligament insufficient knee. Relationship to long-term recovery. Phys Ther 68: 961–965, 1988.
19. Kannus P, Jarvinen M. Knee flexor/extensor strength ratio in follow-up of acute knee distortion injuries. Arch Phys Med Rehabil 71: 38–41, 1990.
20. Kellis E, Baltzopoulos V. In vivo determination of the patella tendon and hamstrings moment arms in adult males using videofluoroscopy during submaximal knee extension and flexion. Clin Biomech (Bristol, Avon) 14: 118–124, 1999.
21. Knapik JJ, Wright JE, Mawdsley RH, Braun J. Isometric, isotonic, and isokinetic torque variations in four muscle groups through a range of joint motion. Phys Ther 63: 938–947, 1983.
22. Knapik JJ, Wright JE, Mawdsley RH, Braun JM. Isokinetic, isometric and isotonic strength relationships. Arch Phys Med Rehabil 64: 77–80, 1983.
23. Krishnan C. Quadriceps and hamstrings muscle control in athletic males and females. In: Physical Therapy and Rehabilitation Science. Iowa City: University of Iowa, 2006. pp. 84.
24. Krishnan C, Allen EJ, Williams GN. Torque-based triggering improves stimulus timing precision in activation tests. Muscle Nerve 40: 130–133, 2009.
25. Krishnan C, Williams GN. Hamstrings activity during knee extensor strength testing: Effects of burst superimposition. Iowa Orthop J 28: 36–41, 2008.
26. Krishnan C, Williams GN. Evoked tetanic torque and activation level explain strength differences by side. Eur J Appl Physiol 106: 769–774, 2009.
27. Krishnan C, Williams GN. Variability in antagonist muscle activity and peak torque during isometric knee strength testing. Iowa Orthop J 29: 149–158, 2009.
28. Krishnan C, Williams GN. Error associated with antagonist muscle activity in isometric knee strength testing. Eur J Appl Physiol 109: 527–536, 2010.
29. Lazarus R, Sparrow D, Weiss ST. Handgrip strength and insulin levels: Cross-sectional and prospective associations in the Normative aging study. Metabolism 46: 1266–1269, 1997.
30. Lewek MD, Rudolph KS, Snyder-Mackler L. Quadriceps femoris muscle weakness and activation failure in patients with symptomatic knee osteoarthritis. J Orthop Res 22: 110–115, 2004.
31. Lindahl O, Movin A, Ringqvist I. Knee extension. Measurement of the isometric force in different positions of the knee-joint. Acta Orthop Scand 40: 79–85, 1969.
32. Mizner RL, Petterson SC, Snyder-Mackler L. Quadriceps strength and the time course of functional recovery after total knee arthroplasty. J Orthop Sports Phys Ther 35: 424–436, 2005.
33. Mizner RL, Petterson SC, Stevens JE, Axe MJ, Snyder-Mackler L. Preoperative quadriceps strength predicts functional ability one year after total knee arthroplasty. J Rheumatol 32: 1533–1539, 2005.
34. Myer GD, Ford KR, Barber Foss KD, Liu C, Nick TG, Hewett TE. The relationship of hamstrings and quadriceps strength to anterior cruciate ligament injury in female athletes. Clin J Sport Med 19: 3–8, 2009.
35. Ortega FB, Silventoinen K, Tynelius P, Rasmussen F. Muscular strength in male adolescents and premature death: Cohort study of one million participants. BMJ 345: e7279, 2012.
36. Pak S, Patten C. Strengthening to promote functional recovery poststroke: An evidence-based review. Top Stroke Rehabil 15: 177–199, 2008.
37. Park J, Hopkins JT. Within- and between-session reliability of the maximal voluntary knee extension torque and activation. Int J Neurosci 123: 55–59, 2013.
38. Patten C, Lexell J, Brown HE. Weakness and strength training in persons with poststroke hemiplegia: Rationale, method, and efficacy. J Rehabil Res Dev 41: 293–312, 2004.
39. Peterson MD, Rhea MR, Sen A, Gordon PM. Resistance exercise for muscular strength in older adults: A meta-analysis. Ageing Res Rev 9: 226–237, 2010.
40. Pietrosimone BG, Park CM, Gribble PA, Pfile KR, Tevald MA. Inter-limb differences in quadriceps strength and volitional activation. J Sports Sci 30: 471–477, 2012.
41. Rantanen T, Harris T, Leveille SG, Visser M, Foley D, Masaki K, Guralnik JM. Muscle strength and body mass index as long-term predictors of mortality in initially healthy men. J Gerontol A Biol Sci Med Sci 55: M168–M173, 2000.
42. Segal NA, Glass NA, Torner J, Yang M, Felson DT, Sharma L, Nevitt M, Lewis CE. Quadriceps weakness predicts risk for knee joint space narrowing in women in the MOST cohort. Osteoarthritis Cartilage 18: 769–775, 2010.
43. Stafford MG, Grana WA. Hamstring/quadriceps ratios in college football players: A high velocity evaluation. Am J Sports Med 12: 209–211, 1984.
44. Sugiura Y, Saito T, Sakuraba K, Sakuma K, Suzuki E. Strength deficits identified with concentric action of the hip extensors and eccentric action of the hamstrings predispose to hamstring injury in elite sprinters. J Orthop Sports Phys Ther 38: 457–464, 2008.
45. Syddall H, Cooper C, Martin F, Briggs R, Aihie Sayer A. Is grip strength a useful single marker of frailty? Age Ageing 32: 650–656, 2003.
46. Urbach D, Nebelung W, Weiler HT, Awiszus F. Bilateral deficit of voluntary quadriceps muscle activation after unilateral ACL tear. Med Sci Sports Exerc 31: 1691–1696, 1999.
47. Williams GN, Buchanan TS, Barrance PJ, Axe MJ, Snyder-Mackler L. Quadriceps weakness, atrophy, and activation failure in predicted noncopers after anterior cruciate ligament injury. Am J Sports Med 33: 402–407, 2005.
48. Williams GN, Snyder-Mackler L, Barrance PJ, Buchanan TS. Quadriceps femoris muscle morphology and function after ACL injury: A differential response in copers versus non-copers. J Biomech 38: 685–693, 2005.
49. Wisloff U, Castagna C, Helgerud J, Jones R, Hoff J. Strong correlation of maximal squat strength with sprint performance and vertical jump height in elite soccer players. Br J Sports Med 38: 285–288, 2004.
50. Zakas A. Bilateral isokinetic peak torque of quadriceps and hamstring muscles in professional soccer players with dominance on one or both two sides. J Sports Med Phys Fitness 46: 28–35, 2006.
Keywords:

quadriceps; hamstrings; muscle strength; isometric; muscle length; length-tension; force-length; torque-angle

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