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Abstract

BACKGROUND:

The ratio of hamstring to quadriceps strength (H/Q), from isokinetic testing, is often used to guide training or rehabilitation.

OBJECTIVES:

The primary objective was to develop an assessment protocol that produces reproducible H/Q data in a single testing session.

METHODS:

Twenty-four healthy subjects, 16 women and 8 men, were tested using a reliability study design (2 sessions, 5 repetitions). The main outcome measure was the dynamic control ratio at 60 ${}^{\circ}$ /s (DCR60). Testing was also done at 120 ${}^{\circ}$ /s, and concentrically at 180 ${}^{\circ}$ /s. Generalizability theory was used to determine the reliability ( $\varphi$ ) coefficient and the minimal detectable change MDC, and to extrapolate the data to develop an optimal assessment protocol, ideally using data from only one session.

RESULTS:

Single-session DCR60 data were reproducible ( $\varphi$ coefficient $=$ 0.868, MDC95 $=$ 0.144) using 5 repetitions, excluding the first repetition from the average. Values were improved by averaging over multiple sessions and repetitions, although little was gained from more than 2 sessions or 5 repetitions. Comparable results were found for testing at 120 ${}^{\circ}$ /s.

CONCLUSIONS:

Reproducible DCR60 values may be derived from a single testing session of the hamstrings (in eccentric mode) and the quadriceps (in concentric mode). We recommend collecting five repetitions, and averaging the data for repetitions 2–5.

Keywords

Knee muscle strength rehabilitation reproducibility dynamometer

1. Introduction

Strength and power of both the hamstrings and quadriceps muscle groups is often a target of rehabilitation following knee injuries or muscle strain injuries [1, 2]. One of the rehabilitation goals may be to normalize the ratio of hamstring-to-quadriceps strength (HQR), derived through isokinetic testing. It has been suggested, however, that the dynamic control ratio (DCR), which is obtained by dividing the peak eccentric moment of the hamstrings by the peak concentric moment of the quadriceps, has a unique differentiating role [3], and may provide the best reflection of the functional, antagonistic actions of these muscles [4]. From a clinical perspective, therefore, having an assessment protocol that can provide reproducible data for the DCR with a realistic minimal detectable change (MDC), using the fewest number of isokinetic measures, would allow the clinician to monitor an individual patient’s progress over time in an efficient way.

Several previous studies have shown that isokinetic testing of the quadriceps and hamstrings can produce reproducible data [1, 4, 5]. Impellizzeri et al. [4], for example, found that peak moment (PM) measurements during isokinetic testing of the hamstrings and quadriceps are highly reproducible over a range of velocities (ICC ${}_{(2,1)}$ from 0.93–0.98 , MDC of 0.123–0.124). These past studies, however, have all reported reproducibility statistics based on data acquired over multiple separate sessions, which is not ideal for clinical use. Preuss [6] has described a method to develop clinical assessment protocols using a reliability-study design and generalizability theory. This approach allows the user to assess the impact of the number of repetitions per session, and the number of testing sessions, on the reproducibility of the acquired data. Increasing the number of repetitions per session, for example, may offset the effects of reducing the number of testing sessions, and in turn may allow for the development of a clinically feasible testing protocol for the DCR, while still producing reproducible data with a small MDC.

While isokinetic measurements at the knee are commonly performed with participants in a seated position (hip flexion 70–85 ${}^{\circ}$ ) [4, 7, 8, 9], this brings the hip well outside its functional range of motion (ROM) for walking or running, and will likely affect the measures taken from the hamstrings and rectus femoris [4]. The prone or supine position has been suggested as a test position that is more reflective of the functional requirements of these muscles [10]. Testing in this study, therefore, will be done in prone.

While the DCR is useful as a primary measure to guide rehabilitation, it is likely not reflective of the full functional capacity of these muscle groups. In addition to the position of the hip (discussed above), the velocity of the movement (including, but not limited to differences between concentric and eccentric movements) and the position of the knee (which affects the length of the muscles and their moment arms at the knee) are also likely to affect the expression of muscular force [11]. Traditional isokinetic testing looks at the PM generated at a specific joint angular velocity [12], but typically does not account for the position at which that PM was generated [13]. Representing muscle function at the knee across multiple joint angular velocities and joint positions, therefore, would add to the information provided by the DCR.

The primary objective of this study, therefore, was to develop a clinical assessment protocol that allows for the acquisition of reproducible DCR data at 60 ${}^{\circ}$ /s, with a realistically achievable MDC, in healthy individuals. It was hypothesized that this was possible using data from a single testing session. This was assessed using generalizability theory, and data acquired over two sessions, with five repetitions per session. The secondary objectives were as follows: 1) to assess the reproducibility of DCR data at 120 ${}^{\circ}$ /s; 2) to examine the change in DCR, at 60 ${}^{\circ}$ /s and 120 ${}^{\circ}$ /s, over the ROM of the knee; 3) to examine the moment-of-force at the knee, produced by the hamstrings and quadriceps, taking into account both joint angle and angular velocity. It was hypothesized that reproducible data for the DCR at 120 ${}^{\circ}$ /s could also be acquired in a single testing session, and that both joint angular velocity and joint position would have an effect on the DCR. Furthermore, it was also expected that the effect of joint angular velocity and joint position would be different for the quadriceps and hamstrings.

2. Methods

2.1 Participants

A sample of 28 healthy participants (mean age: 25 yrs; SD: 3 yrs; range: 19–35 yrs) were recruited via social media. Four of the participants withdrew from the study – two due to knee pain experienced during the first testing session, and two due to an inability to attend their second testing session within the prescribed time frame (see procedures, below) – leaving 24 participants, 16 women and 8 men. Based on the method described by Shoukri et al. [14], it was determined that only 15 participants were required to target a reliability coefficient $\geqslant$ 0.90 (95% confidence interval) for the DCR60, with all participants completing two testing sessions. Additional participants were recruited to ensure sufficient sample size. Demographic and anthropometric information for the 24 healthy participants who completed the study is presented in Table 1.

Table 1
Subject demographic and anthropometric information (N $=$ 24)

Sex	Women: 16	Men: 8
Dominant leg	Right: 23	Left: 1
IPAQ-L7S*	Low: 0	Moderate: 4	High: 19
Age (years)	Mean: 24	SD: 3	Range: 19, 35
Height (m)	Mean: 1.67	SD: 0.09	Range: 1.56, 1.90
Mass (kg)	Mean: 64.0	SD: 12.7	Range: 44.5, 92.5

*N $=$ 23.

Eligible participants were required to be between the ages 18–35 years, and to understand verbal and written English or French. Exclusion criteria were as follows: any history of injury or surgery affecting the knee; a history of hamstrings or quadriceps injury; any lower extremity injury or surgery that affected daily function within the last 12 months; any cardiovascular, neurological, cognitive, systemic disease, or impairment that may have interfered with isokinetic testing of the knee.

Participants were asked to complete the International Physical Activity Questionnaire long form – past 7 days (IPAQ-L7S) prior to the first testing session. The IPAQ-L7S measures the level of physical activity over the previous week, and has been shown to have acceptable measurement properties for both clinical and research purposes [15, 16]. Participants were also instructed to maintain their regular physical activity between the two testing sessions, but not to take part in any new vigorous physical activity for the duration of the study period. We were not able to collect the IPAQ-L7S data from one participant due to time constraints during the testing sessions.

The experiments were undertaken with the understanding and written consent of each participant, and that the study conforms with The Code of Ethics of the World Medical Association (Declaration of Helsinki), printed in the British Medical Journal (18 July 1964). Ethics approval for this study was received from the research ethics board of the CRIR and the CIUSSS Centre-Ouest-de-l’Île-de-Montréal (CRIR-1139-0316).

2.2 Testing procedures

Participants completed two testing sessions within a 7-day interval, with a minimum of 48 hours between sessions to allow for recovery. Isokinetic testing was done for knee flexion (hamstrings) and extension (quadriceps) on the dominant leg (preferred leg to kick a ball), using a CSMI Humac Cybex NORM isokinetic dynamometer (Computer Sports Medicine Inc., Stoughton, MA). The participants were tested in prone, with a pad under the pelvis, placing the hips in $\sim$ 10–20 ${}^{\circ}$ of flexion. The same positions and angles for the dynamometer were used for both testing sessions.

Each session began with a 5-minute warm-up on a stationary bicycle, at a low-moderate intensity. The participant then lay prone on the dynamometer (seatback laid flat), with straps placed around the pelvis and thigh to prevent them from moving during testing. The dynamometer software was set for a knee ROM between 10 ${}^{\circ}$ to 90 ${}^{\circ}$ , with gravity correction to account for the weight of the leg. Mechanical stops were also placed at 0 ${}^{\circ}$ and 100 ${}^{\circ}$ to provide an extra measure of safety, and the participant was given an emergency stop button, which would immediately terminate all testing if pushed. The participants were then instructed to perform 10 submaximal ( $\sim$ 50% maximal effort) repetitions of knee flexion and extension, under both concentric (60 ${}^{\circ}$ /s) and eccentric ( $-$ 60 ${}^{\circ}$ /s) conditions, as a further warm-up, and to minimize learning effects.

The testing protocol followed a standardized, non-randomized protocol for isokinetic testing of the knee. Under each condition, participants had to complete 5 submaximal ( $\sim$ 50% maximal effort) repetitions prior to testing to ensure that they were familiarized with the task [4], after which a 1-minute rest period was given. The participants then completed 5 repetitions of the task with maximal effort, during which they were provided with standardized verbal encouragement from the testers. The order of testing for all participants during both session was as follows: concentric 60 ${}^{\circ}$ /s, eccentric 60 ${}^{\circ}$ /s, concentric 120 ${}^{\circ}$ /s, eccentric 120 ${}^{\circ}$ /s, concentric 180 ${}^{\circ}$ /s. A rest period of 3 minutes was given between each testing condition. The choice not to randomize the order of the isokinetic testing was pragmatic, to more closely reflect typical clinical practice rather than research design.

2.3 Data analysis

The raw data acquired from the dynamometer software were sampled at 100 Hz, and included all 5 repetitions for the hamstrings and quadriceps at each velocity. As this software ‘zeros’ the moment data at the impact point with the digital stop, to limit impact artifacts, the actual ROM available for each repetition was below the 10 ${}^{\circ}$ to 90 ${}^{\circ}$ target range, and was variable between trials. Individual repetitions were identified when the absolute angular velocity was $\geqslant$ 5 ${}^{\circ}$ /s and the absolute moment-of-force was $\geqslant$ 0 Nm. The minimum and maximum joint angle for each repetition were then determined.

Knee angle, angular velocity and moment data for each individual repetition were filtered using a 4 ${}^{\rm th}$ order, dual-pass, zero-phase-lag low-pass Butterworth filter, with a 10 Hz cut-off. The filtered moment and angular velocity data were then interpolated, over the available ROM, using a cubic spline function, with data points at knee angle increments of 0.1 ${}^{\circ}$ .

2.3.1 DCR60 and DCR120

To calculate the DCR60, the main outcome variable for the study, the PM for the hamstrings for each trial of the eccentric 60 ${}^{\circ}$ /s condition, and the PM for the quadriceps for each trial of the concentric 60 ${}^{\circ}$ /s condition, was extracted from the filtered data (prior to interpolation). The DCR60 was then determined for each participant, for all 5 repetitions for each session, and for both sessions, using the ratio of these PM values (hamstrings/quadriceps). Note that these values represent the peak values over the full available ROM, and as such do not account for the knee angle at which they occurred. Similarly, the DCR120 was determined for each participant using 120 ${}^{\circ}$ /s conditions.

2.3.2 DCRROM60 and DCRROM120

As the DCR above do not account for the knee angle at which the PM values occurred, two additional measures were determined. The DCRROM60 represents the DCR at 60 ${}^{\circ}$ /s for each joint position throughout the entire ROM. The DCRROM120 represents the same ratio at 120 ${}^{\circ}$ /s.

2.3.3 Normalized moment

The moment data for each repetition, under all conditions, were normalized to the PM for the same repetition of the quadriceps under the concentric 60 ${}^{\circ}$ /s condition. The mean, normalized moment-of-force was then determined for the study population, for both muscle groups, for each point in the knee ROM (joint angle), for all 5 conditions (3 Con $+$ 2 Ecc).

2.4 Statistical analyses

Independent samples t-tests, along with Levene’s test for equality of variances, were used to compare the mean DCR60 and DCR120 between male and female participants, in order to ensure that no significant sex-related differences were present [17], and that these data could be combined for reliability testing.

Generalizability theory was used to address the reproducibility of DCR60. During the first step, the generalizability study (G-study), the reliability coefficient ( $\varphi$ ), SEM, and MDC (with a 95% confidence interval – MDC95%) were determined using the data from all participants for all 5 repetitions from both sessions. Because $\varphi$ was determined using data from multiple sessions, using a pragmatic approach (multiple testers, non-randomized order), it can be interpreted as a measure of clinical reproducibility [18]. The MDC, which is the most clinically interpretable variable, was calculated as follows:

$\text{MDC}=\text{z-score}\cdot\sqrt{2}\cdot\ \text{SEM}$

where z-score determines the confidence interval of the MDC, based on a normal distribution curve. In this study, a z-score of 1.96 was used, which represents 95% of the data under the normal curve (i.e. a 95% confidence interval). This means that, if the difference between two measures of the DCR60 matches or exceeds this value, the difference is due to real change rather than variability, 19 times out of 20.

During the second step, the decision study (D-study), the $\varphi$ coefficient, SEM, and MDC95% were recalculated by changing the number of occurrences for each of the study facets: number of repetitions and number of testing sessions. Specifically, these values were calculated for 1 to 10 repetitions and for 1 to 3 sessions respectively. For detailed calculation procedures, refer to Preuss [6].

The G-study and D-study were also repeated excluding the first repetitions from each testing session (i.e. using repetitions 2 through 5), and excluding the first two repetitions (i.e. using repetitions 3 through 5). If these analyses produced an improvement in the $\varphi$ coefficient, this would suggest that a learning effect was present during the testing, and that the first (and possibly second) isokinetic repetition was different from subsequent repetitions.

Table 2
Dynamic control ratio means (SD) with comparison for sex-related differences

	Female (N $=$ 16)	Male (N $=$ 8)	Levene’s test	T-test
DCR60	0.398 (0.158)	0.468 (0.090)	P $=$ 0.179	P $=$ 0.261
DCR60 ${}_{2-5}$	0.383 (0.154)	0.459 (0.087)	P $=$ 0.247	P $=$ 0.211
DCR120	0.517 (0.195)	0.575 (0.123)	P $=$ 0.309	P $=$ 0.449
DCR120 ${}_{2-5}$	0.478 (0.185)	0.553 (0.120)	P $=$ 0.357	P $=$ 0.314

Subscript 2–5 indicates that the first repetition was removed from the data.

Figure 1.

DCR60 $\varphi$ coefficient (left) and MDC95% (right). Generalizability study results (based on experimental data) are for 2 sessions, and either 5 repetitions when all data is considered (open diamond), or 4 repetitions when the first repetition is dropped (solid diamond). The remainder of these values represent the findings of the Decision study (extrapolated from the experimental data) when all data is considered (dotted lines), or 4 repetitions when the first repetition is dropped (solid lines).

3. Results

No significant difference were found between male and female participants for DCR60 or DCR120 (Table 2). As such, all further analyzes were done using data from the entire study population (N $=$ 24).

3.1 DCR60

The mean DCR60 for the experimental data (2 testing sessions, 5 repetitions per session) was 0.421 (SD 0.141). These data produced a $\varphi$ coefficient of 0.895, a SEM of 0.046, and a MDC95% of 0.127. By excluding the first repetition from both sessions (i.e. using only repetitions 2–5), the mean DCR60 was 0.408 (SD 0.139). The $\varphi$ coefficient improved to 0.928, the SEM to 0.037, and the MDC95% was reduced to 0.103. Excluding the first 2 repetitions (i.e. using only repetitions 3–5) did not produce any further improvement relative to dropping only 1 repetition ( $\varphi$ coefficient $=$ 0.920; SEM $=$ 0.038; MDC95% $=$ 0.107), and thus this approach was not further assessed.

The D-study indicated that using data from only one testing session, excluding the first repetition, the $\varphi$ coefficient dropped to 0.868, the SEM increased to 0.052, and the MDC95% increased to 0.144. Increasing the number of repetitions beyond 5 did not produce a substantial improvement in the $\varphi$ coefficient or MDC95%.

All data from the D-study, for DCR60, are presented in Fig. 1.

3.2 DCR120

The data for DCR120 followed a similar pattern to the DCR60 data, but with slightly larger ratios (higher relative hamstring moment-of-force), slightly lower $\varphi$ coefficients, and slightly higher MDC95%. The mean DCR120 for the experimental data (2 testing sessions, 5 repetitions per session) was 0.536 (SD 0.174). These data produced a $\varphi$ coefficient of 0.779, SEM of 0.083, and MDC95% of 0.231. By excluding the first repetition from both sessions (i.e. using only repetitions 2–5), the mean DCR120 was 0.503 (SD 0.178), the $\varphi$ coefficient improved to 0.887, the SEM was reduced to 0.057, and the MDC95% was reduced to 0.157. Excluding the first 2 repetitions (i.e. using only repetitions 3–5) did not produce any substantial improvement relative to dropping only 1 repetition ( $\varphi$ coefficient $=$ 0.891; SEM $=$ 0.055; MDC95% $=$ 0.152), and this approach was not further assessed.

The D-study indicated that using data from only one testing session, excluding the first repetition, the $\varphi$ coefficient dropped to 0.801, the SEM increased to 0.079, and the MDC95% increased to 0.219. Increasing the number of repetitions beyond 5 did not produce a substantial improvement in the $\varphi$ coefficient or MDC95%.

3.3 DCRROM60 and DCRROM120

The mean values for DCRROM60 and DCRROM-120 are illustrated in Fig. 2. H ${}_{\textit{ecc}}$ /Q ${}_{\textit{eon}}$ ROM120 was higher than DCRROM60 over the entire ROM, indicating a relatively greater hamstring moment at the higher velocity. Both ratios follow a similar pattern over the knee joint ROM, with higher values closer to the end-range of extension and flexion.

Figure 2.

DCRROM60 (black) and DCRROM120 (grey) over the ROM. Values are illustrated for knee joint angles for which data was available for at least 15 subjects.

3.4 Normalized moment

The mean, normalized (to the peak quadriceps moment at 60 ${}^{\circ}$ /s) moment data for the hamstrings and quadriceps is illustrated in Fig. 3. For both muscle groups, the relative moment increased for slower concentric velocities and for faster eccentric velocities. For the hamstrings, the pattern was similar for all 5 velocity conditions, with only a small change in moment over knee ROM. For the quadriceps, the moment followed a parabolic pattern under concentric conditions, with the highest moment at approximately 50 ${}^{\circ}$ to 60 ${}^{\circ}$ of knee flexion. Under eccentric conditions, however, the moment tended to increase with increasing knee flexion.

4. Discussion

The primary objective of our study was to develop a clinical assessment protocol for the DCR60 that produces reproducible data, and a realistic MDC. We found that this could be achieved using a single-session protocol, collecting 5 repetitions but excluding the first repetition from the average. The same was found for the DCR120, although with a slightly lower $\varphi$ coefficient, and a slightly higher MDC. The reproducibility of the data were improved, at both speeds, by averaging data over multiple session and repetitions, but with greatly diminishing returns when using data from more than 2 sessions or 5 repetitions (Fig. 1). Using data from multiple sessions, however, may not be practical for clinical purposes. The findings related to our secondary objectives, as expected, showed that both joint angular velocity and joint position have an effect on the moments produced by both the hamstrings and quadriceps (Fig. 3), and thus on the DCR (Fig. 2).

Figure 3.

Mean quadriceps and hamstrings moment-of-force data (from data normalized to the individual subject’s peak quadriceps moment-of-force at Concentric 60 ${}^{\circ}$ /s). Concentric (Con) conditions are represented by solid lines, and eccentric (Ecc) conditions by dashed lines. Values are illustrated for knee joint angles for which data was available for at least 15 subjects, for all 5 velocity conditions..

Our findings indicate that isokinetic testing of the hamstrings and quadriceps produces highly reproducible data, which is in line with the findings of previous studies, despite methodological differences. Impellizzeri et al. [4], for example, tested the H/Q ratio in sitting, using data collected over three sessions, and based their analysis on the intra-class correlation coefficient (ICC) model (2,1) [19]. This previous study reported a reproducibility coefficient for the DCR60 of 0.87 for the right leg, and 0.80 for the left, with a MDC of 0.124 and 0.123 respectively. The mean DCR60 reported in this previous study (0.71), however, was quite different from ours (0.421). This may be due to the effect of the test position (sitting vs. prone lying, respectively) on this measure. Changing the hip position may have a similar effect to that of the knee joint angle on the maximum moment produced by the quadriceps (rectus femoris), and to a lesser extent the hamstrings (Fig. 3, discussed below). It may also, however, reflect the fact that 2/3 of the participants in our study were female, who tend to have a lower H/Q ratio than males [17]. This sex-related difference, however, was not significant in the present study (Table 2), nor was the DCR for the male participants as high as previous reports. This effect also cannot be fully considered, as Impellizzeri et al. did not report the sex of their participants.

The effects of joint angular velocity and joint angle on the hamstring and quadriceps moment (Figs 2 and 3) reflect differences in muscle architecture. Lieber and Friden (2001) provide a comprehensive review of the direct relationship between muscle physiological cross-sectional area and force production, and of the effect of muscle fiber length on the rate of force decline at higher velocities (longer muscles show less force decline with increasing velocity of shortening). The greater physiological cross-sectional area of the quadriceps muscles [11, 20], along with the larger moment arm of the quadriceps due to the fulcrum provided by the patella [21, 22], explains the larger moment produced by the quadriceps, relative to the hamstrings, throughout the ROM (Fig. 3). Each of the muscles that comprise the quadriceps muscle group, however, have similar muscle fiber lengths, which are comparable to those of the semimembranosus, but shorter than those of the biceps femoris and semitendinosus [11, 20]. This accounts for the much larger relative drop in moment for the quadriceps at higher velocities, as well as the tendency of the quadriceps to show a more parabolic curve over the knee ROM, with a flatter curve for the hamstrings (Fig. 3). This is also reflected in the DCRROM variables (Fig. 2), as well as in previously reported findings in sitting [13].

It is important for clinicians to keep this effect of muscle architecture in mind when interpreting the DCR. These differences make it unrealistic to expect the DCR60, in particular, to be high (approaching or exceeding 1). The range of DCR60 in our study, based on our recommended single-session assessment protocol, was 0.188 to 0.807. As such, clinicians may only want to target an increase in the DCR if this value is felt to be too low.

As with all studies, the interpretation of our data is subject to certain limitations. When assessing the value of the DCR60 or DCR120 to guide training, it is important to recognize that knee angular velocities during activities such as sprinting may far exceed 120 ${}^{\circ}$ /s [23]. Training or rehabilitation goals, therefore, should look beyond any single H/Q ratio. Our participant population was also composed of healthy, mostly physically active individuals in their early-to-mid 20s. This limits the generalizability of our single-session testing recommendation to older or more sedentary populations, or to populations with an existing knee or muscle injury. Given that isokinetic testing for the quadriceps and hamstrings has routinely been shown to produce reproducible data, it is likely that data from a single-session protocol will be equally robust, but further research is necessary to confirm this. Some participants, many of whom had only a 48-hour rest interval between sessions, complained of mild muscle soreness from the first session, persisting to the second session, which may have affected the results collected from these participants. The fact that our data was highly reproducible, however, suggests that this was not a major problem.

5. Practical applications

Our findings indicate that reproducible data for the DCR60 and DCR120 can be acquired in a single testing session with 5 repetitions, excluding the first repetition from the average. While the exact MDC values in our study will likely change for different patient populations, the MDC produced using this protocol were clinically achievable for individuals with a low DCR. It must, however, be kept in mind that joint angular velocity and joint angle both have an impact on the moment at the knee. As such, the DCR alone (based on the PM over the ROM) does not fully capture the functional capacity of these muscles.

Conflict of interest

The authors have no conflicts of interest, financial or otherwise, to report.

Footnotes

Acknowledgments

Funding for the equipment used in this project was received from the Canada Foundation for Innovation.

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Development of a single-session assessment protocol for isokinetic testing of the hamstrings/quadriceps strength ratio