Exploring the Influence of Quadriceps Peak Torque and Rate of Torque Development on Running Mechanics After Anterior Cruciate Ligament Reconstruction

Abstract

Background:

After anterior cruciate ligament reconstruction (ACLR), chronic changes in knee joint biomechanics during higher level tasks, such as running, may negatively impact long-term knee joint health. Among the factors that contribute to these chronic changes, the influence of quadriceps strength on knee joint biomechanics during running is not well understood.

Hypothesis:

Higher involved limb quadriceps strength (peak torque and rate of torque development [RTD]) and limb symmetry index (LSI) will be positively associated with greater peak knee flexion angle and peak knee extensor moment during running.

Study Design:

Cross-sectional study.

Level of Evidence:

Level 3.

Methods:

Peak knee extensor moment and peak knee flexion angle were analyzed during the stance phase of running, 6 months following ACLR (n = 26; 18 female participants; age, 19 ± 5.0 years). Involved limb quadriceps strength and LSI were calculated for peak torque and RTD. Linear regression models were used to analyze the relationship between involved limb and LSI values of quadriceps peak torque and RTD to peak knee flexion angle and peak knee extensor moment.

Results:

Quadriceps peak torque (R² = 0.37; P < .01) and RTD (R² = 0.31, P < .01) each had a positive relationship to peak knee extensor moment, but not peak knee flexion angle. Quadriceps peak torque and RTD LSI were not associated with peak knee flexion angle or peak knee extensor moment (P > .20).

Conclusions:

Quadriceps peak torque and RTD are positively associated with running kinetics 6 months after ACLR. Peak torque and RTD LSI were not associated with running mechanics after ACLR.

Clinical Relevance:

Quadriceps peak torque and rate of torque development are positively associated with running mechanics after ACLR. Clinicians should consider objective assessments of quadriceps strength before initiating running after ACLR.

Returning to running is a pivotal milestone of rehabilitation after anterior cruciate ligament (ACL) reconstruction (ACLR), as it signifies the transition from early, impairment-based rehabilitation to the more sport-specific phases of recovery. ²⁶ Despite its importance, current clinical practice guidelines lack objective criteria for deciding when to initiate running after ACLR, leaving clinicians to rely solely on time from surgery. ³⁰ Previous work has shown knee joint mechanics during running fail to resolve with time alone, with the ACL-involved limb demonstrating up to a 40% reduction in knee extensor moment 2 years after ACLR. ¹⁶ Considering the potential negative long-term implications (eg, post-traumatic osteoarthritis) of altered knee joint mechanics, it is critical to identify modifiable factors contributing to altered knee joint mechanics in this population.^1,2

Quadriceps strength is considered a primary modifiable factor that is severely impacted after ACLR. Deficits in peak torque have been shown to range between 28% and 40% >2 years after surgery, which likely has negative implications for long-term knee joint mechanics.^10,19,24 Quadriceps rate of torque development (RTD)—a measure of how fast torque is produced—has also been shown to be significantly (>50%) impaired 6 months following ACLR. ¹⁵ Knurr et al ¹⁶ explored the influence of quadriceps strength on running mechanics after ACLR (average, 10.1 ± 5.5 months post-ACLR) and found a moderate-to-strong association between RTD and running mechanics. In contrast, Pamukoff et al ²⁵ found only weak correlations between peak torque (r = 0.38) and RTD (r = 0.26) to running mechanics, after ACLR (average, 48 ± 25 months post-ACLR). Direct comparisons between studies are not possible due to differences in strength testing methodology, calculation of knee joint mechanics, and postoperative testing timeframe. More research is needed to elucidate the association of quadriceps peak torque and RTD to knee joint mechanics during earlier postoperative timeframes when rehabilitation is typically being performed.

Quadriceps peak torque limb symmetry (LSI) is the current standard for clinical decision making after ACLR. Previous work provides support for the use of symmetry indices, finding higher quadriceps peak torque and RTD LSI are associated with more symmetrical knee joint mechanics during running. ¹⁶ However, recent work has critiqued the use of LSI citing the potential to overestimate function due to the variable nature of contralateral limb strength. ³² To overcome this challenge, researchers have proposed using mass normalized quadriceps peak torque in place of LSI as this provides greater insight into knee function. ¹⁸ Normalizing peak torque to mass also allows for easier comparison across individual athletes accounting for differences in body size. However, the use of quadriceps peak torque or LSI to guide return to run after ACLR warrants further investigation.

Peak knee flexion angle and peak knee extensor moment are commonly studied gait mechanics as they provide insight into loading strategies during running. For example, knee flexion is essential for shock attenuation from initial contact to the midstance phase of gait. ⁵ Long-term decreased peak knee flexion angle and peak knee extensor moment are thought to change knee joint loading, which may contribute to the development of early post-traumatic osteoarthritis after ACLR.^6,13 Therefore, identifying modifiable factors that are associated with running mechanics is essential to optimize long-term knee joint health after ACLR.

The primary aim of this study was to assess the relationship between quadriceps strength (peak torque and RTD) and running mechanics (peak knee flexion angle and peak knee extensor moment) 6 months after ACLR. We hypothesized that higher involved limb quadriceps strength (peak torque and RTD) and LSI measures of quadriceps strength would be associated with higher peak knee flexion angle and peak knee extensor moment during running. We aimed to evaluate the clinical utility of different quadriceps peak torque and RTD measures and understand how they influence knee joint mechanics during running 6 months after ACLR.

Methods

Study Design

This cross-sectional study is a secondary analysis of data collected previously from an ongoing clinical trial. A total of 26 people (Table 1) participated in this study following a protocol approved by the University of Kentucky Institutional Review Board (IRB no. 43046). No a priori sample size calculation was performed for this analysis, since the dataset was taken from an ongoing clinical trial that was powered for a different primary outcome specific to the trial. Participants were recruited from University of Kentucky Orthopedic Surgery and Sports Medicine between 2018 and 2023, with all testing completed at the University of Kentucky. The participants in this study had been informed of the risks and benefits of the study and provided written informed consent or parental consent and participant assent for participation in the ongoing clinical trial. Inclusion criteria for the clinical trial were 15 to 35 years old with a unilateral ACL tear confirmed by clinical evaluation and diagnostic testing performed by orthopaedic surgeons from the same practice. Participants were excluded if they had a history of ACL injury or reconstruction, previous surgeries or conditions that may affect their gait, if they were skeletally immature, or had a body mass index >35 kg/m². All data in this study were collected at 6 months postoperatively.

Table 1.

Participant demographics (n = 26)

Age, y	19 ± 5.0
Sex	18 female, 8 male
Height, m	1.68 ± 0.1
Weight, kg	72.4 ± 15.8
Graft type	24 BPTB, 2 QT
Meniscal repair, n	21
Gait speed (m/s)	2.5 ± 0.4
Time post-ACLR, days (range) a	197 ± 22.5 (171-294)
Cincinnati Sport Activity Scale b	96.2 ± 6.5

Data are presented as mean ± SD, unless otherwise stated. ACLR, anterior cruciate ligament reconstruction; BPTB, bone-patellar tendon-bone; QT, quadriceps tendon.

^aDays post-ACLR describes time between surgery and 6-month data collection.

^bPreoperative Cincinnati Sports Activity Scale scores are provided.

Isometric Quadriceps Strength

Participants performed isometric contractions seated on an isokinetic dynamometer with the knee at 90 degrees of flexion according to previously published methods. ¹⁶ Participants performed 5 trials of 5-second maximum voluntary isometric contractions (MVIC) with the uninvolved limb tested first. The first trial was used as a familiarization trial done at 50% of the participant’s maximal volitional effort. Loud verbal encouragement to kick “as hard and as fast as you can” was given to ensure maximal effort for each 5-second effort with 30 seconds of rest between trials and 5 minutes of rest between limbs. The torque signal was sampled at 100 Hz and processed using a custom MATLAB code (Mathworks Inc). The signal was filtered using a fourth-order, low-pass, zero-lag Butterworth filter with a 24-Hz cutoff frequency. Previous work has shown no effect of sampling rate down to 100 Hz on the RTD measures calculated in this study.^29,33 Quadriceps peak torque and RTD were averaged from 4 trials at maximal effort and averaged to participant’s body mass. ¹¹ Visual inspection of data was performed to remove any trials that were <90% of the participant’s peak torque among the 4 trials. RTD was calculated from 20% to 80% of the first 200 ms of the contraction with onset defined using an absolute threshold of 5 Nm, which yields similar values to an onset of 1 Nm. ³³ LSI for quadriceps peak torque and RTD were calculated as follows: ([involved limb/uninvolved limb] × 100).

Three-Dimensional Gait Analysis

Participants were prepared for 3-dimensional (3-D) motion analysis using a previously reported marker set using 52 retroreflective markers. ¹⁰ A 5-minute familiarization period was utilized before running at a self-selected pace on an instrumented treadmill (Bertec). To minimize interaction of shoes, participants wore neutral running shoes (New Balance Fresh Foam Zante V4, New Balance Athletic Shoe Inc). Force plate data were collected at 2000 Hz with concurrent marker position collected using a 12-camera motion capture system (Motion Analysis Corp) at a sampling rate of 200 Hz.

Data Analysis

Data processing was performed using Visual 3-D Software (C-motion) and a custom MATLAB (Mathworks Inc) code to filter data, calculate joint angles, and perform inverse dynamics for the hip, knee, and ankle joints. Maker position data and force data were processed using fourth-order, low-pass, zero-lag Butterworth filter with an 8 Hz and 35 Hz cutoff frequency, respectively.^17,21 Joint angles and moments were calculated using Cardan XYZ angles of rotation with distal segments referenced to the proximal model. Peak knee flexion angle and peak knee extensor moment were calculated for the first 75% of stance phase and averaged across 5 strides. ²² All moments described are in reference to internal joint moments and normalized to height × mass.

Statistical Analysis

A series of linear regression models were fit to examine the relationships between quadriceps peak torque and RTD measures, independently, and peak knee flexion and peak knee extensor moment. Model assumptions were assessed using a combination of visual plots and formal testing, and log transformations were used to correct for right skewness, as needed; 95% CIs for the value of R² for each regression model were computed using a bias-corrected Smithson estimator. ¹⁴ Throughout the study, a P value of <.05 was considered statistically significant. All analyses were completed in R Version 4.3.1 (R Foundation for Statistical Computing).

Results

Descriptive Statistics

Participant demographics are listed in Table 1. Descriptive statistics for quadriceps strength (peak torque and RTD) and lower limb biomechanics are referenced in Table 2. Peak torque and RTD were excluded for a participant who had anterior knee pain that limited maximal effort during testing. RTD was excluded for an additional participant where torque onset was above the 5 Nm threshold.

Table 2.

Quadriceps strength and running mechanics

	Involved limb	Uninvolved limb	LSI
Quadriceps peak torque, Nm/kg	1.74 ± 0.63	2.92 ± 0.96	60.2 ± 14%
Quadriceps RTD, Nm/s/kg	4.74 ± 2.70	9.26 ± 4.97	52.6 ± 20%
Peak knee flexion angle, deg	34.35 ± 5.49	44.34 ± 5.41	77.8 ± 11%
Peak knee extensor moment, Nm/kg×m	0.52 ± 0.26	1.09 ± 0.31	46.7 ± 17%

Data are presented as mean ± SD. Quadriceps peak torque and RTD are represented as mass normalized values. Peak knee flexion and peak knee extensor moment were derived from the stance phase of running gait. LSI = (involved limb/uninvolved limb) × 100. ACLR, anterior cruciate ligament reconstruction; LSI, limb symmetry index; RTD, rate of torque development.

Relationship of Quadriceps Peak Torque and RTD to Knee Joint Mechanics

We found that, for each 0.5 Nm/kg increase in quadriceps peak torque, estimated peak knee extensor moment increased by 30% (R² = 0.37; 95% CI [0.13, 0.62]; r = 0.61; P < .01) (Figure 1). In addition, for each 1.0 Nm/s/kg increase in quadriceps RTD, the estimated peak knee extensor moment increased by 12% (R² = 0.31; 95% CI [0.09, 0.58]; r = 0.56; P < .01) (Figure 2). Models were fit for quadriceps peak torque and RTD to peak knee flexion angle. These relationships were not significant for both peak torque (R² = 0.13; 95% CI [0.04, 0.43]; r = 0.36; P = .07) and RTD (R² = 0.13; 95% CI [0.04, 0.42]; r = 0.36; P = .09).

Figure 1.

Relationship between quadriceps PT and peak knee extensor moment during running. Since knee extensor moment was log-transformed for regression analysis, the trendline was back-transformed to the scale of the original data for visual representation. PT, peak torque.

Figure 2.

Relationship between quadriceps RTD and peak knee extensor moment during running. Since knee extensor moment was log transformed for regression analysis, the trendline was back-transformed to the scale of the original data for visual representation. RTD, rate of torque development.

Relationship of Quadriceps Peak Torque and RTD LSI to Knee Joint Mechanics

Models fit using quadriceps peak torque LSI to peak knee flexion angle (R² = 0.006; 95% CI [0, 0.21]; r = 0.08; P = .71) and peak knee extensor moment (R² = 0.06; 95% CI [0, 0.32]; r = 0.24; P = .26) were not significant. Models fit for quadriceps RTD LSI to peak knee flexion angle (R² = 0.01; 95% CI [0, 0.24]; r = 0.11; P = .60) and peak knee extensor moment (R² = 0.07; 95% CI [0,0.35]; r = 0.27; P = .20) were not significant.

Discussion

The primary purpose of this study was to examine the relationship between quadriceps strength (peak torque and RTD) and running mechanics (peak knee extensor moment and peak knee flexion angle) 6 months after ACLR. We found quadriceps peak torque and RTD to have a positive relationship with peak knee extensor moment, but not peak knee flexion angle during running. In addition, we sought to evaluate whether quadriceps peak torque and RTD LSIs could be used in place of normalized values; however, we found no relationship between either LSI metric and running biomechanics. Our findings indicate a positive and stronger relationship between quadriceps peak torque and RTD to running kinetics compared to the relationship observed with LSI measures of quadriceps strength 6 months after ACLR.

In agreement with our primary hypothesis, quadriceps peak torque was associated with peak knee extensor moment during running (Figure 1). For each 0.5 Nm/kg increase in quadriceps peak torque, estimated peak knee extensor moment increased by 30%. These results corroborate findings from multiple studies that have identified a relationship between quadriceps peak torque and peak knee extensor moment during running after ACLR.^4,25 Whereas knee extensor moment is the summation of all forces across the knee joint, our results suggest that quadriceps strength is an important contributor to generating internal knee extensor moment (Figure 1). Our sample had, on average, a 40% deficit in quadriceps peak torque in the ACL involved limb 6 months after surgery. These deficits in quadriceps peak torque are in line with previous findings, which show a protracted recovery of quadriceps strength after ACLR.^27,28 Given the association between quadriceps peak torque and running kinetics, maximizing quadriceps peak torque should be a primary goal 6 months after ACLR.

In contrast to our initial hypothesis, quadriceps peak torque was not associated with peak knee flexion angle during running. Previous work explored the relationship of quadriceps peak torque and peak knee flexion angle approximately 48 months after ACLR and found no relationship between peak torque and peak knee flexion angle. ²⁶ Arhos et al ³ explored a similar relationship in walking finding that when participants had >80% quadriceps peak torque LSI there was no association between quadriceps strength and gait mechanics. However, Lewek et al ¹⁹ also examined groups with asymmetrical (<80%) and symmetrical (>80%) quadriceps peak torque LSI, finding lower knee flexion angles in the asymmetrical group, suggesting a relationship between quadriceps strength and gait mechanics below a certain threshold of strength. These contrasting studies highlight a potential inflection point at which quadriceps strength may no longer influence knee joint kinematics.

In addition to quadriceps peak torque, we also found a significant relationship between quadriceps RTD and peak knee extensor moment during running. For each 1.0 Nm/s/kg increase in quadriceps RTD, the estimated peak knee extensor moment increased by 12%. Our findings add to a limited body of evidence showing that quadriceps RTD is associated with knee joint kinetics after ACLR.^9,25 As the stance phase of running is brief (~150-250 ms), the quadriceps must produce force rapidly to attenuate forces that cross the knee joint. ³¹ Previous work from Kline et al ¹⁵ found both decreased quadriceps RTD and decreased rate of knee extensor moment during running resulting in poor force absorption after ACLR. Similar to quadriceps peak torque, we found no association between quadriceps RTD and peak knee flexion angle. It is possible that our cohort approached a threshold of quadriceps strength at which running kinematics are no longer improved, suggesting alternative interventions may be needed to improve joint kinematics. Our findings highlight the need to maximize quadriceps peak torque and quadriceps RTD to improve running kinetics.

With reference to our secondary aim, there were no significant relationships between quadriceps peak torque LSI or RTD LSI and running mechanics. Although these results were surprising, there are several potential explanations for our findings. One potential explanation is that LSI alone failed to fully explain the magnitude of peak torque and RTD that can be produced by the ACLR limb. High external forces experienced during the stance phase of running gait require a requisite amount of quadriceps strength to successfully attenuate forces. In addition, the uninvolved limb strength can undergo strength changes across the span of ACL rehabilitation, making LSI an unstable indicator of quadriceps recovery.^12,20 Our findings indicate using quadriceps peak torque and RTD LSI may be insufficient to provide information about peak knee flexion angle and peak knee extensor moments during running. These findings contrast with previous work, which may be attributed to differences in study population (D1 athletes vs recreationally active), average running speed (3.9 m/s vs 2.5 m/s) or methodology for RTD testing (rapid contractions vs 5-second MVICs). ¹⁶ It should be noted our study found that 37% and 31% of the variance in running mechanics was explained by quadriceps peak torque and RTD, respectively, indicating that other factors not explored in this study may also influence running mechanics (eg, joint effusion, knee pain, postoperative timeframe, and psychological readiness).

The findings of this study reveal a positive relationship between quadriceps strength (peak torque and RTD) and running kinetics but not kinematics 6 months after ACLR. These findings reinforce the importance of restoring quadriceps peak torque and RTD as they are positively associated with knee joint kinetics during running. We caution clinicians from relying on visual analyses of running mechanics, as the resolution of kinematics does not indicate symmetrical kinetics. Our findings also indicate that quadriceps peak torque and RTD are the preferred metrics to use as they have a significant relationship to running kinetics. Future work may seek to determine the threshold of quadriceps peak torque and RTD needed to run with symmetrical knee joint mechanics after ACLR.

Limitations

This study has significant limitations. The primary graft type used in this study was a bone-patellar tendon-bone autograft, which limits the generalizability of our findings to other graft types; however, this is the most common graft type used for athletes.^7,8 Quadriceps strength testing was performed isometrically at 90 degrees on an isokinetic dynamometer and results cannot be extrapolated to other forms of testing or other angles of measurement. Nonetheless, the increasing availability of handheld dynamometers and load cells have made isometric testing more clinically accessible and reliable against electromechanical dynamometry. ²³ Running mechanics were assessed cross-sectionally 6 months after ACLR, which does not account for changes that occur with continued rehabilitation, additional exposures to running, or incomplete rehabilitation. However, previous work has found that mechanics remain asymmetrical >1 year after ACLR. ¹⁶ The effect of meniscus repair on running mechanics is unable to be determined as a majority of participants underwent concomitant meniscal repair (Table 1).

Clinical Recommendation

The findings of this study suggest that deficits in peak knee extensor moment are related to an inability to generate sufficient force within the time constraints of running after ACLR. Clinicians should maintain emphasis on restoring quadriceps peak torque and RTD even 6 months after ACLR as quadriceps strength is positively associated with running kinetics. We caution clinicians from using quadriceps strength measures interchangeably with LSI measures as their utility may vary based on postoperative timeframe, population of interest, and contralateral limb strength.