Early sub-maximal quadriceps motor unit firing characteristics and six-month knee extensor strength after anterior cruciate ligament reconstruction: a prospective longitudinal study

Abstract

Objectives

To determine whether quadriceps motor unit firing rates measured pre-operatively and during the first three months after anterior cruciate ligament (ACL) reconstruction are associated with isometric knee extensor strength at six months, and to explore the relationship between motor unit action potential (MUAP) amplitude and firing rate.

Methods

Twenty-seven participants (15 female) underwent surface electromyography of vastus medialis and vastus lateralis during sub-maximal isometric knee extension from pre-operation to three months post-reconstruction. Six-month knee extensor MVC force was modelled using Bayesian regression and interpreted using a region of practical equivalence (ROPE; ±15 N). A secondary hierarchical analysis examined MUAP amplitude and firing rate.

Results

Motor unit firing rate was not consistently associated with six-month knee extensor strength across time points and limbs. In the ACL reconstructed limb at two weeks, a 1-SD greater mean firing rate was associated with 45.8 N greater six-month strength (95% credible interval [CrI] − 18.5 to 114.6 N). Six-month strength was greater in the contralateral limb (β = 198.4 N, 95% CrI 171.6 to 225.1 N), in males (β = 184.3 N, 95% CrI 32.0 to 325.1 N), and with greater body mass (β = 119.9 N per 1-SD, 95% CrI 33.4 to 207.2 N). Greater relative MUAP amplitude was associated with lower firing rate (−3.7 Hz per 1-SD, 95% CrI −3.8 to −3.6 Hz).

Conclusions

Sub-maximal quadriceps motor unit firing rate was not consistently associated with later knee extensor strength, although a stronger positive association was suggested in the reconstructed limb at two weeks. Firing rate was strongly related to relative MUAP amplitude, and its predictive value for later strength appears limited.

Introduction

Anterior cruciate ligament (ACL) rupture carries significant time loss burden and is a complex injury to rehabilitate [1]. Following reconstruction, many patients demonstrate chronic weakness of the knee extensor muscle group compared with the contralateral limb and control uninjured limbs [2,3]. These deficits are related to increased reinjury risk and poor long-term outcomes following reconstruction [4,5] including the development of knee osteoarthritis [6]. Weakness often persists despite strength training interventions employed during rehabilitation [2,7]. Although many factors contribute to knee extension weakness following ACL reconstruction, deficits in neural drive to the knee extensor muscle group are common in ACL reconstruction patients [2], limiting motor unit recruitment and discharge during voluntary contraction.

Assessing knee extensor strength and voluntary drive of the quadriceps muscle group is an important indicator of rehabilitation progression following ACL reconstruction. Patients with higher levels of knee extension strength typically have a greater likelihood of returning to competition than those with lower levels of strength [8]. Strength is difficult to assess during the early phase of rehabilitation due to graft healing, swelling, limited range of motion and pain [9]. Consequently, despite the importance of regaining knee extensor strength, it is challenging to assess maximal strength during early rehabilitation. It is likely patients will become weaker post-operation [2,3], altering the relationship between neural drive and voluntary force output. For instance, if an increase in neural drive is required to produce a specific relative level of sub-maximal force (compared with pre-operation), this may suggest inhibition of the knee extensor muscles and possible future weakness. Understanding whether patients are likely to develop weakness later in rehabilitation may be beneficial for clinicians by highlighting a need for interventions targeting strength adaptations, ultimately creating more personalized rehabilitation and potentially improving outcomes for patients.

Voluntary force production is governed by the recruitment and rate coding of motor units, with increases in force achieved through the recruitment of additional motor units and increases in the discharge rates of active motor units [2]. To produce higher levels of voluntary force, participants will increase the number of recruited motor units and/or increase the discharge frequency of motor units [10]. Inhibition is a common consequence of ACL reconstruction and typically occurs due to presynaptic inhibitory mechanisms [11], leading to reduced discharge of quadriceps motoneurons [7]. While assessing maximal knee extensor strength is not possible during early rehabilitation, assessing motor unit characteristics during sub-maximal knee extensor contractions may provide information on the level of neural drive required to produce a specific level of force. If patients exhibit altered motor unit firing patterns during submaximal tasks early after surgery, such patterns may signal ongoing inhibition and an increased likelihood of persistent strength deficits later in rehabilitation. If these patients can be identified early in rehabilitation, clinicians could intervene, reducing the likelihood of future weakness, ultimately reducing injury risk and improving long term patient outcomes. Motor unit discharge rate is also related to characteristics of the recruited motor unit population. In accordance with the size principle, motor units are recruited in an orderly manner according to recruitment threshold, while surface-detected motor unit action potential (MUAP) amplitude provides complementary information about the electrophysiological characteristics of active motor units [12]. However, surface MUAP amplitude is influenced by factors including motor unit depth and volume conduction and should not be considered a direct measure of anatomical motor unit size.

Previous studies have demonstrated altered quadriceps motor unit behaviour following ACL reconstruction, including reduced motor unit firing rates compared with contralateral or uninjured limbs [3,7]. However, these studies have predominantly used cross-sectional designs or assessed participants at later stages of rehabilitation, typically six months or more after reconstruction. Consequently, little is known about motor unit firing behaviour during the early post-operative period or whether early firing characteristics are prospectively associated with subsequent recovery of knee extensor strength. Addressing this gap may help determine whether sub-maximal motor unit assessment provides useful information about later strength recovery when maximal strength testing is difficult to perform.

This exploratory study aimed to determine whether motor unit firing characteristics measured during sub-maximal knee extensor contractions early in rehabilitation are associated with knee extensor strength at six months post-surgery in ACL reconstructed patients. A secondary exploratory analysis examined the relationship between surface MUAP amplitude and motor unit firing rate, and whether this relationship differed between the ACL reconstructed and contralateral limbs.

Methods

Participants

This study was approved by the University of the Sunshine Coast Human Research Ethics Committee (A211684) and conducted in accordance with the Declaration of Helsinki. All participants provided written informed consent before enrolment. Twenty-seven participants were recruited between June 2022 and December 2024 prior to ACL reconstruction. Participant characteristics and graft type are presented in Table 1. All participants underwent ACL reconstruction within one month of the initial injury, and the pre-operative study assessment was conducted one day during the week prior to surgery for all participants.

Table 1.

Participant characteristics.

Characteristic
Participants, n	27
Female, n (%)	15 (55.6)
Male, n (%)	12 (44.4)
Female age, years	22.3 ± 6.8
Male age, years	25.3 ± 5.3
Female body mass, kg	63.6 ± 8.0
Male body mass, kg	82.6 ± 9.4
Hamstring autograft, n (%)	23 (85)
Bone-patellar tendon-bone autograft, n (%)	4 (15)

Note. Values are mean ± SD unless otherwise stated.

Surgical readiness was determined by the treating orthopaedic surgeon and required full active and passive knee extension, >120° knee flexion, and no or minimal knee oedema on clinical assessment. All participants underwent post-operative rehabilitation under the care of physiotherapists from one of two local physiotherapy clinics. Rehabilitation was not standardized as part of the study protocol; exercise selection, progression, and return-to-activity decisions were determined by the treating physiotherapist according to usual clinical practice. Participants were assessed pre-operatively and followed until six months after ACL reconstruction. Across follow-up assessments, three assessments were missed at two weeks, three at six weeks, and four at three months.

To be included in the study, participants had to have had a unilateral ACL injury, be at least 14 years old, and train for their specific sport at least twice per week for at least one hour. Revision or bilateral ACL reconstructions or other significant lower limb injuries were excluded from the study. This study followed STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) reporting guidelines for cohort studies [13].

Experimental design

This was an observational, prospective longitudinal study with repeated measures at five time points (level of evidence, 2). The study was not pre-registered. Participants were tested pre-operatively, as well as 2-weeks, 6-weeks, 3-months, and 6-months post-operatively. The reconstructed and contralateral limb were tested at each time point. During pre-operative and six-month post-operative testing sessions participants undertook knee extensor MVCs, followed by contractions at 75%, 50% and 20% MVC, in that order. At two weeks post-surgery, participants performed knee extensor contractions at 20% MVC in both limbs. At six weeks post-surgery, participants performed knee extensor contractions at 20% and 50% MVC in both limbs. At three months post-surgery, participants performed knee extensor contractions at 20%, 50%, and 75% MVC in both limbs. During these testing sessions, the pre-operative MVC was used to determine the absolute force level corresponding to the desired sub-maximal contraction intensity, considering the implausibility of MVCs in ACL reconstructed limbs until more than three months post operation.

Instrumentation and participant positioning

Force was measured using a custom-built testing system incorporating an MT501 Universal S-type load cell (Meltrons, Australia). The same load-cell model has previously demonstrated valid and reliable measurement of peak isometric force compared with force-plate assessment during lower-limb strength testing [14]. The load-cell signal was amplified and digitised using an HX711 24-bit load-cell amplifier and analogue-to-digital converter connected to an Arduino Mega 2560 microcontroller. Data were transmitted from the microcontroller to Microsoft Excel using the Data Streamer add-in and recorded for subsequent analysis. The load cell was calibrated using known hanging masses of 5, 10, and 20 kg prior to use. Trigno Galileo surface EMG sensor arrays (Delsys, Natick, MA, USA; sensor head dimensions 23 × 30 × 7 mm) were placed over the vastus medialis and vastus lateralis muscles. Each sensor contained four 2.5-mm-diameter silver contacts arranged in a diamond configuration with a 5-mm inter-electrode distance. Prior to electrode placement, skin was shaved, abraded, and cleansed with an alcohol swab. Electrodes were placed on the most prominent portion of each muscle belly according to SENIAM guidelines [15].

For all contractions, participants were seated on a plinth, with the knee fixed at 65° of knee flexion (0° representing full extension) and the hip fixed at 90° of flexion (see Figure 1). A rigid strap, with custom load cell apparatus attached in series, was fixed to the ankle around the malleoli. Participants were instructed to sit upright, keep the trunk in contact with the support surface, avoid using the upper limbs or contralateral limb to assist, and grip the sides of the plinth during contractions. No additional trunk or pelvic strapping was used. Knee angle was verified using a digital goniometer. Limb-testing order was randomised at each assessment.

Figure 1.

Experimental setup for isometric knee extensor strength testing. (A) Schematic representation of participant positioning during testing. Participants were seated upright on a clinical plinth with the hip flexed to 90° and the tested knee flexed to 65°, with the hands gripping the sides of the plinth; no additional trunk or pelvic strapping was used. (B) Close-up of the distal setup showing the rigid ankle strap, load cell, and attachment to the plinth.

Maximal voluntary contraction and knee extensor force assessment

Before maximal voluntary contraction (MVC) testing, participants completed six isometric knee extension warm-up contractions of 3–5 s duration, progressing from approximately 50–90% of perceived MVC. Warm-up contractions prior to MVCs were separate to familiarization with trapezoidal contractions. Participants then performed two 5-s isometric knee extension MVCs separated by 30 s while receiving visual feedback. If peak force differed by more than 10% between trials, a third MVC was performed and the two highest-force trials were retained. Peak MVC force was determined using a 100 ms window centred on the peak of each force trace, and the two retained MVC values were averaged. MVC testing was undertaken as described in the Experimental Design section.

Submaximal knee extensor contractions

Before recorded submaximal trials, participants were familiarised with the force-matching task using the same visual feedback and trapezoidal contraction format as the recorded trials. Practice continued until participants could consistently reach and maintain the prescribed force target, which typically occurred within two contractions. These familiarisation trials were not included in the analysis. Submaximal contractions followed a trapezoidal template consisting of a 3-s ramp-up, a 10-s steady force phase, and a 3-s ramp-down. Two contractions were performed at each prescribed intensity, separated by one minute. Contractions were repeated when participants were unable to maintain force within 5% of the target. Submaximal intensities and their timing across assessments are described in the Experimental Design section.

EMG acquisition and motor unit decomposition

EMG signals were sampled at 2000 Hz, band-pass filtered between 20 and 450 Hz, and notch filtered at 50 Hz prior to decomposition. Signals were decomposed into motor unit spike trains using NeuroMap software (v1.2.2; Delsys Inc., Natick, MA, USA). Motor unit action potential templates and associated firing patterns were visually inspected following decomposition. Motor units were excluded when firing events occurred outside the identified active contraction period or when only sporadic, isolated firings were present rather than a sustained motor unit discharge train. Decomposition quality was further assessed using the decompose-synthesise-decompose-compare procedure, and only motor units with ≥90% decomposition accuracy were retained. No predetermined minimum or maximum number of motor units was imposed; all motor units satisfying these criteria were retained for analysis.

To identify the steady force phase firing period, firings from all retained motor units within each contraction bout were pooled to provide a single temporal representation of motor unit activity. The expected 16 s contraction template used during testing, comprising a three second ramp-up, ten second steady force phase, and three second ramp-down, was then positioned over the period of pooled motor unit firing activity. The pooled firing pattern corresponded well with the expected 16s contraction window, and the middle ten seconds interval was defined as the steady force phase firing window and used to calculate motor unit firing rate. This procedure was applied consistently across contraction bouts and reliably identified the sustained period of pooled motor unit activity. Force and array EMG data were recorded using separate acquisition systems without a common hardware trigger or shared timestamp. Consequently, the selected ten second interval represents a systematically identified steady contraction window aligned with the expected contraction template. Precise motor unit recruitment time and recruitment force threshold therefore could not be determined and were not analysed.

For the secondary exploratory analysis, the motor unit action potential waveform associated with each retained motor unit was extracted from the NeuroMap output and paired with the corresponding motor unit firing train using the original Delsys motor unit identifier. Peak-to-peak MUAP amplitude was calculated for each of the four recorded MUAP waveforms and averaged to provide a mean peak-to-peak amplitude for each motor unit. Because absolute surface MUAP amplitude may vary between recordings due to factors including electrode position, motor unit depth and volume conduction [12], MUAP amplitude was not interpreted as a direct measure of anatomical motor unit size. Instead, amplitude was natural-log transformed and standardized within each contraction. Motor units were included in the inferential analysis when a calculable steady force phase firing rate and valid positive MUAP amplitude were available.

Sample size estimation and justification

The sample size was determined pragmatically, based on the number of participants undergoing ACL reconstruction through a local clinic during the recruitment period. As such, no formal sample size calculation was undertaken. The study was exploratory in nature and was intended to estimate the magnitude and uncertainty of associations between early motor unit firing characteristics and six-month knee extensor strength rather than to test a single prespecified effect. Although repeated assessments provided multiple observations per participant, the number of independent participants remained modest, and data availability was reduced for some time points and contraction intensities. Consequently, the study may have had limited precision for estimating small associations and interaction effects, particularly at the higher contraction intensities. The Bayesian modelling approach allowed this uncertainty to be quantified directly through posterior distributions and credible intervals, however, it does not overcome the limitations associated with a modest sample size. Findings should therefore be interpreted as exploratory and hypothesis generating. Larger prospective cohorts are required to provide more precise estimates and confirm the observed associations.

Data analysis

The primary outcome variable was isometric knee extensor strength at 6-months post-surgery. Bayesian linear regression with a Gaussian likelihood was used to model the primary outcome. Only motor unit observations obtained during submaximal contractions at 20%, 50%, and 75% MVC were included in the primary prospective analysis; observations obtained during MVC trials were excluded. The model was implemented using the R package brms [16], and included limb (levels: ACL reconstructed or contralateral), sex (levels: male or female), body mass, muscle (levels: vastus medialis, vastus lateralis), contraction intensity (levels: 20%, 50%, or 75% MVC), standardized mean motor unit firing rate, time (levels: pre-surgery, two weeks post-surgery, six weeks post-surgery, or three months post-surgery), and all possible interactions between limb, motor unit firing rate, and time as fixed effects. We also included a random intercept term for participant ID, to account for the correlation between repeated observations on an individual. Body mass was standardized and included as a covariate to account for differences in body size when modelling absolute knee extensor force. Sex was also included as a covariate when estimating the association between early motor unit firing rate and six-month knee extensor strength to account for anthropometric differences between males and females. We used the default brms Student-t prior for the intercept (3, 78.4, 39.3), coefficients were assigned normal priors (0, 10) and the standard deviation of the subject-specific random intercept and the residual standard deviation were assigned half Student-t priors (3, 0, 39.3). Force values in the modelling dataset were recorded in kilograms and the model was fitted on this scale. Posterior coefficient estimates and credible intervals were converted to Newtons for reporting. Accordingly, the ±15 N ROPE corresponded to ±1.53 kg when calculating posterior ROPE probabilities.

Posterior estimates of expected variable values were generated using Hamiltonian Monte Carlo simulations (four chains, 4,000 iterations per chain, 2,000 warm-up). Chain convergence was assessed using R-hat diagnostics from the model summaries, and model fit was assessed using posterior predictive checks. Posterior distributions were summarised as the mean and 95% credible interval (CrI). We also computed the posterior probability that regression coefficients were greater than zero (Pr β > 0) [17,18]. To aid interpretation, we defined a region of practical equivalence (ROPE) around zero. The numerical limits of the ROPE were not derived from the Bayesian model. We calculated the posterior probability that effects were greater than the upper ROPE boundary (Pr β > ROPE) or less than the lower ROPE boundary (Pr β < -ROPE), depending on the direction of the effect. In the absence of a published clinically meaningful change for knee extension strength measured with our custom load-cell apparatus, we defined the ROPE using published measurement error for knee extensor strength after ACL reconstruction of 15 N [19]. This threshold was specified post hoc and was used as a pragmatic benchmark for distinguishing effects from the magnitude of expected measurement error.

The association between relative MUAP amplitude and motor unit firing rate was examined using an additional Bayesian hierarchical model. Steady force phase motor unit firing rate was the outcome and within-contraction standardized log-transformed MUAP amplitude was the primary predictor, with contraction intensity, muscle, limb and time point included as covariates. Random intercepts were included for participant, original motor unit within recording, and contraction to account for the hierarchical and repeated structure of the data. A secondary model included an interaction between MUAP amplitude and limb to determine whether the MUAP-firing rate relationship differed between the ACL reconstructed and contralateral limbs. Sensitivity analyses were performed after restricting observations to motor units with at least five steady force phase firings, applying progressively stricter quality control criteria, and using mean instantaneous firing rate as an alternative outcome.

Missing observations were assumed to be missing at random, with values imputed using classification and regression tree (CART) models across five imputed datasets [20]; the six-month outcome was not imputed. All analyses were conducted in R (version 4.4.1). The analysis code and data are publicly available [21].

Results

Relationship between firing rate and knee extensor force

All 27 participants completed the pre-operative assessment. Follow-up assessments were completed by 24 participants at two weeks, 24 at six weeks, 23 at three months, and 22 at six months post-surgery. Participants who missed an assessment could contribute data at other time points; missing observations were addressed using the multiple imputation procedure described in the Methods. Pre-operatively, absolute knee extensor MVC force was 522 ± 231 N in the ACL injured limb and 762 ± 277 N in the contralateral limb. At six months post-surgery, MVC force was 672 ± 287 N in the ACL reconstructed limb and 875 ± 331 N in the contralateral limb. Descriptive motor unit characteristics across assessment time points, contraction intensities, limbs, and muscles, including the number of retained motor units and the mean and variability of steady force phase firing rates, are presented in supplementary material (see Supplementary Table 1).

Posterior estimates of the fixed-effect model coefficients are presented in Figure 2, with complete numerical posterior summaries provided in Supplementary Table 2. Motor unit firing rate was not consistently associated with six-month knee extensor strength across assessment time points and limbs. At the pre-operative assessment, there was no clear association between mean motor unit firing rate in the ACL injured limb and six-month knee extensor strength (β = −3.3 N per 1SD greater firing rate, 95% CrI −26.5 to 19.9 N), with 77.8% of the posterior distribution falling within the ±15 N ROPE.

Figure 2.

Posterior estimates of model coefficients for six-month knee extensor force. Points represent posterior mean effects, with horizontal bars indicating 95% credible intervals (CrI). The dotted vertical line denotes the null effect, and the shaded region represents the region of practical equivalence (ROPE).

Conditional firing rate associations differed across assessment time points and limbs (Figure 3). In the ACL reconstructed limb at two weeks post-surgery, a one standard deviation greater mean firing rate was associated with an estimated 45.8 N greater six-month knee extensor strength (95% CrI −18.5 to 114.6 N). Although the credible interval included zero, 91.8% of the posterior distribution was above zero and 82.2% was above the +15 N ROPE boundary. Associations in the ACL reconstructed limb were less pronounced at six weeks (β = 9.4 N, 95% CrI −29.9 to 48.7 N) and three months (β = −5.1 N, 95% CrI −30.2 to 20.6 N).

Figure 3.

Conditional effects of mean motor unit firing rate on knee extension strength across time and limb. Solid lines show posterior mean model predictions for knee extension strength (N) across the observed range of mean firing rate (Hz), plotted separately for the reconstructed (ACL) and contralateral (Opp) limbs and faceted by rehabilitation time point (pre-surgery, 2-weeks post-surgery, 6-weeks post-surgery, 3-months post-surgery). Shaded ribbons indicate 95% credible intervals.

In the contralateral limb, the estimated firing rate associations were 18.1 N pre-operatively (95% CrI −4.9 to 41.4 N), −10.1 N at two weeks (95% CrI −71.5 to 46.4 N), 18.2 N at six weeks (95% CrI −7.6 to 45.5 N), and 23.3 N at three months (95% CrI 5.0 to 42.1 N). The three-month contralateral-limb association had 99.4% posterior probability of being greater than zero and 80.9% probability of exceeding the +15 N ROPE boundary.

At six months post-surgery, knee extensor strength was greater in the contralateral than ACL reconstructed limb (β = 198.4 N, 95% CrI 171.6 to 225.1 N), with 100% of the posterior distribution above the +15 N ROPE boundary. Males had greater knee extensor strength than females (β = 184.3 N, 95% CrI 32.0 to 325.1 N), and greater standardized body mass was associated with greater knee extensor strength (β = 119.9 N, 95% CrI 33.4 to 207.2 N). The posterior probabilities that the sex and body-mass effects fell outside the ±15 N ROPE were 99.1% and 99.2%, respectively. There was no clear evidence of a muscle effect (vastus medialis versus vastus lateralis: β = 1.0 N, 95% CrI −15.0 to 17.1 N) or of effects associated with contraction intensity relative to 20% MVC (50% MVC: β = −5.8 N, 95% CrI −26.2 to 14.6 N; 75% MVC: β = −11.3 N, 95% CrI −37.2 to 14.6 N).

Relationship between MUAP amplitude and motor unit firing rate

An additional analysis examined the association between surface-detected MUAP amplitude and motor unit firing rate. Log-transformed peak-to-peak MUAP amplitude was standardized within each contraction, and Bayesian hierarchical models accounted for clustering by participant, original motor unit and contraction. The analysis included 4,241 motor unit observations from 3,806 unique motor units across 510 contractions in 25 participants. Across limbs, greater relative MUAP amplitude was associated with lower firing rate, with a 1-SD greater within-contraction log-transformed MUAP amplitude corresponding to a − 3.7 Hz difference in firing rate (95% CrI −3.8 to −3.6 Hz). This association was consistent in sensitivity analyses restricted to motor units with ≥5 steady force phase firings (−3.7 Hz; 95% CrI −3.8 to −3.7 Hz), stricter quality-control datasets, and when mean instantaneous firing rate was used as the outcome (−3.8 Hz; 95% CrI −3.9 to −3.7 Hz).

The relationship between MUAP amplitude and firing rate also differed between limbs. An inverse association was observed in both the contralateral and ACL limbs; however, it was less pronounced in the ACL limb. The estimated slope was −3.9 Hz per 1-SD greater log-transformed MUAP amplitude in the contralateral limb (95% CrI −4.0 to −3.8 Hz) compared with −3.5 Hz in the ACL limb (95% CrI −3.6 to −3.4 Hz). The ACL-versus-contralateral difference in slope was +0.5 Hz (95% CrI +0.3 to +0.6 Hz) (Figure 4).

Figure 4.

Relationship between motor unit action potential (MUAP) amplitude and steady force phase motor unit firing rate in the contralateral (A) and ACL reconstructed (B) limbs. Transparent points represent individual motor unit observations. MUAP amplitude was log-transformed and standardized within each contraction bout prior to analysis. Solid black lines represent the posterior mean relationship estimated from the Bayesian hierarchical limb-modifier model, which adjusted for contraction intensity, muscle and time point and included random intercepts for participant, original motor unit and contraction bout. Greater relative MUAP amplitude was associated with lower steady force phase firing rate in both limbs, with the inverse association modestly attenuated in the ACL reconstructed limb.

Discussion

The primary aim was to explore whether vastii motor unit firing rates measured at different time points during rehabilitation were associated with isometric knee extensor strength at six months after ACL reconstruction. Motor unit firing rate was not consistently associated with six-month knee extensor strength across assessment time points and limbs. However, posterior estimates suggested a stronger positive association in the ACL reconstructed limb at two weeks post-surgery, although the 95% credible interval included zero. A positive association was also observed in the contralateral limb at three months. In contrast, the clearest associations with six-month knee extensor strength were contralateral limb, male sex, and greater body mass, with 100%, 99.1%, and 99.2% of their respective posterior distributions falling outside the ROPE.

Previous research has examined changes in vastii motor unit firing rates before and after ACL reconstruction [3,7]. Firing rates at different time points during the six-months immediately following reconstruction, and their relationship to strength later in rehabilitation have not been reported. Lower motor unit firing rates have been reported in the vastus lateralis of ACL reconstructed limbs compared with controls at six- and twelve-months post-surgery [7]. Similarly, lower vastus medialis motor unit firing rates at a given level of normalised force are reported in ACL reconstructed limbs (limbs, at least six months post-surgery) compared with controls [3]. While these studies provide important insights into mechanisms contributing to lower voluntary force production in ACL reconstructed limbs, participants were typically assessed at least six months post-surgery. Collectively, their findings suggest altered motor unit discharge behaviour, including slower firing rates and a greater contribution from lower-threshold motor units. Importantly, this is the first study to quantify vastii motor unit firing during early rehabilitation and prospectively examine relationship between these firing rates with six-month knee extensor strength.

An additional analysis demonstrated a strong inverse association between relative surface MUAP amplitude and motor unit firing rate. Within the same contraction, a 1-SD greater log-transformed MUAP amplitude was associated with an approximately 3.7 Hz lower firing rate. This relationship was evident in both limbs but was modestly attenuated in the ACL reconstructed limb, with estimated slopes of −3.9 Hz in the contralateral limb and −3.5 Hz in the ACL limb (between-limb difference 0.5 Hz; 95% CrI 0.3 to 0.6 Hz). These findings indicate that motor unit discharge rate is related to the electrophysiological characteristics of the active motor unit population and that this relationship differs following ACL reconstruction. However, surface MUAP amplitude is influenced by factors including motor unit depth, volume conduction, fibre orientation and electrode position and should not be interpreted as a direct measure of anatomical motor unit size. Accordingly, these findings support interpreting firing rate as one component of motor unit control rather than as a direct measure of recruitment or the Henneman size principle.

Voluntary force production is influenced by both motor unit recruitment and rate coding; however, the present study specifically quantified the discharge rates of motor units active during the steady force portion of submaximal contractions. These firing rate measures therefore characterise motor unit discharge behaviour during the steady force phase period and should not be interpreted as direct measures of motor unit recruitment. Using motor unit behaviour to gain insight into future strength may assist in improving rehabilitation outcomes. However, in the current study, associations between sub-maximal motor unit firing rate and six-month knee extensor strength were variable across assessment time points and limbs. The strongest prospective pattern was observed in the ACL reconstructed limb at two weeks post-surgery, where higher firing rate was associated with greater six-month strength, although uncertainty remained because the 95% credible interval included zero. This contrasts with prior ACL reconstruction studies, which are largely cross-sectional and focus on between-limb comparisons or differences between ACL reconstructed and uninjured limbs [2]. These studies do not directly test whether early firing behaviour provides clinically useful prospective information about knee extensor strength.

Descriptive firing rate data provide useful context for the strength findings (see Supplementary Table 1). In the ACL reconstructed limb, firing rates at 20% MVC generally increased across rehabilitation, although the pattern was not consistent and differed between vastus medialis and vastus lateralis. At 50% MVC, firing rates were numerically lower in the reconstructed limb than the contralateral limb at six weeks, but were more similar by three and six months. At 75% MVC, reconstructed limb firing rates were generally lower than the contralateral limb pre-operatively and at three months, but were similar between limbs by six months. Thus, the lower six-month MVC force in the reconstructed limb occurred despite firing rates that were, by that stage, broadly similar to the contralateral limb at several submaximal intensities. This suggests that persistent strength deficits at six months cannot be explained by firing rate alone and may reflect other factors, including motor unit recruitment, voluntary activation, muscle morphology, and mechanical factors.

Mechanistically, early neural changes may still be important for restoring voluntary activation and generating sufficient tension in skeletal muscle to support later morphological adaptation [22], but our findings suggest that motor unit firing rate during early sub-maximal tasks is unlikely to be a strong predictor of six-month strength. Alternatively, because early post-operative sub-maximal targets were based on the pre-operative MVC, the same absolute force may have represented a higher relative intensity after surgery. Early post-operative weakness, pain, effusion, and arthrogenic muscle inhibition could therefore mean that a target of 20% pre-operative MVC required a greater proportion of the participant’s available strength. This may have influenced motor unit firing behaviour and contributed to the observed associations. Because MVC was not reassessed at the early post-operative time points, this effect could not be quantified.

Some studies report muscle specific differences following ACL reconstruction. We found no clear evidence of a muscle effect on six-month knee extensor strength, with the model coefficient for vastus medialis compared with vastus lateralis close to zero (β = 1.0 N, 95% CrI −15.0 to 17.1 N). Schilaty et al. (2023) observed lower motor unit firing rates in the vastus lateralis motor units at six and twelve months in ACL reconstructed patients. They also reported an increase in vastus medialis motor unit firing rate of ACL reconstructed limbs compared to controls at six months post-surgery. Both vastii muscles receive common and unique supraspinal inputs and the inputs activated during contraction of these muscles are task and contraction mode specific [7]. This variance in input to the vastii muscles may explain the slight differences in muscle specific observations between studies.

At six months post-surgery, knee extensor strength was greater in males than females, greater in the contralateral than reconstructed limb, and positively associated with body mass. These findings are consistent with prior research showing that women tend to exhibit larger and more persistent quadriceps strength deficits after ACL reconstruction [23]. Sex-based differences in motor unit firing may play a role in recovery from ACL reconstruction. Females typically demonstrate slightly higher motor unit firing rates for a given level of voluntary force across multiple muscles, including the vastus medialis [24]. Further work should aim to understand the interaction between motor unit firing in females and its relationship with strength restoration following ACL reconstruction, in order to optimise outcomes for female patients. Additionally, given the consistent observation of increased strength of the contralateral limb, future work should focus on interventions that reduce between limb strength asymmetry without compromising performance of the uninjured limb.

Several limitations should be acknowledged. The study results are specific to participants in the study and may not generalise. The ROPE was defined post-hoc. Ideally, the ROPE should have been pre-specified and the study pre-registered. Second, contractions at 20% MVC were collected at all four follow-up time points, whereas 50% and 75% MVC were collected at fewer time points. As a result, estimates at the higher intensities were based on fewer observations and were therefore less precise. Participants may also develop knee extensor weakness post-surgery, meaning sub-maximal contractions based on pre-surgery MVCs may not reflect the intended contraction intensity. Pre-surgery MVC was typically assessed within the week prior to ACL reconstruction, meaning only three weeks spanned pre-surgery and the first post-surgery assessment. Under normal circumstances, it is unlikely MVC changes substantially in this time frame. When assessing MVCs, although participants were instructed to avoid compensatory movements, the trunk and pelvis were not secured with additional straps during testing. This may have allowed some contribution from trunk or upper-limb movements and introduced variability in measured knee extensor force. Rehabilitation was also not standardized across participants. Although all participants received physiotherapy from one of two physiotherapy clinics, differences in exercise selection and progression may have influenced recovery of strength and motor unit firing characteristics.

Conclusion

This study suggests that submaximal vastii motor unit firing rate is not consistently associated with six-month knee extensor strength after ACL reconstruction, although posterior estimates suggested a stronger positive association in the ACL reconstructed limb at two weeks post-surgery. Contralateral limb strength, male sex, and greater body mass showed the clearest associations with six-month strength. Motor unit firing rate was strongly related to relative surface MUAP amplitude, with this relationship modestly attenuated in the ACL reconstructed compared with the contralateral limb. Submaximal motor unit firing may therefore provide some information about later strength during early rehabilitation, but its prognostic value appears limited.

Funding Statement

This study received in-kind support from Delsys Inc., which provided equipment for the study. Delsys Inc. had no role in the design of the study, collection, analysis or interpretation of data, writing of the manuscript, or the decision to submit the manuscript for publication.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data and analysis code supporting the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.22255496. Additional information regarding the data and materials is available from the corresponding author on reasonable request.