Moment arm and torque generating capacity of semitendinosus following tendon harvesting for anterior cruciate ligament reconstruction: A simulation study

Altered semitendinosus (ST) morphology and distal tendon insertion following anterior cruciate ligament reconstruction (ACLR) may reduce knee flexion torque generating capacity of the hamstrings via impaired ST force generation and/or moment arm. This study used a computational musculoskeletal model to simulate mechanical consequences of tendon harvest for ACLR on ST function by modeling changes in ST muscle tendon insertion point, moment arm, and torque generating capacity across a physiological range of motion. Simulated ST function was then compared between ACLR and uninjured contralateral limbs. Magnetic resonance imaging from 18 individuals with unilateral history of ACLR involving a hamstring autograft was used to analyse bilateral hamstring muscle (ST, semimembranosus, bicep femoris long head and short head) morphology and distal ST tendon insertion. The ACLR cohort was sub‐grouped into those with and without ST regeneration. For each participant with ST regeneration (n = 7), a personalized musculoskeletal model was created including postoperative remodeling of ST using OpenSim 4.1. Knee flexion and internal rotation moment arms and torque generating capacities of hamstrings were evaluated. Bilateral differences were calculated with an asymmetry index (%) ([unaffected limb–affected limb]/[unaffected limb + affected limb]*100%). Smaller moment arms or knee torques within injured compared to uninjured contralateral limbs were considered a deficit. Compared to uninjured contralateral limbs, ACLR limbs with tendon regeneration (n = 7) had minor reductions in knee flexion (5.80% [95% confidence interval (CI) = 3.97–7.62]) and internal rotation (4.92% [95% CI = 2.77–7.07]) moment arms. Decoupled from muscle morphology, altered ST moment arms in ACLR limbs with tendon regeneration resulted in negligible deficits in knee flexion (1.20% [95% CI = 0.34–2.06]) and internal rotation (0.24% [95% CI = 0.22–0.26]) torque generating capacity compared to uninjured contralateral limbs. Coupled with muscle morphology, ACLR limbs with tendon regeneration had substantial deficits in knee flexion (19.32% [95% CI = 18.35–20.28]) and internal rotation (15.49% [95% CI = 14.56–16.41]) torques compared to uninjured contralateral limbs. Personalized musculoskeletal models with measures of ST distal insertion and muscle morphology provided unique insights into post‐ACLR ST and hamstring function. Deficits in knee flexor and internal rotation moment arms and torque generating capacities were evident in those with ACLR even when tendon regeneration occurred. Future studies may wish to implement this framework in personalized musculoskeletal models following ACLR to better understand individual muscle function for injury prevention and treatment evaluation.

generating capacity compared to uninjured contralateral limbs.Coupled with muscle morphology, ACLR limbs with tendon regeneration had substantial deficits in knee flexion (19.32% [95% CI = 18.35-20.28])and internal rotation (15.49% [95% CI = 14.56-16.41])torques compared to uninjured contralateral limbs.Personalized musculoskeletal models with measures of ST distal insertion and muscle morphology provided unique insights into post-ACLR ST and hamstring function.Deficits in knee flexor and internal rotation moment arms and torque generating capacities were evident in those with ACLR even when tendon regeneration occurred.Future studies may wish to implement this framework in personalized musculoskeletal models following ACLR to better understand individual muscle function for injury prevention and treatment evaluation.

| INTRODUCTION
The anterior cruciate ligament (ACL) is the most frequently injured ligament of the knee, with an estimated 400,000 ACL reconstructions (ACLR) performed each year worldwide. 1In Australia, ~90% of ACLRs use a semitendinosus (ST) tendon autograft because of the mechanical strength of the graft, ease of surgical access, and perceived minimal donor site morbidity. 2,3Following harvesting for graft, ST may undergo a regenerative process known as the lizard tail phenomenon, re-attaching neo-tendon to the proximomedial tibia below the knee joint line. 4wever, ~30% of ACLR patients experience no regeneration of harvested ST tendon. 5Most individuals return to physical activity after ACLR 6 but with long-term deficits in knee flexor and internal rotator strength, 7,8 presumably due to postoperative morbidity of harvested muscle. 7These strength deficits following ACLR may contribute to the well-documented elevated risk of secondary ACL rupture, [9][10][11] primary hamstring strain injury, 12,13 and early onset knee osteoarthritis. 14,15derstanding the mechanical consequences of donor tendon regeneration in combination with postoperative muscle morphology is clinically important as it may influence graft choice and surgical and postoperative rehabilitation protocols.
7][18] Following tendon harvesting for ACLR, ST experiences atrophy, 7,8 retraction, 19 shape change, 20 fatty infiltration, 21 and impaired activation. 22Compared to uninjured contralateral limbs, regenerated ST tendons have been reported to insert more proximally and medially on the tibia following ACLR, or within the popliteal fascia. 5Altered ST morphology and distal tendon insertion following ACLR may impair torque generating capacity of the hamstrings through altered muscle force-generating capacity, moment-arm, or both. 23In addition to ST atrophy/retraction, potential compensatory hypertrophic changes in other synergistic hamstring muscles are possible, 7,24 which may mitigate reductions in knee flexion torque generating capacity.
Experimentally, it is challenging to isolate causal effects of muscletendon morphology on ST and hamstring function.Computational modeling enables interrogation of the effects of morphologic alteration of ST on postoperative ST and hamstring muscle function following ACLR. 25,26Recently, patient-specific data from magnetic resonance imaging (MRI) and other imaging modalities have been used to personalize computational models to individual patients, and thus probe specific clinical features of internal muscle morphology and tendon alignment on mechanical function. 27To date, no study has evaluated the mechanical consequences of post-ACLR ST morbidity (atrophy, retraction, and distal tendon migration) on knee function.
The primary aim of this study was to use a personalized musculoskeletal (MSK) model which included ST morbidity following ACLR, to simulate ST moment arm and torque generating capacity across a range of hip and knee motions, and to compare with the uninjured contralateral limb.Our secondary aim was to compare torque generating capacity of the hamstring muscle group [ST, semimembranosus (SM), and the two heads of biceps femoris (BFlh, BFsh)] between ACLR and uninjured contralateral limbs.We hypothesized ST moment arm and torque generating capacity would be lower in ACLR compared to uninjured contralateral limbs across a physiological range of hip and knee motions.Furthermore, within the ACLR limb, torque generating capacity of hamstrings will be lower than the uninjured contralateral limb, with greatest deficits at high degrees of knee flexion.

| Participants
This level 3 cross-sectional study involved an analysis of legacy data from Griffith University of individuals with a history of ACLR (n = 18). 7Inclusion criteria were: (1) an isolated ACL rupture sustained without any other concomitant knee ligament injury, (2) an ACLR with the use of a quadrupled autologous ST-GR tendon graft within DU MOULIN ET AL.
| 1429 the previous 2-4 years, (3) aged between 18 and 45 years, and (4) ability to comply with testing protocol.Exclusion criteria were (1) any contraindications to magnetic resonance imaging (MRI), (2) complex knee injuries with additional ligament surgery or meniscal injury, and (3) previous ACL or lower extremity surgery.Ethics approval was obtained through Griffith University Research Ethics committee (#PES/36/10/HREC), with all participants providing their written informed consent before any testing.

| Magnetic resonance imaging
A 3T MRI unit (Philips Medical Systems) was used to acquire images of both lower limbs from all participants.Participants lay supine on the unit gantry, and continuous images were acquired from top of the iliac crests to ankle mortises.Axial T 1 -weighted three-dimensional fast field echo sequences were performed with 2.4 mm slice thickness and 0.5 mm interslice gap.Voxel size was 1.2 × 1.3 × 1.2 mm and field of view was 300 × 452 mm.

| Magnetic resonance image processing
All MRI data were processed and analysed using the Materialize Interactive Medical Image Control System software (Mimics, Materialize, v21).Within each axial slice of the fast field echo images, outer boundaries of muscles and tendons were visualized and traced as separate objects.These traced boundaries were then used to create a three-dimensional mesh model of hamstrings and distal ST tendon within Mimics (Figure 1).A wrapping factor was applied to each mesh model with 1.3 mm gap closing distance and 0.82 mm smallest detail, followed by 0.4 smoothing factor.Excellent inter-and intra-rater reliability for measured muscle volumes were achieved. 28From the resulting meshes, muscle volume and distal ST insertion point on the tibia were calculated.

| Distal semitendinosus muscle insertion
Distal ST tendon regeneration was defined as "complete" when neotendon was visible below the distal muscle-tendon junction and segmented to the approximate level of pes anserinus below the tibial plateau.Based on this definition, the participants were sub-grouped into those with and without distal ST tendon regeneration.
To measure distal ST tendon insertion on the tibia, meshed bone, muscles and tendons were exported from Mimics to 3-Matics Research (Materialize, v13).In ACLR limbs, injured muscle was mirrored to the uninjured contralateral side.The two meshes (injured and uninjured) were then rigidly aligned using n-point registration using five anatomical landmarks on the tibia, systematically selected by the user.Bilateral differences were then measured along the proximal/distal and anterior/posterior planes (Figure 1).Only participants included within the regenerated sub-group were used for subsequent analyses.
F I G U R E 1 Muscle segmentation from a participant with a unilateral ACLR involving a hamstring autograft.(A) Injured (red) and uninjured contralateral (green) semitendinosus (ST) and ST tendon were manually segmented from magnetic resonance images.In this image, 4 of 512 slices are depicted.(B) Magnified medial view of ST tendon insertion on the tibia for both injured (red, and mirrored) and uninjured contralateral (green) limbs.
Typically the uninjured contralateral limb is assumed to have no long last effects on muscle morphology following an ACLR, previous studies have indicated there are no significant differences in hamstring muscle morphology preoperative to postoperative to the uninjured contralateral limb. 29To authors' knowledge there has been no bilateral comparison of segmented healthy individual hamstring muscle and tendon morphology to assess normal side-to-side variation.Therefore, it is difficult to be confident that the side-toside morphology comparisons are not significantly influenced by natural variation.To assess the suitability of the uninjured contralateral limb as a comparator for the injured ACLR limb, analysis of a healthy control sample (n = 18) 30,31 was performed.Inclusion and exclusion criteria for healthy controls are described in detail. 31Ethics approval was obtained through Griffith University Research Ethics committee (#2017/521), with all participants providing their written informed consent before any testing.The medical imaging acquisition settings and image processing for the healthy controls followed the same methodology outlined above for the ACLR participants.
Following muscle and distal ST tendon segmentation for the healthy controls, meshes from the right limb were mirrored onto the left for analysis of the distal tendon insertion.
There was no significant bilateral difference in hamstring muscle volume within healthy controls.Additionally, no significant bilateral differences in distal ST tendon insertion were found for both proximal/ distal and anterior/posterior (p = 0.91 and p = 0.90, respectively) dimensions.As no significant between-limb differences in muscle volume (cm 3 ) or distal tendon insertion (mm) were found within healthy controls, it was assumed the uninjured contralateral limb within ACLR participants was a good representation of the native anatomical footprint.

| Personalization of musculoskeletal models
A generic full-body model 32 was linearly scaled in OpenSim v4.1 25 to each participant's dimensions using anthropometric measurements taken in a gait laboratory.Tendon slack and optimal fiber lengths were adjusted to preserve each muscle's dimensionless fiber and tendon operating ranges. 33For each participant, their hamstring muscle volumes were based on muscle segmentations from MRI and used to estimate maximum isometric forces (F m Max ).For ACLR limbs, donor muscle morbidity was included by adjusting muscle parameters.
Specifically, ST maximum isometric strength, optimal fiber length (l and tendon slack length (l t s ) were adjusted.Adjusting optimal fiber length for injured ST can be approximated assuming pennation angle is the same in both injured and uninjured contralateral limbs (Equation 1.). 34 Using the new optimal fiber length (l m o Adj ), tendon slack length was adjusted using the same optimization method previously described 33 in which muscle fiber and tendon operating curves were preserved, however, optimal fiber length was fixed to its new value.
The model's muscle tendon unit (MTU) pathways contain both fixed and conditional via points.Via points often introduces discontinuities in MTU kinematics 35 and nonphysiological muscle paths. 36Wrapping surfaces have been used in more recent models to overcome these limitations. 36The ST via-point within the generic (Equation 2).

( ) ( )
Following removal of ST via point and addition and subsequent optimization of the wrap torus object, distal ST tendon insertion point was personalized bilaterally within each participant's MSK model.To do this, MRI measurements of insertions points were transformed from Materialize 3-Matics local coordinate system to tibia body coordinate system in OpenSim.
To minimize discontinuities within ST MTU moment arm after insertion point was adjusted, a second objective, termed smoothing, 36 was used to minimize second derivative of adjusted model ST moment arms (ma knee adj and ma hip adj ) (Equation 3).

| Statistical analysis
All statistical analyses were performed using SPSS v27 (IBM Corp).
Descriptive statistics are presented as mean ± standard deviation (SD), maximum, minimum, and range for parametric variables, and frequencies and proportions for binary variables.Where appropriate, within-group comparisons were performed using paired t-tests.For all analyses, significance was set as p < 0.05.To account for multiple comparisons, bonferroni correction was applied.

| Tendon insertion analysis
Within ACLR limbs with distal ST tendon regeneration, considerable variability in insertion location was found for both anterior/posterior and proximal/distal planes (Figure 2).Notably, six of seven limbs had regenerated ST tendons re-inserted proximal to reference locations (i.e., uninjured contralateral limb), with mean differences in insertion location of 6.64 mm (SD = 16.98,(95% CI = −5.96 to 19.2)) and a range of 56.1 mm (Supplementary Table 1).All regenerated ST tendons re-inserted posterior to reference locations with mean differences of −3.84 mm (SD = 2.42, 95% CI = −5.63 to −2.05) and range of 6.9 mm.
Injured ST demonstrated substantial loss in both flexion/ extension and internal/external torque generating capabilities when muscle moment arm and volume effects are coupled (Supplementary Table 4).Compared to uninjured contralateral ST, surgically reconstructed limbs displayed significantly less flexion torque (mean difference = 19.32%(SD = 3.7, 95% CI = 18.3-20.3;Figure 5) and internal rotation torque (mean difference=15.5% (SD = 3.6, 95% CI = 14.6-16.4;Figure 6) generating capacity.When considering the whole hamstring muscle complex, the injured limb had deficit of 6% (SD = 3.7, 95% CI = 5-6.9) in flexion torque generating capacity (Figure 7) compared to the uninjured contralateral limb.reported recently by Nikose et al., 42  hypothesized to be aided by medial layers of fascia enveloping ST which might provide a tubular sheath and pathway to reinsertion. 44,45If so, preservation of fascial sheath or augmentation of harvesting procedure with the addition of a inducer graft 45 may improve future tendon regeneration outcomes for hamstring autografts.

| DISCUSSION
We found minor deficits in flexion (5.8%) and internal rotation (4.9%) moment arms across a physiological range of knee and hip motions.
Recent systematic reviews 5,23,46 suggested deficits in postoperative knee In conflict with our final hypothesis, no major deficits in knee flexion torque generating capacity of ACLR limbs were observed at angles of deep knee flexion (6% smaller compared to uninjured contralateral limb).
The influence of ST muscle and tendon morphology on the relationship between knee posture and flexion torque generating capacity has been explored experimentally using both isokinetic and isometric dynamometry, with larger strength deficits observed at higher degrees of knee flexion. 41Reduced operating ranges of synergistic muscles, such as bicep femoris long head and semimembranosus, at deep knee flexion angles may partially explain the substantial inter-limb strength deficits observed.
Indeed, these muscles can compensate for an injured ST at shallow knee flexion angles in ACLR patients. 40,47Our observation of no major deficits in knee flexion torque generating capacity of the hamstrings could potentially be explained by the nonphysiological muscle activation (i.e., maximal activation) used within our simulations.Volitional hamstring muscle activation deficits have been observed for several years following ACLR. 8Simulating complete muscle activation throughout a knee range of motion could have masked any potential torque generating deficits at high degrees of knee flexion.Future simulation studies may look to include experimentally detected physiological muscle activation of the hamstring muscle group throughout a flexion/extension cycle of the knee, to improve observed simulated muscle torques.
There are limitations to this study that should be considered.First, the ACLR tendon regeneration subgroup was small (7 from 18 participants), limiting our statistical power.The definition of complete regeneration adopted in this study was ST neo-tendon reaching the level pes anserinus confirmed by MRI and segmentation. 23This was essential for calculating the location of the distal insertion of ST to inform the MSK models.Previous studies have characterized tendon regeneration as the presence of neo-tendon below the musculotendinous junction or more recently below the knee joint line identified via medical imaging. 5No clear definition of regeneration exists in the literature.The MRI effectively identified regenerated tissues but differentiating tendon morphology from scar tissue was challenging, and biopsies are required for confirmation. 23In the present study, 39% of ACLR participants had regeneration of ST to pes anserinus, which is substantially below the rate of ~80% reported within literature.A possible explanation for this discrepancy could be our conservative definition used to classify a tendon as regenerated following ACLR.Second, due the retrospective nature of the study, ACLR participants were not analysed at a standardized followup time (24-48 months postsurgery), and this may have influenced tendon regeneration in some participants.However, previous studies suggest tendon regeneration and remodeling is complete by 12-24 months post-ACLR. 48,49Third, implementing a more physiologically plausible method of muscle activation (e.g., using a neuromusculoskeletal model with electromyographic data) may better inform muscle activity across a physiological range of hip and knee motion.
model was removed and replaced by a torus wrap object anchored to the tibia.Optimization of wrapping surface geometric parameters (translations and rotations along a three-dimensional Cartesian coordinate system, in addition to inner/outer wrap radii) was performed to produce physiologically plausible MTU kinematics, and anatomically plausible MTU pathways.Optimization used MATLAB optimization Toolbox function fmincon with two objective functions.The unadjusted generic model was used as ground truth for the first optimization.The first objective was to maximize correlation between ST moment arms between generic and adjusted models at the knee r

Following personalization and optimization
of each participant's MSK model, ST knee flexion/extension and internal/external rotation moment arm (m) and torque generating capacity (N•m) were simulated across a physiological range of hip 37 (−30°-120°) and knee 38 (0°-110°) motions using OpenSim v4.1 within the model's capability.The torque generating capacity of the entire hamstring muscle complex was calculated across the same physiological range of motion.To simulate capacity, muscle activations were set to maximum (1) for the entire range of tested motions.Muscle moment arms were normalized to participant height (m).Joint torques were normalized to the product of participant body weight (N) and height (m), that is, N.m −1 . 39Bilateral differences were calculated with an asymmetry index (%) ([unaffected limb-affected limb]/[unaffected limb + affected limb] *100%).Smaller moment arms or knee torques within injured compared to uninjured contralateral limbs were considered a deficit.DU MOULIN ET AL.

F I G U R E 2
Distal semitendinosus tendon insertion from MRI segmentations.(A-C) Selected segmentations from healthy uninjured individuals.(D-F) Segmentations from selected ACLR participants illustrating variability of distal tendon insertion following regeneration.(D) Highlighting reinsertion of regenerated tendon relative to native insertion site.(E) Illustrating reinsertion of regenerated tendon distal to native insertion site.(F) Showing reinsertion of regenerated tendon proximal to native insertion site.MRI, magnetic resonance imaging.ACLR, anterior cruciate ligament reconstruction.F I G U R E 3 Normalized semitendinosus flexion (flex) and extension (ext) torque (N•m) across a physiological range of motion of the knee joint with the hip in a neutral (0°) position.Mean torque ± 1 standard deviation (SD) plotted for bilateral limbs (uninjured and injured) from the ACLR cohort (n = 7).F I G U R E 4 Normalized semitendinosus internal (int) and external (ext) torque (N•m) across a physiological range of motion of the knee joint with the hip in a neutral (0°) position.Mean torque ± 1 standard deviation (SD) plotted for bilateral limbs (uninjured and injured) from the ACLR cohort (n = 7).DU MOULIN ET AL. | 1433 moment arms, as well as lower torque generating capacity, compared to homologous muscles in the uninjured contralateral limb.Even when ST distal tendon regeneration occurred, torque generating capacity of the hamstring muscle group was lower compared to uninjured contralateral limbs.Mechanical consequences of ACLR simulated in this study agree with experimental observations of chronic strength deficits, 40,41 indicating even if the "best" possible outcome is achieved (complete tendon regeneration at level of pes anserinus), deficiencies in ST and hamstring function post-ACLR remain and are modulated by remodeling of ST morphology.For those ACLR participants who had tendon regeneration, we observed substantial bilateral differences in distal ST tendon insertion, ranging between 56 mm and 6.9 mm in proximal/distal and anterior/ posterior tibial planes, respectively.Within the ACLR regeneration subgroup, 6 of 7 participants had ST tendon reinsertion proximal to their insertion point on their uninjured contralateral limb.Similar results were F I G U R E 5 Normalized semitendinosus flexion (flex) and extension (ext) torque (N•m) across a physiological range of motion of the knee joint with the hip in a neutral (0°) position.Mean torque ± standard deviation (SD) plotted for bilateral limbs (uninjured and injured) from the ACLR cohort (n = 7).F I G U R E 6 Normalized semitendinosus internal (int) and external (ext) torque (N•m) across a physiological range of motion of the knee joint with the hip in a neutral (0°) position.Mean torque ± standard deviation (SD) plotted for bilateral limbs (uninjured and injured) from the ACLR cohort (n = 7).F I G U R E 7 Normalized hamstring (semitendinosus, semimembranosus, biceps femoris long head, biceps femoris short head) flexion (flex) and extension (ext) torque (N•m) across a physiological range of motion of the knee joint with the hip in a neutral (0°) position.Mean moment arm ± standard deviation (SD) plotted for bilateral limbs (uninjured and injured) from the ACLR cohort (n = 7).
flexion strength are due to reductions in harvested muscle moment arms and alteration of morphology following surgery.In theory, a more proximally and posteriorly inserted distal ST would reduce knee flexion and internal rotation moment arms, and the remodeled ST would have impaired contraction function and line of action of the force.Combined with changes to ST moment arms and maximum isometric force generating capabilities (derived from measured muscle volumes), deficits were found in knee flexion (19.6%) and internal rotation (15.5%) torque generating capacity when compared to uninjured contralateral knees.Joint torque analysis suggested altered muscle morphology (i.e., smaller volumes and retraction of muscles in ACLR compared to contralateral limbs) was the dominant factor dictating torque generating capacity in these simulations.Future research should investigate and optimize rehabilitation programs to restore harvested muscle morphology following ACLR.
Further analyses are warranted to examine the accuracy of personalization of MSK models against experimentally collected strength measures when estimating muscle torque generating capacities.Lastly, components within a MSK model uniquely influence muscle force generation.Muscle force production is highly sensitive to tendon slack length and maximum isometric force,50,51 determined by factors such as specific muscle tension, muscle volume, pennation angle, and optimal fiber length.However, the influence of muscle moment arm on joint torque is relatively minimal, with the expected sensitivity of torque production to moment arm changes being small to moderate.Due to the inherently limited and confined characteristics of moment arms (i.e., insertions in close proximity to joints), any alterations in moment arms represent significant proportions of their original magnitudes.Consequently, recognizing the modest comparative effects on joint torques but significant proportional changes relative to the natural anatomic footprint, efforts were made to personalize these model components for each participant, avoiding generic assumptions about internal components and insertion modifications based on previous literature.5 | CONCLUSION Personalization of the distal insertion and injured muscle morphology in this simulation study provided unique insight into post-ACLR ST and hamstring function, highlighting mechanical deficits previously only reported in whole muscle group experimental strength tests.Following ST tendon regeneration to the level of pes anserinus, substantial deficits in ST torque generating capacity remain, which DU MOULIN ET AL. | 1435 may have implications for load sharing amongst the hamstrings and future lower limb injury risk.Future studies may wish to implement this framework to personalize musculoskeletal models following ACLR to better understand individual muscle function for injury prevention and treatment evaluation.
indicating ST regeneration involves proximal migration of distal ST insertion by ~28 mm.Conversely, Choi et al 43 found distal ST insertion changed 4.3 ± 7.6 mm distal for 36 of 45 ACLR patients compared to their preoperative MRI.Neither previous studies report distal ST insertion changes within a tibial coordinate system (e.g., proximal/distal, anterior/posterior dimensions), nor is it clear what explains the conflicting results across studies.Indeed, the mechanism of distal ST tendon regeneration has not been clearly identified but is