Literature search and study selection

The following databases were searched: PubMed, ScienceDirect, Google Scholar, and IEEE Xplore. Different combinations of the terms “Knee”, “Model”, “Musculoskeletal”, “Ligament”, “load”, ‘‘force”, “tension “, “length”, ‘‘strain”, “elongation” and ‘‘lengthening” was used. The reference lists of identified original articles were also searched manually for relevant articles. The search was limited to English and full-text articles only, and all duplicate papers were first removed. A team of two reviewers (SSF and DD) then independently screened the titles and abstracts of the remaining papers for eligibility. Disagreements between reviewers were resolved by consensus.

Data extractions

A customised data extraction form was created to extract each selected study’s critical musculoskeletal model development parameters. One author (SSF) undertook the data extraction, and the other (DD) checked the final table to ensure reliability. Specific parameters of the musculoskeletal knee model used in each eligible study were independently extracted, including the (1) musculoskeletal model characteristics (i.e., software used for modelling, knee type, source of geometry, the inclusion of cartilage and menisci, and articulating joints and joint boundary conditions (i.e., number of degrees of freedom (DoF), subjects, type of activity, collected data and type of simulation)), (2) specifically ligaments modelling techniques (i.e., ligament bundles, attachment points, pathway, wrapping surfaces and ligament material properties such as stiffness and reference length), (3) sensitivity analysis, (4) validation approaches, (5) predicted ligament mechanics (i.e., force, length or strain) and (6) clinical applications if available.

These items were chosen to overview each selected study’s modelling and validation techniques and the presented sensitivity assessment, ligament mechanics, and associated results. In the absence of the published numerical data, data was obtained from the graphs. When a method was partially described in the original study, detailed information was retrieved from the authors’ references and previous works to provide comparable data across the selected studies.

Quality assessment

A customised checklist consisting of 16 appraisal questions was developed based on previous reviews in computational modelling of the human motion for prediction modelling studies with clinical/translational outcomes [11] and human motion analysis [12, 13], assessing the quality of the selected studies. Each question was rated two (satisfying description or justification), one (limited details) or zero (no information). The 16-item quality checklist used in this review is listed in in Table 1.

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Table 1. The checklist used for quality assessment of the included publications in the systematic review.

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Each study was evaluated independently by the two authors (SSF, DD). The original article was checked to ensure the correct rated scores, and the authors found a consensus in case of discrepancy.

Search yield

The electronic database search revealed 999 records: 246 studies from PubMed; 291 from ScienceDirect; 446 from Google Scholar; and 16 from IEEE Xplore. After removing 404 duplicates, 572 studies were excluded based on the exclusion criteria, leaving 28 potentially relevant studies. Most of the excluded studies did not report ligament loading data despite the inclusion of ligaments in the models. Others were based on finite element modelling or other non-musculoskeletal modelling approaches. Three of these studies were also excluded due to repeated data. Of the 1004 original records only 25 meet the inclusion criteria and were included in this review. The study selection process is reported in Fig 1. Quality assessment and data extraction results are reported below. Details can be found in Tables 2–4, respectively.

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Fig 1. PRISMA flow diagram of literature search for the systematic review.

The PRISMA flow diagram depicts the flow of information throughout the different phases of this systematic review, including the number of records identified, included, and excluded and the reasons for the exclusions.

https://doi.org/10.1371/journal.pone.0262684.g001

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Table 2. Quality assessment results of included publications database (25 publications).

https://doi.org/10.1371/journal.pone.0262684.t002

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Table 3. Musculoskeletal knee joint modelling characteristics of included publications (in descending chronological order).

https://doi.org/10.1371/journal.pone.0262684.t003

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Table 4. Ligament model characteristics of included publications (in descending chronological order).

https://doi.org/10.1371/journal.pone.0262684.t004

Quality assessment

The quality of the reviewed studies is summarised in Table 2. Each article’s overall score is calculated by the sum of the rated questions divided by the sum of relevant questions. The selected studies demonstrated high quality in the areas of objectives, study design, modelling technique, movement tasks, simulation, validation, statistics, results, key findings, limitations, and conclusion.

According to the quality assessment results presented in Table 2, several articles had limited modelling technique descriptions [15, 16, 19, 20, 27, 33] and validation methods [16, 18, 25, 27, 35, 37, 38]. In 12 of the selected studies [14–17, 20, 24–27, 31, 37, 38], the sensitivity of the model outputs on ligament model parameters has not been assessed. In one study [26], findings were not fully supported by the literature. Overall, the selected articles demonstrated high content quality, with scores ranging between 81.25% and 100%.

Musculoskeletal model definition

Details of the extracted musculoskeletal model definitions are summarised in three sections: geometry, degrees of freedom/joint boundary conditions, and ligament modelling, with detailed information presented in Tables 3 and 4, and Fig 2.

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Fig 2. Distribution of studies by model characteristics.

Pie charts representing the distributions of studies according to various modelling parameters: modelling software (A), knee type (B), model type (C), source of geometry (D), inclusion of cartilages (E), inclusion of menisci (F), and articulating joints forming the knee (G).

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A range of musculoskeletal modelling software packages has been used across the selected studies (Fig 2A and Table 3). 14 studies [15–17, 20–25, 27, 29, 32, 34, 35] used OpenSim [39], four studies [18, 36–38] used SIMM [40], two studies [26, 28] used AnyBody Modelling System (AnyBody Technology, Aalborg, Denmark), one study [30] used ADAMS [41], one study [14] used SimWise-4D platform (Design Simulation Technologies, DST, Canton, MI, USA), one study [19] used KneeSIM (LifeModeler Inc., San Clemente, CA), one study [33] used Musculoskeletal Joint Modeler [42], and one study [31] used Working Model 3D (Working Model 3D, MSC, Software Corp., Santa Ana, CA, USA).

Sensitivity analysis

Several different methods have been reported to assess ligament loading behaviour’s sensitivities to the modelling parameters using computer simulation models [18, 19, 21–23, 28, 29, 32, 35] (Table 5).

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Table 5. Comparison of different validation approaches and sensitivity analysis between included publications (in descending chronological order).

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Three studies focused on the sensitivity of the active knee kinematics to varying ligament lengths [19, 22, 23]. For instance, Tanaka et al. [19] found that active knee kinematic are sensitive to ACL slack length, and Blache et al. [23] found a similar sensitivity to LER attachment site, with a postero-proximal femoral LER attachment site leading to active kinematics closer to an intact knee. In another study, Smale et al. [22] found that the model’s knee kinematics and ligament length were very sensitive to the joint geometry and contact surfaces during highly dynamic tasks.

Passive knee kinematics have been shown to be sensitive to ligament parameters [28, 29]. Schmitz et al. [29] found that passive knee kinematics are sensitive to the slack length and stiffness of the ACL, PCL, and MCL. Kang et al. [28] showed that tibiofemoral translations and internal tibial rotation were sensitive to the stiffness and strain values at full extension within the PFL, LCL, and PT ligaments.

The sensitivity of ligament model parameters on forces experienced by ACL [18, 21, 35] and MCL [19, 35] have also been assessed. Vignos et al. [18] found that forces in the ACL during walking were sensitive to vertical graft angle, tibial translation, and initial tension in the graft. Tanaka et al. [19] reported that the MCL tension during deep knee bend, gait, and stair descent activities was sensitive to ACL length change. Charles et al. [21] demonstrated the sensitivity of ACL force predictions to subject-specific anatomy, specifically musculoskeletal joint geometry and ligament resting lengths. They showed that during walking, ACL forces were highly sensitive to the ligament resting length with ±10% variations resulting in force differences of up to 84%. Shao et al. [35] revealed the sensitivity of ACL and MCL forces during the stance phase to variations in different anterior tibial translations.

One study assessed the effect of variation in the slack length and ligament strain on the ligament strain errors [32]. It was found that in an OpenSim generic ligament model, ligament strain error was highly sensitive to variations in ligament strain and slack length.

Validation approaches

An essential stage of modelling is validation, which compares the performance of the models against experimental measurements. Two different types of measurements were used for validation: in vivo experimental data and in vitro experimental data (Table 5). Only three reviewed papers did not include any form of validation [16, 25, 27].

Among the selected studies in this systematic review, 15 studies used in vivo experimental datasets to validate their model predictions [14, 15, 18–21, 23, 24, 26, 28, 31, 34–37]. Common in vivo datasets used to validate simulation data includes kinematics derived from the fluoroscopic analysis [19], CT/MR/X-ray image analysis [21, 23, 24, 28]; motion capture analysis [14, 20]; EMG results [15, 31]; or a combination of these techniques [18, 26, 31, 34–37]. A combination of active [14, 15, 17–19, 21, 23, 26, 31, 34–37] and passive [18, 20, 24, 28] activities were used to generate these data sets.

In vitro validation methods compare model performance against kinematic and kinetic data measured in cadaveric testing. For example, Smale et al. [22] used a modelling method previously validated against cadaveric passive flexion data [44] and Kia et al. [30] collected ligament forces and experimental kinematics during the passive flexion of a cadaveric knee to validate their model. Among the nine studies which validated their models against in vitro cadaveric experiments [18, 20, 22, 29, 30, 32, 33, 35, 38], some used knee kinematics [18, 22, 38]; others used ligament strain/force data [20, 32]; some used a combination of these [29, 30, 33, 35].

Model predictions

All models in this systematic review report ligament mechanics in one form or another (Table 4). Depending on the research question, either the ligaments’ force, strain, or length has been reported.

Predicted forces.

Fourteen studies reported ligament forces [18–20, 23, 25, 26, 28–31, 34–38], incorporating passive and active activities. Typically, walking [14, 17, 18, 21, 26, 28, 35, 36] and squatting [28, 31, 37] are used for simulating active movements, and passive knee flexion [30, 38] and the anterior drawer test [31] are used as passive movements. Figs 3 and 4 show the comparative ligament force values across the different studies for active movements, including walking and squatting. Fig 5 reports the ligament for passive knee flexion.

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Fig 3. Reported ACL, PCL, MCL, and LCL forces vs percentage of the gait cycle during walking in different studies [14, 18, 21, 26, 28, 35, 36].

Curves represent the trends of ligament forces (in Newton) experienced by ACL (A), PCL (B), MCL (C), and LCL (D) during the stance phase (0–60%) and the swing phase (60–100%) of the gait cycle.

https://doi.org/10.1371/journal.pone.0262684.g003

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Fig 4. Reported ACL, PCL, MCL and LCL forces vs knee flexion angle during passive [31] and active [28, 37] squatting in three different studies.

Curves represent the trends of ligament forces (in Newton) experienced by ACL (A), PCL (B), MCL (C), and LCL (D) in 0° to 90° of knee flexion along with the squat movement. To highlight the trend more clearly, the MCL and LCL forces are presented in the 0-300N range.

https://doi.org/10.1371/journal.pone.0262684.g004

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Fig 5. Reported ACL and PCL forces vs knee flexion angle during passive knee flexion in two different studies [30, 38].

Curves represent the trends of ligament forces (in Newton) experienced by ACL (A) and PCL (B) in 0° to 90° of knee flexion along with the passive flexion movement.

https://doi.org/10.1371/journal.pone.0262684.g005

Walking (active). Six studies [14, 18, 21, 26, 35, 36] calculated the ACL forces of healthy knees using their models under simulated dynamic walking conditions (Fig 3A). Five showed the ACL tensions ranging between 50-300N [14, 18, 21, 35, 36]. They generally found the ACL active during the stance phase. All three studies showed peaks in the ACL force in the midstance phase (15%–45% of the gait cycle). However, there was considerable variation in the distribution of those peaks. In contrast, Hu et al. [26] reported low tensions (less than 50N) in the ACL throughout the whole gait cycle. Three studies [14, 26, 36] (Fig 3B) reported two force peaks in the PCL associated with the ipsilateral heel strike and toe-off, with a comparatively high peak of PCL force (approximately 700N) reported by Frigo et al. [14] at toe-off. In contrast, Hu et al. [26] suggest that the PCL is loaded throughout the stance phase, while the other three studies report comparatively minimal loading during the stance phase [14, 35, 36]. During walking, the MCL force patterns were variable across four different studies [14, 26, 35, 36] (Fig 3C). Shao et al. [35] found high fluctuating tension with two peaks at heel-strike and mid-swing; Frigo et al. [14] and Hu et al. [26] reported higher forces in the swing phase compared with the stance phase; whilst Shelburne et al. [36] calculated a relatively low constant force of about 20N throughout the gait cycle. The LCL forces were similarly variable. However, three studies [28, 35, 36] (Fig 3D) generally show all loading occurring in the stance phase. Frigo et al. [14] and Hu et al. [26] again differed from the other models, suggesting that loading occurs throughout the stance and swing phase.

Squatting (active/passive). Three studies reported ligament loads during squatting [28, 31, 37] (Fig 4). Shelburne et al. [37] generally showed minimal activity across all the ligaments (Fig 4A, 4C and 4D) except for the PCL, which increased from 35° of knee flexion up to about 600N at full knee flexion (Fig 4B). Bersini et al. [31], via modelling the passive squatting, also showed increased PCL force with increasing knee flexion (Fig 4B) and a similar load profile for MCL (Fig 4C). An inverse loading profile, which decreased with increasing flexion, was reported for the ACL (Fig 4A) and LCL (Fig 4D). The LCL experienced relatively low loads; these loads were fairly constant for Shelburne et al. [37] at 0N and Kang et al. [28] at 90N (Fig 4D) modelling the active squatting.

Knee flexion (passive). The ACL and PCL knee flexion forces of a musculoskeletal model under passive knee flexion are only calculated and reported by two studies [30, 38] (Fig 5). Shelburne et al. [38] showed that the ACL generally experiences a high force (~100N) at full extension, which reduces to nil by about 60° of flexion [38] (Fig 5A). In contrast, the PCL experiences no force from 0° to 40° of flexion, followed by a steadily increasing force with increasing knee flexion [38] (Fig 5B). Kia et al.’s model showed comparatively low forces with minimal variation throughout the ACL and PCL flexion range [30] (Fig 5B and 5A).

Anterior-posterior drawer test (passive). Of all 25 studies in this systematic review, only one study calculated the ACL and PCL force pattern during the passive tibial anterior-posterior drawer test [31]. Bersini et al. [31] found that the force required to draw the tibia forward (equivalent to 5mm displacement) was higher (328N) when the knee was extended than when it was flexed (226N). In contrast, the force required to draw the tibia backward (again, equivalent to 5mm displacement) was higher (298N) when the knee was flexed than when it was extended (138N).

During anterior drawing, they showed approximately 400N (at 0°) and 50N (at 90°) of force experienced in the ACL, and almost zero forces at 0° and 90° of flexion in the PCL. The posterior drawer, instead, produced a significant load on PCL, with approximately 110N (at 0°) and relatively higher force values of 319N (at 90°), while in the ACL, zero forces (at 0°) and 75N (at 90°) was reported. It is clear that increasing the flexion angle reduces the ACL force and decreases the PCL force, which is consistent with the results presented in Figs 3 and 5 above.

Predicted strain/elongation.

Ligament strain data was reported in five studies [24, 25, 29, 32, 34]. These studies either refer to a reference length [24, 32, 34] or a slack length [25, 29] extracted from the literature. A reference length is the ligament length in a defined body posture (e.g., full extension in passive movements or heel-strike in walking), whereas the slack length refers to the length at which the ligament is slack. Three of these studies separated the cruciate ligaments into their respective bundles and investigated the passive knee motion using OpenSim [25, 29, 32]. Fig 6 shows the strain values for the cruciate and collateral ligaments over 90° of passive flexion. The strain magnitudes of the different ligament bundles were found to exhibit different patterns throughout flexion (Fig 6), with considerably higher strains reported for the ACL and PCL ligament bundles (Fig 6A and 6B). Also, MCL Strain values within different bundles of MCL displayed considerable variation (Fig 6C). Although most of the MCL bundles had declining strain patterns, anterior bundles of the MCL are tensioned almost constantly during the flexion, while intermediate bundles of the MCL showed small strain values than the posterior bundles. LCL strain values were in a similar range and pattern to that of MCL bundles (Fig 6D), having a slow declining strains trend throughout the range of flexion. However, Schmitz et al. [29] suggested positive LCL strain values with a maximum at full extension.

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Fig 6. Reported ACL, PCL, MCL and LCL percentage of strain vs knee flexion angle during passive knee flexion in 3 different studies [25, 29, 32].

Curves represent the trends of ligament strains (in per cent) within different bundles of the ACL (A), PCL (B), MCL (C), and LCL (D) in 0° to 90° of knee flexion along with the passive flexion movement. The MCL and LCL strains are presented in the -20 to +20% range to highlight the trend more clearly.

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Two other studies also reported the ligament strain patterns: Kar et al. [34] reported active ACL strains and forces under stop-jump activities, with strains reported between 6–10%. Barzan et al. [24] reported cruciate and collateral ligament strains calculated based on optimisation routines within three different ligament models and validated using MRI scans of paediatric subjects at various flexion angles.

In two studies, ligament length/elongation was reported by measuring the ligament’s distance between origin and insertion points [22, 33]. In those studies, the ligament length at each knee joint pose was compared to quantify the relative length change throughout the activity. The length change of knee model ligaments was investigated under passive knee motions by Ozada et al. [33]. Their results demonstrated that by increasing the flexion angles from 0° to 90°, the ACL shortened, consistent with the average ACL strain values within anterior and posterior bundles, reported above [25, 29, 32](Fig 7). Considering the contact between the tibia and femur, Smale et al. [22] used extensive optimisation methods [44] to ensure realistic joint contact behaviour, reporting knee ligament lengths for a side cut task. Their models covered a wide range of possible ligament lengths.

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Fig 7. The reported percentage of ACL strain and length in 4 different studies [25, 29, 32, 33].

Grey curves represent the trends of ACL strains (in per cent), and the black curve represents the ACL length (in millimetre) in 0° to 90° of knee flexion along with the passive flexion movement. To highlight the trends more clearly, ACL strain values within the anterior (aACL) and posterior (pACL) bundles of three studies were averaged and presented here.

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Analysis of the model predictions

Various modelling techniques under different boundary conditions have been used to predict knee joint kinematics and ligament mechanics. Because of these differences, there is considerable variability in the resulting ligament mechanics. Geometric input, boundary conditions, and ligament modelling parameters are used to define the unique characteristics of each specific musculoskeletal model (Fig 8). All these parameters have, to varying degrees, been found to affect the predicted ligament mechanics behaviour. Below is a discussion relating to each of these parameters.

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Fig 8. Categorised parameters of musculoskeletal knee model.

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Effect of boundary conditions on the predicted ligament mechanics

DoFs. Five studies [25, 29, 30, 32, 38] assessed ligament mechanics during passive knee flexion/extension tests (Figs 5 and 6). As summarised in Table 6, each applied different boundary conditions as they tried to simulate the tibia’s passive movement relative to the femur. The variable knee kinematics results throughout the range of knee flexion indicate the effect of different degrees of freedom on the model performance [25, 29, 30, 32, 38] (Fig 9).

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Fig 9. Reported kinematics of the knee joint during passive knee flexion [25, 29, 30, 32].

Curves represent the kinematic of the knee joint in forms of internal tibial rotation (in degrees) (A) and anterior tibial translation (in millimetres) (B) in 0° to 90° of knee flexion along with the passive flexion movement.

https://doi.org/10.1371/journal.pone.0262684.g009

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Table 6. Comparison of the tibiofemoral joint boundary conditions among five studies [25, 29, 30, 32, 38] which reported the knee kinematics during the passive knee flexion test.

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Table 6 summarises the available degrees of freedom for each model and the respective ligament tensions. Marieswaran et al.’s [25] and Xu et al.’s [32] models both constrained all DoFs except for the flexion-extension axis. These highly constrained models result in the presence of low tension in the aACL and aPCL, with all other ligaments producing negative strains. In practical terms, negative strains indicate laxity in those soft tissues throughout the full range of motion (ROM). In contrast, Kia et al.’s model [30], which allowed the full 6-DoFs, experienced some small forces in all ligaments during passive flexion for most of the ROM.

In general, we know that the collateral ligaments experience higher tensions when there is an increase in activity in the adduction/abduction, int/external tibial rotation, or medial/lateral translation directions. Looking at Fig 9, Schmitz et al. [29] and Kia et al. [30] both had increased internal rotations and thus should expect to see increased collateral ligament tensions. Table 6 verifies this assumption; both models report strains of up to 8% or up to 10N of force in the collaterals.

Similarly, increased anterior-posterior tibial translations lead to an increase in the tensions in the cruciate ligaments. For example, in Fig 9B, Kia et al. [15] experienced increased anterior translation as the knee flexed as opposed to the increased posterior translation reported by Schmitz et al. [29], which locked three extra DoFs. Therefore, we expect the ACL and the two collaterals to undergo tension, which is verified in Table 6.

In another study, Smale et al. [22] compared different knee models with either three or 6-DoFs. The generic 6-DoFs model experienced a greater range of movement and ligament length changes. However, an MRI-based model with 6-Dof in the same study showed lower length change when validated against quasi-static MR images [22]. The authors hypothesised that the ligament lengths were too short, leading to an over-constrained joint. Also, the MRI based knee model was found to be very responsive to the kinematics and ligament lengths of highly dynamic tasks.

Type of activity. Load bearing activities that generate a reaction force are generally referred to as closed chain activities; open-chain activities typically do not generate a reaction force and include the swing phase in walking and passive motions. An example of the difference can be seen in the cruciate ligament forces during active (squatting) (Fig 4) and passive (knee flexion) activities (Fig 5). They follow a similar pattern, but the magnitude of the forces is significantly higher for the active results. This difference is most likely due to the closed-chain, load-bearing nature of active squatting [30, 31, 37, 38] (Fig 10B and 10C).

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Fig 10. Comparison of reported PCL forces vs knee flexion angle during walking, squatting, and passive knee flexion in different studies [14, 26, 30, 31, 35–38].

Curves represent the trends of PCL forces (in Newton) during active walking (A), passive and active squatting (B), and passive knee flexion (C) in 0° to 90° of flexion. As a typical gait curve, the red curve represents the knee flexion angles vs the percentage of the gait cycle. Blue dashed lines are used to determine the corresponding flexion angle.

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The difference between open- and closed-chain activities is also highlighted when comparing the PCL force during active walking (Fig 10A) with those reported by Shelburne et al. [37] during squatting (Fig 10B). Although both are active tasks, the PCL force drops to nil during the swing phase of the gait cycle, which is equivalent to 30°-60° of flexion (see red gait curve in Fig 10A); for active squatting, in this same flexion range, the PCL load is monotonically increasing. This is because the swing phase of active walking is open-chain, exerting a minimal force on the ligament. As a result, the passive knee flexion curve (Fig 10C) aligns better with the swing phase of the active walking curves (i.e., 30°-60° of flexion) since it is also an open-chain configuration.

Notably, there is a greater agreement concerning the swing phase in the active walking figure, with three studies all showing no load in the PCL (Fig 10A). In contrast, the stance phase of active walking (0–60° of knee flexion in Fig 10A) shows a large amount of variation. This indicates that joint load distribution during closed-chain activities, such as the stance-phase of walking, is more sensitive to various patient-specific parameters [62, 63]. In contrast, open-chain activities such as the swing phase of walking allow relaxation of the surrounding soft tissues and the joint mechanical behaviour relies more on any external forces and moments for passive motion [64] or momentum in active motion [65].

During the stance phase of active walking (0–60%), the knee flexion angle (Fig 10A, red curve) generally remains below 30°. Shelbourne et al. [36] and Shao et al. [35] both agree that there is minimal loading in the PCL throughout much of the stance phase, which agrees well with the results for this flexion range during active squatting (Fig 10B). As discussed below, the higher loads in Hu et al. [12] can be attributed to variations in ligament properties.

The effect of ligament modelling parameters on predicted ligament mechanics

Ligament stiffness. The ligament stiffness values used in the various studies may explain some of the differences observed in ligament forces (Fig 3B) between the multiple studies. In Hu et al.’s model [26], the referencing regarding ligament stiffness values is unclear; for instance, the PCL stiffness values have a possible range of 1500-9000N (Table 7) compared to values of 1900-2600N in the Shelburne et al. model’s [36] and Shao et al.’s model [35]. This possible discrepancy may explain the differences between ligament stiffness values.

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Table 7. ACL/PCL stiffness values from active models of walking and passive models of knee flexion.

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In general, the ranges of stiffness values listed for the ligament stiffnesses are often large (Table 7). This leads to some issues with the reproducibility of the data presented in studies. It would be ideal if the final values were listed for each ligament bundle, allowing for better verification of previous findings.

Method of calculating the ligament strain. Many studies report a negative strain in ligaments (e.g., Fig 6). This is because their calculations are based on the relative distance between the insertion points rather than the actual strain. For instance, Xu et al. [32] and Marieswaran et al. [25] measured the relative distance between the insertion points to find the strain; this fails to account for the wrapping of the ligament around the bones and the change in strain patterns that this may create.

In contrast, Schmitz et al. [29] calculated strains based on predicted forces (i.e. indirect strain measurement) using ligament nonlinear force-strain equations [66–70]. This calculation method allows the wrapping of the ligament around the bone geometry to be incorporated in the strain calculation.

In addition, while many studies simply report the calculated value for strain (positive or negative), Schmitz et al. [29] recognised that negative strain represents the laxity of the ligament; they set a zero strain threshold to incorporate this into their model.

Sensitivity assessment

Our review reveals the need for and importance of running a sensitivity analysis when analysing joint ligament behaviour. Sensitivity analyses are important for several reasons: (¡) they indicate the accuracy of the model in the given scenario [71, 72]; (¡¡) they provide a means of investigating a window of possible outcomes given any uncertainty about analysed parameters [71, 73]; and (¡¡¡) they can potentially provide insights into the importance of different ligament parameters on such factors as knee kinematics and forces [74, 75], which can have implications for such translational concepts as graft placement as discussed below.

Ligament loading values have been shown to be sensitive to most parameter variations in all studies [14–38]. This suggests that using patient-specific data to determine the exact ligament insertion points and develop accurate contact surface geometries will play an important role in future MSK models. The variation of the ligament sensitivity assessment techniques and results reported in the literature (Table 5) makes it difficult to determine how different modelling parameters affect the ligament results. However, investigating the sensitivity of ligament loading to changes in various modelling parameters using patient-specific models as a starting point may improve our understanding of these relationships.

Quality of input data

Another source of error in knee ligament dynamics predictions between different models is the quality of the kinematics and/or kinetics data input into the model [76, 77]. Kinematic information is typically captured using motion capture methods or fluoroscopy. Both techniques have limitations that have an impact on the quality of data [78]. For example, motion capture methods can vary depending on the different marker sets used (i.e., The modification of the Helen Hayes markers set [79]), which can vary across different research groups. Also, the actual placement of the markers will vary in accuracy depending on the skill of the operator. Dealing with the data at the processing stage can add further potential errors and is dependent on the software, level of filtering, scaling and other software specific parameters. Kinetic input can be sourced from ground reaction forces and EMG data, each of these has similar limitations, regarding user error and researcher-specific measurement protocols.

Therefore, even in the case of two well-calibrated (and validated) models, the model predictions may not agree, as they will be dependent on operator error at several stages in the process before the modelling even occurs; and this is the main focus of this systematic review.

Clinical application

Among the selected studies, in addition to models which examined the intact knee joint [14–17, 19–22, 24–27, 29–34, 37, 38], some considered aspects of knee injuries and surgical treatments, including ACL deficient [35, 36] and ACL-reconstruction [18], PCL-deficient [28] and LER reconstruction [23]. Those studies were developed for clinical applications to investigate the impacts of injuries and surgical treatments on the knee joint’s biomechanical functioning.

Shelburne et al. [36] aimed to predict the pattern of shear force and ligament loading in the ACL-deficient knee during walking. They found that increasing anterior tibial translation (ATT) reduced patellar tendon angle and reduced anterior tibial shear force. They suggested that while the MCL acts as the primary restraint to ATT in the ACL-deficient knee, patellar tendon angle changes can decrease the knee’s total anterior shear force. Shao et al. [35] investigated the influence of increasing tibial slope on ligament loading and anterior tibial translation in healthy and ACL-deficient knees during gait. Their model results gave a more in-depth insight into how the patients adapted their gait following the ACL deficiency. They found an increase in ATT throughout the stance phase for the ACL-deficient knee compared to the healthy knee. They also reported that the primary passive restraint of anterior shear force was the ACL in the healthy knee, and the MCL was the primary passive restraint to anterior shear force in the ACL-deficient knee. They also showed that the knee flexors were used as active restraint to help balance anterior shear force in the ACL-deficient knee. Based on their model results, they anticipated that increasing the tibial slope would increase the resulting ATT and ligament forces in both healthy and ACL-deficient knees.

Vignos et al. [18] explored the relationship of ACL graft angle with tunnel location with tibiofemoral kinematics in patients with ACLR. They found that post-operative cartilage loading is sensitive to the graft angle. Their results suggest that even a slight change of the graft tunnel placement leads to a small deviation from the anatomic ACL angle and an increase in knee osteoarthritis risk after ACLR.

Kang et al. [28] investigated the effect of PCL deficiency on the posterolateral corner structure forces, including the LCL, Popliteus tendon (PT), and Popliteofibular ligament (PFL), and tibiofemoral and patellofemoral contact forces under dynamic-loading conditions. They showed that PCL deficiency affects the variability of force on the popliteus tendon in dynamic-loading conditions, suggesting potential degeneration of the patellofemoral joint resulting from high flexion dynamic activity.

Blache et al. [23] assessed the effect of different LER graft tunnel locations on graft tensioning and altered knee joint kinematics. By simulating a pivot-shift test, they revealed the importance of the LER in ACL rupture patients. They suggest a postero-proximal femoral LER attachment site in LER surgery since it provides the desired behaviour during physiological knee flexion.

Kim et al. [15] investigated the effect of hip abductor weakness on the altered lower extremity joint moments and kinematics, which leads to an increased risk of ACL injury during single-leg landing. They suggest that subject-specific musculoskeletal simulations estimating ACL loading can help clinicians predict potential ACL injuries during dynamic movements.

In a similar study, Moon et al. [16], using musculoskeletal modelling techniques, found that the ACL load, following hamstring fatigue, did not show statistically significant differences; instead, there was a significant reduction in ACL load after quadriceps fatigue. This reduction after quadriceps fatigue reconfirms that the quadriceps is the major muscle group causing ACL injuries by reducing the extension and adduction moment of the knee joint and thereby increasing the ACL load.

Moon et al. [27] evaluated the effectiveness of wearing commercialised sports knee braces and sleeves on knee kinematics, kinetics, and ACL force during drop jumps using musculoskeletal modelling analysis. They found that knee braces and sleeves reduced flexion and abduction movement and adduction moment but did not reduce the knee joint shear force, internal rotation moment, or the ACL force. They suggested that a sports knee brace that controls the knee joint’s shear force and internal rotation moment needs to be developed to prevent ACL injuries during high impact activities.

Recommendations

Based on the results of this systematic review, we recommend attention be given to the following stages of the modelling process:

Limitations

The studies selected for this systematic review were limited only to those reporting ligament loading data in a musculoskeletal knee model. Therefore, several musculoskeletal studies modelling the knee joint were excluded accordingly. For example, four studies [74, 87–89] considered the effect of their modelled ligaments on the knee kinematics but did not report the ligament loading, excluding them from this review. By extending the range of studies considered to those who assessed the knee joint kinematics and kinetics, without reporting the ligament mechanics, it might be possible to better evaluate the effect of passive ligament performance on the knee functions during inverse or forward simulations.

Only a few activities were investigated in the selected database, i.e., walking, squatting, and passive knee flexion. There was insufficient data to draw any meaningful conclusions about ligament loading during each type of activity.

The limited number of studies, wide variety of simulation techniques used, and the model’s apparent sensitivity to a large number of interdependent parameters means that a comparison between the loading results did not reveal any discernible trends for the predicted ligaments loading.

Moreover, the limited number of studies specific to this systemic review criteria have frequently been conducted by members of the same research groups, likely leading to an increased risk of bias towards similar types of methodologies and results.