Predictions of Anterior Cruciate Ligament Dynamics From Subject-Specific Musculoskeletal Models and Dynamic Biplane Radiography

Abstract

In vivo knee ligament forces are important to consider for informing rehabilitation or clinical interventions. However, they are difficult to directly measure during functional activities. Musculoskeletal models and simulations have become the primary methods by which to estimate in vivo ligament loading. Previous estimates of anterior cruciate ligament (ACL) forces range widely, suggesting that individualized anatomy may have an impact on these predictions. Using ten subject-specific (SS) lower limb musculoskeletal models, which include individualized musculoskeletal geometry, muscle architecture, and six degree-of-freedom knee joint kinematics from dynamic biplane radiography (DBR), this study provides SS estimates of ACL force (anteromedial-aACL; and posterolateral-pACL bundles) during the full gait cycle of treadmill walking. These forces are compared to estimates from scaled-generic (SG) musculoskeletal models to assess the effect of musculoskeletal knee joint anatomy on predicted forces and the benefit of SS modeling in this context. On average, the SS models demonstrated a double force peak during stance (0.39–0.43 xBW per bundle), while only a single force peak during stance was observed in the SG aACL. No significant differences were observed between continuous SG and SS ACL forces; however, root mean-squared differences between SS and SG predictions ranged from 0.08 xBW to 0.27 xBW, suggesting SG models do not reliably reflect forces predicted by SS models. Force predictions were also found to be highly sensitive to ligament resting length, with ±10% variations resulting in force differences of up to 84%. Overall, this study demonstrates the sensitivity of ACL force predictions to SS anatomy, specifically musculoskeletal joint geometry and ligament resting lengths, as well as the feasibility for generating SS musculoskeletal models for a group of subjects to predict in vivo tissue loading during functional activities.

Introduction

Insights into knee ligament dynamics during gait, such as strains and passive forces, are crucial for understanding injury mechanisms and informing rehabilitations and clinical interventions following these injuries [1]. However, passive forces from these ligaments are very difficult to directly measure in vivo during dynamic activities such as gait, and as such have often been estimated using biomechanical modeling or similar methods [2–12]. These studies have reported a wide range of passive forces from the anterior cruciate ligament (ACL) during various functional activities, with estimates ranging from 0.5 x body weight (xBW) [13] to 3.5 xBW [6] during walking. There is clearly little consensus over exactly how much force is developed by the ACL during gait, with this large range of values suggesting that results are largely dependent on the level of complexity within the models, or the anatomy of the single individual upon which these models are often based. There is therefore justification for addressing the limitations of previous studies by using a cohort of subject-specific (SS) musculoskeletal models to predict ACL forces during gait in multiple subjects.

The benefits of patient-specific models relative to the more-often used scaled-generic models are becoming more accepted, with several studies reporting high sensitivity of models to individualized anatomical factors such as bone geometry, muscle attachment points, and joint centers of rotation [14–23]. These models can be further improved by including precise multiple-degree-of-freedom (DoF) joint kinematics obtained from dynamic biplane radiography (DBR), which can replicate bone positions and orientations with submillimeter accuracy [24]. This can demonstrably improve the accuracy of musculoskeletal models compared to exclusively using traditional skin-mounted surface marker motion capture methods [25].

Regardless of how detailed these individualized models are, the accuracy of ligament force predictions is inherently dependent on the accuracy of their input parameters, particularly resting length (or the length beyond which these tissues begin generating passive forces). This, however, is a difficult measurement to obtain in vivo during dynamic movements such as gait, and as such is usually estimated in studies into knee ligament dynamics, for example, by using a standardized correction percentage of 85% of the ligament's maximum length throughout the full knee flexion/extension range of motion, as described by Guess et al. [26].

This study aims to create a set of subject-specific lower limb musculoskeletal models using a validated framework [23,27,28] to estimate the passive forces exerted by the ACL during a full cycle of level treadmill walking in uninjured knees. The models will include individualized bone geometries, muscle attachments, joint centers of rotation, muscle force generating properties, and six DoF knee joint kinematics from a biplane radiography system. The outputs from these models will be compared to those from corresponding scaled-generic models, which will give important insights into the sensitivity of ligament force predictions to patient-specific properties, the intersubject variability in predicted passive forces in the aACL and pACL forces during gait, and the necessity of creating subject-specific models for answering detailed clinical questions in future studies. Furthermore, a sensitivity analysis where ligament resting lengths will be altered to test the effect on predicted passive forces will give insight into the importance of this parameter in obtaining individualized predictions of knee joint dynamics during gait. These analyses will be used to address two hypotheses: (1) due to the inclusion of individualized bone and muscle data, the subject-specific musculoskeletal models will produce significantly different and more plausible and precise predictions of knee ligament dynamics relative to their scaled-generic equivalents; and (2) predictions of passive knee ligament forces will be highly sensitive to resting length input values.

Methods

Subject-Specific Model Construction.

To create the SS lower limb musculoskeletal models (Fig. 1), musculoskeletal geometry of the right lower limbs of ten individuals (5 males, 5 females; age—27 ± 4 years; body mass—76 ± 12 kg) was obtained from magnetic resonance imaging (MRI). Each subject signed informed consent prior to taking part in this IRB approved study. Imaging primarily consisted of three sequences: T1-weighted anatomical turbospin echo (voxel size 0.47 × 0.47 × 6.5 mm³, repetition time (TR)—650 ms, echo time (TE)—23 ms, number of slices—35 per segment, number of signal averages (NSA)—1, acceleration factor—2) to image from the iliac crest to the ankle joint; T2 (sagittal, voxel size—0.29 × 0.29 × 0.59 mm³, TR—29 ms, TE—16 ms, NSA-1) to image the knee joint ±7.5 cm above and below the joint line; and diffusion-weighted single-shot dual-refocusing spin-echo planar (voxel size 2.96 × 2.96 × 6.5 mm³, TR/TE 7900/65 ms, 12 direction diffusion gradients, b value—0 and 400 s/mm², strong fat suppression—spectral attenuated inversion recovery, number of slices—35 per segment, NSA—2, acceleration factor—2, bandwidth—2440 Hz/pixel) to determine in vivo muscle fiber lengths and pennation angles using a validated framework of fiber tractography. See Charles et al. [28] for details of this method, and Charles et al. [27] for an extensive dataset of in vivo lower limb muscle architecture from the same individuals in this study. All subjects were imaged in a supine position in the same 3T scanner (Biograph mMR, Siemens, Munich, Germany), with a total scanning time of ∼37 min.

Fig. 1.

Framework for constructing subject-specific lower limb musculoskeletal models from T1, T2 MRI, and DTI. Muscles, ligaments, and bones were manually segmented from these images to create 3D meshes, and musclulotendon unit and ligament attachments and via points were manually placed based on these meshes. Muscle force generating properties for each individual were determined for 20 lower limb muscles using a validated framework of DTI and fiber tractography [27], which have formed a reference dataset of in vivo muscle architecture data [28].

The T1 MR images were digitally segmented in Mimics (Materalise, Leuven, Belgium) to create three-dimensional (3D) volumetric meshes of 20 lower limb muscles, as well as the pelvic bones, femur, tibia, fibula, and foot bones. The T2 MR images were similarly segmented to create detailed 3D meshes of the distal femur, proximal tibia and fibula, patella, and the ACL. The meshes of the femur, tibia, and fibula bones segmented from the T1 and T2 MR images were each merged, to create full bone models with detailed articular surfaces at the knee.

Each subject-specific lower limb model was assembled in NMSBuilder [29]. Muscle force generating properties for 21 musculotendon unit (MTU) models were derived from a previously published dataset of in vivo muscle anatomy from the same subjects used in this study [27], which was generated using a combination of anatomical MRI and diffusion tensor imaging (DTI). Including subject-specific muscle force generating properties derived from DTI fiber tractography has been shown to significantly improve the accuracy of model outputs relative to using more generic data [23], and so was included in the models here to optimize their subject-specificity and accuracy. The points of origins and insertions and via points for these MTUs were placed based on the 3D muscle meshes segmented from the T1 MR images (Table 1). The Adductor magnus muscle was represented by two MTUs (lateral and medial) due to its broad origin on the ischium and two insertions on the medial femur separated by the adductor foramen. To account for this, maximum isometric force of the whole muscle [27] was split evenly between these MTUs, while optimal fiber length and pennation angle remained the same, which is common practice in musculoskeletal modeling [21,30–32]. See Tables S1–S10 available in the Supplemental Materials on the ASME Digital Collection for the force generating properties included in each individual musculoskeletal model. This method of attachment point placement is similar to that described previously and has an overall median error of 6.1 mm along all 3 axes [15].

Table 1.

The musculotendon units included in each subject-specific musculoskeletal model, as well as associated wrapping surfaces and properties

		Wrap surface properties
Muscle	Abbreviation	Wrap surface	Body	Cylinder/sphere	Radius (mm)	Length (mm)
Adductor magnus (lateral)	AM1
Adductor magnus (medial)	AM2
Adductor longus	AL
Adductor brevis	AB
Gracilis	GRA
Semimembranosus	SM	Hip extensors at tibia	Leg	Sphere	35	n/a
Semitendinosus	ST
Biceps femoris- long head	BFL
Biceps femoris- short head	BFS
Popliteus	POP
Sartorius	SAR	Hip extensors at tibia	Leg	Sphere	35	n/a
Rectus femoris	RF
Vastus lateralis	VL	Knee extensors at femur	Thigh	Cylinder	25	75
Vastus medialis	VM
Vastus intermedius	VI
Tibialis anterior	TA
Extensor digitorum longus	EDL
Extensor hallucis longus	EHL
Medial gastrocnemius	MG	Gastrocs at femur/Gastrocs at tibia	Thigh/leg	Cylinder	25	75
Lateral gastrocnemius	LG
Soleus	SOL

Ligament Model Properties.

Attachment points of the ACL were determined from 3D meshes from the T2 MR images, as described by Nagai et al. [33]. Similar to Nagai et al. [33], and to ensure consistency with current musculoskeletal models, which include knee ligaments [34], the ACL was modeled by two ligament models representing the anteromedial bundle (aACL) and posterolateral bundle (pACL) in each subject. The dynamic properties of the ligaments were modeled as described by Stanev et al. [35], where input parameters include the ligament's resting length (L_r), stiffness, and damping. Stiffness and damping values were taken from previous literature [34] and were consistent between all subjects (1500 N and 390 N, respectively, for the aACL, and 1600 N and 403 N for the pACL), while L_r values were estimated for both bundles in each subject using a standardized correction percentage [26,36]. These resting lengths are shown in Tables 2 and 3.

Table 2.

Resting lengths of the aACL in each subject-specific and scaled generic model

	aACL resting lengths (m)
	Subject-specific			Scaled-generic
Subject	Initial	+10%	−10%	Initial
S01	0.0352	0.0387	0.0317	0.0283
S02	0.0329	0.0362	0.0296	0.0296
S03	0.0315	0.0347	0.0283	0.0299
S04	0.0306	0.0336	0.0275	0.0295
S05	0.0321	0.0353	0.0289	0.0328
S06	0.0310	0.0341	0.0279	0.0310
S07	0.0307	0.0338	0.0276	0.0320
S08	0.0277	0.0305	0.0249	0.0312
S09	0.0427	0.0469	0.0384	0.0336
S10	0.0382	0.0420	0.0344	0.0330

Table 3.

Resting lengths of the pACL in each subject-specific and scaled generic model

	pACL resting lengths (m)
	Subject-specific			Scaled-generic
Subject	Initial	+10%	−10%	Initial
S01	0.0270	0.0298	0.0243	0.0215
S02	0.0251	0.0276	0.0226	0.0240
S03	0.0239	0.0263	0.0215	0.0234
S04	0.0216	0.0238	0.0195	0.0195
S05	0.0252	0.0278	0.0227	0.0252
S06	0.0290	0.0319	0.0262	0.0291
S07	0.0258	0.0284	0.0232	0.0245
S08	0.0204	0.0225	0.0184	0.0219
S09	0.0340	0.0373	0.0306	0.0246
S10	0.0276	0.0304	0.0248	0.0239

Wrap surfaces were added to the model to prevent muscles passing through bones surfaces (Table 1), and were placed based on those in a generic full body opensim model [37] and subsequently manually optimized in size and location to minimize muscle-bone penetration during joint rotations. Coordinate systems and joint centers for the hip, knee, and ankle joints were determined based on the lower extremity anatomical landmark sets recommended by the International Society of Biomechanics [38] (Fig. 2). Each model was exported to opensim 3.3 [39] for further analysis.

Fig. 2.

Joint centers for the hip (a), knee (b), and ankle (c) joints in each subject-specific musculoskeletal model constructed in NMSBuilder [29]. The position and orientation were determined by the position of anatomical landmarks defined by the International Society of Biomechanics [38]. The coordinate system origin for each body in the model (pelvis, thigh, leg, and foot) was set as the joint center of the respective parent joint. RPSIS/LPSIS—right/left posterior superior iliac spine, RASIS/LASIS—right/left anterior superior iliac spine, RHC/LHC—right/left hip center, RLE/RME—right lateral/medial femoral epicondyle, RLC/RMC—right lateral/medial femoral condyle, RLM/RMM—right lateral/medial malleolus, RPA_CA—right posterior aspect of calcaneus, RPA_II—right posterior aspect of second metatarsal.

Data Collection.

Lower limb joint kinematics and kinetics were gathered from the same ten individuals (Fig. 3) with a 12-camera motion capture system (Vicon vantage, Oxford, UK; 100 Hz) measuring full-body motion for one whole stride (heel strike to heel strike) of level treadmill walking (four trials, 13 s at 1.5 m s⁻¹). A total of 55 reflective markers were placed on each subject.

Fig. 3.

Workflow to create subject-specific and scaled generic musculoskeletal simulations from kinematic and kinetic data collection. Whole body kinematics were obtained from maker based motion capture, while precise six degree-of-freedom knee joint kinematics were obtained from dynamic biplane radiography and a validated model based tracking algorithm [24]. Combined with GRFs, these data were used to develop simulations of treadmill walking with subject-specific and scaled generic musculoskeletal models.

A customized DBR system imaged the knee joint through these same walking steps (100 Hz), with two trials recording one half of the gait cycle (midswing to midstance), and two recording the other half (midstance to midswing). Ground reaction forces (GRFs) were recorded using a dual-belt instrumented treadmill (Bertec Corporation, Columbus, OH).

High-resolution CT scans (voxel size—0.6 × 0.6 × 0.6 mm) of both knee joints were then collected for each individual. The acquired CT images were then digitally segmented (Mimics 17.0, Materalise, Leuven, Belgium) to obtain models of the femur and tibia bones. A validated volumetric model-based tracking process determined the precise 3D six degree-of-freedom knee joint kinematics (Fig. 4) through the recorded walking steps using the biplane radiographs and digitally reconstructed radiographs [24]. The kinematics from the four walking trials for each subject were averaged and then combined to obtain full gait cycle, six degree-of-freedom knee joint kinematics. See Gale and Anderst [40] for full details regarding the acquisition and analysis of these knee joint kinematics from the DBR system. Motion capture marker coordinates and GRF data (low-pass filtered at 20 Hz) were processed and prepared for subsequent modeling steps using the freely available “C3D extraction toolbox” for matlab.2

Fig. 4.

Mean (±1 SD) knee extension (a), adduction (b), and internal rotation (c) joint angles and anterior–posterior (d), lateral–medial (e), and proximal–distal (f) tibial translations determined from DBR, biplane radiographs and model based tracking, and input into subject-specific and scaled-generic musculoskeletal models. The vertical dashed line indicates average toe-off time.

Simulations.

For each subject-specific lower limb model, the standard opensim simulation protocol of inverse kinematics and residual reduction algorithm was applied. The inverse kinematics step was modified to allow for the predefined knee joint kinematics from DBR to be combined with the hip and ankle joint kinematics from motion capture marker positions. Static optimization was used to estimate knee ligament forces during walking, with the objective function of minimizing the sum of muscle activations squared.

An initial validation of each SS model was performed by comparing predicted knee joint loads to previously published in vivo knee joint forces [41]. The model predictions of joint contact force were obtained using the Joint Reaction Analysis within opensim 3.3, while in vivo forces were measured during treadmill walking in six individuals with instrumented knee joint replacements (24 total gait cycles; 1.1 m s⁻¹, sports shoes. Data available online3).

Full body generic musculoskeletal models [37] were then scaled to match the anthropometry of each subject. The same simulation protocol was applied to these scaled generic (SG) models, which provided direct comparisons to the subject-specific models. In these models, the muscle and ligament attachment sites remained unchanged from their default settings. Resting lengths in the aACL and pACL were altered using the same correction percentage applied to the subject-specific models.

Data Analysis.

Ligament forces predicted from static optimization in SG and SS models were normalized to body weight (xBW) for comparison. A paired t-test was used to test for significant differences between aACL and pACL forces predicted by the SS (F_SS) and SG (F_SG) models at all time points of the gait cycle using the freely available statistical parametric mapping (SPM) toolbox [42]. Here, this calculation reported statistically significant differences (p < 0.05) when the t statistic, also referred to as SPM{t} [42], exceeded a threshold value. These thresholds were >4.18 or < −4.18 for the aACL, and >4.37 or < −4.37 for the pACL.

To quantify the agreement of the ligament forces predicted in both ACL bundles by the SG models relative to the SS models, root-mean-squared (RMS) differences were calculated for each subject through the entire walking gait cycle $\left(\sqrt{\overline{(F_{\mathrm{ss}}\hspace{0.17em}-\hspace{0.17em}{F_{\mathrm{SG}})}^2}}\right)$. Intrasubject variability in predicted ACL bundle forces was quantified by the average standard deviation of those forces throughout the gait cycle.

Sensitivity Analysis.

To test the effect of predictions of knee ligament forces to uncertainties in resting length values, these values in the aACl and pACL were altered ±10% of their initial value within the SS models (see Tables 2 and 3). Static optimization was then rerun for each SS model within opensim to predict the resulting ligament forces.

Results

Ligament Forces.

Subject-specific simulations predicted a double peak of knee ligament forces in both the aACL and pACL during a walking gait cycle (Figs. 5(a) and 5(b)). The first peak occurred at early stance phase, and the second peak occurred during midlate stance phase. There was also an increase in ligament force at the end of the swing phase, just prior to heel strike. These peaks appear to correspond to peaks of ligament strain measured previously within the same individuals (Nagai et al. [33]) (see Fig. 5). Average force in the aACL was 0.42 ± 0.05 xBW at the first peak, and 0.43 ± 0.05 xBW at the second peak in the SS models. In the pACL, average force was 0.38 ± 0.06 xBW at the first peak, and 0.41 ± 0.06 xBW at the second peak. Intersubject variability in aACL and pACL forces predicted by the SS models averaged 0.14 xBW and 0.13 xBW, respectively, over the entire gait cycle (Fig. 5).

Fig. 5.

Comparison of mean (±1 SD) forces (xBW) in the anterior–medial bundle of the anterior cruciate ligament (aACL; a) and posterior–lateral bundle (pACL; b) as predicted from subject-specific (SS) and scaled generic (SG) simulations of one stride of walking gait. The vertical dashed line indicates average toe-off time. SPM{t} values (aACL, c; pACL, d) through the gait cycle indicate the level of statistical significance between the model predictions. Red horizontal dashed lines represent respective thresholds of statistical significance (SPM{t} > 4.18 or < −4.18 for the aACL, and >4.37 or < −4.37 for the pACL).

Scaled generic models predicted a similar double-peaked behavior during walking in the pACL (Fig. 5(b)), and similar peak forces as in the SS models (0.38 ± 0.04 at the first peak, and 0.39 ± 0.07 at the second peak). This was not seen in the aACL (Fig. 5(a)), which exhibited only one peak of force during midstance (at around 0.41 ± 0.05 xBW on average), with only a slight reduction in force through the swing phase (Fig. 5(a)). In the SG models, intersubject variability averaged 0.15 xBW in both the aACL and the pACL over the gait cycle (Fig. 5).

Statistical parametric mapping showed no statistically significant differences between forces predicted by the SS and SG models in either the aACL or the pACL throughout the entire gait cycle (Figs. 5(c) and 5(d)). However, individual subject RMS difference values showed substantial variability between individuals, with differences between SS and SG simulations ranging from 0.08 xBW (21.1% of maximum force; subject 1) to 0.26 xBW (30.6%; subject 8) in the aACL, and from 0.05 xBW (17%; subject 10) to 0.18 xBW (43.3%; subject 3) in the pACL (Table 4).

Table 4.

Subject demographics and RMS differences of anterior cruciate ligament forces predicted by SG models relative to subject-specific (SS) models

					RMS difference (SS versus SG; xBW)
Subject	Sex	Age	Body mass (kg)	Height (cm)	aACL	pACL
S01	Male	23	90.7	182	0.08 (21%)	0.13 (35%)
S02	Male	26	82.1	173	0.11 (26%)	0.17 (40%)
S03	Male	29	81.1	182	0.10 (25%)	0.18 (43%)
S04	Female	26	71.2	162	0.12 (29%)	0.11 (28%)
S05	Female	23	59.8	170	0.26 (44%)	0.09 (12%)
S06	Female	35	80.2	169	0.13 (31%)	0.09 (33%)
S07	Female	25	80.7	168	0.09 (21%)	0.13 (28%)
S08	Female	26	40.6	162	0.27 (31%)	0.09 (10%)
S09	Male	26	84.8	187	0.21 (64%)	0.06 (15%)
S10	Male	34	82.5	192	0.12 (30%)	0.05 (17%)

RMS differences expressed as % of maximum SS force are displayed in parentheses, which highlights the variability of the accuracy of ACL force prediction by the SG models.

Sensitivity Analysis.

Altering the resting lengths of both the aACL and pACL in the subject-specific models had substantial effects on predictions of force during walking (Fig. 6). Increasing resting lengths by 10% resulted in decreases of peak forces up to 0.18 xBW (57% change) and 0.13 xBW (65%) at the first force peak during the stance phase in the aACL and pACL, respectively. Similar reductions in peak forces were seen at the second peak (54% and 60% in the aACL and pACL, respectively). Reducing ligament resting lengths by 10% resulted in large increases in peak forces in the aACL and pACL. In the early stance phase, peak forces increased by 69% and 73% in the aACL and pACL, respectively (increased to 0.71 and 0.66 xBW). In the late stance phase, peak aACL force increased by 71% (to 0.72 xBW), while peak pACL increased by 84% (to 0.70 xBW).

Fig. 6.

Sensitivity analysis of mean forces (xBW) in the anterior–medial bundle of the anterior cruciate ligament (aACL; a) and posterior-lateral bundle (pACL; b) predicted from subject-specific (SS) simulations of the stride of walking gait, where resting lengths were changed ±10% from the original value. The vertical dashed line indicates average toe-off time.

Knee Joint Contact Forces.

Predicted knee joint contact forces followed similar patterns in the SS models to those measured in vivo [41], and peak forces were similar, with forces of ∼3 xBW in the SS models and ∼2.3 xBW in the in vivo data (Fig. 7).

Fig. 7.

Mean (±standard deviation) knee joint contact forces predicted by the subject-specific (SS) models using the Joint Reaction Analysis in opensim, compared to in vivo knee contact forces measured using instrumented knee joint replacements [41]. The vertical dashed line indicates the average toe-off time in the SS simulations.

Discussion

The main goal of this study was to compare high-fidelity subject-specific musculoskeletal models to scaled generic models of the lower limb for predicting anterior cruciate ligament dynamics during gait. Secondary goals were to quantify the sensitivity of ligament forces predictions to variations in individualized musculoskeletal and ligament anatomy and to characterize the among-subject variability in predicted ACL forces during gait. Two hypotheses were formulated to attempt to achieve these goals, where it was hypothesized that (1) due to the inclusion of individualized bone and muscle data, the subject-specific musculoskeletal models will produce significantly different and more plausible and precise predictions of knee ligament dynamics relative to their scaled-generic equivalents; and (2) predictions of passive knee ligament forces will be highly sensitive to resting length input values.

Previous plausible estimates of peak ACL force during walking range from 0.5 to 1.7 xBW [2,5,7–12], which model the ACL as one whole structure. Our peak force estimates from the SS and SG models, which model the ACL as two bundles, fall within this range when forces from both bundles are summed to provide a total force from the entire ACL structure (0.80–0.84 xBW). It is important to note that these ACL force values are the average over our entire group of ten subjects, which showed variability in peak force that ranged from 0.32 to 0.87 xBW (in the aACL). This large range of values (and standard deviations) points to a potentially large intersubject variability in ACL forces, and suggest that previous studies have not necessarily provided incorrect predictions of forces but have instead been limited by their relatively small sample sizes. The ability of a valid subject-specific modeling framework to capture intersubject variations in musculoskeletal anatomy, and by extension musculoskeletal and ligament function, is an inherent advantage of this method over generic or scaled generic models; however, in the absence of a “gold standard” reference for in vivo knee ligament forces, these estimates are difficult to validate.

The patterns of ligament forces in both ACL bundles predicted here in the SS models follow the patterns of relative elongation reported by Nagai et al. [33], whose analyses used the same subjects. Nagai et al. [33] showed two relative elongation peaks during the stance phase and a peak toward terminal swing phase in both bundles, with the relative elongation of the aACL higher than that of the pACL, which is also similar to the forces seen here. These patterns are, however, different to those seen in previous models and predictions of ACL dynamics [2–4,12], some of which predicted two peaks of relative strain or elongation, at midlate stance phase and terminal swing phase. Potential reasons for these differences may be due to more accurate kinematics relative to Taylor et al. [4] and higher walking speeds relative to Wu et al. [3] (see Nagai et al. [33] for further discussion of these differences).

However, while the SS models exhibited similarities to previous data, the SG models did not, particularly in the aACL, where a double force peak during stance was not observed and forces remained high throughout the swing phase. Despite the peak force being within a physiological range, and the differences from the SS models not being statistically significant throughout the gait cycle, the peak force during midstance and relatively high loading throughout the swing phase are unlikely to be representative of true aACL dynamic behavior during walking. Therefore, these data partially supported hypothesis 1, although it is possible that small adjustments to the ligament attachment points within the scaled-generic models, particularly those of the aACL, could improve the force predictions of the scaled-generic models and result in closer matches to the subject-specific predictions.

However, this good agreement in ligament forces between the model types did not appear to be consistent across all the subjects in this study. The large variation in RMS difference values between the subjects (ranging from 0.08 xBW to 0.27 xBW in the aACL) showed that the SG models lack precision in predicting knee ligament dynamics in subjects with a range of anthropometries. There are many potential reasons for this variability in the accuracy of the SG models, such as inconsistencies in scaling and discrepancies in ligament attachment points. The attachment point location (onto the femur and tibia) and orientation of the ACL are known to vary considerably between individuals due to variations in the anatomy of the knee joint complex [43], and these are important factors which cannot be precisely incorporated into scaled-generic models. Given that ligament resting lengths in the SG models were determined with the same correction percentage to the SS models, but attachment sites coordinates remained unchanged from their generic values, these discrepancies in force highlight the importance of accurately identifying and incorporating individualized ligament attachment sites into musculoskeletal models in order to accurately estimate ligament forces during gait. This sensitivity of knee ligament forces to origin and insertion location was also suggested by Beynnon et al. [44] and lends further support to the use of subject-specific musculoskeletal modeling within clinical or sports biomechanics, where high resolution MR images can be used to determine individualized muscle and ligament geometry. Within these fields, a valid framework to generate high fidelity predictive models of the knee joint complex in a range of subjects provides a platform upon which to test various functional hypotheses of in vivo tissue loading, and could also be used to generate personalized predictions of postsurgical outcomes or inform tailored injury rehabilitation protocols.

Ligament Resting Lengths.

The comparison between subject-specific and scaled generic models suggests that estimates of ligament dynamics are highly sensitive to attachment sites and bony geometry. However, the resting length of these ligaments (the length beyond which they begin to develop a passive force) is another important input factor into these ligament models, but one which is usually estimated rather than directly measured in studies modeling the dynamic behavior of knee ligaments. The results of the sensitivity analysis, where initial resting length values were changed ±10%, supported hypothesis 2 and quantified the high sensitivity of force predictions to uncertainties in certain input values, with a 10% decrease in resting length resulting in increases in peak passive forces of up to 84% from the pACL during the late stance phase. Using estimates of resting lengths is an inherent limitation of studies modeling knee ligament dynamics due to difficulty in obtaining such values in vivo, with the “optimal” approach currently being calculating this value using a correction percentage based on maximum ligament length [26,36]. While various medical imaging techniques such as ultrasound, shearwave or magnetic resonance elastography have shown promise as potential methods for obtaining in vivo estimates of ligament resting lengths, as well as other in vivo muscle/tendon parameters [45–49], they may prove unsuitable for obtaining similar parameters from the ACL due to occlusion from the femoral condyles or tibial plateau. It is therefore likely that estimating resting lengths will remain the most feasible method of enabling individualized predictions of knee ligament dynamics using musculoskeletal modeling, but one which can be optimized with knowledge of individualized ligament geometry obtained through subject-specific modeling.

It should be noted that while attempts were made to individualize the resting length values of the ACL in each model, the stiffness and damping values remained unchanged from their generic values [34]. This was due to a lack of knowledge about how these parameters vary between individuals and further difficulty in measuring these in vivo, but regardless reduced the subject-specificity of each model. These assumptions further contributed to what could be seen as a relatively simple model of ligament dynamics used here [35], particularly when compared to more complex models such as that described by Nasseri et al. [50]. However, the model developed by Stanev et al. [35] has the advantage of being easily incorporated into the open-source, user friendly opensim modeling environment, meaning it can be readily used in a range of studies to accurately predict ligament dynamics in multiple individuals, which this study succeeded in demonstrating.

Limitations.

While this study represents an initial and important insight into the necessity of detailed subject-specific modeling and kinematics in estimating knee ligament dynamics, a few limitations and assumptions inherent to musculoskeletal modeling hinder the clinical relevance of these findings.

As mentioned, in vivo measurements of knee ligament forces are impossible to obtain during dynamic activities such as walking. Therefore, while a good agreement in predicted ACL forces was seen in the SS models to previous musculoskeletal modeling studies, comparisons such as these do little to assess the true validity of the models or their outputs. But good matches between predicted knee joint loads in the SS models relative to in vivo data raised confidence in this modeling framework and in the model's functional predictions, and suggested that they were accurately replicating the dynamics of the knee joint complex. Of course, an exact match between knee joint forces predicted from models of young, healthy individuals and those measured from older individuals with knee joint replacements should not be expected, due to differences in age, gait kinematics and walking speed (1.5 m s⁻¹ versus 1.1 m s⁻¹). Therefore, the lack of in vivo data against which to truly compare predictions of ligament forces from musculoskeletal models make validation attempts difficult and may limit their immediate clinical applicability. However, it is possible that incorporating an improved ligament model into these musculoskeletal models, such as that described by Nasseri et al. [50], which was validated against cadaveric data obtained through a drop-landing task, could raise confidence in the force predictions generating using this subject-specific modeling framework.

Despite the high accuracy of the knee joints in each subject-specific model created here, with high-resolution musculoskeletal geometry, 6 deg of joint freedom and individualized joint centers of rotation based on anatomical landmarks, these centers of rotation were fixed throughout each walking gait cycle. There are questions regarding how this assumption affects the accuracy of predicted model outcomes, as van den Bogert et al. [51] showed that knee joint center of rotation moves and changes orientation substantially during gait, which could have a large effect on muscle and ligament moment arms. While implementing a moving center of knee joint rotation within the opensim subject-specific modeling framework presented here was out of the scope of this study, doing so could provide more realistic personalized predictions of muscle and ligament forces in future studies.

Our study focused on level treadmill walking; however, investigating downhill running, cutting, or pivot maneuvers, which place more load on the ACL would be more relevant to predictions of postsurgical rehabilitation. Furthermore, given that the force from both ACL bundles seen here was homogenous, something also noted by Wu et al. [3] during walking, analyzing more demanding movements may give further insights into the dynamic differences between the aACL and pACL bundles. These two bundles have also been seen to wrap over each other during knee flexion–extension [52], however ligament wrapping was not included in this study. Ultrasound imaging of the ACL could also provide insights into how the two bundles interact during knee rotations and translations and may allow more accurate representations of this behavior in musculoskeletal models using wrapping surfaces.

Future Directions

Here, we establish an efficient framework for developing highly detailed subject-specific lower limb musculoskeletal models and simulations of knee ligament dynamics, which incorporate individualized musculoskeletal geometry, muscle architecture, and high precision knee joint kinematics from dynamic biplane radiographs.

Predictions of ACL forces from the subject-specific models through walking are slightly lower than values reported in previous literature, although without “gold-standard” reference values of in vivo ligament forces, it is assumed that these values are not physiologically unfeasible during a low-demand movement such as walking. The more physiologically plausible and precise predictions of ACL dynamics predicted by the subject-specific models relative to the scaled-generic models, as well as the high sensitivity of these predictions to ligament input parameters, support the need for a high degree of personalization in models such as these for clinical uses. However, further study and refinements to this framework are needed before these models can be used clinically. More accurate measurements of ACL resting lengths, or the use of more complex ligament models, will optimize predictions of its dynamic behavior during gait, and attempts to automate the process of creating the subject-specific models are crucial for applying this framework to clinical cases. Nevertheless, this study provides solid support to the notion that highly accurate subject-specific musculoskeletal models can be developed for groups of individuals (healthy or pathological) and used within freely available musculoskeletal modeling software for hypothesis testing related to postsurgical ligament dynamics. This is particularly important for future work, as while it is possible to predict ligament forces without the creation of detailed inverse dynamics based musculoskeletal models, generating predictive simulations of functional postsurgical and rehabilitation outcomes cannot be done using purely kinematics-based methods. Furthermore, a large set of individualized models such as that presented here would also be an ideal platform upon which to investigate the relationships between musculoskeletal anatomy, physiology and ligament forces, which could help to increase understanding surrounding ACL injury risk factors in various patient populations. Furthermore, if these methods were to be applied to other joints, this could lead to an extensive set of highly detailed subject-specific models of the human musculoskeletal system with potentially greater clinical applicability than scaled-generic models.

Supplementary Material

Supplementary Material

Supplementary Tables

Funding Data

• •National Institutes of Health (No. 2R44HD066831-02A1; Funder ID: 10.13039/100000002).