AI-powered biomechanical modeling for ACL-reconstructed knees: predicting knee joint contact forces via computer vision and deep learning

Abstract

Background

Patients undergoing anterior cruciate ligament reconstruction (ACLR) are at high risk of osteoarthritis or secondary injuries, with abnormal knee contact forces (KCFs) identified as a key factor in joint degeneration. Traditional KCF assessment relies on expensive lab systems while advances in computer vision and AI now enable low-cost alternatives. However, currently available methods oversimplify knee mechanics and neglect compensatory movements, highlighting the urgent need for intelligent, real-time monitoring tools for personalized rehabilitation. Therefore, the aim of this study was to develop and validate an integrated, non-invasive framework for accurate KCFs prediction in ACLR patients during daily activities. We hypothesized that combining enhanced musculoskeletal modeling with a deep learning architecture incorporating spatiotemporal attention would improve the prediction accuracy across multiple movement tasks.

Methods

This study simultaneously recorded three daily movements of 29 post-ACLR patients using both Vicon and OpenCap. Motion trajectories captured by Vicon were imported into OpenSim for musculoskeletal modeling and KCFs calculation. Dataset comprising OpenCap-derived kinematics and OpenSim-computed KCFs was used to train 3 learning models for the prediction of KCFs in ACLR patients across different movements.

Results

Among three models, CNN-BiGRU-Attention model demonstrated the best predictive performance across all three movement tasks (R2walking = 0.973 ± 0.003, R2running = 0.982 ± 0.004, R2descending stairs = 0.951 ± 0.007). CNN and self-attention mechanism collectively enhanced the model's ability to capture key features in ACLR patients' movement data, thereby improving KCF prediction accuracy. Furthermore, for the three daily activities, all models showed superior KCFs prediction performance in running and stair-descent tasks compared to walking.

Conclusion

The developed framework successfully achieved high-precision prediction of KCFs. This technological breakthrough not only provides a real-time quantitative tool for rehabilitation monitoring in patients with ACLR, but also facilitates a paradigm shift from static laboratory analysis to dynamic real-time monitoring, with broad application prospects in sports medicine, rehabilitation engineering.

Introduction

In the field of sports medicine, anterior cruciate ligament reconstruction (ACLR) has become one of the most critical orthopedic surgical interventions, with well-established standardized treatment protocols globally [1]. Epidemiological data indicate that the annual volume of ACLR surgeries has exceeded 200,000 cases and continues to rise steadily, driven by the growing population engaged in sports activities [2, 3]. Despite continuous improvements in surgical techniques and rehabilitation protocols, long-term follow-up studies have revealed concerning clinical outcomes: approximately 15–25% of patients develop knee osteoarthritis (KOA) within 5–10 years postoperatively, and the re-injury rate remains as high as 15% [4, 5]. This clinical dilemma highlights the limitations of current postoperative assessment systems in biomechanical monitoring, prompting researchers to focus on the potential mechanisms linking abnormal dynamic knee loading to postoperative complications, particularly the prognostic value of abnormal knee contact forces (KCFs) distribution [6, 7].

Recent advancements in sports biomechanics have revealed that patients after ACLR exhibit KCFs patterns during functional movements (e.g., running, jump-landing, and cutting) that differ significantly from those of healthy individuals [8]. Specifically, instrumented analyses show that the peak KCFs on the affected limb during gait cycles, landing, and sudden deceleration can reach 3 to 5 times body weight, 20%–30% higher than the contralateral side and well beyond the physiological range observed in healthy subjects [9, 10]. Compared with normal individuals, ACLR patients often display imbalanced anterior–posterior and medial–lateral KCF distribution, altered force trajectories, and delayed time to peak loading [11]. These abnormal loading patterns not only affect the mechanical environment of cartilage and meniscus but may also induce localized microdamage through stress concentration, thereby accelerating joint degeneration [12]. Therefore, precise quantification of the spatiotemporal characteristics of KCFs during movement is of great clinical importance for establishing objective and sensitive postoperative evaluation systems, predicting KOA and other complications, and developing individualized rehabilitation strategies based on patient-specific loading responses [13].

Currently, Instrumented knee implants represent the gold standard for the direct in vivo measurement of knee contact forces, as demonstrated by the datasets released through the Grand Challenge initiatives. However, the highly invasive nature of instrumented implants, together with ethical and practical constraints, severely limits their applicability to routine clinical assessment and large-scale studies. Consequently, non-invasive approaches based on motion capture and musculoskeletal modeling have become the most widely adopted solution for estimating knee contact forces in both research and clinical settings [14]. While this approach yields high accuracy, its clinical application faces substantial barriers, including high cost, stringent space and personnel requirements, time inefficiency, and limited ecological validity [15]. These constraints significantly hinder the widespread adoption of such technology in routine clinical and community rehabilitation settings and restrict its use in large-scale longitudinal studies [16, 17].

In recent years, advances in computer vision and artificial intelligence have opened new avenues for research in sports biomechanics [18–20]. The OpenCap system, developed at Stanford University, represents a significant breakthrough in this domain [21, 22]. Utilizing two or more smartphone cameras and deep learning algorithms, OpenCap achieves near-laboratory precision in 3D motion capture at a fraction of the traditional cost, offering a viable solution for large-scale and efficient KCF assessment in clinical and community settings. Based on this foundation, researchers have begun exploring machine learning-based approaches for predicting KCF and have made promising progress. N.M. Brisson et al. achieved relatively accurate predictions of peak KCFs using a dataset from KOA patients and LASSO regression modeling in their study [23]. While J. Lavikainen et al. trained a feedforward neural network using datasets from inertial measurement units (IMU) and video cameras respectively, thereby achieving prediction of KCFs [24]. J. Holder et al. enhanced the prediction accuracy of KCFs in individuals with knee deformities by incorporating knee joint moments and an optimized linear mixed-effects model [25]. In separate investigations, the research groups led by H.J. Bennett and J. Zou independently implemented long short-term memory (LSTM) neural network architectures to predict KCFs under walking conditions, demonstrating the applicability of deep learning approaches for gait analysis [26, 27].

However, applying the OpenCap system and advanced algorithms to ACLR patients still faces several key challenges. In terms of biomechanical modeling, current OpenSim models often simplify ACL grafts as linear elastic components, which fail to capture the complex mechanical behavior of the ligament, including: nonlinear stress–strain relationships, with stiffness increasing when strain exceeds; time-dependent behaviors such as stress relaxation and creep; and pronounced anisotropy, with distinct mechanical responses in longitudinal versus transverse directions [28]. These simplifications can lead to KCFs estimation errors, especially during high-impact tasks such as jump landing. On the algorithmic side, a lot of existing deep learning methods are based on data from healthy individuals, making them ill-suited to accurately capture the compensatory movement patterns characteristic of ACLR patients. These include: kinematic features such as a 20%–30% reduction in knee flexion angle during the stance phase accompanied by compensatory increases in hip motion; kinetic changes such as reduced peak ground reaction forces (GRFs) and delayed time to peak; and neuromuscular control alterations such as quadriceps inhibition and hamstring overactivation [29]. These deviations collectively limit the predictive accuracy and clinical applicability of current models in postoperative populations.

To address these challenges, this study proposes an integrated framework combining biomechanical modeling and deep learning for KCFs prediction, specifically tailored for ACLR patients. Building upon OpenCap-based motion capture, we integrated an enhanced OpenSim model to develop a personalized system for estimating knee contact forces. The main contributions of this study include: (1) Collecting data from ACLR patients under non-invasive conditions using OpenCap video motion capture technology to provide an accurate dataset for the model. (2) implementing a hyperelastic constitutive model for the ACL within the OpenSim platform to better represent the nonlinear mechanical behavior of the ligament; and (3) designing a deep learning network with spatiotemporal attention mechanisms to enhance recognition of characteristic compensatory movement patterns in ACLR patients. The outcomes of this study are expected to provide a valuable biomechanical tool for personalized rehabilitation monitoring and to promote a more intelligent, individualized, and predictive approach in sports medicine.

Methods

The complete procedure of the prediction from kinematic data to KCFs (kinetics) can be divided into three parts, which are outlined in Fig. 1. Three daily movements from 29 patients after ACLR were simultaneously recorded by the Vicon 3D motion capture system and two iOS devices equipped with OpenCap. The motion trajectories captured by Vicon were imported into OpenSim for musculoskeletal modeling, and simulation calculations were performed to obtain KCF.s Dataset consisting of kinematics from OpenCap and KCFs from OpenSim was used to train the developed CNN-BiGRU-Attention model to predict KCFs of ACLR patients based on input joint angles and accelerations of the lower limbs.

Fig. 1.

Schematic overview of the integrated framework for predicting knee contact forces in ACLR patients. A Simultaneous motion capture during three daily activities (walking, running, and stair descent) from 29 ACLR patients using a Vicon optical system and two smartphone-based OpenCap systems. Reflective markers were placed on anatomical landmarks, and ground reaction forces were collected via embedded force plates. B Vicon-derived marker trajectories and force plate data were processed, filtered, and imported into OpenSim for musculoskeletal modeling. A subject-specific model was scaled, and inverse dynamics combined with a nonlinear hyperelastic ACL model were used to compute KCFs. C OpenCap-extracted lower limb joint angles and accelerations served as input to a hybrid deep learning model (CNN-BiGRU-Attention), which was trained to predict KCFs. The model integrates convolutional layers for spatial feature extraction, bidirectional GRU for temporal dependencies, and a self-attention mechanism to emphasize biomechanically critical gait phases

Participants

A total of 29 patients at different rehabilitation stages after ACL reconstruction were recruited to participate in this experiment, which included 22 males (ages = 29.1 ± 4.6 years old, height = 1.73 ± 0.05 m, body mass = 71.52 ± 4.31 kg, postoperative duration = 6.3 ± 3.1 months, International Knee Documentation Committee (IKDC) score = 78.19 ± 1.77) and 7 females (ages = 25.8 ± 3.2 years old, height = 1.64 ± 0.03 m, body mass = 51.14 ± 3.91 kg, postoperative duration = 7.4 ± 2.6 months, IKDC score = 80.76 ± 3.27) participants. Before the official recruitment, all patients were told to complete an IKDC survey to assess the rehabilitation status of their knee joint [30]. The inclusion criteria for recruitment were as follows: (1) The participant was able to perform daily activities after diagnosed by a specialist; (2) The participant had no other severe lower limb injuries or neuromuscular diseases and other conditions that could affect gait; (3) The participant had no significant complications during the postoperative rehabilitation process and had reached the corresponding rehabilitation milestones (IKDC score above 70) [31]. All participants were informed of the purpose, requirements, and procedures before the experiment began, and then signed a written informed consent form and confirmed that they had no history of knee-related surgery other than anterior cruciate ligament reconstruction.

Experimental procedure

The experimental data in this study were all collected in the Biomechanics Laboratory of Ningbo University. The Vicon 3D motion capture system (Vicon Metrics Ltd., version 2.14.0, Oxford, UK) with 16 cameras was set up around the runway, equipped with two Kistler force plates to collect the participants' motion trajectories and ground reaction forces during movement. The sampling frequencies of the Vicon system and the force plates were 200 Hz and 1000 Hz, respectively, and they were synchronized on a workstation computer. Two iOS devices (iPhone 16 Pro Max, Apple, USA) equipped with the OpenCap App (Stanford University, CA, USA) were placed on both sides of the runway. In accordance with the OpenCap user guidelines, at least two devices are required to achieve accurate motion capture. This configuration ensured adequate coverage of the motion plane while minimizing the risk of occlusion, and at the same time provided a practical and efficient setup compatible with the experimental environment. A checkerboard panel (440 × 310 mm), positioned perpendicular to the ground, was used to calibrate both the motion plane and the cameras [21, 22]. The video capture frequency of OpenCap was set to 60 Hz (Fig. 1A).

The recruited participants were required to wear designated tight-fitting sportswear and have reflective markers attached during the experiment (Fig. 1A). For all three movement tasks (level walking, running, and stair descent), participants performed the trials at a self-selected and comfortable pace that best represented their habitual daily movement patterns. To ensure consistent and reliable kinetic measurements of the reconstructed knee, participants were instructed to initiate ground contact with their affected limb on the force plate during each trial. Prior to formal data collection, all participants completed a standardized familiarization and warm-up session, during which they practiced each task multiple times to adapt to the experimental setup and reduce potential alterations in movement patterns associated with force plate targeting. This procedure was implemented to balance the need for accurate kinetic data from the affected limb with the preservation of task naturalness. During the formal experiment, participants were instructed to complete three daily movement tasks: walking, running, and descending stairs. For the walking and running tasks, participants followed the researchers’ instructions to walk at their natural gait or run at their self-selected pace across the runway and were required to step onto the force plate first with their affected limb. For the stair descent task, a three-step staircase with a standing platform was placed in front of the first force plate. Participants were instructed to descend the stairs naturally from the platform and step onto the force plate first with their affected limb [32, 33]. Each movement task was performed 10 times without any discomfort. Participants were allowed to take breaks as needed to prevent fatigue or discomfort from affecting their performance. All three daily movement tasks were simultaneously recorded by both the Vicon 3D motion capture system and the OpenCap video-based motion capture system [34, 35]. Meanwhile Electromyography (EMG) sensors (Delsys, Boston, MA, USA) with a frequency of 1000 Hz were placed on the subject’s vastus lateralis (VL), vastus medialis (VM), rectus femoris (RF), biceps femoris (BF), tibialis anterior (TA), medial gastrocnemius (MG), lateral gastrocnemius (LG), and soleus (SL), and the sensors were positioned following SENIAM guidelines [36, 37] (Fig. 2C). After shaving the test area, abrading the skin, and applying alcohol to minimize impedance between the skin and electrodes, surface EMG signals were recorded, and all data collection processes were conducted by professional and experienced biomechanics researchers. This study complied with the principles laid down in the Declaration of Helsinki. The Ethics Committee of Ningbo University has accepted the study protocol (Approval Number: TY2025035). All participants were informed of the purpose, requirements, and procedures before the experiment began, and then signed a written informed consent form.

Fig. 2.

Musculoskeletal Modeling Process Based on OpenSim. A Subject specific model scaling and static optimization was processed based on the original model, while inverse dynamics computed KCFs. B ACL was explicit modeled based on nonlinear materials to improve biomechanical accuracy. C Model validation involved comparing simulated muscle activations with experimental EMG data and verifying joint kinematics against DFIS-measured bone displacements, ensuring accuracy

Musculoskeletal modeling

The motion trajectories collected by the Vicon 3D motion capture system were exported as C3D format files. MATLAB R2024a (MathWorks, Natick, MA, USA) was used to process the experimental data, including procedures such as coordinate transformation and low-pass filtering. We applied a fourth-order zero-phase-lag Butterworth low-pass filter to process the data, with cutoff frequencies set at 10 Hz and 20 Hz. Specifically, the 10 Hz cutoff frequency was used to extract the motion data to effectively smooth the marker trajectory while preserving meaningful motion details, while the 20 Hz cutoff frequency was applied to minimize noise for maintaining the integrity of the ground reaction force signals. After preprocessing, motion capture and force plate data stored in C3D format were converted into OpenSim-compatible formats using a custom data-processing pipeline developed in MATLAB. Specifically, three-dimensional marker trajectories were first extracted from the C3D files and resampled to ensure consistent sampling frequency across trials. The marker positions were then organized according to the OpenSim marker set definition and exported as.trc files, with appropriate coordinate system alignment and unit conversion applied where necessary. This conversion procedure ensured temporal alignment between kinematic and kinetic datasets and compatibility with subsequent musculoskeletal simulations in OpenSim. In this study, biomechanical parameters were processed and calculated using OpenSim. First, a generic musculoskeletal model was scaled to each participant using subject-specific anthropometric information derived from motion capture markers. During the scaling process, segment dimensions and joint center locations were adjusted by minimizing the distance between experimental marker trajectories and corresponding virtual markers on the model, thereby ensuring geometric consistency between the scaled model and the participant’s anatomy. Body segment masses and inertial properties were simultaneously scaled based on individual body mass and segment lengths. Inverse kinematics (IK) was then performed to estimate joint angles by minimizing weighted marker tracking errors across all segments over the entire movement cycle. The resulting joint kinematics, together with experimentally measured ground reaction forces, were subsequently used as inputs for inverse dynamics to compute joint moments. KCFs were estimated using joint reaction analysis (JRA), which integrates joint kinematics, external forces, and joint moments to resolve the resultant joint reaction forces and moments acting at the knee. In the present study, JRA was implemented using OpenSim’s built-in analysis tools, with knee joint reaction forces expressed in the tibial reference frame and decomposed along anatomically meaningful directions. This approach enabled the estimation of knee contact force profiles throughout the movement cycles while maintaining consistency between kinematic and kinetic inputs.

This study employed an upgraded musculoskeletal model derived from the standard OpenSim2392 model, which was previously developed and validated by the authors in earlier work [38]. While the original OpenSim2392 model represents each knee joint with a single degree of freedom (flexion/extension), such a simplification is insufficient for investigating anterior cruciate ligament (ACL) mechanics and knee joint loading. Therefore, the base model was further modified to explicitly account for multi-planar knee motion and ligament behavior, providing a more physiologically realistic representation of knee joint mechanics. In particular, the upgraded model incorporates an explicit constitutive formulation of the ACL, in which nonlinear and non-elastic strain behavior is modeled to capture the ligament’s characteristic force–elongation response under physiological loading conditions. The upgraded model consists of 10 rigid body segments, 27 degrees of freedom (DOFs), and 92 muscle–tendon units. Compared to the standard OpenSim2392 model (23 DOFs), each knee joint was modeled with three rotational degrees of freedom, including flexion/extension, abduction/adduction, and internal/external rotation. These additional DOFs, together with the explicit modeling of ACL nonlinear strain behavior, enable the representation of secondary knee motions and ligament loading mechanisms that are closely associated with knee joint contact force distribution.

When exploring the injury mechanisms of the ACL and knee joint, traditional models in OpenSim typically assume that the ligament follows a linear force–length relationship and neglect its dependence on strain rate. However, as a dense connective tissue (DCT), the ACL typically exhibits short-term viscoelastic strain behavior, which consequently affects its force–length characteristics [39]. Therefore, the musculoskeletal knee model developed and validated in former study was applied to achieve a more accurate biomechanical simulation of ACL and knee joint injuries, which redefines the ACL ligament as a nonlinear, short-term viscoelastic material with strain rate dependency, thereby enhancing the biological realism of the simulation (Fig. 2B). The ACL explicit model used in this study calculates the instantaneous strain rate () by computing the time derivative of ligament strain length:

1

Within this computational framework, the calculation function for nominal axial stress developed based on DCT mechanism is given as follows:

2

where α and β represent the shape factor and scale factor, respectively, of the probability distribution function during the sequential stretching of collagen fibers under stress loading, while x and y denote the initial length and strain length of the ligament [38]. Based on the calculated , the internal ligament loading force based on this model was :

3

where is the average physiologic cross-sectional area of the DCTs. When the ACL is explicitly modeled in OpenSim, the KCFs derived from inverse dynamics can be calculated as:

4

where is the simulated force of the joint-related muscle, is the ground reaction force, is the force generated due to the mass and acceleration of the knee joint and its connected parts, is the passive support force provided by the knee joint ligaments, and are the weighting coefficients of each part [29].

To quantitatively validate the musculoskeletal simulations, the EMG signals of VL, VM, RF, MG, LG, SL in running movement were compared with the result of the Opensim simulation. EMG data were first processed using standard procedures, including band-pass filtering, rectification, and normalization. Simulated muscle activations obtained from the OpenSim model were time-normalized to the gait cycle and aligned with the corresponding EMG profiles. Quantitative agreement between simulated and measured muscle activity was evaluated using the coefficient of determination (R²) computed over the entire time series [39]. Besides, a rotatable liquid helium-free MRI scanner (XGY-SpinMRI-CS001, XinGaoyi Medical Equipment Co., Ltd., Zhejiang, China) was used to acquire imaging data of the affected knee and constructed a 3D model, with mesh sizes for soft tissues, bones, cartilage, and ligaments set to 2 mm, 2 mm, 0.5 mm, and 0.5 mm, respectively. In addition, a high-speed dual fluoroscopic imaging system was used to analyze the patient's bone displacement during movement. Two fluoroscopes positioned at 90° captured knee images from anterolateral and anteromedial projections. A cubic calibration frame and XMAlab (v2.1.0, Brown University, Prov, USA) was used for spatial calibration and calculating X-ray tube and detector positions. The calibration file was imported into Rhinoceros (v7.4, Robert McNeel Ltd., WA, USA) to create a virtual biplanar fluoroscopy system, with two virtual cameras representing the X-ray sources. The knee model was adjusted in Rhinoceros to align its projection contours with actual fluoroscopic images, using the 3D model as a reference. Coordinate systems for the femur, tibia, and patella were established, and bone displacement was calculated using Rhinoceros tools (Fig. 2C). The relative displacement of the femur-tibia, femur-patella, and tibia-patella in the sagittal plane during walking was calculated and used to validate the accuracy of the OpenSim simulation model [40].

Data preprocessing

After completing the experiment and musculoskeletal modeling process, a total of 862 sets of knee joint contact force data and corresponding OpenCap-collected kinematic data were saved. Among them, there were 287 sets of walking data, 289 sets of running data, and 286 sets of stair descent data. Each set of data included lower limb joint (hip, knee, ankle) angles and velocities from the subjects in 3 motion planes: the sagittal, the frontal, and the transversal. The gait cycle of all three daily movements was defined as a complete phase from 0 to 100% in this study, corresponding to the interval from the participant’s foot contacting the force plate to leaving it. The stance phase was defined as the period from initial foot contact, identified when the vertical GRF exceeded 10 N, to toe-off, which was defined as the complete liftoff of the forefoot from the ground, corresponding to the instant when the GRF dropped below 10 N. The kinematic data collected by OpenCap was intercepted according to the video frame and saved as a complete gait cycle data series. A MATLAB (Visual R2022a, MathWorks, Natick, MA, USA) script was used for filtering and interpolation. In the script, a fourth-order Butterworth low-pass filter was applied to both the knee joint contact force and kinematic data, with cutoff frequencies set at 10 Hz and 20 Hz. The filtered data were then interpolated and resampled to 101 data points to correspond to the 0–100% gait cycle. After filtering and interpolation, the script conducted missing data checks and outlier elimination to ensure dataset accuracy. Following these preprocessing steps, 280 datasets for each movement type were ultimately retained as the input dataset for validating the deep learning model using a ten-fold cross-validation. In each dataset, the input data consists of joint angles and accelerations from three lower extremity joints (ankle, knee, and hip) across three planes of motion (sagittal, frontal, and transverse planes), while the output data was KCF during the stance phase of various movements [41].

Deep learning prediction

A combined deep learning model: CNN-BiGRU-Attention, was developed in this study and used to predict KCFs of patients after ACL reconstruction during 3 kinds of daily movements. The development, training, and testing of the model were conducted with the PyTorch deep learning framework in PyCharm (V2024.2.3, JetBrains, Prague, Czech Republic). The CNN-BiGRU-Attention model employed a multimodal feature extraction strategy to achieve accurate prediction of KCFs through a three-stage processing architecture. In the first stage, convolutional neural networks (CNN) were utilized to extract spatial local features from kinematic/dynamic data, capturing instantaneous spatial correlations in joint movement patterns. The second stage leverages the bidirectional temporal processing capability of bidirectional gated recurrent units (BiGRU) to model biomechanical relationships between pre- and post-movement states, thereby analyzing the dynamic evolution patterns of lower limb joint movements. The final stage incorporates an attention mechanism to dynamically weight temporal features, with particular emphasis on enhancing mechanical feature representation during critical movement phases (such as mid-stance and push-off phases in gait cycles). This approach significantly improves prediction accuracy for peak KCFs.

The proposed hierarchical feature fusion architecture can effectively address the limitations of traditional methods in mechanical prediction under complex movement patterns. The complete structure of CNN-BiGRU-Attention model and the construction of each block are shown in Fig. 3.

Fig. 3.

The structure of CNN-BiGRU-Attention model. The input data was first passed through the CNN block for feature extraction, then entered the BiGRU block optimized with the self-attention mechanism

Convolutional neural network

In this study, targeting the KCFs prediction task, we constructed a one-dimensional (1-D) CNN to extract discriminative features from the time-series kinematic and kinetic data (Fig. 3). Unlike traditional feature engineering methods that rely on handcrafted variables, the 1-D CNN automatically learns hierarchical feature representations directly from the raw temporal signals, such as joint angle trajectories, angular velocities, and GRFs profiles. Specifically, the convolutional kernels slide along the temporal dimension of the input sequences, capturing localized motion patterns and short-term temporal dependencies that are closely related to the dynamic loading of the knee joint. For example, small kernel sizes are capable of detecting fine-grained variations in joint movement during rapid gait transitions, while larger receptive fields formed through stacked convolutional layers allow the model to integrate contextual information across multiple gait cycles [42]. The local perception and weight-sharing properties of the 1-D CNN contribute to both efficiency and generalization. Local perception ensures that each filter focuses on a specific temporal neighborhood of the input, enabling the extraction of phase-specific biomechanical signatures, such as the sharp increase in knee flexion moment during the loading response phase. Weight sharing across the entire sequence reduces the number of learnable parameters, alleviates overfitting, and ensures that the same motion patterns can be recognized regardless of their temporal position in the sequence. In addition, pooling operations following convolution further condense the learned representations, filtering out redundant or noise-sensitive fluctuations in the sensor data while retaining the most salient features related to knee joint loading [43].

Bidirectional gated recurrent unit

Gated recurrent unit (GRU) is an improved recurrent neural network (RNN) architecture which introduces update and reset gates, which allow it to more effectively update the network state and selectively forget previous state information, thereby improving the capture of long-term dependencies while avoiding excessive computational complexity (Fig. 3). The hidden state update equations of GRU are as follows:

5

where represents the hidden state at the current time step, while represents the hidden state at the previous time step. is the candidate hidden state at the current time step. The update gate has a value range of [0,1] and controls the weighting between old and new information, determining the degree of hidden state update. Additionally, the symbol represents element-wise multiplication, which is used for per-element computations [44, 45].

Compared to traditional unidirectional GRUs, bidirectional gated recurrent Unit (Bi-GRU) simultaneously propagates information in both forward and backward directions, allowing for a more comprehensive capture of the sequential dependencies:

6

7

8

Here, represents the forward hidden state, which is passed from time step to , and the input ​ is the input feature at the current time step. Meanwhile, ​ represents the backward hidden state, which is passed from time step to . This means that the backward GRU propagates information from the end of the sequence to the beginning, opposite to the forward GRU. The final hidden state ​ is formed by concatenating the forward hidden state ​ and the backward hidden state ​.

In this study, we constructed a bidirectional gated recurrent unit (BiGRU) module, which receives the temporal features extracted by the CNN module and subsequently predicts KCFs under three different movement patterns. The rationale for employing BiGRU lies in its ability to effectively model sequential dependencies and long-range contextual information within kinematic and kinetic data. Unlike standard recurrent architectures, the gating mechanism of GRU selectively updates and resets hidden states, enabling the network to adaptively filter irrelevant inputs while retaining critical biomechanical information. This characteristic significantly reduces the interference of redundant signals, thereby enhancing the stability and robustness of prediction across variable movement conditions [46].

Moreover, the bidirectional design allows the model to simultaneously process the time series data in both forward and backward directions. This dual perspective is particularly advantageous in biomechanical analysis, as KCFs are influenced not only by preceding movement states but also by subsequent motion patterns within a gait cycle. By integrating contextual cues from past and future frames, BiGRU captures more comprehensive temporal dependencies, leading to a more physiologically meaningful representation of joint loading dynamics. In addition to its representational capacity, BiGRU demonstrates computational efficiency compared with more complex recurrent structures such as LSTM. With fewer parameters and simplified gating operations, BiGRU achieves faster convergence and lower computational cost while maintaining predictive accuracy. This efficiency makes it well suited for large-scale datasets and real-time applications in clinical and sports biomechanics [47].

Self-attention mechanism

Self-attention is a mechanism that captures dependencies between elements at different positions in a sequence. It works by calculating the similarity between each element and others in the sequence, dynamically adjusting the attention given to other elements, thereby obtaining richer contextual information:

9

The query matrix , key matrix , and value matrix are obtained by applying linear transformations to the input data. The scaling factor ​ represents the dimensionality of the key vectors (typically the same as the query vectors). Since the dot product computation may result in large numerical values, affecting gradient stability, a scaling factor of ​ is applied to maintain numerical stability. The similarity between queries and keys is measured by computing their dot product , which evaluates the association between a word in a sequence and other words. Then, the Softmax function is applied to the similarity matrix for normalization [48].

This study introduces a self-attention mechanism into the model, enabling it to dynamically allocate attention weights by calculating the correlation between different time steps in the input data (Fig. 3). With this mechanism, joint angles and joint velocities that have a greater impact on KCFs receive higher weights, while irrelevant or less significant information is assigned lower weights. By computing attention scores between Q, K, and V, the model can flexibly adjust the attention each time step pays to others, thereby capturing key patterns in motion data more comprehensively [49].

Model training and evaluation

This study employed a combined approach of k-fold cross-validation and a hold-out independent test set to systematically evaluate the performance of three deep learning models [50]. Specifically, k-fold cross-validation was used for model training and validation, while a separate hold-out test set was reserved for the objective assessment of final model performance. For the tenfold cross-validation, the shuffled dataset was evenly split into ten subsets of equal size. The model underwent ten iterations, with each iteration selecting nine subsets as the training set while reserving the remaining subset for validation. The dataset was first partitioned at the subject level to create an independent test set using a leave-one-out scheme. This test set was completely excluded from the subsequent model training and validation processes. In small-sample machine learning scenarios like this study, each data point plays a critical role in evaluating model performance. A 9:1 training-to-testing split ensures the independence of the test set, serving as a reliable benchmark for assessing the model’s generalization ability [51]. The remaining data were then used to perform k-fold cross-validation, which was applied solely for model training, hyperparameter tuning, and internal validation. This separation ensured a strict independence between the test set and the cross-validation folds. Additionally, the Min–Max normalization technique was applied to standardize the data, ensuring consistency and improving model efficiency. The normalization process follows the algorithmic formula presented below:

10

In this formula, represents the value of a single data point, is the minimum value in the column of data, is the maximum value in the column of data. This technique scales the original data to a range between 0 and 1. This method not only preserves the original distribution of the data but also unifies the scale of the data, making different features or variables comparable.

The squared correlation coefficient (R²), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) of each fold were calculated to assess the performance of the CNN-BiGRU-Attention model. These metrics were computed with Matplotlib in Python, providing a comprehensive evaluation of the model’s predictive accuracy:

11

12

13

In these formulas, represents the true value of the data, denotes the predicted value, and refers to the total sample size. Meanwhile, the value of and MAE ranges from 0 to 1( can theoretically take negative values when the predictive performance of a model is substantially worse than that of a baseline predictor.), a higher indicating better model performance, while a lower value of MAE stands for good. The values of MAPE range from 0 to 100, where values closer to zero indicate better model performance. Using MAE and MAPE together provides a more comprehensive model evaluation. MAE directly measures the absolute error of predictions, making it suitable for assessing the overall error magnitude while remaining stable and unaffected by outliers. MAPE reflects the relative error proportion, making it ideal for datasets with different scales and ensuring better comparability. Combining both metrics helps identify the source of errors (whether in large or small values), avoids the limitations of a single metric, and aids in precisely optimizing deep learning models for time series forecasting tasks [52, 53].

To ensure the generalizability of the deep learning models and prevent overfitting, several strategies were implemented during model development and training. First, a tenfold cross-validation scheme was employed, ensuring that the model was evaluated on multiple independent data splits. Second, dropout layers (dropout rate = 0.3) were incorporated within both the CNN and BiGRU modules to reduce neuron co-adaptation. Third, early stopping was applied during training by monitoring validation loss with a patience of 20 epochs. Fourth, L2 weight regularization (λ = 0.001) was applied to all fully connected layers to penalize large weight values. Finally, hyperparameter optimization was conducted via a grid search over learning rate (0.001, 0.0005), batch size (128, 256), and layer configurations, with selection based on validation performance. These measures collectively ensured robust model performance and minimized overfitting, as evidenced by the consistent R² values across cross-validation folds and the independent test set.

Results

Musculoskeletal model validation and simulation

The validation and KCFs calculation results of the OpenSim musculoskeletal model used in this study are shown in Fig. 4. For the muscle activation validation, EMG data during running were compared with the muscle activation results simulated by OpenSim. The waveforms of both were highly similar, confirming the accuracy of the musculoskeletal model. (Fig. 4A) Additionally, we calculated bone displacements of the lower limb using a rotatable liquid helium-free MRI scanner and DFIS. The DFIS-derived results were compared with the relative displacements of the femur-tibia, patella-tibia, and femur-patella obtained from OpenSim simulations. The waveforms and standard deviations of both were also highly consistent, further validating the accuracy of the musculoskeletal model used in this study. (Fig. 4B) KCF calculated by the ligament-inclusive musculoskeletal model exhibits distinct waveform patterns across the three movement types. Specifically, the walking KCF demonstrates a relatively smooth double-peak curve, while running produces a single-peak waveform. Notably, the stair descent KCF displays a pronounced and steep double-peak pattern (Fig. 4C).

Fig. 4.

The visualization results of musculoskeletal model validation. A The simulation results of muscle activation from OpenSim were compared with the real EMG data collected by Delsys sensors. B The relative displacements of tibia, femur and patella were compared between the results of the DFIS calculation and the Opensim simulation. C KCFs calculated by the validated model for the three types of movements are also presented, where the solid lines represent the mean values and the dashed lines denote the standard deviations

Deep learning models configurations and training

Three deep learning models (CNN-BiGRU-Attention, CNN-BiGRU, and BiGRU) were developed in this study and trained for the KCFs prediction, respectively. The parameter configuration of each model is shown in Table 1.

Table 1.

Parameter configuration of 3 deep learning models in this study

	Name of Models	Layer of CNN	Layer of GRU	Layer of Self-Attention	Batch Size	Number of Epochs
Model 1	CNN-BiGRU-Attention	2	2	1	256	200
Model 2	CNN-BiGRU	2	2	/	256	200
Model 3	BiGRU	/	2	/	256	200

The training and testing loss curves of the three models for predicting KCFs are shown in Fig. 5. In the prediction tasks across all 3 daily movements, the CNN-BiGRU-Attention model, which is equipped with 2 CNN layers and a self-attention module, achieved the lowest test loss (Loss_Walking = 0.0123, Loss_Running = 0.0018, Loss_{Descending Stairs} = 0.0113) among the three models during both training and testing in 200 epochs. Moreover, compared to the other two movements, both the CNN-BiGRU-Attention and CNN-BiGRU models exhibited lower training and testing losses when inputting the dataset collected from the running task.

Fig. 5.

The loss curves of 3 deep learning models in the tasks of knee contact force prediction in 3 daily movements. A Loss curves of BiGRU. B Loss curves of CNN-BiGRU. C Loss curves of CNN-BiGRU-Attention

The study employs a k-fold cross-validation (k = 10) to evaluate the performance of three deep learning models during training. In the process of model training, R², MAE, MAPE of each fold were calculated and recorded during the cross-validation are shown in Table 2. Figure 6 visualizes the prediction errors per fold across different activities in the KCFs prediction task under tenfold cross-validation.

Table 2.

The mean value and standard deviation of R², MAE, MAPE from each model in each fold in different prediction tasks under tenfold cross validation

Models	Movements	R2	MAE	MAPE
BiGRU	Walking	0.795 ± 0.025	0.811 ± 0.045	23.53 ± 2.45
	Running	0.856 ± 0.005	0.821 ± 0.034	19.27 ± 0.88
	Descending Stairs	0.801 ± 0.012	0.874 ± 0.039	25.01 ± 1.61
CNN-BiGRU	Walking	0.861 ± 0.021	0.794 ± 0.014	19.19 ± 3.06
	Running	0.927 ± 0.005	0.760 ± 0.027	15.36 ± 0.98
	Descending Stairs	0.852 ± 0.024	0.806 ± 0.024	21.50 ± 2.38
CNN-BiGRU-Attention	Walking	0.912 ± 0.033	0.650 ± 0.021	12.90 ± 2.29
	Running	0.981 ± 0.004	0.633 ± 0.033	9.78 ± 0.54
	Descending Stairs	0.924 ± 0.029	0.661 ± 0.019	13.87 ± 1.97

Fig. 6.

The visualization of R², MAE, MAPE from each model in each fold during different prediction tasks under tenfold cross-validation. A R² of 3 models in 3 KCF prediction tasks under tenfold cross-validation. B MAE of 3 models in 3 KCF prediction tasks under tenfold cross-validation. C MAPE of 3 models in 3 KCF prediction tasks under tenfold cross-validation

As shown in Table 2, in the KCFs prediction tasks for three types of daily movements, the CNN-BiGRU-Attention model demonstrated the highest R² with the lowest MAE and MAPE in the K = 10 cross-validation among the three models, indicating its strong performance across different prediction tasks. Furthermore, in the prediction tasks for all three movements, all three models exhibited the highest R² and the smallest standard deviation of R² in the running task (R²_{CNN-BiGRU-Attention} = 0.981 ± 0.004, R²_CNN-BiGRU = 0.927 ± 0.005, R²_BiGRU = 0.856 ± 0.005), which suggests that the series of deep learning models with BiGRU as the core architecture possess excellent capability in handling single-peak time-series data of KCFs during the stance phase of running.

KCF prediction and model performance

The study employed three deep learning models—CNN-BiGRU-Attention, CNN-BiGRU, and BiGRU—to simultaneously predict KCFs in patients after ACLR during three daily activities: walking, running, and descending stairs. The models' performance was evaluated using tenfold cross-validation, and 28 out of the 280 input data samples were set as the test dataset for combined validation.

Figure 7 presents a comparison between the predicted outputs of the three models and the test set curves across different motion prediction tasks. As illustrated in Fig. 7, the R² values of all three models are indicated for each motion prediction task. By analyzing both the waveform curves and R² values, the CNN-BiGRU-Attention model demonstrates superior performance compared to the other two deep learning models, while maintaining consistent stability across all three motion tasks (R² ≥ 0.95).

Fig. 7.

The output curves and test dataset curves of the three models in different KCFs prediction tasks. The thicker solid lines indicate the mean values and the thicker dashed lines represent the standard deviations. A Output curves of BiGRU. B Output curves of CNN-BiGRU. C Output curves of CNN-BiGRU-Attention

Figure 8 displays the scatter plot of the mean values of the predicted results versus the actual collected results, along with the fitted curve. As shown in Fig. 8, the prediction results of the standalone BiGRU model exhibit a well-fitted slope, but the standard deviation of the predictions far exceeds that of the actual results. The initially optimized CNN-BiGRU model significantly improves the issue of excessive standard deviation. Furthermore, after incorporating a self-attention mechanism module, the CNN-BiGRU-Attention model achieves a fitted slope close to 1 while maintaining an ideal range of standard deviation (m _Walking = 0.987, m _Running = 1.075, m _{Descending Stairs} = 1.164.

Fig. 8.

The scatter plot of the mean values between the collected actual results and the model-predicted results. The shaded area in the plot represents the standard deviation, and m is the slope of the fitted curve. The closer m is to 1, the higher the correlation between the mean values of the actual results and the predicted results. A Scatter plot of BiGRU. B Scatter plot of CNN-BiGRU. C Scatter plot of CNN-BiGRU-Attention

The study employed a hold-out method with a fixed test set comprising 28 data groups to validate the prediction results. For the validation results on the test set, Table 3 presents the R², MAE and MAPE values of the output results from the three models in KCFs prediction tasks across three daily movements. The metrics were calculated and recorded for all 28 test output samples, while Fig. 8 presents the visualization of loss metrics for the three models across all three motion prediction tasks.

Table 3.

The mean value and standard deviation of R², MAE, MAPE from the results of 3 deep learning models under the separate hold-out test set validation

Models	Movements	R2	MAE	MAPE
BiGRU	Walking	0.861 ± 0.004	0.841 ± 0.025	20.61 ± 1.63
	Running	0.889 ± 0.008	0.829 ± 0.026	19.47 ± 1.45
	Descending Stairs	0.849 ± 0.003	0.834 ± 0.019	21.08 ± 1.17
CNN-BiGRU	Walking	0.899 ± 0.006	0.776 ± 0.021	16.19 ± 1.16
	Running	0.927 ± 0.004	0.754 ± 0.023	13.86 ± 1.46
	Descending Stairs	0.901 ± 0.002	0.780 ± 0.024	15.50 ± 0.98
CNN-BiGRU-Attention	Walking	0.973 ± 0.003	0.647 ± 0.014	11.41 ± 1.29
	Running	0.982 ± 0.004	0.629 ± 0.013	9.23 ± 0.91
	Descending Stairs	0.951 ± 0.007	0.631 ± 0.011	12.08 ± 1.32

As shown in Table 3 and Fig. 9, the CNN-BiGRU-Attention model achieved the highest R² with the lowest MAE and MAPE among the three models in predicting KCFs for all movements. Additionally, all three models demonstrated the highest R² with the lowest MAE and MAPE when predicting KCFs during running, compared to the other two motions. This result further highlights the robust performance and stability of BiGRU-based deep learning models in processing running movement data.

Fig. 9.

Visualization of loss metrics for the three models across all knee joint contact force prediction tasks. In each diagram, the Sample Size on the horizontal axis represents the 28 test datasets, where the waveform illustrates the distribution of test results across different metric magnitudes. The vertical axis whiskers provide detailed visualization of these distributions. A R² of 3 models in 3 KCF prediction tasks. B MAE of 3 models in 3 KCF prediction tasks. C MAPE of 3 models in 3 KCF prediction tasks

In Table 4, the previous related studies mentioned in the article are compared with the deep learning model used in this study, including participant demographics, experimental movements, and prediction errors. While most previous studies collected data from different populations, they only employed relatively simple motor tasks. In contrast, the CNN-BiGRU-Attention model developed in this study demonstrates stable performance in predicting KCFs in ACLR patients across multiple daily activities.

Table 4.

Comparison of the studies mentioned in the article with this study

Study (Authors)	Models (Name)	Participants (Type)	Movements	Error (Type)
Brisson et al. [23]	LASSO	KOA	Walking	0.81 (R2)
Lavikainen et al. [24]	Feedforward- ANN	Healthy & KOA	Walking	0.96 ± 0.10 (R)
Holder et al. [25]	Linear Mixed-effects Model	Knee Malalignment	Walking	0.97 (R2)
Bennett et al. [26]	LSTM	Healthy	Walking	0.77 (R2)
Zou et al. [27]	Transferred MF-LSTM	Instrumented Prostheses	Walking	0.987 (ρ)
This study	CNN-BiGRU-Attention	Post ACLR	3 Movements	0.969 ± 0.005 (R2)

Discussion

The study simultaneously collected lower limb biomechanical data from ACLR patients during three daily activities (walking, running, and descending stairs) using both Vicon and OpenCap systems. The motion trajectories captured by Vicon were utilized for musculoskeletal modeling in OpenSim to calculate vertical-direction KCFs on the affected limb during these movements. To achieve more accurate KCF estimation, we explicitly modeled the anterior cruciate ligament with nonlinear strain characteristics, overcoming the limitation of traditional OpenSim musculoskeletal models that lack ligament modeling. Subsequently, using OpenCap-derived lower limb joint angles and accelerations as input data, we developed three deep learning models to predict KCFs during the three activities and compared their performance. The results demonstrated that the CNN-BiGRU-Attention model consistently outperformed the other two deep learning models across all three movement tasks (R² ≥ 0.95).

KCFs of ACLR patients from precise musculoskeletal model

The study integrated the Vicon motion capture system with OpenSim to successfully construct a biomechanical model of the knee joint for patients after ACLR during three daily activities, and accurately calculated the vertical KCFs. In standard OpenSim models, knee joint stability is typically achieved solely through geometric constraints and muscle synergy, while overlooking the active mechanical contributions of key soft tissues such as the anterior cruciate ligament. By explicitly modeling the nonlinear strain characteristics of the anterior cruciate ligament and employing a hyperelastic constitutive relationship based on strain energy to characterize its mechanical behavior, this study significantly enhanced the biomechanical realism of knee joint dynamics simulations. To ensure the reliability of the model, a multi-level validation was conducted: First, for muscle activation validation, the activation timing of six major lower limb muscles simulated in OpenSim was compared with synchronously acquired surface EMG signals. The results showed high consistency in waveform morphology, peak timing, and activation amplitude between the two (Fig. 4A). Besides, a DFIS was used to obtain precise three-dimensional bone motion trajectories of the knee joint, which were then quantitatively compared with OpenSim simulation results. The relative displacements between the femur, tibia, and patella calculated by OpenSim also exhibited high agreement with DFIS measurements, further validating the accuracy of the musculoskeletal model in this study (Fig. 4B).

During walking, ACLR patients maintained the characteristic biphasic KCF curve, but with a reduced first peak magnitude compared to healthy controls. This alteration may be attributed to diminished dynamic knee stability secondary to postoperative muscle inhibition [54, 55]. Although the second peak amplitude showed no significant difference, its reduced rising slope reflects compromised generation efficiency of the knee extension moment during the propulsion phase. During running, the patients demonstrated a modified single-peak KCF profile characterized by both attenuated peak magnitude and earlier timing compared to normal subjects. This "low-amplitude early-peak" pattern likely represents a protective gait adaptation, where patients subconsciously reduce GRFs and shorten the braking phase to minimize ACL loading [56, 57]. When ACLR patients take tasks of descending stairs, the curves exhibited the most pronounced pathological KCF pattern: a significantly heightened initial impact peak with increased rising slope relative to healthy individuals. This "high-magnitude steep-slope" characteristic suggests impaired eccentric quadriceps control and compromised energy absorption mechanisms at the knee joint. Concurrently, the delayed second peak timing may indicate altered neuromuscular coordination patterns following ACL reconstruction [58, 59] (Fig. 4C).

Instrumented implant data from the Grand Challenge studies provide an important benchmark for evaluating the physiological plausibility of non-invasive knee contact force estimations. Previous reports have shown that peak tibiofemoral contact forces during level walking typically range between approximately 2.5- and 3.5-times body weight, with peak values occurring during the early to mid-stance phase. In the present study, the predicted knee contact forces exhibited peak magnitudes and temporal patterns that were consistent with these reported ranges. Specifically, peak KCFs occurred within the stance phase and followed similar loading–unloading trends to those observed in Grand Challenge datasets. While direct point-by-point numerical agreement is not expected due to differences in subject populations, movement tasks, and the absence of instrumented implants, the overall agreement in magnitude and timing supports the physiological validity of the proposed framework. In the present study, the estimated KCFs exhibited peak magnitudes and temporal patterns that were broadly consistent with those reported in the Grand Challenge, particularly with respect to the occurrence of peak contact forces during the stance phase. While inter-subject variability prevented exact numerical matching, the overall loading trends and muscle activation timing showed good qualitative agreement with Grand Challenge observations as well as with previously published musculoskeletal simulation studies. These comparisons support the physiological plausibility and reliability of the proposed framework, while highlighting the inherent variability associated with individualized knee joint mechanics. These findings indicate that the present non-invasive approach is capable of capturing the dominant biomechanical characteristics of knee joint loading observed in in vivo measurements, while offering a practical and scalable alternative suitable for longitudinal monitoring and personalized rehabilitation in ACLR patients [14].

Notably, the modeling methodology in this study also exhibits excellent extensibility. By adjusting the constitutive parameters of ligament materials, the method can adapt to simulations of mechanical properties for different surgical reconstruction techniques (e.g., autografts, allografts, or synthetic ligaments). Additionally, by modifying muscle force generation algorithms, it can further investigate the effects of muscle compensation strategies on KCFs. These features make the model not only suitable for scientific research but also hold potential for development into a personalized clinical assessment tool in the future [29].

Performance of the CNN-BiGRU-attention model

Among the three deep learning models evaluated, the CNN-BiGRU-Attention architecture demonstrated the most outstanding performance across all testing scenarios (Fig. 5–9). The model's exceptional predictive capability stems from its sophisticated hybrid architecture that synergistically integrates three powerful computational mechanisms: The CNN layers effectively extract local spatial features from OpenCap-acquired joint kinematic data, capturing important spatial relationships between different lower limb segments; The BiGRU components excel at modeling temporal dependencies in movement patterns, which is particularly crucial for understanding the dynamic characteristics of gait cycles; The self-attention mechanism employs adaptive weighting to focus on biomechanically critical time points in movement sequences, such as heel strike and toe-off events during gait cycles.

In the study, we compared the performance of three deep learning models designed for multi-task prediction. The results demonstrated that the CNN-BiGRU model achieved significantly higher prediction accuracy compared to the model using only BiGRU. This finding indicates that the CNN module plays a critical role in extracting motion-related features, particularly in the context of processing dynamic data from patients who have undergone ACLR to predict KCFs. Specifically, CNNs are effective at capturing local spatial features from input signals, which enhances the quality and discriminative power of the representations used for subsequent temporal modeling. In contrast, although the BiGRU model alone possesses strong capabilities for modeling time series, it may fall short in comprehensively capturing the complex temporal variations in joint angles and accelerations of the lower limbs across different motion tasks, especially when the data involve multi-scale characteristics or nonlinear dynamic changes. By incorporating the CNN module, the model can perform feature enhancement before sequence modeling, thereby improving overall prediction performance [42, 43]. Furthermore, the integration of a self-attention mechanism on top of the CNN-BiGRU architecture led to additional performance improvements across the predictive tasks. This enhancement may be attributed to the advantages of the attention mechanism in feature selection and weighting. By modeling the relationships among Keys, Queries, and Values, the self-attention mechanism dynamically adjusts the importance of features at each time step [60]. This allows the model to focus more effectively on relevant information while suppressing redundant or noisy signals, thereby significantly boosting the expressiveness and accuracy of the predictions [48].

In summary, the synergy between the CNN module and the self-attention mechanism demonstrates strong complementarity within the multi-task learning framework, collectively enhancing the model's ability to capture key features in ACLR patient movement data and improving the precision of KCFs prediction. This level of accuracy holds significant value for clinical applications, demonstrating that the model can reliably assess joint loading during daily activities in ACLR patients without requiring complex laboratory-based motion analysis. The CNN-BiGRU-Attention model's ability to maintain high accuracy across different movement tasks makes it particularly suitable for longitudinal monitoring of rehabilitation progress, where patients typically transition gradually from walking to more challenging activities like running and stair descending.

Hybrid framework of the OpenCap data-driven deep learning

The study directly utilizes joint kinematic data acquired through the OpenCap system to predict KCFs in ACLR patients during various daily activities, overcoming the limitations of traditional reliance on expensive laboratory equipment. This innovative approach helps break the dependence of conventional knee biomechanical analysis on laboratory-grade devices (such as Vicon motion capture systems and force plates), providing new perspectives for conducting precise biomechanical assessments in clinical settings. Although OpenCap's accuracy is slightly lower than Vicon's, its portability and low-cost characteristics make it more suitable for clinical or community applications. By effectively mining OpenCap data using deep learning models, we obtained prediction results comparable to high-precision simulations.

Particularly noteworthy is that the open architecture of the OpenCap platform allows researchers to develop customized biomechanical assessment modules for special populations (e.g., patients with Alzheimer's disease, cognitive impairments, or amputees) [21]. While this study primarily focuses on knee joint mechanics analysis in ACLR patients, this technical framework can be seamlessly extended to multiple rehabilitation medicine fields, including gait assessment in Parkinson's disease and balance function monitoring in stroke patients. Our practice demonstrates that by deploying lightweight sensors on tablets or smartphones combined with cloud-based data-driven modeling, a comprehensive three-tier "laboratory-clinic-home" biomechanical assessment network can be established. This new technological paradigm not only addresses the pain points of traditional methods in achieving long-term continuous monitoring but also enables the creation of personalized rehabilitation trajectory models for each patient through big data accumulation, providing critical technical support for implementing precision rehabilitation medicine [61, 62].

Limitations and future perspectives

This study has several limitations that warrant consideration. First, the sample size, comprising 280 datasets derived from only three types of functional movements—walking, running, and stair descent—limits the generalizability of the findings. Future studies should aim to include a larger and more diverse cohort of participants, as well as a broader range of movement tasks, such as stair ascent, jumping, or cutting maneuvers, to better capture the complexity of real-world neuromuscular demands. Second, while OpenCap offers a portable and scalable motion capture solution, its data may be affected by sensor noise and environmental variability, potentially compromising model robustness in uncontrolled settings. This highlights the need for further refinement of sensor fusion algorithms and data preprocessing pipelines to improve signal fidelity and reliability. The requirement for participants to contact the force plate with the affected limb represents a common methodological trade-off in kinetic gait analysis. While force plate targeting may influence spatiotemporal gait parameters, this approach was adopted to ensure consistent and accurate measurement of ground reaction forces from the reconstructed knee, which was the primary focus of the present study. Importantly, participants were provided with a familiarization and warm-up period prior to data collection, allowing them to adapt to the experimental protocol and thereby reducing potential disruptions to natural movement patterns. Nevertheless, we acknowledge that such instructions may partially affect the ecological validity of the recorded movements. Future studies will aim to adopt multi-force-plate setups or force-plate-free approaches to further enhance the naturalness of daily activity assessment.

When interpreting the estimated knee joint kinematics and contact forces in relation to the Grand Challenge benchmark datasets, several limitations of the present study should be acknowledged. Knee joint kinematics were derived from marker-based motion capture and inverse kinematics, which inherently rely on simplified joint representations and are susceptible to soft tissue artifacts. Although such approaches are widely adopted in non-invasive gait analysis, they cannot fully capture subject-specific joint translations and cartilage-level interactions that are directly measured using instrumented implants. Knee contact forces were estimated through joint reaction analysis within a musculoskeletal modeling framework, which integrates kinematic data, external forces, and model-based assumptions regarding joint mechanics. While this pipeline enables practical and scalable estimation of joint loading, it differs fundamentally from direct in vivo measurements reported in the Grand Challenge studies; therefore, exact numerical agreement is not expected, and comparisons are more appropriately focused on force magnitudes, temporal characteristics, and overall loading trends. The present framework prioritizes non-invasive applicability and individualized monitoring over implant-level accuracy, and future work will aim to further refine knee joint representations, incorporate improved subject-specific modeling strategies, and explore hybrid validation approaches that leverage Grand Challenge data to enhance the physiological fidelity of non-invasive knee contact force estimation [14].

Moreover, the current deep learning model adopts a generalized architecture without incorporating individualized anatomical and physiological differences, such as variations in muscle strength, ligament laxity, or joint geometry, which may influence knee biomechanics. Future work should explore the integration of personalized calibration mechanisms, possibly through subject-specific parameter estimation or adaptive modeling strategies, to enhance prediction accuracy and clinical relevance.

Looking ahead, this study establishes a promising foundation for the next generation of intelligent and accessible biomechanical monitoring systems. By integrating deep learning with portable motion capture platforms such as OpenCap, the framework enables real-time, non-invasive analysis of joint loading in natural environments, minimizing reliance on costly laboratory infrastructure. This technological advancement paves the way for future research in several key directions. Clinically, embedding real-time prediction systems into wearable or mobile health platforms could provide continuous biomechanical feedback for ACLR patients, facilitating personalized therapy adjustments and reducing reinjury risk. Additionally, coupling the model with assistive technologies such as rehabilitation robots or intelligent exoskeletons may enable adaptive movement retraining based on joint loading dynamics [63]. The framework’s architectural flexibility also allows extension to other joints and conditions, including hip, ankle, or spine analysis in patients with musculoskeletal or neurological disorders. Incorporating additional data modalities like EMG, IMUs, or imaging could further enhance its capacity for multimodal biomechanical assessment. Moreover, the convergence of AI-driven analysis with cloud computing and edge AI opens new avenues for large-scale, remote movement monitoring, early abnormality detection, and the development of personalized digital twins for simulation-based intervention planning [64].

Conclusions

The proposed CNN-BiGRU-Attention hybrid neural network architecture exhibited outstanding predictive performance across three core movement patterns, achieving accuracy on par with gold-standard laboratory-based biomechanical simulations, yet with markedly reduced computational complexity and resource demands. These results highlight the model’s capacity to serve as a scalable and efficient alternative for real-time biomechanical monitoring, offering a transformative framework for intelligent rehabilitation support in patients following ACL reconstruction. Furthermore, the adaptive and generalizable design of the architecture positions it as a promising foundation for broader applications in the assessment and management of other musculoskeletal disorders, potentially advancing personalized, data-driven rehabilitation across multiple clinical domains, paving the way toward more accessible, precise, and proactive musculoskeletal healthcare.

Author contributions

TC: Writing-original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Conceptualization; ZZ: Writing-review & editing, Methodology, Investigation; DX: Writing-original draft, Resources, Methodology, Investigation, Conceptualization; YY: Resources, Writing-review, Methodology, Investigation; HZ: Writing- review & editing, Methodology, Investigation; QG: Writing- review & editing, Methodology, Investigation; TJ: Writing- review & editing, Methodology, Investigation; MW: Writing- review & editing, Methodology, Investigation; LX: Writing-review & editing, supervision, resources, methodology, conceptualization; GF: Writing-review, Methodology, Investigation; UU: Writing- review & editing, Resources, Methodology; YG: Writing- review & editing, Supervision, Software, Methodology, Investigation, Funding acquisition, Conceptualization.

Funding

This study was sponsored by Zhejiang Provincial Natural Science Foundation of China for Distinguished Young Scholars (LR22A020002), Zhejiang Provincial Key Research and Development Program of China (2023C03197), Ningbo key R&D Program (2022Z196), National Key Research and Development Program of China (2024YFC3607305), and Zhejiang Rehabilitation Medical Association Scientific Research Special Fund (ZKKY2023001), Ningbo 2035 Science and Technology Innovation Yongjiang Key Technology Breakthrough Plan (2024Z200).

Data availability

The knee model with ACL explicit modeling used in this study is available at https://simtk.org/projects/ligament_dct. The deep learning model developed in this research, along with partial datasets, has been open-sourced and can be accessed at https://github.com/tianxiaochen1108/ACLR-Patients-KCFs-Prediction/tree/main.

Declarations

Ethics approval and consent to participate

This study complied with the principles laid down in the Declaration of Helsinki. The Ethics Committee of Ningbo University has accepted the study protocol (Approval Number: TY2025035).

Consent for publication

All authors have read and approved the final manuscript and consent to its publication. No identifiable personal data are included in this article.

Competing interests

The authors declare no competing interests.