A Data-Driven Approach to Estimate Changes in Peak Knee Contact Force With Exoskeleton Assistance.

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Published in final edited form as: IEEE Trans Neural Syst Rehabil Eng. 2025;33:3116–3128. doi: 10.1109/TNSRE.2025.3596261 Search in PMC Search in PubMed View in NLM Catalog Add to search A data-driven approach to estimate changes in peak knee contact force with exoskeleton assistance Delaney E Miller Delaney E Miller 1 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA Find articles by Delaney E Miller 1 , Ashley E Brown Ashley E Brown 2 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA Find articles by Ashley E Brown 2 , Nicholas A Bianco Nicholas A Bianco 3 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA Find articles by Nicholas A Bianco 3 , Scott L Delp Scott L Delp 4 Departments of Mechanical Engineering, Bioengineering, and Orthopaedic Surgery Stanford University, Stanford, CA 94305 USA Find articles by Scott L Delp 4 , Steven H Collins Steven H Collins 5 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA Find articles by Steven H Collins 5 Author information Copyright and License information 1 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA 2 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA 3 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA 4 Departments of Mechanical Engineering, Bioengineering, and Orthopaedic Surgery Stanford University, Stanford, CA 94305 USA 5 Department of Mechanical Engineering Stanford University, Stanford, CA 94305 USA ✉ Email: [email protected] PMC Copyright notice PMCID: PMC13075458  NIHMSID: NIHMS2153764  PMID: 40768472 The publisher's version of this article is available at IEEE Trans Neural Syst Rehabil Eng Abstract Lower-limb exoskeletons could benefit individuals with knee osteoarthritis by reducing knee loading. Real-time estimation of knee loads could accelerate the development of load-reducing exoskeletons. However, measuring or estimating internal knee forces remains challenging due to the rarity of force-sensing knee implants and complexity of simulation-based methods. We developed two data-driven models to separately estimate the peaks in knee contact force during early and late stance using a limited set of features from electromyography (EMG), ground reaction force (GRF), and knee angle recordings. These models were trained on experimental data from healthy young adults (N = 6) walking with a wide range of knee-ankle exoskeleton torque assistance conditions. Peak knee contact forces were obtained from EMG-informed musculoskeletal simulations in OpenSim Moco. The data-driven models were evaluated using leave-one-subject-out cross validation on their ability to accurately compare exoskeleton assistance conditions. The data-driven models identified directional changes in peak knee contact force larger than 0.1 body weights (BW) with 90% accuracy for early-stance peak and 79% accuracy for late-stance peak. Both models included GRF and knee angle features, but EMG features reflected phase-specific muscle activity: quadriceps appeared in the early-stance model, plantar flexors in late stance, and hamstrings in both. We developed a simple method to rapidly estimate changes in peak knee contact force. This approach is suitable for systematic interventions that aim to reduce knee load, such as human-in-the-loop optimization of exoskeleton assistance. 1. Introduction The growing prevalence of knee OA poses a major burden to individuals and society. Due to the limited effectiveness of non-invasive treatments, many individuals with knee OA eventually undergo knee arthroplasty, an effective yet invasive and costly surgical intervention [ 1 , 2 ]. Compressive knee loading is correlated with pain and disease progression [ 3 - 6 ]. There is a need for new treatment approaches, such as assistive exoskeletons, that can reduce knee loading to beneficial levels in individuals with knee OA. Assistive exoskeletons could potentially reduce knee loading by assisting muscles that span the knee joint. Compressive forces generated by knee-spanning muscles make up 50-75% of total knee contact force during walking [ 7 , 8 ]. By providing assistive joint torques during walking, an exoskeleton could reduce the muscle forces required to produce knee extension and flexion moments. This approach could reduce total knee contact force, even if knee loads resulting from ground contact are unchanged. McLain et al. (2022) demonstrated a 10% reduction in early-stance peak contact force during incline walking with a knee exoskeleton that provided extension assistance [ 9 ]. Dai et al. (2024) achieved a nearly 18% reduction in early-stance peak contact force during decline walking with a rigid-soft hybrid knee exoskeleton [ 10 ]. These promising results were obtained through manual tuning of the applied assistance pattern. It is possible that greater reductions in knee loading could be achieved by optimizing assistive torques to minimize joint force. One of the major challenges in exoskeleton development is understanding what assistance strategies might be most beneficial for the user. Human-in-the-loop optimization has enabled large improvements in outcomes of interest by directly evaluating user responses to exoskeleton assistance in real time and systematically adapting the applied assistance [ 11 ]. Optimization has identified exoskeleton assistance strategies that have substantially improved user outcomes like the energy cost of walking [ 11 - 13 ] and running [ 14 , 15 ], walking speed [ 16 ], muscle activity [ 11 , 17 - 19 ], and user preference [ 20 , 21 ]. However, human-in-the-loop optimization requires a method to rapidly measure the outcome of interest during the human-robot interaction. Some outcomes, such as metabolic rate, can be time-consuming to measure or challenging to collect outside of the laboratory. Instead, data-driven models have been developed to estimate changes in metabolic rate from readily available sensor data [ 22 - 26 ]. Estimation of knee contact force is essential to advance the development of exoskeletons for knee OA, but current simulation-based methods are ill-suited for real-time use. In the absence of a force-sensing implant, musculoskeletal simulations are used to estimate knee contact force [ 7 , 27 , 28 ]. Electromyography (EMG)-informed approaches [ 8 , 29 - 34 ] are commonly used to estimate knee contact force and can outperform static optimization in estimating knee contact forces when compared to instrumented implant data [ 35 ]. By incorporating measured muscle activity, EMG-informed approaches capture changes in muscle coordination strategy that may not be evident from kinematics and kinetics alone. Measuring muscle activity may be particularly important in motor learning tasks, such as adapting to a new exoskeleton assistance pattern, where increased muscle co-activation is expected [ 36 , 37 ]. Although musculoskeletal simulation approaches produce state-of-the-art estimates of knee contact force, they are computationally expensive and thus ill-suited for real-time applications [ 38 ]. Thus, there is a need to develop a data-driven model to rapidly estimate changes in peak knee contact force from available sensor data so that we can optimize exoskeleton assistance to reduce peak knee loading. There are a number of data-driven approaches to rapidly estimate knee contact force, but it is unclear how these methods could generalize to assessing interventions like gait modifications and assistive devices. Several machine learning models have been trained on static optimization estimates of knee loading during normal walking [ 39 - 43 ]; this approach poses a few limitations for identifying helpful exoskeleton assistance strategies. First, static optimization typically assumes a muscle coordination strategy that minimizes some measure of muscle effort ( e.g. sum of squared activations). This assumption may not hold for exoskeleton-assisted walking, as individuals may choose activation patterns that prioritize other objectives, such as stability. A second limitation is that these models were trained using only normal walking data from each participant. These models may have learned features of typical coordination patterns rather than a more general relationship between input data (e.g. muscle activity, ground reaction forces, etc.) and knee load. Finally, the majority of these methods use kinematic and kinetic input features to encode muscle forces, which may not be able to capture how exoskeleton joint torques affect muscle contributions to net joint moments. By replacing some of the muscle contributions to the net joint moment, an exoskeleton can reduce muscle forces without altering the observed kinematics or external forces. Models that do not incorporate measures of muscle activity may not adequately capture this effect. Some data-driven models have been developed using instrumented implant force measurements from participants walking with gait modifications [ 44 ], which may better capture certain features of exoskeleton-assisted walking. By training on direct measurements of knee contact forces, the limitations of static optimization are avoided. These models use EMG signals along with some combination of ground reaction forces and marker trajectories to estimate medial [ 45 - 47 ] and total knee contact force [ 48 ], suggesting that EMG signals contain valuable information for capturing intra-subject variations in knee load. However, due to the limited variation in training data from a small number of gait modifications, these approaches may not generalize to exoskeleton-assisted walking or any novel coordination patterns that alter total knee load. For human-in-the-loop optimization of exoskeleton assistance, it is important that a data-driven model accurately distinguish between exoskeleton conditions that produce meaningful differences in peak knee contact force. Evolutionary optimization algorithms such as CMA-ES, commonly used in human-in-the-loop optimization experiments, depend on the relative ranking of the outcome measure across conditions rather than the absolute magnitude. Pairwise comparison accuracy can capture how well a data-driven model might perform in this setting by producing every possible pairwise comparison between exoskeleton conditions and assigning an accuracy of 1 if the data-driven model agrees with the reference outcome measure. Slade et al. (2022) found that a data-driven model for metabolic rate with pairwise comparison accuracy of 76.2% achieved comparable performance to using respirometry data in human-in-the-loop optimization of ankle exoskeleton assistance [ 24 ]. Another key performance consideration is the minimum threshold required to capture meaningful changes in peak knee contact force. Similar to Kaneda et al. (2023), we set a threshold of 0.1 body weights (BW) based on the clinical effects of weight loss on knee OA outcomes [ 49 ]. Studies suggest that weight loss of approximately 10% of body weight is needed to achieve clinically significant symptom improvements [ 50 , 51 ]. Because peak contact force decreases by approximately 0.2-0.4 BW per 0.1 BW of weight loss [ 52 - 54 ], we estimate that a minimum contact force reduction of 0.2-0.4 BW would result in improved clinical outcomes. Setting a detection threshold of 0.1 BW provides sufficient resolution to assess changes in contact force without overfitting to measurement noise. The goal of this study was to develop a method to rapidly estimate changes in peak knee contact force with exoskeleton assistance. To achieve this goal, we had participants walk on a treadmill while wearing tethered bilateral knee-ankle exoskeletons. Motion capture, force plate, electromyography (EMG), and exoskeleton torque data were recorded. We used EMG-informed musculoskeletal simulation in OpenSim Moco [ 55 ] to obtain best estimates of early- and late-stance knee contact force [ 56 ]. For early- and late-stance peaks in knee contact force, separately, we developed a linear model to map peak lower-limb EMG signals, ground reaction forces, and knee joint encoder angles to peak knee contact force. Models were trained on data from participants walking in approximately 30 different exoskeleton conditions. Input features were selected from an exhaustive search of possible feature combinations using leave-one-subject-out cross validation. Model performance was evaluated based on data from a separate experimental session in which participants walked in a wide variety of exoskeleton conditions. 2. Methods 2.1. Knee-ankle exoskeleton emulator Participants wore tethered bilateral knee-ankle exoskeleton emulators with a mass of 3.4 kg each ( Figure 1 ) [ 57 ]. The exoskeletons were actuated by six offboard motors through a series-elastic Bowden cable transmission. Each device had three directions of actuation: knee extension, knee flexion, and ankle plantarflexion. The exoskeleton was attached to the user through a boot and padded nylon straps at the upper thigh, lower thigh, and upper shank. The straps applied normal forces to the participant’s leg and were placed far apart to minimize force applied to the user when generating assistive torque. The exoskeleton connected rigidly to the sole of the boot near the heel and below the metatarsophalangeal joints. Forces from the boot and nylon pads resulted in joint torques on the user’s leg. Shoe size, shank length, and device width were customized to each user. Sensors on the exoskeleton end effector directly measured applied ankle joint torque, knee flexion and extension cable forces, knee joint angle, and ankle joint angle. All data were low-pass filtered at 100 Hz. A previously developed low-level controller accurately applied the desired knee and ankle torques [ 58 ]. Figure 1: Open in a new tab Experimental overview. (A) A participant walks on the treadmill wearing bilateral knee-ankle exoskeletons. (B) Assistive exoskeleton torques were applied by offboard motors. Motion capture, EMG, and ground reaction force data were recorded. (C) Knee and ankle exoskeleton torques were varied by adjusting 11 parameters defining the shape of the assistance curve. At the knee, these parameters included (1) extension ramp time, (2) extension stiffness constant, (3) extension off time, (4) flexion rise time, (5) flexion peak time, (6) flexion peak torque magnitude, (7) flexion fall time, and (8) flexion damping constant. At the ankle, these parameters included (9) torque onset time, (10) peak torque time, and (11) peak torque magnitude. 2.1.1. Torque parameterization Desired knee and ankle torques were prescribed as functions of stride and stance time, respectively, which were measured using an instrumented split-belt treadmill (Bertec Corporation, Columbus, OH, USA). Desired knee torque was defined by eight parameters ( Figure 1c ), which generated a spring-like knee extension torque in early stance, followed by timed knee flexion torque in late stance and early swing, and knee flexion damping torque during swing. Desired ankle torque was defined by three parameters ( Figure 1c ), which generated a timed ankle plantarflexion torque during mid- to late-stance. Ankle torque was constrained to end at toe-off. Parameter values were constrained to a comfortable range established in previous work [ 59 ]. Exoskeleton torque magnitudes were scaled to participant body mass. 2.2. Data collection Participants experienced two experimental sessions: a model-training session and a model-evaluation session. During each session, participants walked with and without bilateral knee-ankle exoskeletons on an instrumented split-belt treadmill. Participants walked at a constant speed of 1.25 m/s for up to 90 minutes and took breaks as needed. 2.2.1. Participants Six healthy adults (4 M, 2 F; 1.73 m, 67.8 kg, 28 y.o.) participated in this study. The study protocol was approved by the Stanford University Institutional Review Board under Protocol 73489 on March 12, 2024. All participants provided written informed consent before participating in the study. Individuals were excluded if they had any ongoing orthopedic conditions, such as arthritis or ligament injuries to the knee. Two participants had extensive prior experience walking with lower-limb exoskeletons, while the other four participants were novice users. 2.2.2. Sensor instrumentation Surface electromyography (EMG) signals (Delsys Inc., Boston, MA USA) were collected at 1250 Hz from 9 lower-limb muscles on the right leg: soleus (medial aspect), medial gastrocnemius, lateral gastrocnemius, tibialis anterior, semitendinosus, biceps femoris long head, vastus medialis, vastus lateralis, and rectus femoris. Before placing each electrode, an experimenter shaved and cleaned the electrode location with isopropyl alcohol. After electrode placement, participants performed a series of maximum voluntary contraction (MVC) exercises that were later used to normalize EMG data. Twenty-eight retroreflective markers were placed on anatomical landmarks on the arms, torso, pelvis, thighs, lower legs, and feet. Additionally, 28 markers were used to aid in limb tracking. Four markers that were placed on anatomical landmarks were removed after the calibration trial due to potential interference during walking. Participants donned a fitted athletic shirt and full length tights before marker placement. Marker data were collected using a 12-camera optical motion capture system at 100 Hz (Vicon Motion Systems Ltd, Oxford UK). Ground reaction forces collected from a split-belt treadmill (Bertec Corporation, Columbus, OH, USA) at 1250 Hz. After markers were placed, participants performed a static and range-of-motion calibration trial without the exoskeleton, which were used to estimate hip joint centers and tracking marker reference locations. 2.2.3. Session A: Model training During the first experimental session (Session A), each participant gained experience with the exoskeleton and walked in a range of randomly generated exoskeleton assistance strategies. Data were collected from each exoskeleton condition to train a data-driven model for rapidly estimating changes in peak contact force (see “ Data-driven model ” below). After sensor placement, the participant walked for two minutes on the treadmill without the exoskeleton to obtain baseline walking data. The exoskeleton was sized to the participant and the participant walked in the unpowered device for at least 5 minutes and until they felt comfortable. The participant then experienced several minutes of walking with varying magnitudes of knee and ankle assistance until they felt comfortable. The participant then experienced a series of randomly generated knee-ankle assistance strategies for 1 minute each. Each participant experienced between 26 and 38 conditions. Data were collected from the last 30 seconds of each condition. 2.2.4. Session B: Model evaluation During the second experimental session (Session B), which was conducted on a separate day, the participant walked in a wide range of exoskeleton assistance strategies, for a total of approximately 1.5 hours of walking. Data were used to evaluate the performance of the data-driven model (see “ Data-driven model ” below). The participant underwent the same sensor instrumentation process. The participant walked without the exoskeleton for 2 minutes and in the unpowered exoskeleton for 2 minutes before walking in various exoskeleton assistance conditions. Each participant experienced approximately 80-90 different assistance conditions for 1 minute each. Data were collected from the last 30 seconds of each condition, including the baseline walking condition. 2.3. EMG-informed simulation Experimental data were passed through an EMG-informed musculoskeletal modeling pipeline to estimate total knee contact force, as described in detail in [ 56 ]. To evaluate model accuracy, we compared simulated peak knee contact forces with data from an instrumented knee implant (Third Grand Challenge). For standard gait modifications, the root-mean-square error was 0.29 ± 0.23 body weights (BW) in early stance and 0.14 ± 0.24 BW in late stance. For three extreme conditions (bouncy, crouch, medial thrust), early-stance error increased to 1.62 ± 0.49 BW. These values match or improve upon static optimization results [ 49 ]. Our EMG-informed model achieved 92% pairwise ranking accuracy for early stance and 81% for late stance in directional comparisons of peak contact force, metrics that may better reflect utility for optimizing exoskeleton assistance strategies. Kinematics and kinetics were obtained using OpenSim 4.4 [ 60 ]. We scaled a generic full-body musculoskeletal model [ 61 , 62 ] using marker data from the static pose. We performed an optimization procedure to preserve muscle-tendon operating ranges [ 7 , 63 ] and scaled maximum isometric forces according to participant mass and height [ 64 ]. The added mass of each knee-ankle exoskeleton (3.4 kg per leg) was distributed across the leg according to the existing mass distribution of the anatomical model. We calculated joint kinematics from marker trajectories using the Inverse Kinematics tool in OpenSim. We performed inverse dynamics to compute net joint moments using ground reaction force and kinematic data, which were low-pass filtered at 8 Hz. Electromyography signals were high-pass filtered at 20 Hz, full wave rectified, low-pass filtered at 6 Hz, and normalized to the maximum values seen across MVC and gait trials. Signals were visually inspected to remove erroneous data resulting from motion artifact or sensor attachment issues; approximately 5% of data were discarded. We estimated total knee contact force using an EMG-informed simulation approach in OpenSim Moco [ 55 ]. Twelve musculotendon units drove ankle and knee flexion on the EMG-instrumented leg. In addition to the nine muscles for which we collected surface EMG data, we mapped three signals to adjacent muscles that shared the same innervation and mechanical action but were not readily accessible using surface electrodes [ 30 , 65 ]: vastus medialis to vastus intermedius, biceps femoris long head to biceps femoris short head, and semitendinosus to the semimembranosus. Remaining coordinates of the anatomical model were driven by torque actuators to achieve dynamic consistency. Reserve torques at the knee and ankle provided additional strength in the model to enforce dynamic consistency despite errors arising from the data. For each EMG-informed simulation, we solved a trajectory optimization problem to obtain muscle excitations. Each simulation was a single stance phase of the EMG-instrumented leg. While prescribing experimental kinematics, ground reaction forces, and exoskeleton torques, we solved for muscle excitations and reserve torques that minimized a combination of EMG tracking error, reserve torque effort, and muscle excitation effort. Unlike static optimization, which solves for muscle activations by minimizing estimated muscle activations, our EMG-informed approach uses measured EMG signals to track subject-specific coordination strategies and incorporates activation dynamics and tendon compliance. The cost function for our EMG-informed simulation approach is given by: J = w exc J excitation + w ka J knee ∕ ankle + w res J reserve + w EMG J EMG (1) Here, J excitation is excitation effort, J knee ∕ ankle is reserve torque effort at the stance knee and ankle, J reserve is reserve torque effort at remaining model coordinates, and J EMG is the EMG tracking error. Each term is given by the sum of squares and integrated across all time steps. The weights w were selected such that the EMG tracking error and knee/ankle reserve torque effort terms contributed similarly to the total cost. The terms related to excitation effort and remaining reserve torques were assigned small weights and primarily served to regularize the solution. Additional details on the cost function formulation are available in Appendix 6 ( Section 1.1 ). Before processing all exoskeleton walking trials, we used a subset of data from the baseline walking condition to scale the magnitudes of our EMG reference signals (“Calibration” stage). For each simulation, we obtained the scale factor for each EMG signal such that the muscle-driven joint moments most closely matched the net joint moments computed from inverse dynamics. We used 10 strides of data to obtain scale factors for each muscle. These scale factors, which could range between 0.5 and 1, were used to adjust the magnitude of the experimental EMG signals for each trial that were used to estimate knee contact force. Simulation-adjusted muscle excitations, along with known musculotendon states from the scaled anatomical model and prescribed kinematics, were used to compute muscle forces. Knee contact force was computed using the JointReaction analysis in OpenSim [ 27 ]. Total knee contact force was taken as the axial component in the tibia reference frame. Early- and late-stance peak knee contact force values were obtained between 15-40% of stance and 60-90% of stance, respectively. 2.3.1. Simulation outcomes We computed peak reserve torques at the knee and ankle to assess the error between muscle-driven and inverse dynamics joint moments. To evaluate how well the simulations tracked experimental EMG signals, we computed maximum and root-mean-square error between simulation-adjusted and experimental EMG for each muscle. Simulation outcomes were computed per stride, then aggregated by assistance condition and session. 2.3.2. Sensitivity analysis of cost function terms We chose simulation cost function weights such that the EMG tracking error and reserve torque effort terms contributed similarly to the final cost function value. Unlike purely EMG-driven or moment-driven methods, this hybrid approach leveraged both sources of data in an effort to reduce sensitivity to experimental noise and modeling uncertainties. Adjusting the relative weighting on EMG tracking and reserve torque effort could affect estimations of knee contact force, especially when there is disagreement between measured muscle excitations and inverse dynamics. We performed a sensitivity analysis by running additional simulations on data from Session A in which we separately doubled the cost function weight first on EMG tracking error and then on knee/ankle reserve torque effort. We assessed the effects of the adjusted cost function weights on the performance of the data-driven models. 2.4. Data-driven model We developed simple linear regression models to separately map early- and late-stance peaks in readily available sensor data to the corresponding peaks in knee contact force. Using data from Session A, we trained models using all possible feature combinations and selected the best feature set using leave-one-subject-out performance. We then evaluated the performance of the model with the best feature set on data from Session B using the same leave-one-subject-out approach, such that data from a participant’s Session A were not used to generate the coefficients of the model evaluated on that participant’s Session B data. 2.4.1. Data preparation for model variables We extracted features from EMG signals, ground reaction forces, and the exoskeleton knee joint encoder on the instrumented limb during the stance phase. Features used for the early-stance model were taken as the peak signal values between 15 and 40% of stance. Features used for the late-stance model were taken as the peak signal values between 60 and 90% of stance. EMG signals were used from the knee spanning muscles and the soleus, as it can affect knee loading by altering ground reaction forces and kinematics during times of peak knee contact force [ 62 , 66 ]. The tibialis anterior EMG signal, although recorded for the EMG-informed simulation approach, was excluded because it does not contribute directly to knee contact force. Vertical, anterior-posterior, and medio-lateral components of ground reaction force were used to generate GRF features. Other features such as stance and stride time, peak exoskeleton torque, and peak ankle angle were explored but ultimately excluded from final analyses because they did not improve model performance. To normalize data across participants and experimental sessions, EMG, ground reaction forces, and knee contact force were normalized to the average peak values during stance from baseline walking without the exoskeleton. Knee joint angles were not normalized. 2.4.2. Assessing model performance Model performance was evaluated using pairwise comparison accuracy across exoskeleton conditions. Across all strides in a given exoskeleton assistance condition, we computed the average peak knee condition force obtained through the EMG-informed simulation approach. For every unique comparison between two exoskeleton conditions, we evaluated the directional accuracy of the data-driven regression model when compared to simulation. If the data-driven model correctly identified the larger of the two peaks, we assigned an accuracy of 1, and 0 otherwise. We implemented a 0.1 body weight (BW) threshold, as we expect changes in peak contact force above this level to result in clinically meaningful improvements in knee OA outcomes. If two exoskeleton conditions differed in peak contact force by less than 0.1 BW according to simulation, the comparison was excluded from the accuracy calculation. Accuracy was averaged across all remaining pairwise comparisons for a given participant. Random chance would result in approximately 50% accuracy. In addition to assessing pairwise comparison accuracy, we computed the average root-mean-square error for each pairwise comparison. More specifically, we computed the peak contact force difference (in BW) between each pair of exoskeleton conditions for both the simulation estimates and data-driven model estimates, then computed the average RMSE between these values. Differences below 0.1 BW were not excluded from this calculation. This measure indicates how well our data-driven models captured differences in peak contact force magnitude between exoskeleton conditions. 2.4.3. Model training and feature selection Using data from Session A, separate regression models were trained to estimate early- and late-stance peaks in knee contact force. Input features were taken from the respective portions of stance. We generated all possible combinations of the EMG, GRF, and knee angle input features, resulting in 2,047 ( 2 n − 1 ) combinations. To assess the generalizability of each model on unseen participants, we used leave-one-subject-out cross-validation (LOSO-CV) to train a linear regression model on the majority of participants and evaluate on the held-out participant. To aid interpretability of relative coefficient magnitudes, each input feature was standardized to have 0 mean and unit variance using the mean and standard deviation of the training data. The best feature combination was selected based on the average performance across held-out participants. 2.4.4. Model evaluation We used experimental data from Session B to evaluate the performance of the chosen early- and late-stance data-driven models against simulation estimates of knee contact force. We again used LOSO-CV to assess pairwise comparison accuracy. For each fold, the model coefficients were obtained using training data (Session A) of the remaining 5 participants, excluding the data of the held-out participant. Although the selected feature set was influenced by the held-out participant’s training data, we believed that this approach would provide a more accurate measure of how well the models might generalize to a new group of participants, rather than holding out a separate test participant. This method also allowed us to maximize the use of available data by incorporating data from all participants into the training process. 2.5. Statistical analyses To assess the extent to which each feature in our linear regression models affected peak knee contact force, we calculated the p-value associated with each model coefficient. Residuals were visually inspected using Q-Q plots and were approximately normally distributed. During model training, our models were trained using approximately 3,600 observations across five participants and evaluated on the final held-out participant. Each observation was taken from a single stance phase of gait, and each exoskeleton assistance condition resulted in approximately 30 observations. Due to the dependent nature of our dataset resulting from repeated measures within exoskeleton conditions and participants, a standard power analysis for linear regression was not appropriate. To assess whether we had sufficient data to train our models effectively, we conducted two simulations. First, we systematically reduced the total number of observations while maintaining a balanced representation from each participant and evaluated model performance using leave-one-subject-out cross-validation (LOSO-CV). Observations were reduced on a per-condition basis, meaning that all observations from a specific assistance condition for a given subject were either retained or excluded together. The excluded conditions were randomly selected, and the total number of observations was progressively reduced to 5% of the initial dataset in 5% increments. This process was repeated for 100 iterations and the results were averaged across all iterations. Second, we reduced the total number of subjects, again evaluating model performance using LOSO-CV. We evaluated every possible combination of subjects. We found that reducing the total number of observations had a small effect on pairwise comparison accuracy. When only 5% of the training observations were retained, the models experienced less than a 4% reduction in accuracy. Similarly, retaining only 1 training subject resulted in less than 4% reduction in pairwise comparison accuracy from the original 5 subjects ( Appendix 6 , Figure A7 ). These results suggest that the selected feature set captures relationships between experimental data and changes in peak contact force that are relatively agnostic to exoskeleton condition and individual participant differences in our dataset. The significance level for all analyses was α = 0.05 . Statistical analysis was performed using MATLAB (Mathworks, Inc.). 3. Results 3.1. Feature selection For the early-stance data-driven model, the feature set that achieved the highest LOSO-CV performance contained 7 features: EMG from semitendinosus, vastus medialis, vastus lateralis, and rectus femoris; vertical GRF; anterior-posterior GRF; and knee flexion angle. For the late-stance model, the best feature set contained 8 features: EMG from soleus, medial gastrocnemius, lateral gastrocnemius, semitendinosus, biceps femoris (long head), and vastus lateralis; vertical GRF; and knee flexion angle. Performance was defined as the average pairwise comparison accuracy across held-out participants. The average model coefficients are shown in Figure 3 and listed in Table 1 . Figure 3: Open in a new tab Model coefficients. Average coefficients across leave-one-subject-out cross validation folds are shown for the selected early-stance peak contact force model (red) and late-stance peak contact force model (blue). The standard deviation across folds is indicated by the error bars. Each input feature is the peak signal value during the relevant portion of stance. Input features were standardized to have mean of 0 and unit variance, so that the magnitude of each coefficient indicates how much the input feature affects peak knee contact force. Table 1: Model coefficients and significance Early-stance peak model Feature Coefficient Std. dev. p-value Semitendinosus 0.083 0.009 <0.001 Vastus medialis 0.050 0.007 <0.001 Vastus lateralis 0.074 0.019 <0.001 Rectus femoris −0.012 0.015 0.09 a Vertical GRF 0.063 0.007 <0.001 Anterior-posterior GRF −0.040 0.009 <0.001 Knee flexion angle 0.060 0.015 <0.001 Intercept 1.239 0.051 <0.001 Late-stance peak model Feature Coefficient Std. dev. p-value Soleus −0.024 0.010 <0.001 Medial gastrocnemius 0.058 0.007 <0.001 Lateral gastrocnemius 0.017 0.007 <0.001 Semitendinosus 0.029 0.009 <0.001 Biceps femoris (long head) 0.040 0.014 <0.001 Vastus lateralis 0.011 0.006 0.02 b Vertical GRF 0.101 0.026 <0.001 Knee extension angle −0.010 0.021 0.005 Intercept 1.104 0.037 <0.001 Open in a new tab a This feature was highly significant (p < 0.001) for all LOSO-CV folds except when subject 6 (p = 0.54) was held out. b This feature was highly significant (p ≤ 0.003) except when subject 5 was held out (p = 0.10). Pairwise comparison accuracy was similar across top performing models as shown in Figure 4 . For the early-stance model, approximately 500 feature combinations (25% of models) resulted in pairwise comparison accuracy within 5% of the best model. For the late-stance model, approximately 300 feature combinations (15% of models) achieved performance within 5% of the best model. Most of the early-stance models with highest accuracy included the vasti and semitendinosus EMG signals, vertical component of ground reaction force, and knee flexion angle. In late stance, most of the models with highest accuracy included EMG signals from the gastrocnemii, biceps femoris, vertical ground reaction force, and knee extension angle. These results suggest that strong performance could be achieved with several feature sets, provided that they include some of the signals with the strongest correlation to peak knee contact force. Figure 4: Open in a new tab Pairwise comparison accuracy for all feature combinations. Models were separately trained to estimate early-stance peak (left) and late-stance peak (right) in knee contact force. For each possible combination of input features, pairwise comparison accuracy was computed on data from Session A using leave-one-subject-out cross-validation. Models are ranked in descending accuracy order along the horizontal axis, and pairwise ranking accuracy indicates how well the model ranked exoskeleton assistance conditions. The black line represents the mean across held-out subjects and the shaded region represents the standard deviation. 3.2. Data-driven model performance The best early-stance and late-stance data-driven models achieved similar performance on the evaluation data from Session B as seen in the training data from Session A ( Figure 5 ). For each held-out participant, the early-stance data-driven model correctly ranked pairs of assistance conditions by peak knee contact force with 89.9 ± 3.4% accuracy on average. This value was similar to the 87.9 ± 8.4% accuracy obtained in training. The late-stance model achieved an accuracy of 79.1 ± 10.3% on the evaluation data compared to 79.5 ± 10.8% on the training data. When combined, the models achieved an accuracy of 85.8 ± 7.2% in identifying directional changes in root-mean-square contact force, compared to 85.7 ± 7.4% for the training data. All accuracies are reported with a 0.1 BW threshold according to simulation estimates of peak knee contact force. After discarding peak contact force comparisons within 0.1 BW, between 63% and 85% of comparisons remained in the held-out participant’s evaluation dataset from Session B (56-90% in Session A). Figure 5: Open in a new tab Pairwise comparison accuracy of best early- and late-stance models. We used leave-one-subject-out cross-validation to assess how well the chosen models ranked various exoskeleton conditions for an unseen participant. Model contact force estimates were compared against estimates from EMG-informed simulations. For early-stance (red), late-stance (blue), and the root-mean-square (purple) peaks in knee contact force, similar performance was retained between the training (Session A) and evaluation (Session B) sessions. The pairwise comparison accuracy of a previously successful data-driven model used to optimize exoskeleton assistance for metabolic cost [ 24 ] is shown in gray. For the evaluation data from Session B, the models estimated differences between exoskeleton conditions with 0.18 BW root-mean-square error on the early-stance peak and 0.21 BW error on the late-stance peak. These results were similar to the pairwise comparison errors from the training data (Session A), which were 0.22 BW for the early-stance peak and 0.24 BW for the late-stance peak. 3.3. Simulation results The reserve torques supplied at the knee and ankle to achieve dynamic consistency in our simulations were similar across training and evaluation sessions. In the region of interest (10-90% stance), the maximum knee reserve torques for training and evaluation, respectively, were 0.044 ± 0.024 Nm/kg and 0.050 ± 0.033 Nm/kg (7.3 and 8.3% of maximum knee joint moment), averaged across participants. The maximum ankle reserve torques for training and evaluation were 0.020 ± 0.011 Nm/kg and 0.040 ± 0.009 Nm/kg (1.1 and 2.3% of maximum ankle joint moment). The reserve torques across stance are shown for each participant in Appendix 6 ( Figure A1 ). The root-mean-square EMG tracking error during the region of interest (10-90% stance) was 0.028 ± 0.015 for training data (18.7 ± 13.9% error) and 0.032 ± 0.017 for evaluation data (22.8 ± 16.3% error). The maximum EMG tracking error in the same region was 0.067 ± 0.031 for training data (45.3 +/− 29.5% error), 0.075 ± 0.037 for evaluation data (53.9 +/− 35.0% error). Due to greater observed variations across muscles rather than participants, the standard deviation is expressed across muscles. Muscle excitations could range from 0 to 1, although typical muscle excitations were much lower than 1. On average, the highest maximum and root-mean-square tracking errors were observed for the soleus ( Appendix 6 , Figure A2 ). Doubling cost function weights on EMG tracking error and reserve torque effort had little effect on data-driven model performance. Despite training the data-driven models on simulation contact force estimates with the original cost function weights, adjusting the cost function weights did not have a significant effect on pairwise comparison accuracy (paired t-tests, p > 0.55). Increasing EMG tracking weight led to the largest change in accuracy of 1.0% in late-stance, averaged across participants. Peak contact force estimates from the adjusted cost functions were highly correlated with the original estimates across all participants for both early- and late-stance (r > 0.94). 4. Discussion This study reveals that simple linear models using available sensor data can identify directional changes in early- and late-stance peak knee contact force with sufficient accuracy for human-in-the-loop optimization. We obtained estimates of peak knee contact force from filtered electromyography, ground reaction force, and knee joint encoder signals, which can be easily calculated with minimal processing. Unlike musculoskeletal simulation methods that are computationally costly, this approach allows for rapid estimation of changes in peak knee contact force on a per-stride basis, which could enable systematic identification of exoskeleton assistance strategies for reducing peak knee loading. By achieving pairwise ranking accuracies of 90% and 79%, these models exceed the performance of a previously-successful data driven model (76.2%) for human-in-the-loop optimization [ 24 ]. In early-stance, changes in peak quadriceps and hamstrings EMG, ground reaction force, and knee flexion angle captured changes in peak knee contact force with 90% accuracy. This feature set aligns well with the underlying biomechanical factors that contribute to peak knee contact force. In early stance, the vastus muscles dominate muscle force contributions to peak knee contact force [ 66 ], so we expected that these muscles would appear in the model. Although small in magnitude, the negative coefficient on rectus femoris may indicate a kinematic adaptation that reduces knee contact force, such as maintaining a straighter knee in early stance. Semitendinosus activity also emerged as an important feature in the model, likely as a result of hamstring co-activation, which may facilitate motor learning of exoskeleton assistance strategies [ 36 , 67 ]. Increases in peak ground reaction forces increase the intersegmental portion of peak knee contact force as these forces are transmitted up through the body. Increasing peak knee flexion angle in early stance requires a larger knee extension moment to straighten the leg, which is expected to increase peak contact force through increased knee extensor muscle forces. In late-stance, changes in plantarflexor and hamstring EMG, vertical ground reaction force, and knee extension angle captured changes in peak knee contact force with 79% accuracy. The best model assigned a large positive coefficient to peak vertical ground reaction force, as it directly relates to intersegmental force at the knee. Also prominent in the model were EMG features for the gastrocnemii, which dominate muscle force contributions to peak knee contact force in late stance while generating knee flexion and ankle plantarflexion moments [ 66 ], as well as the hamstrings, which produce knee flexion and hip extension. The negative coefficient on soleus activity indicates that reducing gastrocnemius reliance during late-stance ankle plantarflexion by increasing soleus activation is beneficial for reducing knee contact force [ 62 ]. A small positive coefficient on vastus lateralis activity may be attributed to co-activation, similar to the hamstrings in the early-stance model. Finally, as represented through a negative coefficient on peak knee extension angle in the model, knee extension in late stance requires a larger knee flexion moment to prepare for swing, which increases peak contact force. Out of all of the evaluated feature sets, many combinations achieved similar performance on the held-out training data, which suggests that a feature set can be adapted to some extent based on available sensor data. Major muscle contributors to each peak in knee contact force appear critical for model performance, as does knee angle and vertical ground reaction force. However, the number of input features could be reduced by selecting a single EMG sensor for muscles with similar functional roles, such as the medial and lateral gastrocnemii. For out-of-laboratory testing, ground reaction force features could be replaced with acceleration-based features from inertial measurement units [ 68 , 69 ]. To evaluate devices or interventions for which knee angle cannot be directly measured using an encoder, inertial measurement units [ 70 ] or video-based motion capture [ 71 ] could be used. Data-driven model performance varied across participants and experimental sessions. This variation can be attributed to a variety of factors, including differences in participant morphology, noise in experimental data, and variability in coordination strategies. In this study, we used a generic anatomical model with geometric and musculotendon parameters that had been averaged across individuals from the literature [ 61 ]. In the present study, there may have been greater differences between some participants and the generic model, which could result in larger discrepancies between joint moments estimated from measured muscle activity and those estimated from inverse dynamics. Experimental error resulting from marker and EMG sensor placement, or even the fit and alignment of the exoskeleton, could also affect outcomes. Finally, some participants and experimental sessions had less variation in coordination strategies and peak knee contact force. Our models did not perform as well when capturing small changes in peak knee contact force across conditions, which led to overall lower accuracies for these data. The early-stance model generally achieved higher pairwise comparison accuracies than the late-stance model on held-out participant data. In the training data from Session A, there was higher variation in early-stance peak knee contact force than in late-stance. More peak contact force variation in training data can improve performance of linear regression models by uncovering the true relationships between input features and the outcome of interest. It is possible that the late stance model was more susceptible to overfitting to noise due to a reduced signal-to-noise ratio. Additionally, in the EMG-informed simulations, we observed higher EMG tracking errors and knee reserve torques in late-stance, indicating a mismatch between measured muscle excitations and net joint moments. This phenomenon could result from both experimental noise and inaccuracies in the musculoskeletal model used in simulation. An important limitation of this study is the use of musculoskeletal simulation to estimate changes in knee contact force and train the data-driven models. Unlike force measurements from instrumented knee implants, simulation estimates of knee contact force include errors from several sources, including anatomical modeling assumptions, noise in experimental data, and cost function formulation. More specifically, our EMG-informed simulation approach created a trade-off between leveraging experimental EMG data and computed net joint moments. Surface electromyography is susceptible to several sources of noise, including motion artifacts, changes in skin properties, and cross-talk from nearby muscles. Placing a single pair of electrodes on a muscle may not accurately represent the net muscle excitation [ 72 ]. While marker trajectories and force plate measurements can be more reliable data sources than electromyography, inaccuracies resulting from center of pressure estimates, marker registration errors, simplified joint models, incorrect segment mass and inertial properties, and misaligned joint centers can result in substantial errors in computed net joint moments [ 73 - 75 ]. Despite careful data collection and modeling, these sources of error (and others) can result in disagreement between EMG-driven joint moments and those computed through inverse dynamics. We used a hybrid cost function to solve the trajectory optimization problem that balanced the minimization of inverse dynamics joint moment error with tracking experimental EMG signals. We found that modifying the relative weighting between these cost function terms did not have an effect on data-driven model performance. Although we developed data-driven models that primarily use features extracted from EMG data, the effectiveness of these data-driven models are not sensitive to how closely experimental EMG signals are tracked in simulation. It is possible that more drastic changes to the cost function weights, such that the simulation becomes nearly exclusively EMG-driven or dynamics-driven, could result in greater changes in data-driven model performance. However, such approaches may also produce less accurate estimates of knee contact force by relying too heavily on one source of data. This study had several limitations which could affect the interpretation of our findings. It is unclear how this approach might generalize to different assistive devices with different mass distributions or assistance methods. Due to the small number of study participants, it is also unclear how this approach might generalize to larger populations and to individuals with OA. We found that reducing the number of participants did not have substantial effects on pairwise comparison accuracy in the held-out participant. However, it is possible that these models would not perform well on individuals with different coordination patterns not captured in our study cohort, such as individuals with knee OA [ 76 - 80 ]. It may also be challenging to obtain sufficient EMG signal quality from individuals with knee OA due to higher prevalence of obesity and muscle atrophy [ 81 - 83 ]. Finally, we used surface EMG from superficial muscles to infer activation in nearby deep muscles that shared mechanical function and neural innervation. While this mapping strategy is supported in prior EMG-driven modeling work, it may limit accuracy when those muscle pairs exhibit distinct coordination patterns. There are also limitations introduced by our choices of surrogate model architecture and input features. Linear models, such as those used in this study, allow for interpretable relationships between features and predicted contact force and tend to be less prone to overfitting in problems with few training data. However, it is possible that a more complex modeling approach that allows for nonlinear relationships between input features and peak contact force could improve performance. We only considered a subset of possible features to estimate peak knee contact force. It is possible that greater performance could be achieved by incorporating additional sensor inputs or more complex features engineered from time-varying data. Finally, the input features in this study—electromyography, ground reaction force, and knee angle—required measurements from multiple laboratory sensors. This limits the practicality of the approach for widespread deployment. Future work could explore feature sets derived from more accessible modalities, such as inertial measurement units or video-based motion capture, to enable cost-effective and out-of-laboratory use. In this study, we developed simple linear models to capture changes in peak knee contact force from EMG, ground reaction force, and joint angle data. We found that the highest performing models contained easily interpretable input features that contributed to peak knee loading. When comparing exoskeleton assistance conditions from a held-out participant, the early- and late-stance models achieved comparison accuracies of 90% and 79%, respectively, when compared to EMG-informed simulation estimates. These models can be employed to enable more rapid exploration of exoskeleton assistance strategies to reduce knee loading. This approach could also be used to quickly identify the effects of changing muscle coordination strategy on knee loading and communicated to individuals through biofeedback [ 38 , 62 ]. Beyond knee loading, data-driven models have the potential to supplement musculoskeletal simulations in assessing many gait outcomes of interest that cannot be measured directly. While simulation can provide a comprehensive understanding of human gait, the specialized equipment, computational time, and domain expertise required to perform these analyses can limit the accessibility of gait monitoring. Data-driven models could enable longitudinal monitoring of gait in clinical populations on a broader scale and speed the process of identifying and deploying useful interventions to enhance mobility. 5. Conclusion We present two data-driven models to separately estimate early-stance and late-stance peaks in knee contact force during exoskeleton-assisted walking. These simple regression models use a limited set of features from electromyography, ground reaction force, and knee angle data and can be implemented in real time to estimate changes in knee loading. The models were trained on experimental data from healthy adults walking in a wide range of exoskeleton torque conditions, and knee contact forces were obtained using EMG-informed musculoskeletal simulations in OpenSim Moco. The models identified directional changes in peak knee load with sufficient accuracy to assess the effect of load-reducing interventions, such as through human-in-the-loop optimization of exoskeleton assistance. Our models and data are freely available ( https://simtk.org/projects/kcf_exo_model ), and we invite others to implement these models and expand upon our work. Supplementary Material Appendix A NIHMS2153764-supplement-Appendix_A.pdf (9MB, pdf) Additional results and details of this study are available as a separate document. The contents of this appendix are listed below. Figure 2: Open in a new tab Model overview. In Session A, participants walked in 30 different exoskeleton assistance conditions. Peak EMG, ground reaction force, and joint angle features were extracted. Experimental data were passed through an EMG-informed simulation pipeline to estimate knee contact force. The simulation estimated peaks in knee contact force were used to train separate data-driven models for early- and late-stance to predict peak knee contact force from extracted input features. In Session B, participants walked in 80 different exoskeleton assistance conditions. The models obtained from Session A were used to predict knee contact force peaks for Session B. The data-driven model predictions were compared against EMG-informed simulation estimates of peak knee contact force. Pairwise comparison accuracy (a measure of how well the data-driven models ranked exoskeleton assistance conditions) was evaluated using leave-one-subject-out cross-validation. Acknowledgment We thank Russell Martin and Gwen Bryan for assistance in exoskeleton controller development, as well as Michael Raitor for help in setting up data collection tools. Footnotes EMG-informed simulations Cost function Solver settings and computer specifications Knee and ankle reserve torques EMG tracking error by muscle Knee contact force waveforms Sensitivity analysis of cost function weights Data-driven models Ranking of all feature combinations Model coefficients for each cross-validation fold Simulation vs. data-driven estimates of peak KCF Pairwise comparison accuracy by subject Effects of reducing observations and subjects Contributor Information Delaney E. 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