Cerebral palsy (CP) is the most common motor disability in childhood, with a prevalence of 1 per 1,000 live births in Europe (Arnaud et al., 2018). In spastic CP, which is the most common form of CP, symptoms such as tremor, hypertonia, and limb weakness are often reported (Gage et al., 2009; Forni et al., 2018). To deal with these symptoms, individuals with CP present diverse compensatory strategies during walking, leading to pathological gait patterns (Rodda and Graham, 2001). To understand these compensatory strategies and identify their causes, instrumented clinical gait analysis (CGA) has become increasingly commonplace, and is also used for supporting clinical decision making regarding treatment planning and monitoring (Armand et al., 2016).

During CGA in children with CP, kinematic and kinetic information is collected by means of optical motion capture, 3D tracking systems, and ground reaction force (GRF) plates (Armand et al., 2016). However, to enable a complete understanding of the patient-specific motor impairment, quantification of the internal joint kinetics is required (Sloot and van der Krogt, 2018), which can be estimated using inverse dynamics analysis (Derrick et al., 2020). Here, the musculoskeletal system is generally modeled as a rigid body system starting from the acquired kinematic data (skin-mounted marker trajectories), from which segment and joint center locations and velocities, as well as linear and angular accelerations are derived. The inertial forces associated with the motion are then computed based on assumptions regarding the inertial characteristics of the body segments (Dumas and Wojtusch, 2018), while additional information on the external forces applied to the body is required before a complete dynamic characterization of the motion can be achieved. During CGA, this information can be obtained through force plates integrated into the floor, which commonly provide the magnitude, orientation, and point of application of the GRF vector. These data can also be equivalently reported in the form of three force and three moment vectorial components [ground reaction forces and moments (GRF&Ms)] in a force plate based coordinate system.

Collecting GRF&Ms remains challenging, even in advanced laboratory settings. Here, targeting clean force plate hits might change the natural movement pattern and corresponding measured kinetics (Challis, 2001). Force plates are also subject to error, e.g., hysteresis of the sensors, linearity errors, electrical inductance, and signal interference, which can all affect the estimated external kinetics (Psycharakis and Miller, 2006; Pamies-Vila et al., 2012). Finally, force plates are rarely available in external, unconstrained, environments, which limits measurements in real-life settings (Dorschky et al., 2019). As a result, a number of techniques to predict GRF&Ms solely from kinematic input data have recently emerged (Oh et al., 2013; Fluit et al., 2014; Skals et al., 2017; Dorschky et al., 2019; Lim et al., 2020). One of the more promising techniques is based on musculoskeletal modeling (Smith et al., 2021), in which the external GRF&Ms can be calculated based on the need for all segment forces to balance those of the body’s motion (Andersen, 2021; De Pieri et al., 2022c). Previous investigations using these techniques to predict GRF&Ms within the AnyBody Modeling System (AMS, AnyBody Technology, Aalborg, Denmark) have shown promising results in healthy subjects, with Pearson correlation coefficients of 0.80 and higher (Fluit et al., 2014; Skals et al., 2017). While such predictive models have been tested in patients with orthopedic (Peng et al., 2018; Zhang et al., 2020; Oh et al., 2021) and neurological (Eltoukhy et al., 2017) disorders, it remains unknown how they perform for locomotor pathologies that include toe-walking, such as children with CP who are the primary beneficiaries of CGA, where the outcome can influence clinical decision-making. Specifically, capturing GRF&Ms in children with CP can be extremely challenging as they often use walking aids or take very small steps, hence, making the collection of clean force plate hits, where only one whole foot completely contacts the force plate, difficult. Therefore, the goal of our study was to investigate if GRF&Ms can be predicted from pathological gait kinematics to a similar level achieved for asymptomatic gait patterns. In addition, we aimed to estimate the influence of predicted GRF&Ms on the resulting ankle, knee, and hip joint moments, toward understanding the suitability of applying these methods to support clinical decision making.

In this study, we firstly tested the reproducibility of previous results from healthy individuals (Fluit et al., 2014; Skals et al., 2017) in a pathological cohort affected by CP. Next, model performance was assessed for both the unaffected and affected limbs in hemiplegic gait patterns. Finally, the effect of predicted vs. measured GRF&Ms on the calculation of joint moments was quantified to provide an understanding of the applicability of this method for determining internal joint contact forces and for supporting clinical decision-making.

Ground reaction forces and moments has been successfully predicted in research settings for assessing human kinetics during various activities of daily living (Fluit et al., 2014; Jung et al., 2017; Skals et al., 2017). This prediction of GRF&Ms is able to support our understanding of muscle requirements during different complex motions, or to estimate joint loading conditions in real life scenarios. However, the applicability of such approaches for supporting clinical decision-making in subjects with pathological gait patterns, and specifically toe-walkers, has not yet been investigated. In the current study, we evaluated the performance of an available GRF&Ms prediction algorithm on spastic hemiplegic gait patterns in children with CP. For both the affected and unaffected legs, differences between predicted and measured GRF&Ms were comparable to those observed in healthy individuals (Fluit et al., 2014). The performance of the prediction algorithm was also similar across different spastic hemiplegic gait patterns. The levels of error found in the determination of joint moments derived from the predicted GRF&Ms, however, suggest that caution should still be taken when using such approaches in clinical decision-making.

In general, the vertical component of the GRF and sagittal plane GRM were best predicted by the algorithm, with strong to excellent PCC, which is in-line with previous findings (Fluit et al., 2014; Skals et al., 2017). While PCC for antero-posterior and medio-lateral components of the GRFs were also strong to excellent (0.71–0.95, Table 2 and Supplementary Figure 1), the corresponding GRM correlations in the frontal and transverse planes were only weak to moderate (0.31–0.43, Table 2 and Supplementary Figure 1). The largest deviations between predicted and measured GRMs were found in the transverse plane, which also agrees with previous reports (Fluit et al., 2014). The relatively higher error observed for the GRF&M components with lower magnitudes is plausibly due to the increased signal-to-noise ratio resulting from soft-tissue artifact (Leardini et al., 2005). The absolute errors found in this study were, however, slightly higher than values reported in literature (GRFs our study vertical: 1.09 ± 0.22 vs. 0.74 ± 0.13 N/kg, antero-posterior: 0.45 ± 0.09 vs. 0.38 ± 0.07 N/kg, medio-lateral: 0.18 ± 0.05 vs. 0.17 ± 0.04 N/kg, GRMs sagittal: 0.27 ± 0.06 vs. 0.18 ± 0.05 Nm/kg), which is not entirely surprising as previous investigations mainly comprised of healthy individuals (Fluit et al., 2014).

Sharp peaks were observed within the predicted GRF&M components during the transition from double to single stance and vice-versa, hence, resulting in a more discontinuous appearance than actual measured forces and moments. This discontinuity of the predicted signals was more prominent than in previous reports, probably because previous investigations have presented the average of multiple activity trials instead of reporting only single trials, thereby artificially “smoothing” the predicted signals. Interestingly, these discontinuities were observed equally for both the unaffected and affected limbs, as well as across different spastic hemiplegic gait patterns, likely due to the approach used to distribute GRF&Ms across two limbs in such closed-chain scenarios. During these phases of double support, the predicted GRF&Ms are computed as part of the muscle recruitment problem, hence, finding the most optimal solution. The optimality of this solution, however, might not hold true for individuals with pathological gait patterns, who could have impairments in controlling their motion optimally, or could choose to move with different motor control strategies. For example, CP subjects commonly present sub-optimal muscle activation patterns, due to e.g., contractures or spasticity (Kim et al., 2018a), or might move with the goal of avoiding pain rather than maintaining efficient motion (Veerkamp et al., 2019). Different control strategies could also lead to an imbalance in the relative loading patterns between limbs. Here, no large differences were observed in performance of the GRF&M prediction algorithm between the sides of the hemiplegic spastic gait patterns (Figure 4). However, the vertical component of the GRF on the affected limb was overestimated during initial contact, but underestimated contralaterally during pre-swing. No such difference between sides was reported when applying the prediction algorithm on healthy walking patterns (Fluit et al., 2014). It is possible that this side-to-side difference results from the non-optimality of the pathological locomotor patterns, as children with unilateral CP rely more on their unaffected limb than on their affected one, especially during double support phases, potentially due to a lack of strength and confidence in their affected limb (Kim et al., 2015).

To estimate GRF&Ms during movement, a full-body marker protocol, including upper extremities, trunk, and head, with a sufficient number of markers to characterize all segment motions, is required. From this kinematic data, a musculoskeletal model reproducing the captured motion is created. Typical modeling assumptions and simplifications, such as a rigid foot segment, a 1-DOF hinge joint at the knee, and a rigid trunk segment, might limit the capacity of the model to represent the real kinematics, thus leading to errors in the prediction of the internal kinetics of the musculoskeletal system. In this study, we observed a mean marker tracking error of 1.4 cm across all subjects (range: 1.1–1.9 cm). Similarly, segments’ dimensions and inertial properties are linearly scaled within the AMS musculoskeletal models, using an adult cadaver as a reference (Carbone et al., 2015). The assumption that such an adult healthy subject is representative of the anatomy and segmental inertial properties of pathological children could introduce considerable errors in the computation of internal forces during the reproduced motion (Camomilla et al., 2017; Hainisch et al., 2021). During a typical AMS inverse dynamics analysis based on force plate data, all kinetic mismatches between the reproduced motion of the scaled human model and the measured GRF&Ms are compensated by artificial actuators located at the pelvis, which balance the kinetics of the modeled motion. When using force plate data as input, we found the mean magnitude of the residual force and moment vectors at the pelvis across all patients to be 0.81 N/kg (range: 0.44–1.61) and 0.25 Nm/kg (range: 0.17–0.30), respectively. Within the workflow to predict GRF&Ms, these actuators are necessarily deactivated, and therefore any kinetic mismatch (error in internal forces) is propagated to the predicted GRF&Ms. This could partially explain some of the observed differences between measured and predicted signals. Future studies should devise segment-specific and gait-phase-specific marker-tracking and force residual metrics to assess potential improvements in experimental marker protocols and modeling assumptions, such as joint DoFs and segmental inertial properties. In particular, the simplified foot model, which cannot account for foot bending (e.g., mid-foot break) that is a key characteristic of pathological gait patterns (Stebbins et al., 2010), could also potentially influence the predicted position of the contact nodes with respect to the ground. A more detailed foot model would likely go a long way toward mitigating these limitations (Kim et al., 2018b). Similarly, more realistic knee and thoracic models could improve the accuracy of the predictions (Fluit et al., 2014; Ignasiak et al., 2016; Dejtiar et al., 2020).

The current results did not indicate a difference in performance of the GRF&M prediction algorithm across different spastic hemiplegic gait patterns, which presented rather consistent RMSD values. This might be due to the fact that only high functioning children with CP (GMFCS level I) were included in this investigation. Although toe-walking was predominant in our population, their gross motor function impairments were only low, and not as severe as can be expected in children with GMFCS level II. It should be noted, however, that the rather small sample size (n = 5 unilateral CP subjects per category) limits the possibility to perform sub-group statistical analysis. It would therefore be interesting to further assess the impact of specific locomotor impairment patterns on prediction performance, including varying degrees of severity, with larger sample sizes.

While the GRFs were relatively well predicted, errors between measured and predicted GRMs were relatively high, indicating that the algorithm had difficulties identifying the location at which the force vector acted. These errors in GRMs propagated toward the moments at the ankle, knee, and hip joints, to an extent that could influence clinical decisions. Pathological gait patterns in CP are identified through a number of kinematic and kinetic features (Brunner and Rutz, 2013; Sloot and van der Krogt, 2018). For instance, toe-walking gait patterns are often characterized by a double-peak profile of the ankle plantar flexion moment, and an erroneous prediction of these profiles (Figure 5, unaffected ankle sagittal moment) could misinform clinical decisions. Furthermore, the peak ankle plantar flexion moment during push-off provides information on the severity of toe-walking and serves as an indicator of the effectiveness of certain treatments (Sloot and van der Krogt, 2018). Predicting GRF&Ms led to an underestimation of the peak moment, which could translate into erroneous clinical conclusions. Deviations in sagittal knee moments in patients compared to controls can be used in CGA to infer quadriceps weaknesses, patellar pain, or quadriceps overload (Armand et al., 2016; De Pieri et al., 2022c). Furthermore, the knee adduction moment is often used as a surrogate measure for the load distribution between the medial and lateral compartments of the knee (Holder et al., 2020; De Pieri et al., 2022b), while reduced hip abduction moment in patients can be associated with a functional deficit of the hip abductors in the presence of altered femeral morphologies (Thielen et al., 2019; Alexander et al., 2022; De Pieri et al., 2022a). However, significant differences between the two methods in the computed sagittal and frontal moments for both knee and hip between the two methods suggest that this these metrics should be interpreted carefully while predicting GRF&Ms. Overall, a more accurate prediction of the joint moment profiles, as well as their peak values, is warranted to translate these predictive algorithms into trustworthy diagnostic tools and to expand the applicability of musculoskeletal modeling in clinical settings (Smith et al., 2021), particularly for subjects with CP.

In conclusion, our study demonstrates that musculoskeletal modeling-based approaches to predict GRF&Ms are able to estimate external kinetics for affected and unaffected limbs in different spastic hemiplegic gait patterns, with error levels similar to those previously reported for gait in healthy individuals. By estimating GRF&Ms solely based on kinematics, without the need for measured force plate data, this approach therefore presents potential to expand biomechanical investigations beyond confined motion laboratories into real-life scenarios (Larsen et al., 2020; Skals et al., 2021). Moreover, the approach can be combined with novel motion-tracking technologies such as inertial measurement units (IMUs), depth-sensor cameras, and markerless techniques (Karatsidis et al., 2017; Ripic et al., 2022), to offer less-constrained application possibilities. Although promising, the error levels for the derived joint moments might still influence clinical decisions, and further improvements are required before the approach can be reliably translated into clinical settings.

The datasets analyzed for this study can be found in the ETH Research Collection (doi: 10.3929/ethz-b-000597686). Further inquiries can be directed to the corresponding author.

The studies involving human participants were reviewed and approved by the Cantonal Ethics Committee Zurich (KEK 2018-01640). Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.

RV and EDP: conceptualization and data curation. JK: investigation and visualization. JK, RV, and EDP: methodology and writing—original draft. JK and EDP: software. JK and RV: formal analysis. RV, WT, EV, and EDP: project administration. WT, EV, and EDP: supervision. JK, RV, WT, EV, and EDP: writing—review and editing. All authors contributed to the article and approved the submitted version.