2.1 Perturbation experiments
The perturbation experiment was performed by utilizing a custom-designed gait-perturbing device. A brushless servo motor was fixed onto the mechanical frame, and perturbation force was applied to subjects’ pelvis through transmission mechanism (see Fig. 1a). The magnitude and duration of the perturbation force were controlled by the main control board, and real-time perturbation force data were measured by the tension load cell (see Fig. 1b). A wireless microprocessor controller was devised to detect gait event of the leading leg by monitoring changes in plantar pressure of the force-sensing resistor (FSR) attached at plantar heel region (see Fig. 1c). To reduce mechanical response delay, admittance control was used to keep transmission mechanism at a pre-tension state before imposing perturbation forces, and the duration was limited in loading response phase at 90ms. The magnitude of the perturbation force was set equal to 8% of the subjects’ bodyweight and tested before experiment for ensuring safety and feasibility. Perturbed walking group and unperturbed walking group (zero perturbation force) were randomly imposed onto the subject’s pelvis to minimize subject’s anticipatory postural adjustments. The trial that induced multiple-steps response would not be included in the analysis.
Five healthy young adults volunteered to participate in this study [Male; age = 23 ± 1 year, height = 1.70 ± 0.09 m, mass = 63.8 ± 12.1 kg (mean ± SD)], and informed consent was obtained. This study was conducted in accordance with the Declaration of Helsinki and approved by the ethics committee of the regional hospital and registered with ChiCTR.org.cn (www.chictr.org.cn, 17/12/2021, ChiCTR2100054453). All trials were performed in a Motion Capture lab utilizing eight camera motion capture system (see Fig. 1) and plug-in-gait full body model marker protocol (Vicon Nexus 1.8.5, VICON, Oxford Metrics Ltd, UK) (see Fig. 1). Skin marker data was sampled at 100Hz and filtered by forth order, zero-lag Butterworth filters, with a cut-off frequency of 6Hz respectively. Ground reaction force sampled at 1080 Hz was simultaneously recorded from four AMTI force-plates (Advanced Mechanical Technology Inc, Watertown, MA, USA). Electromyography signals from four muscles(rectus femoris, biceps femoris, gluteus medius and adductor longus) were recorded using a wirless device(Delsys Inc, Boston, USA) and sampled at 1000Hz. Subsequently, the recorded signals were rectified and filtered using a fourth-order Butterworth filter with a cutoff frequency of 6 Hz. Participants walked at self-selected walking speed (averaged at 1.0 ± 0.15 m/s). Each subject performed 40 trials, including 20 normal walking trials and 20 perturbed walking trials
2.2 Model Analysis
Neuromusculoskeletal modelling (NMS) is a computation way to investigate the muscle functions of body system by the means of inverse dynamic analysis. However, a generic model will not meet the experimental requirement for joint reaction force calculation due to the unappropriated estimation of subject’s anthropometric data.
Thus, the current subject-specific musculoskeletal model was modified based on the GaitFullBody model from Anybody modeling system (AnyBody Technology, Denmark) for model repository with 42 degrees of freedom (see Fig. 2a), which is one of the most dedicated human full-body musculoskeletal models. Parameters optimization and segments’ scaling were performed to match subject’s morphology to reduce a global error metric between experimental and virtual motion marker positions before performing simulation. Mass-fat scaling algorithm was adapted to estimate each individuals’ segments length and mass, according to the measured anthropometric data (body weight, body height, pelvis width, thigh, shanks, and foot length). The subject-specific neuromusculoskeletal model was driven by in-vivo marker motion data obtained through motion capture system, enabling the capturing of dynamic motor variations during perturbed and unperturbed walking conditions (see Fig. 3).
In NMS, all skeletal muscles were modelled by the hill type muscle model. Muscle redundancy problem and muscle activations were solved and calculated by inverse dynamics approach and third-order polynomial muscle recruitment algorithm, which calculated as follows:
$$\begin{gathered} Min{\text{ }}G({f^{(M)}}) \hfill \\ s.t.{\text{ }}{\mathbf{ Cf=d}} \hfill \\ {\text{ }}f_{i}^{{(M)}} \geqslant 0,{\text{ }}i \in \{ 1,2,...,{n^{(M)}}\} \hfill \\ \end{gathered}$$
1
$$G({f^{(M)}})={\sum\limits_{i} {(\frac{{f_{i}^{{(M)}}}}{{{N_i}}})} ^p}$$
2
Where \(G\) represents the optimal objective function. \({f}^{\left(M\right)}\) is the muscle force, which together with joint reaction force constitute a n-dimensional vector f. C represents the system’s coefficient matrix associated with anatomy, and the vector d denotes external force. \({N}_{i}\) are the normalizing factors, typically muscle strength.
Joint moments were normalized by subject’s mass(M), leg length(L) and graviton acceleration(g). For validating muscle dynamics, comparison between model-simulated and experimentally-measured muscle electromyographic signals was conducted. Specifically, we compared the normalized muscle activation levels of four major surface muscle bundles, including hip flexor (rectus femoris), extensor (biceps femoris), abductor (gluteus medius) and adductor (adductor longus) in unperturbed walking and perturbed walking. Pearson’s correlation coefficients (r) were used to evaluate the relationships between the two methods.
To better analyze the gait phase-dependent joint responses, T-tests with SPM (statistical parameter mapping) were employed to identify gait phases where joint responses showed significant differences (p < 0.05) between the unperturbed walking and perturbed walking, and would permit a time-wise continuous analysing for the significant changes in hip kinematics and kinetics within a complete gait cycle.[27].
Muscle coactivation index (CI) was calculated by identifying the overlap between the agonist and antagonist muscles activation curves as[28]:
$$CI=100 \times \frac{{\int_{{{t_1}}}^{{{t_2}}} {\hbox{min} [EMG{{(t)}_{{\text{M}}1}},EMG{{(t)}_{{\text{M2}}}}]dt} }}{{\int_{{{t_1}}}^{{{t_2}}} {\hbox{max} [EMG{{(t)}_{{\text{M}}1}},EMG{{(t)}_{{\text{M2}}}}]dt} }}$$
3
Where \({M}_{1 }\)is agonist muscle group and \({M}_{2}\) is antagonist muscle. In this study, iliacus, rectus femoris (RF) and sartorius (SA) were selected as hip flexor muscles, gluteus maximus (GMax), biceps femoris (BF), semitendinosus (ST), semimembranosus (SB) as hip extensor muscles, gluteus medius (GMed), gluteus minimus (GMin) and tensor fascia (TF) as abductor muscles, adductor magnus (ADM), adductor longus (ADL) and adductor brevis (ADB) as adductor muscles (see Fig. 2b). And \({t}_{1}\)denoted the time of leading leg heel strikes and\({t}_{2}\) denoted the time of the trailing leg consecutive heel strikes in current study. The time of consecutive heel strikes is the step time when the new BoS formatted. We compared results between perturbed walking and unperturbed walking by using paired t-test. The level of statistical significance was set at P < 0.05.