Mechanical effort predicts the selection of ankle over hip strategies in nonstepping postural responses

First, we investigated the relation between effort minimization and the selection of a postural response in the continuum of potential ankle and hip strategies. We found that ankle strategies can be explained by minimizing mechanical work, whereas hip strategies can be explained by minimizing instability. Second, although previous studies showed that center of mass (COM) feedback is important, our results indicate that a COM feedback-controlled, torque-driven model cannot accurately track the experimental hip strategies.

Abstract

Experimental studies have shown that a continuum of ankle and hip strategies is used to restore posture following an external perturbation. Postural responses can be modeled by feedback control with feedback gains that optimize a specific objective. On the one hand, feedback gains that minimize effort have been used to predict muscle activity during perturbed standing. On the other hand, hip and ankle strategies have been predicted by minimizing postural instability and deviation from upright posture. It remains unclear, however, whether and how effort minimization influences the selection of a specific postural response. We hypothesize that the relative importance of minimizing mechanical work vs. postural instability influences the strategy used to restore upright posture. This hypothesis was investigated based on experiments and predictive simulations of the postural response following a backward support surface translation. Peak hip flexion angle was significantly correlated with three experimentally determined measures of effort, i.e., mechanical work, mean muscle activity and metabolic energy. Furthermore, a continuum of ankle and hip strategies was predicted in simulation when changing the relative importance of minimizing mechanical work and postural instability, with increased weighting of mechanical work resulting in an ankle strategy. In conclusion, the combination of experimental measurements and predictive simulations of the postural response to a backward support surface translation showed that the trade-off between effort and postural instability minimization can explain the selection of a specific postural response in the continuum of potential ankle and hip strategies.

NEW & NOTEWORTHY

First, we investigated the relation between effort minimization and the selection of a postural response in the continuum of potential ankle and hip strategies. We found that ankle strategies can be explained by minimizing mechanical work, whereas hip strategies can be explained by minimizing instability. Second, although previous studies showed that center of mass (COM) feedback is important, our results indicate that a COM feedback-controlled, torque-driven model cannot accurately track the experimental hip strategies.

an improved understanding of the neuromechanics of human balance control has the potential to improve the assessment and treatment of balance disorders. However, until to date, the factors determining postural control strategies in response to perturbations of standing remain unclear. Computer simulations are a useful tool to investigate causal relations that cannot be directly measured experimentally.

Ankle and hip strategies are the two main nonstepping postural responses to a perturbation of standing (Nashner and McCollum 1985). Using an ankle strategy, the postural equilibrium is maintained by rotating the body as a rigid segment around the ankle joint (Nashner and McCollum 1985). Using a hip strategy, the postural equilibrium is maintained by flexing the hips and plantar flexing the ankles (Nashner and McCollum 1985). Ankle and hip strategies are the extremes in the continuum of nonstepping postural responses (Alexandrov al. 2001; Horak and Nashner 1986; Kuo 1995a; Runge al. 1999). The ankle strategy is mainly used by healthy subjects to cope with small perturbations of balance (Horak and Nashner 1986; Runge al. 1999). In more challenging conditions, subjects gradually switch their postural response from an ankle toward a hip strategy (Horak and Nashner 1986). Examples of more challenging conditions are an increased perturbation magnitude (Horak and Nashner 1986) or a reduced base of support, e.g., when standing on a narrow beam (Horak and Nashner 1986). The selection of a postural response not only depends on the perturbation conditions, but is also influenced by experience, adaptation (Welch and Ting 2014), and fear of falling (Adkin al. 2000). However, the determinants for selecting an ankle or hip strategy remain unclear. It has been suggested that an ankle strategy is advantageous to maintain an upright pose with minimal head movements, which is thought to improve sensory feedback from the vestibular and visual systems (Assaiante and Amblard 1995; Kuo 1995a). On the other hand, Kuo and Zajac (1993b) showed that using a hip strategy increases the capability for accelerating the center of mass (COM) without stepping, and that the instantaneous muscle activity for a desired COM acceleration is lower during a hip than during an ankle strategy. This might explain why a hip strategy is used in more challenging conditions. However, only the instantaneous muscle activity needed to accelerate the COM was investigated. Therefore, it remains unclear whether the total muscle effort during the postural response is smaller for a hip strategy than for an ankle strategy.

Perturbed standing is controlled based on integrated feedback from visual, vestibular and somatosensory systems (Winter 1995), and this complex feedback signal has been modeled in different ways. Park and colleagues used full-state feedback to control a torque-driven double-inverted pendulum model (Park al. 2004; Kim al. 2009, 2012). They showed that this model could accurately track experimental kinematics and kinetics. Alternatively, Ting and colleagues used delayed COM position, velocity and acceleration feedback to control a muscle-driven inverted pendulum model (Lockhart and Ting 2007; Welch and Ting 2007). They showed that, for each muscle a set of feedback, gains could be determined such that the model accurately reconstructed the measured muscle activity in response to forward and backward perturbations (Welch and Ting 2007). However, since COM and full-state feedback are equivalent when controlling a single inverted pendulum, it is still unclear whether COM feedback is sufficient to control a model with more than one degree of freedom.

It has been suggested that, in the aforementioned feedback models, a specific postural response is selected from a redundant set of responses by optimizing performance (Kuo 1995a; Lockhart and Ting 2007; McKay and Ting 2012). Different performance criteria have been used; including minimization of 1 COM movement, 2 deviation from upright position, and 3 muscle activity squared. Kuo (1995b) showed that minimizing COM movement of a double-inverted pendulum model resulted in a hip strategy, whereas minimizing deviation from the upright position resulted in an ankle strategy. On the other hand, measured muscle activity and COM kinematics of a muscle-driven inverted pendulum model can be predicted by minimizing the weighted sum of muscle activity squared (i.e., neural effort) and deviation from the upright position (Lockhart and Ting 2007; Welch and Ting 2007, 2014). In addition, Welch and Ting (2014) showed that, during adaptation to perturbations of standing, experimental muscle activity patterns shift closer toward the minimal muscle effort activity patterns. Furthermore, McKay and Ting (2012) showed that muscle activity and ground reaction forces can be predicted for perturbed standing in cats by a cost function that minimizes muscle activity squared, while satisfying the measured forces and moments around the COM. Hence, these studies suggest that postural responses are optimized to minimize neural effort, which is related to energy consumption. Although simulations showed that the optimization criterion influences the predicted strategy and that postural responses can be predicted by effort minimization, it is still unclear whether and how minimizing effort influences the selection of a specific postural response from the redundant set of ankle and hip strategies.

The main goal of this study was therefore to investigate whether the selection of a postural response to recover from a backward translation of the support surface can be explained by the trade-off between mechanical work, which is related to energy consumption, and postural instability. Experiments and predictive simulations were combined to evaluate the correlation between the peak hip angle, indicative of the use of a hip strategy, and mechanical work, muscle effort, and metabolic energy used by the subject. We hypothesized that the relative importance of minimizing mechanical work vs. postural instability can explain the continuum of observed postural responses. To test this hypothesis, kinematics predicted by an optimal feedback control model were compared with measured kinematics. In addition, two sensory architectures, i.e., COM feedback and full-state feedback, and the effect of more demanding conditions, more specific a decreased base of support, on the postural response were evaluated.

METHODS

An overview of the hypothesis, research question and various methods can be found in Fig. 1.

Fig. 1.

Workflow. A: the experimental measurements of the 10 healthy subjects where the posture was perturbed by means of a posterior platform translation. B: the motion capture and ground reaction forces (GRF) data were combined with a scaled musculoskeletal model to conduct the inverse analysis of the postural response. Joint kinematics, joint moment, muscle forces and metabolic energy consumption were calculated to evaluate if three estimates of effort are correlated with the peak hip angle during the postural response (research question Q1). C: the computed joint kinematics were used in the tracking simulations to evaluate if COM feedback is sufficient to model the measured postural response (research question Q2). Furthermore, the joint kinematics prior to perturbation and after the perturbation were used to constrain the predictive simulations. Predictive simulations were used to evaluate the influence of minimizing mechanical work vs. postural instability on the postural response (research question Q3). Minimizing mechanical work was compared with an objective function proposed by Kuo 1995a to evaluate if mechanical work explains the ankle strategy as well as upright posture. Finally, predictive simulations were used to evaluate the influence of a reduced FBOS on the predicted postural response (research question Q4).

Experiments.

During the experiments, the posture of 10 healthy adults [21 ± 2 SD (standard deviation) yr] was perturbed by a sudden backward translation of the motion base (MotekMedical). The measurement protocol was submitted to and approved by the commission of medical ethics of KU Leuven, Belgium. All participants gave written, informed consent before participating in the study.

The subjects were instructed to stand on marked foot positions corresponding to a stance width that equaled their shoulder width. The subjects knew that the platform could move randomly in mediolateral and anterior-posterior directions and were instructed to maintain stability without stepping. The data were controlled visually and automatically to exclude postural responses with heel-lift or stepping. The motion base translated in anterior-posterior or mediolateral direction over a distance of 0.16 m with three different acceleration profiles (Fig. 2). To minimize anticipation, the perturbation protocol was semi-randomized. Random perturbation directions were applied in the three blocks of, respectively, medium, fast and slow acceleration profiles. These acceleration profiles were sufficient to elicit a wide range of postural responses. Two trials were measured for each perturbation acceleration profile and direction. Only the posterior platform translations were used in the present study, resulting in a total of six trials for each subject. Integrated motion capture was used to measure the postural response of the subjects: three-dimensional marker coordinate data and the ground reaction forces under both feet were measured using a Vicon system (100 Hz) and two AMTI force plates (1,000 Hz). An extended plug-in gait marker protocol (58 makers) was used to capture the full-body movement (Davis al. 1991). The functional base of support (FBOS) was measured for each subject. To this aim, the subjects were asked to move their trunk maximally anteriorly and posteriorly without lifting their feet. Subsequently, the extreme positions of the center of pressure (COP) with respect to the ankle quantified the FBOS.

Fig. 2.

Feedback control model. The feedback control model is similar to the model of Park al. 2004. In the sensory information block, either the full-state of the model (ankle and hip joint angles and angular velocities) is used, or only the COM position and velocity are used. The sensory information is compared with the desired values corresponding to quiet standing. The error on the desired state is multiplied by a feedback gain matrix K to compute the ankle and hip joint torque (eight feedback gains for full-state feedback and four feedback gains for COM feedback). The different acceleration profiles of the platform as a function of time were approximated by cubic splines and imposed as external forces acting on the skeletal model.

Inverse analysis of the experimental data.

The experimental data of each individual trial were analyzed in OpenSim (Delp al. 2007) to evaluate the correlation between the peak hip flexion angle, characterizing the use of a hip strategy, and the mechanical work, muscle effort and metabolic work used by the subject. A scaled skeletal model with 23 degrees of freedom and 92 hill-type muscles (Gait2392 model) (Delp al. 1990, 2007) was used to calculate joint kinematics from the recorded marker trajectories using a Kalman smoothing algorithm (De Groote al. 2008). Joint kinetics were calculated with the inverse dynamics tool.

Subsequently, muscle activations and forces were estimated using static optimization. Static optimization assumes that muscles are coordinated to optimize performance while satisfying the kinetic constraints of the movement. Static optimization solves the muscle redundancy problem at each time frame individually by minimizing muscle activity squared, a commonly used objective function (Zajac 1989). Subsequently, three estimates of effort were computed over the duration of the postural response (2 s). First, the total positive and negative mechanical work needed for balance control was computed from the measured joint kinematics and kinetics

$$\text{Total}\hspace{0.17em}\text{mechanical}\hspace{0.17em}\text{work}\left(\text{J}\right)={\displaystyle {\int }_{t_0}^{t_{\text{end}}}{\displaystyle {\sum }_{j=1}^{n\text{DOF}}\sqrt{{\left({\stackrel{․}{q}}_j{T}_j\right)}^2}\text{d}t}}$$

where t₀ is the start of the perturbation; t_end is 2 s after the start of the perturbation; nDOF is the number of degrees of freedom (ankle, knee and hip joint angles in the sagittal plane), q̇_j is the joint angular velocity; and T_j is the joint moment. Second, the increase in muscle activity was integrated over the duration of the postural response:

$$\text{Muscle}\hspace{0.17em}\text{effort}\hspace{0.17em}(-)={\displaystyle {\int }_{t_0}^{t_{\text{end}}}{\displaystyle {\sum }_{i=1}^{n\text{Muscles}}\left(a_i-a_{i,0}\right)\text{d}t}}$$

where muscles = 92 is the number of muscles in the Gait2392 model, and a_i is the computed muscle activity. Third, the increase in metabolic power was integrated over the duration of the postural response:

$$\text{Metabolic}\hspace{0.17em}\text{work}\hspace{0.17em}\left(\text{J}\right)={\displaystyle {\int }_{t_0}^{t_{\text{end}}}{\displaystyle {\sum }_{i=1}^{n\text{Muscles}}\left({\stackrel{․}{E}}_i-{\stackrel{․}{E}}_{i,0}\right)\text{d}t}}$$

where Ė_i is the estimated metabolic energy consumption, and Ė_i,0 is the estimated metabolic energy consumption before perturbation.

Simulation model.

Forward simulations with a linearized double-inverted pendulum model proposed by Park al. (2004) were generated for each measured postural response (Fig. 2). The model has two rotational degrees of freedom, four states (ankle and hip angle and angular velocity x = [q_ankle q_hip q̇_ankle q̇_hip]^T) and two controls (ankle joint moment and hip joint moment, u = [T_ankle T_hip]^T). The ankle joint angle is defined as the angle between the leg and the vertical; the hip joint angles is defined as the angle between the torso and the leg. The inertial parameters of the segments were derived from the scaled OpenSim models that were used to analyze the experimental data (Delp al. 1990). Acceleration of the motion base was implemented as an external force acting on the feet in the simulation. A feedback loop was added to model control of postural responses (Fig. 2). Two different sensory information architectures were evaluated. First, the four states were used as feedback signals (Park al. 2004). Second, only COM position and velocity were used as feedback signals, similar to the work of Ting and colleagues (Lockhart and Ting 2007; Welch and Ting 2007, 2009, 2014; Ting al. 2009). Subsequently, the feedback signals were compared with the desired values corresponding to quiet upright standing and multiplied by a set of feedback gains to compute the ankle and hip joint moments that drive the model. The feedback gains K were selected through optimization, as discussed below.

Optimization.

To evaluate the ability of the feedback controlled double-inverted pendulum model to describe nonstepping postural responses to perturbations of standing, feedback gains were determined for the full-state and COM feedback models by minimizing the difference between the experimental and simulated kinematics:

$$J\left(\mathit{K}\right)={\displaystyle {\int }_{t_0}^{t_{\text{end}}}{\left(\mathit{x}-\widehat{\mathit{x}}\right)}^2\text{d}t}$$

where J is the name of the objective function, t₀ is the onset of the platform translation, and t_end = t₀ + 2 s and corresponds to the end of the response. x and x̂ are the simulated and measured joint kinematics, respectively. These simulations will be referred to as tracking simulations.

Predictive simulations with the double-inverted pendulum model were used to evaluate the relative importance of minimizing mechanical work vs. postural stability. A first objective function consisted of a weighted sum of 1 the integral of the extrapolated COM position with respect to the quiet standing position, a measure of stability accounting for the COM velocity (Hof et al. 2005); and 2 ankle and hip mechanical work, a measure for the energy needed for postural control (2.5):

$$J\left(\mathit{K}\right)={\displaystyle {\int }_{t_{\text{0}}}^{t_{\text{end}}}\left[f\text{w}{\left(\text{Xcom}-{\text{Xcom}}_{\text{0}}\right)}^2+\left(1-\text{w}\right){\left({\stackrel{․}{\mathit{q}}}^{\mathit{T}}\mathit{T}\right)}^2\right]\text{d}t}$$

where f = 2e⁵ is a scale factor to account for the different magnitude of both parts of the objective. Xcom is the extrapolated COM (Hof et al. 2005), and Xcom₀ is the position of the extrapolated COM prior to perturbation. T is a vector containing the ankle and hip joint moment, q̇ is a vector containing the ankle and hip angular velocities, and w is the relative weight between both parts of the objective function. This value was varied between 0 and 1 in steps of 0.03 to investigate the influence of both terms of the objective function on the predicted kinematics. We will refer to this function as the instability-effort objective function. Note that Xcom₀ is equal to the COM and COP position during quiet standing prior to perturbation. The deviation of the Xcom from the COP during quiet standing and not from the instantaneous COP was minimized because the instantaneous COP might be close to the boundaries of the base of support (BOS), and, in that case, an Xcom close to the boundaries of the BOS and hence a small margin of stability would not be penalized. In addition, this modeling choice allows easy comparison with previous studies (Kuo 1995a; Lockhart and Ting 2007; Welch and Ting 2009).

The weight (w) was varied between 0 and 1 in steps of 0.03 to investigate the influence of both terms of the objective function on the predicted kinematics. The weight that best predicted the measured joint kinematics was selected based on the root mean square (RMS) difference between the experimental and measured joint angles.

A second objective function consisted of a weighted sum of 1 the integral of the extrapolated COM position with respect to the quiet standing position, a measure of stability; and 2 the integral of the ankle and hip joint angle, a measure for the deviation from upright posture:

$$J\left(\mathit{K}\right)={\displaystyle {\int }_{t_{\text{0}}}^{t_{\text{end}}}\left[2e^2\text{w}{\left(\text{Xcom}-{\text{Xcom}}_{\text{0}}\right)}^2+\left(1-\text{w}\right){\mathit{q}}^2\right]\text{d}t}$$

where q is a vector containing the ankle and hip angles. This objective function was used to investigate whether mechanical work explains the selection of an ankle strategy as well as upright posture and is similar to the function proposed by Kuo (1995a). We will refer to this function as the instability-upright objective function.

To provide a hot start for the optimization, the initial feedback gains were computed from the experimental joint kinematics and kinetics. For each joint, the feedback gains were computed by solving the linear set of equations expressing that the measured joint moments equal the measured states times the feedback gains:

$${\mathit{K}}_{\mathit{0}}\mathit{\left[}\begin{array}{cccc}{\widehat{\mathit{x}}}_{\mathit{0}}& {\widehat{\mathit{x}}}_{\mathit{i}}& \mathrm{...}& {\widehat{\mathit{x}}}_{\mathit{n}}\end{array}\mathit{\right]}\mathit{=}\mathit{\left[}\begin{array}{cccc}{\widehat{\mathit{T}}}_{\mathit{0}}& {\widehat{\mathit{T}}}_{\mathit{i}}& \mathit{\dots }& {\widehat{\mathit{T}}}_{\mathit{n}}\end{array}\mathit{\right]}$$

where K₀ is the initial guess for the feedback gains, x̂ are the experimental joint angles and velocities and T̂_i are experimental joint moments. This overdetermined set of equations was solved for K₀ in a least squares sense.

Task and physiological constraint.

Constraints were added to make the simulation physiologically and mechanically more realistic. First, the movement of the COP was constrained based on the measured FBOS. As the feet were welded to the ground, the ankle joint moment was directly related to the distance between the COP and the ankle joint. Therefore, the FBOS of each subject was imposed by constraining the ankle joint moment during the simulation:

$$\text{m}\left({\stackrel{‥}{\text{com}}}_y+g\right){\text{COP}}_{\min }<T_{\text{ankle}}<\text{m}\left({\stackrel{‥}{\text{com}}}_y+g\right){\text{COP}}_{\max }$$

where m is the mass of the subject; com̈ is the vertical acceleration of the COM; and COP_max and COP_min are, respectively, the measured maximal and minimal position of the COP with respect to the ankles. The influence of a reduced FBOS on the predicted kinematics was evaluated by decreasing the FBOS in steps of 3 mm until no feasible solution could be found (i.e., the constraints could no longer be satisfied). These simulations were performed to evaluate if the predicted postural response shifts from an ankle toward a hip strategy in more demanding conditions. In this case, the weight w was kept constant to exclude the influence of a change in objective (w = 0.1).

Second, the initial joint angles and joint moments of the model were constrained based on the experimental joint angles and moments prior to perturbation:

$${\widehat{\mathit{T}}}_{t0}-10\hspace{0.17em}\text{Nm}<T_{t0}<{\widehat{T}}_{t0}+10\hspace{0.17em}\text{Nm,}\hspace{0.17em}{\widehat{\mathit{x}}}_{t0}={\mathit{x}}_{t0}$$

This prevented the feedback controlled double-inverted pendulum model to anticipate the perturbation and therefore models the anticipatory feed-forward control used by the subject. Third, the final state of the model was bounded based on the measured joint angles after perturbation:

$${\widehat{\mathit{x}}}_{\text{tend}}-[5°\hspace{0.17em}5°\hspace{0.17em}20°\hspace{0.17em}{s}^{-1}\hspace{0.17em}\hspace{0.17em}20°s^{-1}]<{\mathit{x}}_{\text{tend}}<{\widehat{\mathit{x}}}_{\text{tend}}+[5°5°20°s^{-1}\hspace{0.17em}\hspace{0.17em}20°\hspace{0.17em}{s}^{-1}\hspace{0.17em}]\hspace{0.17em}$$

where x̂_tend is the measured state, and x_tend is the predicted state 2 s after the perturbation. Fourth, the feedback gains were constrained to result in a stable closed-loop system. A closed-loop system is stable if the real parts of the eigenvalues are negative. For numerical reasons, this condition was not directly imposed. Instead, the property that the states of a stable system are bounded over time was used. Therefore, an additional constraint was imposed that the ankle and hip joint angles returned within the boundaries of normal standing after 20 s of simulation, starting from six different initial body configurations (angle joint angles between −3° and 3° and hip joint angles between −6° and 6°). The real parts of the eigenvalues of the system matrix were calculated post hoc to evaluate if this constraint resulted in a stable system. Finally, the rate of change of the ankle and hip joint moments was bounded between −250 Nm/s and 250 Nm/s. This value is similar to the average maximal rate of change in joint moments found in the experimental trials and resulted in the best prediction of joint moments.

All constrained dynamic optimization problems were solved using the direct collocation software GPOPS II (Rao al. 2010). The sensitivity of the optimized feedback gains to the initial guess was investigated using 150 simulations with random initial feedback gains. The random feedback gains were selected using Latin hypercube sampling. The sensitivity of predicted postural response to a 10% change in the optimal feedback gains was investigated to evaluate the robustness of the control strategy to parameter variations.

The experimental data, models, simulations, and more details on the sensitivity analysis and the optimization problem are available to the reader on the Simtk project “Mechanical effort preducts postural responses” (https://simtk.org).

Statistical analysis.

To evaluate if minimizing mechanical work can explain the selection of a postural response in the continuum of potential ankle and hip strategies, statistical analyses on both the experimental and simulation results were conducted. A linear mixed-effect analysis was used to evaluate the correlation between the measured peak hip angle in each postural response and 1 the measured mechanical work, 2 the estimated muscle activity, and 3 the estimated metabolic energy consumption (IBM SPSS Statistics for Windows, Armonk, NY). The estimates of effort were used as a fixed effect, and intercept and slope for each subject were used as random effects, to account for subject variability. The same linear mixed model was used to evaluate the correlation between the optimal value of w and the measured peak hip angle. The optimal value of w that weights both parts of the instability-effort and instability-upright objective function was used as a fixed effect, the slope and intercept were used as random effect.

RESULTS

Experimental data.

The measured peak knee angle during the postural response was limited (5 ± 3.8° SD). There were significant strong positive correlations between 1 the measured peak hip angle and mechanical work [F(1,8.6 = 31.37), P < 0.001]; 2 the measured peak hip angle and the increase in muscle activity following the perturbation [F(1,10.4 = 35.39), P < 0.001]; and 3 the measured peak hip angle and the metabolic work [F(1,8.2 = 45.02), P < 0.001] (Fig. 3).

Fig. 3.

Correlation between measured peak hip angle and the databased approximations of effort used during the postural response. Each point represents a single trial of a subject. Different shades of gray were used for each subject. Significant strong correlations were found between the measured hip range of motion and mechanical work (A), increase in muscle activity (B), and metabolic work (C). The black line is constructed from the mean slope and mean intercept of the different subjects in the linear mixed model.

Sensitivity analysis.

The sensitivity of the optimized feedback gains to the initial guess of the feedback gains showed that the initial guess influenced the optimization results due to local minima. However, the optimization starting from the hot start (i.e., computed from the recorded kinematics and kinetics) resulted in the minimal objective values. The sensitivity of predicted postural response to a 10% change in the optimal feedback gains showed that for the predicted ankle strategies (i.e., minimizing effort) variations in the feedback gains of the ankle and hip joint angle have a strong impact on the predicted postural response, and small variations result in an unstable system. Variations in the optimal feedback gains of the predicted hip strategies (i.e., minimizing postural instability), on the other hand, have a smaller impact on the predicted postural response.

Tracking simulations.

The RMS difference between the experimental and simulated joint angles was computed for each measured postural response. The average RMS difference of all measured postural responses was 1.1 ± 0.8° (SD) for the tracking simulation with full-state feedback. This RMS difference was 10.7 ± 15.1° (SD) for the tracking simulations with COM feedback only. In the tracking simulation with COM feedback, the RMS error increased with increasing peak hip angle during the response (Fig. 4C). The results of the tracking simulation with full-state feedback and with COM feedback for a randomly selected postural response are visualized in Fig. 4, A and B.

Fig. 4.

Comparison of COM feedback and full-state feedback. Results of tracking simulation in a randomly selected postural response are shown for the ankle (A) and the hip angle (B). In this case, the RMS difference between the measured and simulated angles was 0.7° and 4.5° for the tracking simulation with full-state feedback and COM feedback, respectively. C: the RMS error as a function of the peak hip angle for all measured trials is shown. The RMS error for the simulations with COM feedback (FB) increases when the measured peak hip angle increases.

Predictive simulations.

A low value of w (i.e., minimizing mechanical work) predicted the experimental kinematics best when the subject used an ankle strategy, whereas a high value of w (i.e., minimizing postural instability) predicted the kinematics best when the subject used a hip strategy (Fig. 5). The RMS difference between the experimental and the simulated joint angles was 3.2 ± 2.4° (SD) for the predictive simulations with instability-effort objective function with optimal weights. For the simulations with the upright-instability objective (Kuo 1995a), the RMS difference between the experimental and the simulated joint angles was 3.9 ± 2.4° (SD).

Fig. 5.

Results of the predictive simulation for a typical measured ankle strategy (A) and hip strategy (B). The black dashed lines represent the experimentally measured joint angles of a single trial of one subject in response to the perturbation; the gray lines represent the results of the predictive simulations with various values of w. The left and middle graphs show, respectively, the ankle and hip joint angle as a function of time. The right graphs show the root mean square (RMS) difference between the experimental and simulated kinematics as a function of w. The predicted postural response with the lowest RMS difference is selected as and is highlighted with the vertical dashed line in the right graphs, and as a bold line in the left and middle graphs. A typical ankle and hip strategy was selected based on the measured peak hip angle, which was, respectively, in the 25th and 75th percentile of the measured peak hip angles.

There was a clear correlation between the optimal value of w and the experimental peak hip angle for energy-postural instability objective [F(1,8.023 = 13.62), P = 0.006] and for the upright posture-postural instability objective [F(1,12.049 = 10.869), P = 0.006] (Fig. 6).

Fig. 6.

Correlation between optimal weight and measured peak hip angle. The optimal value of w that weights the two parts in the objective function was selected for each trial. Each dot represents the optimal value of w for an experimental perturbation trial. A: significant correlation between the measured peak hip angle and optimal w for the instability-energy objective. B: significant correlation between the measured peak hip angle and w-optimal for the instability-upright objective.

The predicted peak hip angle increased when the FBOS decreased (Fig. 7).

Fig. 7.

Simulated peak hip angle as a function of the functional base of support. Each dot represents the result of a predictive simulation with a different FBOS. The vertical black solid and dotted lines represent, respectively, the mean FBOS in the 10 subjects and the standard deviation. The stick figures show the postural response for each simulation.

DISCUSSION

The aim of this study was to investigate if minimizing mechanical work influences the selection of a postural response from the continuum of ankle and hip strategies capable of restoring balance after a posterior surface translation. The experimental results showed that there is a relation between peak hip angle and different measures of effort. The simulation results confirmed the hypothesis that the relative importance of mechanical work vs. postural instability influences the predicted peak hip angle during the postural response. Hence, our results demonstrated that the selection of a postural response can be explained by the trade-off between energy consumption and postural stability.

Tracking simulations.

The low RMS error between the experimental and simulated kinematics of the tracking simulation with full-state feedback confirmed the results of Park al. (2004). It showed that this model can accurately describe a range of nonstepping postural responses to posterior support surface translations of different magnitudes in a control population. Although previous studies showed that COM feedback is important (Welch and Ting 2007), the high RMS differences between the experimental and simulated kinematics in the tracking simulations with COM feedback, especially for high peak hip angles, indicate that COM feedback is not sufficient to track the full range of experimental postural responses using a torque-driven, double-inverted pendulum model. These results seem to contradict the study of Welch and Ting (2007) who showed in a similar task that measured muscle activity can be modeled by delayed COM feedback of an inverted pendulum model driven by a single muscle. Several factors might have influenced the finding that COM feedback is not sufficient to track the experimental kinematics. First, different acceleration profiles of the motion base were used to perturb the posture in our study compared with the study of Welch and Ting. Second, COM feedback and full-state feedback are equivalent in a single inverted pendulum model, since COM position and velocity are linearly related to and fully determine the state. Nevertheless, Welch and Ting demonstrated that COM kinematics explains to a large extent the experimental muscle activity, suggesting that COM feedback is of major importance during postural responses. Third, the RMS error in the tracking simulations with COM feedback was low for ankle strategies but increased with increasing peak hip angle, suggesting that COM feedback might be sufficient to explain ankle strategies. Fourth, the discrepancy between the current study and the results from the study of Welch and Ting might also be explained by the contributions of muscle dynamics to the control of postural equilibrium. It is known that intrinsic muscle properties (such as force-length and force-velocity characteristics) and history-dependent muscle dynamics help stabilize dynamic movements (John al. 2013). In our simulations, the states were linearly transformed to joint torques, whereas muscles will nonlinearly transform the feedback signals to joint torques. Finally, the properties of the feedback control system can also influence the postural response. Individual feedback gains for each muscle rather than joint level feedback gains will increase the capability to control posture. More specific, individual control of bi-articular muscles allowing energy transfer between joints would influence the postural response (Prilutsky 2000). Other researchers suggested that the central nervous system does not control muscles individually but by activating combinations of muscle synergies (Ting and McKay 2007). To study the influence of muscle dynamics and muscle control, more detailed musculoskeletal and control models are needed. Hence, there are inherent limitations to the use of torque-driven simulations that may limit the insights gained by the current study. Nevertheless, the low RMS error between the experimental and simulated kinematics indicates that this model can be used to predict ankle and hip kinematics during postural responses.

Predictive simulations.

The significant positive correlations between the peak hip angle and estimates of effort in the experimental data (Fig. 3) and between the peak hip angle and the optimal weight in the predictive simulation (Figs. 5 and 6) confirmed the hypothesis that the relative importance of minimizing mechanical work vs. postural instability can explain the selection of a hip vs. an ankle strategy. The predictive simulations allowed us to investigate cause-effect relationships between changes in the objective and postural responses without the influence of confounding variables. All possible confounding variables, such as FBOS, initial and final posture, were modeled and kept constant in the simulation, which is not possible in experimental conditions. Minimizing mechanical work resulted in an ankle strategy, whereas minimizing postural instability resulted in a hip strategy (Fig. 5). The finding that minimization of mechanical work resulted in an ankle strategy seems to contradict the finding of Kuo and Zajac (1993b) that less muscle effort is required for a given magnitude of horizontal acceleration when using a hip strategy. This contradiction might be explained by the different definitions of effort. Kuo and Zajac defined effort as the percentage of the feasible acceleration needed to restore posture. The feasible acceleration was computed based on maximal mus cle activity, taking into account heel lift and toe lift constraints. Hence, Kuo and Zajac used a relative measure of effort that does not account for the work needed for the postural response. Furthermore, there is a difference in time horizon of both analyses. Kuo and Zajac only evaluated the instantaneous effort, whereas the current study evaluated effort over the duration of the postural response. Our results confirm the findings of Lockhart al. that effort-related objective functions can be used to predict postural responses (Lockhart and Ting 2007; Welch and Ting 2007). Furthermore, by using a double instead of a single inverted pendulum, we showed that the relative importance of mechanical work vs. postural stability can explain the continuum of ankle and hip strategies. When using the upright-instability objective function that is similar to the objective proposed by Kuo and Zajac (1993b), a similar correlation between the measured peak hip angle and the optimal weight was found (Fig. 6). This indicates that both upright posture and mechanical work can explain the selection of a postural control strategy equally well.

The higher sensitivity of the postural response to a change in the optimal feedback gains in ankle strategies compared with hip strategies emphasizes the finding that hip strategies are more stable postural responses (Kuo and Zajac 1993a). These results suggest that hip strategies are more robust to inaccuracies and noise in the sensory system. This could be an additional reason for the increase in hip strategies in the elderly with age-related deterioration of the sensory system (Hsu al. 2013; Shaffer and Harrison 2007). However, additional experiments and simulations are needed to confirm this hypothesis.

To test if the model was able to predict a change in postural response following a change in the perturbation conditions, the influence of a decreased FBOS on the postural response was evaluated. A gradual shift toward a hip strategy was found with decreasing FBOS (Fig. 7). The shift from an ankle toward a hip strategy for a constant objective indicates that the ankle strategy is not a feasible solution when the FBOS decreases. This is in accordance with experimental studies that found an increased occurrence of hip strategies when balancing on a narrow beam (Horak and Nashner 1986). Previous experimental studies showed a correlation between a decrease in FBOS and a reduced ability to restore balance without stepping (Fujimoto al. 2013). This is highly relevant in understanding falling hazards in the elderly. Indeed, the FBOS is known to decrease with aging (King al. 1994), reducing the balance-restoring ability. It has been suggested that reduced ankle muscle strength contributes to a decreased FBOS and explains the increased number of stepping responses in the elderly (Fujimoto al. 2013). Our results emphasize the importance of training the FBOS in nonstepping postural control.

In conclusion, both the objective of the movement (i.e., relative importance of minimizing mechanical work vs. postural instability) and the FBOS influence the postural response. Hence, the modeling framework captures the dependence of the selection of a postural response both on the performance criteria (minimizing mechanical work vs. maximizing stability) and on changes in the perturbation conditions (modeled by the FBOS). As a result, the simulation method proposed in this study can be used to evaluate if a subject's postural response is the result of a decreased FBOS or rather a change in objective. Therefore, this method can be used to identify how the age-related reduction of the FBOS vs. age-related changes in objective (e.g., as a result of fear of falling) contribute to the higher incidence of hip strategies in elderly and has therefore the potential to identify whether ankle strength training is needed.

Strengths, limitations and future directions.

Although the cause-effect relationship between changes in the objective and the postural response was demonstrated, more complex biomechanical models and further experiments are needed to study control of posture in more detail. These results should therefore be interpreted within the limitations of the study. First, only three acceleration profiles of the motion base were used. Different profiles could elicit different responses. For example, higher perturbation velocities elicit hip flexion torques with increasing magnitudes (Runge al. 1999). Since measured peak hip flexion torques were small in this study, peak hip angles instead of peak hip flexion torques were used to classify hip and ankle strategy. Nevertheless, the range of acceleration profiles in the present study was sufficient to elicit a wide range of peak hip angles. Second, the simulations did not include a neural time delay and muscle dynamics. An effect of neglecting time delay is that the maximal hip angle occurs faster in the predictive simulations compared with the tracking simulations (Fig. 3). Therefore, we expect the RMS differences between the measured and simulated kinematics to decrease when accounting for the neural time delay. However, without any muscle dynamics or passive joint stiffness, a neural time delay in torque-driven simulations results in constant joint torques equaling the joint torques during quiet standing and as a consequence unrealistically high angular accelerations during the first time interval after the perturbation. This contradicts the experimentally observed increase in joint moments during the first time interval after the perturbation. This initial response in joint moments could be caused by muscle force-length and force-velocity properties, tendon stiffness, short range stiffness (Cui al. 2008; Loram al. 2007), and stretch reflexes. Third, we simplified the multidegree of freedom skeletal system to a model with two degrees of freedom. This simplification is motivated by the limited peak knee angle observed in the experimental data. Furthermore, the internal joint moments that would be required to stabilize the knee in the simulations are physiologically realistic and in the same order of magnitude as those observed in the experiments. Nevertheless, additional degrees of freedom (such as motion around the knee, lumbar and shoulder joint) should be considered to predict stepping postural responses. Therefore, we believe that future work should concentrate on implementing muscle dynamics and neural time delays as well as additional degrees of freedom in simulations of postural responses that allow stepping responses.

Conclusion.

The combination of experimental measurements and predictive simulations of postural responses following a backward support surface translation suggests that effort minimization influences the selection of a postural response in the continuum of potential ankle and hip strategies. More specifically, the relative importance of minimizing postural instability vs. mechanical work is correlated with the peak hip angle used during the postural response. Hence the selection of an ankle or hip strategy can be explained by a trade-off between effort and stability.

GRANTS

M. Afschrift is a research fellow of the Flemish Agency for Scientific Research (FWO-Vlaanderen).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

M.A., I.J., J.D.S., and F.D.G. conception and design of research; M.A. performed experiments; M.A. and F.D.G. analyzed data; M.A., I.J., and F.D.G. interpreted results of experiments; M.A. prepared figures; M.A. drafted manuscript; M.A., I.J., J.D.S., and F.D.G. edited and revised manuscript; M.A., I.J., J.D.S., and F.D.G. approved final version of manuscript.