Energetic cost landscape of human standing balance

In our first experiment (N = 13), we measured participants’ energy expenditure at preferred and prescribed postures using indirect calorimetry to determine how energy expenditure varies over natural postures. During preferred posture trials, participants self-selected a lean angle throughout the trial (eyes open and eyes closed, 2 x 5 min each, Fig 1A, 1C, 1E). Most participants adopted a slight forward lean in both the eyes-open (12/13) and eyes-closed (13/13) conditions (Fig 2B). The range of average preferred postures across participants spanned from -0.03 to 2.54° for eyes-open and 0.70 to 2.91° for eyes-closed standing (see Table 1 and Fig 2B). On average, these whole-body lean angles did not differ significantly between the eyes open and closed conditions (t(12) = -2.10, p = 0.058). Similarly, there was no significant difference in measured energy expenditure between eyes open and closed standing (see Table 1; Fig 2A inset).

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Table 1. Energy expenditure (measured and simulated) and balance characteristics for Experiment 1.

https://doi.org/10.1371/journal.pcbi.1013522.t001

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Fig 1. Overview of Experiments 1 and 2.

(A) The setup of Experiment 1. Participants stood on two force plates and had a total of 43 motion capture markers on their bodies to measure their three-dimensional movement. The back-worn metabolic analyzer measured the flow and air composition at the facemask worn by the participant. The EMG amplifier recorded EMG signals of 8 muscles on the right leg (medial gastrocnemius, soleus, tibialis anterior, vastus medialis, rectus femoris, biceps femoris, semitendinosus, and erector spinae). During target trials, the screen presented a target circle and a cursor of the center of pressure (CoP) in real-time. In Experiment 2, a single force plate was used, and energy expenditure was only estimated from our musculoskeletal model. (B) Workflow to estimate muscle activation and energy expenditure from motion data, depicted with simulations from a representative participant. Motion capture data (first panel, blue dots) were used to scale the musculoskeletal model ([13], https://simtk.org/projects/full_body, available under MIT license) to each participant in OpenSim ([14], https://simtk.org/projects/opensim, available under Apache 2.0 license). Inverse kinematics (IK) were then performed for all trials to find their joint angles (second panel). The ground reaction forces (green arrows) were then applied to calculate forces and activations in all 80 modeled muscles using static optimization (SO, implementation by Uhlrich, Jackson [45], including passive forces) at 20 Hz (third panel). Lastly, the model by Umberger, Gerritsen [32] was used to compute the energy expended by each muscle. (C) Preferred posture trial; participants self-selected a posture throughout the trial without any feedback on the screen. (D) Target trials; whole-body lean angles were prescribed by asking participants to maintain the CoP cursor in a target, which was estimated as the projection of the CoM on the ground plane at the given angle. (E) Protocol for Experiment 1. Participants performed two blocks, both consisting of a preferred (panel C, 5 min eyes open and 5 min eyes closed) and target (panel D, 6 targets for 2 min each) trial set with a ~ 10 min sitting break between each block. The starting set (i.e., preferred vs. target) was random in the first block and reversed in the second. (F) Gait initiation trials; participants stood at a preferred posture or at a CoP target, and after 5-10 seconds, the screen depicted a prompt (Forward or Backward) to walk in the corresponding direction. Both prompts were paired with a unique sound cue, and a second tone was played 3.1 s after the first prompt to end the trial. (G) Protocol for Experiment 2. In the first block, participants stood at a self-selected preferred posture (panel C) and performed three sets of gait initiation trials (panel F) in random order (Forward, Backward, Random). During the second block, participants were presented with CoP targets (panel D) and received a prompt to walk in the forward or backward direction chosen at random.

https://doi.org/10.1371/journal.pcbi.1013522.g001

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Fig 2. Metabolic energy expenditure of different postures in Experiment 1.

(A) The means and bootstrapped 95% confidence interval of measured (blue) and simulated (red) metabolic expenditure at each of the target lean angles (-1.15, 0, 1.15, 2.29, 3.44, 5.73°) and the preferred posture with eyes open (EO) and eyes closed (EC). The main panel shows the mass-normalized energy expenditure difference relative to the preferred posture EO condition (subtraction performed for each participant independently). The inset shows the mass-normalized absolute energy expenditure. Note that the simulated expenditure as computed from the musculoskeletal simulation only considers lower-limb skeletal muscles and omits contributions from any other source, whereas indirect calorimetry measurements represent whole-body energy expenditure. (B) Participant means for whole-body angle θ, within-trial standard deviation of whole-body angle θ_SD, and average magnitude of the CoP velocity in the anteroposterior (AP) direction during target and preferred posture trials. The radius of the target (0.3°) is denoted as r_target. The range between the most posterior and anterior preferred postures observed in the EO condition (-0.03 to 2.54°) is marked in gray in both panels. ^a Significant difference w.r.t. all other targets, ^b Significant difference w.r.t. targets in the range of 0 to 3.44°, *: p ≤ 0.05, **: p ≤ 0.01, ***: p ≤ 0.001.

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In the target condition trials, six whole-body lean angles were prescribed (-1.15, 0, 1.15, 2.29, 3.44, and 5.73°) using real-time feedback of the center of pressure (CoP) position on a screen (Fig 1A, 1D). The energetic cost measured through indirect calorimetry was minimal at the 1.15° target (anterior) and increased in both lean directions (Fig 2A). For visualization, the offset due to the basal metabolic cost (i.e., the energy expended by non-motor processes to uphold bodily function) and model simplifications (i.e., muscles beyond the lower limbs) was removed by subtracting the cost of the preferred posture trial with eyes open per participant for both the measured and simulated data (Fig 2A; data without this subtraction are shown in the inset). At the minimum-cost target (1.15° anterior), the energy expenditure was not significantly different from the preferred posture trials with eyes open (Table 1, Fig 2A). Across all postures, the energy expenditure varied significantly with the prescribed target (F(5, 55) = 13.83, p_target < 0.001, Table 1, Fig 2A), increasing total energy expenditure by up to ~31% at the most anterior target. To assess how energetic cost increased with respect to the minimum-cost posture, we performed planned post-hoc comparisons of energy expenditure across targets to the minimum-cost target using one-sided t-tests. The difference with respect to the minimum-cost target was significant for all posterior postures and for most more anterior postures (Table 1, Fig 2A inset). This pattern of increasing energy expenditure at larger anterior and posterior lean angles was accompanied by a small increase in minute volume (total air circulated per minute) and breath frequency at both outer targets relative to the minimum-cost target (see S1 Appendix for statistics and values). For minute volume, there was no significant difference between the minimum-cost target and the preferred posture (t(11) = -0.15, p = 0.883), while breathing frequency was ~ 25% higher at the minimum-cost target (t(11) = -2.99, p = 0.012).

To test whether the increase in metabolic cost was symmetric around the minimum-cost target (1.15°), we calculated the average rate of change in energy expenditure across adjacent targets in both the anterior and posterior directions from this minimum. The average slope in the posterior direction was -0.21 ± 0.14 W/kg/°, whereas the slope in the anterior direction was 0.11 ± 0.05 W/kg/°. The absolute values of these slopes differed significantly (t(11) = 3.62, p = 0.004), indicating that the energetic cost of anterior-posterior lean was asymmetric, increasing at almost twice the rate in the posterior direction. Overall, these results show that energy expenditure during quiet standing is a function of whole-body lean angle, with a clear energetic minimum near a slight forward lean.

Preferred postures are variable but centered around the minimum-cost whole-body lean

Although participants generally preferred postures near the energetic minimum, their whole-body lean angle also showed substantial variation both within and across individuals (see Fig 2B). To assess within-trial variability, we analyzed the CoP velocity in the forward-backward direction and the standard deviation of whole-body lean angle. We first compared responses from the preferred posture trials (eyes-open) with the minimum-cost posture (i.e., 1.15°), which was also the target nearest to the preferred posture (Fig 2A). The average magnitude of the CoP velocity, which is an indication of the magnitude of postural corrections, did not differ between the preferred posture and the minimum-cost target posture (t(12) = 0.16, p = 0.873; Table 1 and Fig 2B). The within-trial standard deviation of lean angle during preferred posture was roughly double that of the minimum-cost target (t(12) = 5.77, p_Holm < 0.001; Table 1 and Fig 2B), likely because the absence of a target allowed the participants’ posture to drift. This indicates that variability in whole-body lean (i.e., standard deviation of lean angle) was greater during preferred standing than at the minimum-cost target, but did not translate into increased postural corrections (CoP velocity) or higher energy expenditure. Overall, these findings suggest that minimizing whole-body variability, a common objective in postural control models, may not be a prerequisite for minimizing energy expenditure during quiet standing.

Next, we compared these same responses across the target trials. Average anteroposterior CoP velocity differed across the targets (F(2.62, 31.4) = 19.61, p_target < 0.001), with pairwise comparisons showing significant increases (~30%) observed only at the most posterior and anterior targets compared to all others (see Fig 2B and S1 Appendix for statistics). Similarly, the standard deviation of the whole-body angle was also significantly different across postures (F(2.07, 24.87) = 13.22, p_target < 0.001); however, pairwise comparisons revealed that only the most anterior target was significantly increased from all others (see Fig 2B and S1 Appendix for statistics). Finally, closing the eyes did not change the within-trial variability of whole-body lean (t(12) = -0.75, p = 0.466, Fig 2B), but increased the CoP velocity by around 18% (t(12) = -4.39, p = 0.001, Fig 2B) compared to preferred posture with eyes open.

To identify possible mechanical sources of across-participant variability, we assessed whether individual variability in ankle stiffness could account for differences in preferred posture. When standing is simplified as a single inverted pendulum, the actively generated moment is minimal when the passive moments generated by the tissues around the ankles counteract the gravitational moment acting on the body. We used a published model of ankle stiffness [46] to estimate a distribution of whole-body lean angles where the passive ankle moment is in equilibrium with the gravitational moment of a body with a height equivalent to our group average (see Materials and Methods). Using a Monte Carlo analysis, we found that the simulated equilibrium angles formed a right-skewed normal distribution with a median of 1.25° and an interquartile range of 0.51° [1.02, 1.53°] (data reported in non-parametric metrics to account for skewness of the distribution). For comparison, the preferred postures measured in Experiment 1 had a median of 1.68° and an IQR of 1.14° [0.93, 2.07°]. This suggests that individual ankle mechanics may partly explain between-participant differences in preferred posture though participants generally adopted more forward-leaning postures than predicted by the passive equilibrium angles alone.

Musculoskeletal model simulations predict the trend of metabolic cost across postures

To better understand the physiological basis of postural energy expenditure, we used a musculoskeletal model in OpenSim [13,14] to estimate muscle-level energetic cost during standing (Fig 1B). Muscle energy expenditure was computed for 80 muscles using a physiological model [32] that accounted for the muscle’s activation, mass, fiber composition, and (tendon) stiffness. Similar to our experimental data, the energy expenditure in our simulations was lowest at 1.15° and varied significantly with the target lean angle (F(1.62, 19.4) = 15.63, p_target < 0.001), increasing at both posterior and anterior leans. Relative to the minimum-cost posture, the simulated cost increased significantly at all posterior postures and at the most anterior posture (Fig 2A, Table 1). Overall, simulations captured the trends in measured energy expenditure, though they underestimated the cost for anterior-leaning postures.

To validate the simulated muscle activations and explore posture-dependent muscle recruitment, we compared experimental EMG recordings with simulated activations for eight major postural muscles (Fig 3). Overall, the simulations captured the qualitative trends in EMG across postures, although absolute magnitudes likely differed due to normalization [47]. Muscles responsible for dorsiflexion (tibialis anterior) and knee extension (rectus femoris, vastus medialis) were highly active in backward postures, with activation declining as the body leaned forward. In contrast, forward postures increased reliance on ankle plantarflexors (soleus, gastrocnemius) and hip extensors (semitendinosus, semimembranosus). The gluteal muscle activation in our simulation results also increased with lean angle, but to a lesser extent than the plantarflexors (see S1 Fig for activations of all simulated muscles). As the erector spinae was not included in our simulations, we compared the model’s lumbar extension moment to the experimentally measured muscle activity. Both signals followed a slight upward trend, suggesting that the contributions of trunk muscles gradually increase with greater anterior leaning.

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Fig 3. Measured (black) and simulated (colored) activity of major postural muscles on the right side of the body during Experiment 1.

Solid lines indicate the mean activity across participants, and the shaded areas represent the bootstrapped 95% confidence interval of the mean. The EMG activity is shown for the rectus femoris, vastus medialis, tibialis anterior, semitendinosus, biceps femoris (long head), soleus, and medial gastrocnemius muscles. The EMG activity of the erector spinae was compared against the trend of the lumbar extension moment (dashed line), as the muscle was not present in the musculoskeletal model [13]. Activations for all muscles included in the model are provided in S1 Fig. The simulated activations of the semimembranosus and semitendinosus are shown in the same panel as they share a similar function. Electromyography data were normalized to the largest value observed during maximal voluntary contraction, and simulated muscle activations were inherently constrained between zero and one. The central model visualization was generated with the unscaled musculoskeletal model ([13], https://simtk.org/projects/full_body, available under MIT license) with the left leg muscles hidden for clarity and muscle colors matched to the activation traces shown in each panel.

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To better understand the different physiological contributions to energy expenditure, we decomposed the total metabolic cost from the simulations into activation maintenance, fiber shortening rate, and mechanical work [32]. The activation maintenance reflects the metabolic losses of sustaining a constant, isometric muscle force, including processes such as calcium cycling and cross-bridge turnover [32]. The shortening rate accounts for additional losses occurring when the muscle fibers change length, while mechanical work represents the muscle’s idealized external work [32]. During preferred posture trials, nearly all energy expenditure was attributed to activation maintenance costs (99.4 ± 0.6%), with only a minimal contribution from the fiber shortening rate (0.6 ± 0.6%) and none from mechanical work. This confirms that static standing primarily expends energy through sustained low-level muscle activation, rather than dynamic contraction or external work.

Interestingly, the proportion of energy expended by muscles consisting mostly of more energy-intensive fast-twitch muscle fibers (type II) also varied with lean angle. At the most posterior target (-1.15°), 70.0 ± 9.4% of the simulated energy expenditure came from muscles with relatively high (> 52%) fast-twitch fibers, such as the rectus femoris and vastus lateralis [31]. In contrast, at the most anterior target (5.73°), only 42.6 ± 13.8% of expended energy came from such muscles, with the remainder of the energy being consumed by muscles consisting primarily of slow-twitch fibers (type I), such as the soleus [31]. This result suggests that posterior leaning may recruit less metabolically efficient muscles for prolonged activation maintenance, contributing to the higher energetic cost observed when leaning in that direction.

Preferred quiet standing posture is not affected by the metabolic cost of gait initiation

So far, we observed that participants preferred whole-body angles close to the minimum-cost angle (Fig 2). However, the optimization of posture may reflect more than just minimizing the cost of static standing; it may also be shaped by the need to initiate movement quickly, efficiently, and frequently [41,43]. To explore this proposition, Experiment 2 investigated how the energetic cost and time required to initiate gait vary with posture, and whether participants adjust their static posture in anticipation of the movement direction. Participants (N = 20) stood on a force plate at a target or at their preferred posture and initiated gait when prompted to start walking in a forward or backward direction (Fig 1F-1G, see Materials and Methods).

First, we assessed whether participants adjusted their preferred standing posture in preparation for the upcoming gait initiation direction. Participants were explicitly informed as to which set of trials (Forward only, Backward only, Random) they would have to perform, and could therefore anticipate the probability of the walking direction but not the timing of the walking prompt. The lean angle during standing before gait initiation did not differ significantly between sets of randomized or known walking directions, and was also not different between walking forward or backward only (Fig 4B, Table 2). Similarly, the time required to reach steady-state walking (i.e., when the center of mass velocity reached 90% of their average maximum velocity for that direction) was not significantly different when the direction was randomized or known in either direction (Table 2). Between forward and backward walking with known directions, the time to reach steady state walking was around 19% shorter during backward as compared to forward walking initiation, likely because the maximal absolute velocity in backward walking was also roughly 19% lower (Fig 4B, Table 2).

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Table 2. Results and statistics for Experiment 2.

https://doi.org/10.1371/journal.pcbi.1013522.t002

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Fig 4. Gait initiation results for preferred posture and target trials of Experiment 2.

In preferred posture trials, the participant could self-select a posture during the period before the cue. In target trials, participants were prescribed a lean angle using the CoP target. (A) Mean forward velocity of the center of mass (v_com) for all participants (N = 20) grouped by trial. Blue and red lines correspond to the Forward- and Backward-only block, respectively, where participants were aware that they would only initiate gait in the corresponding direction (repeated as dashed lines in the right figure for comparison). The gray lines (lagging slightly behind the blue and red lines) show the initiation in the Random direction block, where the direction was unpredictable. The colored lines (yellow, purple, green) correspond to the three prescribed targets (-1.15, 1.15, 3.44°, respectively). (B) Results of gait initiation metrics. The gray band in the whole-body lean angle plot indicates the range of preferred postures for prolonged standing as observed in Experiment 1. Forward and backward-only initiation differ significantly for all metrics except θ (Table 2). For reference, simulated activations of all muscles are provided in S2-S3 Figs. Variables shown are θ: whole-body lean angle, t_v90%: time to reach 90% of steady-state velocity with respect to the start of movement, v_peak: peak forward or backward velocity (absolute value), E_musc: simulated muscle energy expenditure between prompt and foot strike, Δx_com: change in center of mass location over that period, CoT: cost of transport, equal to E_musc/ Δx_com. *: p ≤ 0.05, **: p ≤ 0.01, ***: p ≤ 0.001.

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Next, we assessed the energetic cost of gait initiation. Our simulations of Experiment 1 showed that activation maintenance costs drive energy expenditure during quiet standing. However, many idealized representations of gait initiation only consider kinetic and potential energy [48–51], overlooking the cost of losses from muscle activation and likely underestimating total energy expenditure. To address this, we used the same musculoskeletal modeling approach as Experiment 1 (Fig 1B) to estimate energy expended by the lower-limb muscles during gait initiation from the prompt (i.e., during standing) to the first foot strike (heel or forefoot). The cost of gait initiation was quantified as the cost of transport (CoT; [11]), computed as the weight-normalized energy expended by the simulated muscles (E_musc) divided by the change in center of mass location in the forward direction (Δx_CoM, Table 2, Fig 4B). During the sets with known walking direction (Forward and Backward only sets), the CoT of backward walking was ~ 38% higher than that of forward walking (Fig 4B, Table 2). When walking direction was random, the CoT of forward walking increased by ~3% compared to when it was known, whereas there was no difference for backward walking (Table 2). For each direction, there were no significant differences between known or random conditions for the simulated muscle energy expenditure or center of mass distance (Table 2). Together, these results indicate that participants did not adjust their standing posture in anticipation of the expected movement direction, even though we observed a marginal but significant improvement in the energetic cost of forward gait initiation when the direction was known.

Static lean angle only minimally affects the time and energy expended for gait initiation

In the second block of Experiment 2, we used the target trials to test whether initiating gait from a more anterior or posterior leaning whole-body angle reduces the time required and/or the energetic cost of initiating gait. Participants stood at one of three prescribed whole-body angles (-1.15, 1.15, 3.44°; Fig 1D) and initiated walking in either the forward or backward direction five times each in random order following a prompt (Fig 1F).

During forward gait initiation, the time to reach steady-state velocity varied significantly with lean angle (Table 2), with post-hoc tests showing that participants reached steady-state walking around 0.2 seconds faster from a forward than backward lean angle (Fig 4B, S1 Appendix for statistics). However, comparisons of the outer two targets with the central target were not significantly different, suggesting that postural adjustments beyond the central posture did not yield significantly faster gait initiation times. In contrast, during backward gait initiations, lean angle did not significantly affect time to reach steady-state velocity (Table 2). We further observed that the peak center of mass velocity did not differ across targets for forward initiation, but was marginally (~2%) and significantly higher when initiating backward walking from a forward-leaning posture versus a backward-leaning posture (Table 2, Fig 4B). Overall, these results suggest that the time required to initiate forward gait can be improved slightly with small adjustments to whole-body lean during quiet standing.

Next, we assessed whether lean angle changes the energetic demands of gait initiation. The CoT differed with lean angle for both forward and backward gait initiations (Table 2, Fig 4B). Interestingly, post-hoc tests revealed that for both initiation directions, the CoT was ~ 10% higher when leaning at the posterior target as compared to the central target (Fig 4B), contrary to the hypothesis that posterior lean would facilitate more efficient backward initiation. Conversely, the CoT did not differ between the anterior and central target for both initiation directions (Fig 4B), suggesting that maintaining a posture close to 1.15° was sufficient to optimize the CoT of upcoming gait initiation regardless of direction.

To better understand what drives the difference in CoT between anterior and posterior leaning postures, we examined the total muscle energy expended (E_musc) and the CoM displacement (Δx_com). The total simulated muscle energy expenditure between the cue to walk and the first foot strike decreased by < 2% when leaning in the direction of movement for both forward and backward initiations (Table 2, Fig 4B, see S2-S3 Figs for simulated muscle activity of all muscles). Differences between the central target and the target aligned with the direction of movement were not significant, whereas initiating gait from a lean angle opposite to the movement direction incurred a higher muscle energy expenditure than both other targets (Fig 4B, S1 Appendix for statistics). In addition, the CoM displacement between the starting position and the first foot strike decreased by around 3–4 cm when leaning further in the direction of movement for both forward and backward trials (Table 2, Fig 4B), likely because the prescribed lean already placed the CoM toward the desired direction. Because CoT is energy expenditure per distance traveled, these combined reductions in both energy and displacement canceled each other out, suggesting that leaning further in the direction of movement does not necessarily improve the energetic cost of gait initiation.

Preferred human posture aligns with the energetic minimum

The first aim of our study was to determine how energy expenditure varies with standing posture. The alignment of preferred posture with the energetic minimum (Fig 2) suggests that participants naturally adopted an energetically efficient posture during quiet standing. We also found that removing vision did not significantly affect energy expenditure or lean angle, although CoP velocity increased slightly. This indicates that while visual feedback aids postural control (for review, see [27,52,53]), its absence does not substantially alter the selection or energetic cost of the preferred posture. Our results further revealed that the increase in energy expenditure with lean angle was not symmetric (Fig 2A), increasing at about twice the rate during posterior lean as compared to anterior lean. This directional asymmetry in energetic cost likely reflects underlying anatomical and physiological asymmetries in the human body, which may have evolved under selection pressures for efficient (forward) locomotion [54,55] and shape the energetic landscape of standing balance. For instance, the relatively short calcaneus, while advantageous for energy-efficient running [56], limits posterior stability because it is much shorter than the forefoot and therefore requires faster CoP corrections (Fig 2B) to prevent backward falls. Similarly, passive ankle stiffness increases with forward lean [46,57], reducing the proportion of active muscle contributions needed to generate stabilizing torques. Lastly, we found that backward-leaning postures may engage muscles dominated by fast-twitch fibers, which are less metabolically efficient, whereas forward lean more prominently engages muscles with slow-twitch fibers suited for economical tonic activation [32,55]. Together, these biomechanical and muscular properties make it less costly to allow greater excursions in the anterior direction than in the posterior, helping to explain why humans typically adopt a forward-leaning stance.

Additional non-metabolic factors may also drive our preference for a slight forward lean. Sinha and Maki [58] proposed that this orientation simplifies control by only relying on tonic plantarflexor activity, while also increasing the gain of short-latency reflexes through increased tonic activity [59]. A second possibility is that a forward lean positions the center of mass closer to the center of our asymmetric base of support, which may help optimize stability boundaries [60,61]. This preference may also prepare us to initiate movement [43], although our direct examination of this possibility in Experiment 2 showed that participants remained near their energy-optimal stance regardless of the expected walking direction. Other factors not assessed here may also contribute, including stabilizing the head [62], reducing the cognitive demands of control [63,64], or allowing exploratory variability [65]. Thus, while our findings suggest that humans preferentially adopt near-optimal postures from an energetic perspective, the control mechanisms underlying this selection remain unresolved. Possible explanations include optimal control theory [66], synergy- or repertoire-based learning [67,68], or even evolved or learned priors that bias behavior towards sufficiently optimized solutions [69,70].

Costs of gait initiation do not drive quiet standing posture

The second and third aim of this study were to determine how quiet standing posture affects the cost of gait initiation and whether this cost influences our choice of standing posture. We found that leaning further in the intended direction of movement provided no significant energetic benefit or reduction in time spent initiating gait when compared to the minimum-cost static posture. For forward walking, leaning further forward as compared to a central posture only slightly reduced the time to reach steady-state velocity (Fig 4B) and increased the CoT of the first step by just 0.17 ± 0.49 J/m/kg, consistent with prior reports that posture has little impact on the characteristics of forward gait initiation [44]. For context, humans adjust their steady-state walking speed to minimize CoT differences in the order of ~0.42 J/m/kg (0.1 kcal/km/kg), and continuously expend around 3.8 J/m/kg [6]. Initiating forward gait from the least efficient posture tested (-1.15°), which increased energy expenditure by 0.42 ± 0.27 J/kg relative to initiation from the minimum-cost posture, would raise total expenditure over 10 m of walking by only ~1%. While significant, such marginal differences indicate that the energetic penalties of starting gait from a suboptimal stance may be too small to drive systematic adjustments, especially when compared against the substantial cost increase associated with lean angle (Fig 2A). Consistent with this finding, participants maintained their preferred static posture even when the direction of gait initiation was predictable (Fig 4A). Together, these findings suggest that while posture can modulate the cost and timing of gait initiation at larger lean angles, the influence is negligible relative to the continuous cost of walking and standing, and thus unlikely to shape postural choice under typical everyday conditions.

Instead, time and task constraints may have a stronger influence on postural selection for gait initiation [43]. For example, sprinters adopt a crouched start to maximize acceleration [42,43], while marathon runners primarily start upright. Clearly, urgency can drive changes in posture when the task demands it [43]. In our experiment, participants had no strong incentive to minimize the time spent initiating gait, as their initiation speed did not hinder their ability to perform the task effectively. We hypothesize that stricter time demands, such as reaching the end of the walkway as quickly as possible, would have led them to prioritize acceleration at the expense of energetic efficiency [48]. Future work could assess how humans optimize energy expenditure through postural adjustments during gait initiation tasks with greater time pressure.

Variability and flexibility in postural control

In both experiments, participants naturally converged on an energetically efficient posture when no target was prescribed, yet also exhibited substantial variability both across participants and within trials (Figs 2 and 4). A Monte Carlo analysis of a passive ankle stiffness model showed that differences in participants’ stiffnesses could explain only part of this variability. The simulated equilibrium angles (where active contributions to the ankle moment are minimal) were slightly more posterior than the actual postures adopted in Experiment 1. This suggests that a participant’s preferred forward lean is not solely the result of minimizing active contributions to the ankle moment, consistent with earlier work showing that humans typically adopt a more forward-leaning stance than predicted by inverted pendulum models [23,71] and that ankle stiffness alone cannot stabilize the human body [72–74].

We further found that both metrics for within-trial postural variability (i.e., standard deviation of lean angle and CoP velocity, Fig 2B) did not differ across central targets (0 to 3.44°). This aligns with recent work showing that variability in postural control signals (i.e., ankle torque) remains relatively constant within this range, but rises beyond it, likely because higher force demands increase motor noise [75]. Furthermore, when standing at preferred postures, the within-trial standard deviation of lean angle was roughly twice that of the minimum-cost target (Fig 2B, Table 1), consistent with larger postural variability and low-frequency sway previously reported in unconstrained standing [76–79]. This greater dispersion of lean angles did not coincide with higher CoP velocity or metabolic cost (Fig 2), suggesting that the target successfully constrained the natural sway without substantially increasing the control demand. Strictly limiting the permitted CoM or CoP variability can increase energetic expenditure due to the higher incidence and magnitude of postural corrections [28,39], though energetic costs also rise when variability is artificially increased using more challenging experimental conditions [38]. Intermittent balance control models [80–82] formalize this tradeoff between effort and variability by permitting postural sway until a stability threshold is exceeded, thereby reducing energetic demands compared to continuous control [83]. Overall, minimizing variability does not appear to be a prerequisite for minimizing energy expenditure, suggesting that efficient postural control does not require constraining posture at a single energetic minimum. Furthermore, our findings suggest that interpretations of postural control without a fixed reference angle, such as intermittent control [80–82] or random walk (i.e., Brownian motion, [77–79]), are not at odds with energetically optimized standing as long as posture remains within the central region of measured costs (Fig 2). The implications of these observations on modeling methods are discussed further below.

Towards improved models of cost in posture

Postural control is commonly simplified as a continuous minimization of deviations from a reference lean angle of an inverted pendulum [21–24], resulting in a symmetric linear or quadratic cost function with a single optimum in the center. However, our experimental data show that energy expenditure increases at almost twice the rate with backward lean than with forward lean, which is not captured by these cost functions. To improve the predictive and exploratory power of inverted pendulum models, we recommend penalizing posterior-leaning postures more strongly than anterior-leaning postures to account for the asymmetries observed in energy expenditure (Fig 2A) and to use caution when equating the idealized ankle moment to physiological effort. Future work could evaluate whether multi-objective control models (e.g., a linear quadratic regulator minimizing control action and kinematic state [21,24,28,30]) and intermittent control [80–82] can be improved by incorporating asymmetric weights to control actions in the anterior and posterior directions, which may better represent the cost of accelerating the body in these directions. We hypothesize that this adjustment may explain the human tendency to maintain an anterior-leaning posture during quiet standing as a precaution to avoid the steeper cost gradient associated with a posterior lean. Furthermore, our work suggests that energy expenditure in posture is sufficiently optimized by limiting sway within a central region of lower-cost lean angles, providing experimental support for balance interpretations that do not rely on a reference angle to optimize control (e.g., intermittent control [80–82] or Brownian motion [77–79]). More broadly, it is also important to consider whether a model’s mechanical representation may limit inferences about energy expenditure. A single-link inverted model cannot capture multi-segment coordination and may not accurately represent higher-frequency dynamics [30,84], possibly underestimating the control effort and highlighting the need to select appropriate model mechanics and cost functions for the problem at hand.

Alternatively, musculoskeletal simulations may offer an approach grounded in anatomy and muscle physiology to represent the energetic costs of posture. Such models have been applied to simulate quiet standing [25,26,85,86] and estimate the energetic cost of postural responses [87]. Our study extends this work by validating musculoskeletal inverse simulations as a computational approach for capturing trends in measured energetic cost of standing across lean angles, including the asymmetric increase for posterior lean. While the model estimated the shape of the metabolic cost landscape, it underestimated the increase in energetic cost for anterior lean angles (Fig 2A). One possibility is that contributions from muscles not included in the model, such as those of the back, arms, and neck, increase energy expenditure during anterior postures. The measured EMG activity of the erector spinae muscle (Fig 3) showed a small increase in activity with more anterior postures, suggesting that it could contribute to changes in energy expenditure together with other trunk muscles, though this trend was considerably smaller than that observed in the plantarflexor muscles. Another explanation is the model’s high passive ankle stiffness: for a participant with parameters close to the unscaled model (male, 1.77 m, 80 kg), the summed tendon force of the inactive soleus and gastrocnemius (medialis and lateralis) muscles generated 400 N at a plantarflexed ankle angle of 5 degrees, resulting in a moment of 17 Nm. By comparison, previous literature reported the moment contribution of passive ankle stiffness to be around 10 Nm at this angle [46,57], suggesting that the model’s larger passive contributions may reduce the required plantarflexor muscle activations for maintaining equilibrium. Future work could investigate how stabilization of the spine and upper body, individual (sex) differences in morphology and muscle strength [88,89], weight distribution, physiological and behavioral changes with ageing [61,90], and passive ankle stiffness [46,72,91] affect energy expenditure and optimal posture.

Ethics statement

All experiments were conducted in accordance with the Declaration of Helsinki and under the approval of the Erasmus Medical Center Medical Ethics Review Committee (MEC-2023-0205). Participants received the information letter of the experiment at least 24 hours prior to participating. Before the experiment was conducted, participants provided written informed consent for their participation, and all participants provided the optional permission to publish the coded data collected during the experiment under a Creative Commons Attribution (CC BY) license.

Participants

A total of 33 healthy adult participants aged 18–50 with no history of balance, neurological or musculoskeletal disorders were recruited for this study (Experiment 1: 8 male, 5 female, age = 24.2 ± 2.1 years, height = 175.3 ± 7.3 cm, weight = 72.4 ± 9.7 kg; Experiment 2: 9 male, 11 female, age = 24.1 ± 3.3 years, height = 178.1 ± 11.1 cm, weight = 70.0 ± 10.5 kg, one participant completed both experiments).

Methods and protocol

This study aimed to determine the energy expenditure required for maintaining a static posture and initiating gait. We performed two experiments: (1) a metabolic assessment of static standing at six prescribed target positions and at preferred postures with eyes open and closed, and (2) a walking initiation experiment where participants stood ready and started walking when presented with a cue.

Experiment 1: Static standing protocol.

The aim of Experiment 1 was to measure the metabolic cost of anterior and posterior postures and to determine whether this cost could be predicted from motion data using a musculoskeletal model of human standing. A motion capture system (Qualisys AB, Göteborg, Sweden), consisting of 12 Oqus 700 cameras, was used to track the locations of 43 passive motion capture markers placed on the participant at 100 Hz. Marker placement followed the IOR gait marker set (used by [92]) with the addition of four markers on the head, two on each arm, and the omission of the T7 marker due to obstruction by the back-worn metabolic analyzer (See S1 Appendix for list of markers). Ground reaction forces on both feet were measured at 500 Hz using two force plates (9260AA6, Kistler Group, Winterthur, Switzerland; CoP error < 2.0 mm), which were zeroed before each set of measurements (four sets per participant) to account for potential signal drift.

Energy expenditure was measured throughout the experiment using a breath-by-breath indirect calorimetry metabolic analyzer (K5 9260AA6, COSMED, Italy). This type of indirect calorimetry system has been validated during resting conditions against Douglas bag measurements and metabolic simulators [93,94]. Before each session, the device was calibrated following the manufacturer’s instructions using a certified gas mixture (16% O₂, 5% CO₂), a CO₂ scrubber (C04408-01-07, COSMED, Italy), and a 3 L calibration syringe (C00600-01-11, Hans Rudolph, United States). The analyzer recorded minute ventilation (VE) as well as the O₂ and CO₂ concentrations in both inhaled and exhaled air, and reported energy expenditure using the Brockway equation [95]. Caloric and caffeine intake are known to affect metabolic assessments [96], so participants were asked not to consume caffeine or food for at least 3 hours prior to the experiment’s start time. In addition to this measurement, the energy expenditure was also computed using musculoskeletal simulations (see Analysis). Indirect calorimetry data were excluded for one participant (S09) because their ventilatory equivalent (VE/VO2) was highly elevated compared to that of the other participants (26.0 ± 4.0 for the remaining included participants, around previously reported rest ranges of 25–30 [97]).

Electromyography (EMG) data were collected from 8 muscles on the right side of the body, including the medial gastrocnemius, soleus, tibialis anterior, vastus medialis, rectus femoris, biceps femoris, semitendinosus, and erector spinae. The ground electrode was connected to the right ankle on the lateral malleolus, and the SENIAM 8 guidelines [98] were used for electrode placement. Signals were amplified with a gain of 20 and recorded at 2000 Hz using an ExG amplifier (Porti7-8b8at, TMSi, Netherlands). The amplifier was connected to a laptop computer (Windows 10, USB 3.0, i7-1195G7, 16 GB RAM, MSI, Taiwan) using a USB connector to start, stop, monitor, and store the EMG data using a modified version of the TMSi MATLAB interface. The measurements were normalized to the maximal observed activation during exercises described by Uhlrich et al. [45,99] to evoke a maximal voluntary contraction. These exercises consisted of prone knee flexion, supine ankle dorsiflexion, hip flexion kicks, and maximum height jumps with knees initially at ~90°. A prone lumbar extension exercise without arm support was added to maximize activation of the erector spinae. A synchronization signal was sent from the “sync out” port on the first Oqus camera to the trigger port of the EMG amplifier at the start of each measurement, allowing for the synchronization of the two measurements. The indirect calorimetry measurement was synchronized by manually reading the device measurement time at the start of each measurement.

At the start of the experiment, participants were shown the equipment and explained the protocol before signing the informed consent. A short survey was used to collect basic participant information, including age (24.2 ± 2.1 years), sex (8 male, 5 female), dominant hand (12/13 right), and dominant leg (12/13 right, based on which leg they would use to kick a ball). General physical activity was assessed using the short International Physical Activity Questionnaire (Aug 2002 English version) to determine a three-level scale [92,100]. Almost all participants (11/13) were rated at the high activity level, while the remaining participants were rated at the middle level. This distribution was insufficient for making informative comparisons between scores. Next, basic anthropometric measurements were collected, including body length (175.3 ± 7.3 cm), ankle height at the lateral malleolus (6.8 ± 0.6 cm), and hip width at the greater trochanter (34.2 ± 2.1 cm). Body weight (72.4 ± 9.7 kg) was calculated by summing the vertical forces on the force plates and subtracting the weight of the metabolic analyzer (900 g). The foot placement on the force plate was standardized by positioning the centers of the ankle joints at hip width, estimated as 0.532 times the measured distance between the greater trochanters following Bennett et al. [101]. The center of rotation of the ankle joint was assumed to lie at the anterior edge of the medial malleolus [102]. During quiet standing, whole-body lean was computed through a static inverted pendulum approximation, where the CoM was assumed to be directly above the CoP. The length of the pendulum was approximated as the center of mass height with respect to the ankle joint (h_CoM), estimated by multiplying the body height by 0.56 for female and 0.57 for male participants [103], and subtracting the ankle height. The lean angle θ was then estimated in radians by dividing the distance of the CoP with respect to the ankle joint [102] by the center of mass height.

Experiment 1 consisted of two trial types: preferred posture trials and target trials (Fig 1C-1E). In preferred posture trials, participants stood quietly facing forward with their arms at their sides, maintaining a comfortable posture with their arms by their side (but not in their pockets) with either their eyes open (EO) or closed (EC). Each trial lasted five minutes. In target trials, participants were instructed to match their CoP to a visual target displayed on a screen 3.20 m in front of them, at a height of 1.67 m. This target was necessary to limit natural drifts in quiet standing posture [76–79], which would invalidate the indirect calorimetry assessment of a specific lean angle. A black circle represented the target, and participants controlled a red cursor corresponding to their CoP location. The cursor turned green when it was within the target area, providing real-time feedback. While the target circle was always drawn in the center of the screen, participants had to maintain a lean angle θ_target of -2, 0, 2, 4, 6, or 10 ⋅ 10^-2 rad (i.e., -1.15, 0, 1.15, 2.29, 3.44, 5.73°) to get the cursor in the center. These lean angles correspond to a subset of the targets used by Mensink et al. [75], where the variability of ankle torques was investigated. The corresponding CoP target positions were calculated as:

(1)

The radius r_target of the target circle was normalized to body length so that a similar whole-body angle excursion would result in a similar deviation from the target for all participants. The target radius is shown in Fig 2B to allow direct comparison with the natural within-trial variability of lean angle, indicating whether participants successfully restricted their spontaneous sway to the target range. The radius of the target was computed as

(2)

The circle was green when the participant was within the radius of the target, computed as

(3)

A 5-minute break was scheduled midway through the experiment. To minimize order effects, the order of the blocks (Preferred or Target) was reversed before and after the break. A total of 3 out of 208 trials were excluded due to technical issues or experimenter error (EO and targets 0 and 1.15°, all from different participants). In these cases, participant mean data were computed using the remaining valid trial of that condition.

Experiment 2: Walking initiation protocol.

The aim of Experiment 2 was to determine the energetic cost of gait initiation across natural postures and to evaluate whether humans select postures that minimize this cost based on the expectation of walking direction. Participants (9 male, 11 female, Age = 24.1 ± 3.3 years, Height = 178.1 ± 11.1 cm, Weight = 70.0 ± 10.5 kg) stood on a force plate and initiated gait when a prompt on a screen asked them to start walking in the forwards or backwards direction (Fig 1F-1G). Because the initiation of walking takes far less time than the time constant of indirect calorimetry (~42 seconds [104]), the metabolic cost of gait initiation could not be measured. Instead, we estimated metabolic cost using musculoskeletal simulations on the kinetic and kinematic data measured through the force plate and motion capture system (see Computation of metabolic cost below).

The motion capture system consisted of 8 cameras running at 100 Hz (4 Miqus M3 and 4 Miqus M5, Qualisys AB, Göteborg, Sweden), an analog measurement board (Qualisys Analog Interface 16 Channels, 230597, Qualisys AB, Göteborg, Sweden), a sync box (Qualisys Sync Box, 410850, Qualisys AB, Göteborg, Sweden), and a single force plate running at 1000 Hz (Plate: BMS 400600HF-1K, Amplifier: Optima OPT-SC, AMTI, MA, US; CoP error < 0.5 mm) embedded in a wooden walkway (740 cm long, 80 cm wide, > 2mm clearance gap with the force plate and wooden walkway). The foot placement and motion capture marker locations were identical to those used in Experiment 1, with the addition of a marker on the T5 vertebra, which could now be placed since the back-worn metabolic analyzer was no longer used (see S1 Appendix for list of markers). A TV screen was placed at eye level at the anterior-facing end of the walkway (3.2 m away) to show the CoP target in some trials and to prompt the participant to start walking at the start of the trial. The data was stored in 12-second trials, with the prompt appearing at the 6-second mark.

Experiment 2 consisted of two sets of trials: preferred and target posture trials. The preferred posture set was always performed first to avoid influencing the participants’ preferred posture at gait initiation. In the preferred trials, the participant was instructed to stand calmly with their arms resting at their sides while looking straight ahead. During these trials, there were three distinct blocks to evaluate whether the known probability of gait initiation influenced posture: Forward-only (20 trials), Random (15 trials forward, 15 trials backward), and Backward-only (20 trials). In all three blocks, the participant was explicitly informed of the probabilities associated with the prompts, but not as to when they would be delivered. In the Random block, a random permutation determined the order of the prompts, and neither the participant nor the experimenter (to prevent experimenter bias) was aware of the direction presented for each trial.

In the set with target trials, participants received the same visual feedback on CoP position as used in Experiment 1 (Fig 1D, Eq 1–3), but only at target locations of -1.15, 1.15, and 3.44°. For each target, participants were prompted to walk forward or backward 5 times each, resulting in a total of 30 trials. The trials were ordered using a random permutation, ensuring that the target order and initiation direction were unpredictable. Trials that contained an error, such as initiating gait in the wrong direction or with the incorrect leg, were repeated and shuffled among the last five trials so that participants could not predict which direction would be repeated.

Prompts to initiate walking were provided using the TV screen. Forward trials were indicated by a blue screen displaying “Forward”, an upward-facing arrow, and a sound tone of 532 Hz; backward trials were indicated with an orange screen displaying “Backward”, a down-facing arrow, and a 440 Hz sound tone. After 3.1 seconds, a stop tone of 329 Hz was played to signal to participants that the trial had been completed. The period was selected to approximate the time by which participants should have made their fourth foot strike. Participants were asked to step with the same leg consistently and could choose a different leg for forward or backward walking. The time between a participant being ready and the delivery of a prompt was standardized to be a random integer in the range of 5–10 seconds, so that the timing of the prompt would not be predictable. The participant was considered ready when the absolute time derivative of the CoP remained below a threshold for 1000 consecutive samples (1000 ms). This threshold was determined at the start of the experiment using a baseline trial of 2 minutes and computed as:

(4)

where is the vector containing the CoP time derivative of the entire baseline trial. A MATLAB script was used to detect when the participant was ready and start a timer, indicating to the experimenter that the prompt could be sent.

Quantification and statistical analysis

Monte-Carlo analysis of ankle stiffness and equilibrium lean angle.

To investigate whether individual differences in passive ankle stiffness could account for variations in preferred lean angle (Experiment 1), we estimated how this variability affects the equilibrium whole-body lean angle. This analysis helps infer whether individual differences in the mechanical properties of the ankle could lead to different energetically optimal postural lean angles. We performed a Monte Carlo simulation based on the parameter distributions for ankle stiffness reported by Moseley et al. [46], as this model includes the progressive increase of ankle stiffness with ankle angle [46,57] and provides the uncertainty ranges of the fit parameters, allowing the stochastic generation of ankle stiffness curves. The equilibrium lean angle was defined as the whole-body angle at which the moment produced by passive ankle stiffness balanced the gravitational moment acting on the body. The mass-normalized ankle stiffness of one ankle was modeled as

(5)

Where θ is lean angle in degrees, k = 56.09 · 10^-3 ± 8.36 · 10^-3, b = 1.871 ± 0.282, and m = 68.5 kg. These values were obtained from the study [46] and normalized by dividing the ankle moment by the average mass. We generated 50,000 samples from the distributions of k and b, assuming a normal distribution for both. Next, we computed the equilibrium angle θ for each combination by finding the intersection of the mass-normalized ankle moment (M_norm(θ)) and gravitational moment (gLθ) using MATLAB for an assumed body with the mean parameters of the participants in Experiment 1 (center of mass height = 0.954 m, weight not required). Because the resulting distribution of equilibrium angles was skewed, we reported the median and interquartile range of the estimated equilibrium angles.