Understanding the influence of context on real-world walking energetics Free

Walking is an integral part of daily life in humans, enabling movement in the environment and contributing to overall health and well being. Studies investigating the relationship between walking kinematics and energetic cost conducted in the lab have demonstrated that humans tend to select movement patterns that minimize cost of transport (Clark, 2015). Net cost per unit distance – gross cost adjusted for resting metabolic rate – is often used to identify energetically optimal movement patterns in controlled experimental studies, and provides insights into the requisite daily energy expenditure for prescribed walking distances. For unconstrained movement during daily life, the gross cost per unit distance may more closely align with the maximal range speed that is observed during typical walking behaviors (Srinivasan, 2009). Studies in controlled environments have demonstrated that key gait parameters (e.g. step width, step height, swing limb trajectory, arm motion) are self-selected to minimize energetic cost using both net and gross metabolic rate (Abram et al., 2019; Minetti and Alexander, 1997; Zarrugh et al., 1974; Wong et al., 2019; Selinger et al., 2015). However, work has also demonstrated that gait observed in laboratory settings differs from unconstrained movement in the real world (Dal et al., 2010; Lee et al., 2022; Hutchinson et al., 2019; Foucher et al., 2010).

Many of the advantages of in-lab gait analyses, such as increased control over participant behavior, may result in movement patterns that are not representative of daily life. For example, steady-state treadmill walking reduces variability during extended bouts of gait, but human movement during daily life has been observed to consist of many short bouts or longer walks with punctuated stops, such as standing idle waiting to cross a street (Baroudi et al., 2022; Orendurff et al., 2008). Differences have also been observed in walking kinematics in different environments (inside versus outside walking), depending on behavioral context (purposeful versus recreational walks) (Slade et al., 2022; Kim et al., 2020; Wang and Adamczyk, 2019). Direct observation of human walking also offers greater control during an experiment. However, researchers have shown that individuals alter their performance when observed compared with their natural behavior (a phenomenon known as the ‘white-coat effect’) (Warmerdam et al., 2020; Hillel et al., 2019).

Compact wearable sensing technologies can be used to measure kinematics and physiology during daily life to investigate walking biomechanics. Small low-power sensors, such as accelerometers, have been embedded in shoe soles and belts, and are also commonly found in phones and watches (Benson et al., 2018; Motl et al., 2012). Sensing systems designed around accelerometers can make continuous measurements for weeks (Wu et al., 2022; Baroudi et al., 2022). Inertial measurement units (IMUs) combine accelerometers with gyroscopes and magnetometers to measure additional kinematics. IMUs require more power than an accelerometer alone, limiting recording duration to day scale. But, these sensor data can be used to estimate parameters such as foot orientation and speed, enabling position estimates of the foot during gait. The accuracy of the step-to-step position estimates has been shown to be comparable to measurements made using motion capture (Ojeda and Borenstein, 2007; Rebula et al., 2013; Potter et al., 2019). Using wearable sensors to persistently monitor an individual enables the investigation of real-world movement patterns; however, behavioral and environmental context can also be used to explain the variability observed in real-world movement patterns.

Contextual information can have many forms, from the location of a walk, to its purpose. Prior work has identified a dependency between terrain type and metabolic cost (Gast et al., 2019; Kowalsky et al., 2021). Researchers have leveraged GPS data, as location is closely associated with activity (Kim et al., 2020; Wang and Adamczyk, 2019). Gast et al. (2019) demonstrated how humans might prefer a slower speed than the energetically optimal speed when walking on difficult terrains to increase stability. However, these experiments were focused on a specific contextual aspect over a short period. To gather contextual information over longer periods, technologies such as cameras can offer a direct observation of the environment someone is moving in, but they are highly invasive and image analysis can be burdensome. These issues impact the feasibility of using camera data for long-term monitoring. Alternatively, researchers have asked participants to keep a manual log of their daily activities to gain additional information on context (Cleland et al., 2014; Chang et al., 2017).

The objective of this work was to investigate the relationship between both gross and net cost of transport, real-world walking speed, and context during the daily life of young able-bodied adults. Specifically, we quantified whether participants self-selected walking speeds that minimize their gross or net cost of transport in the real world, where walking is highly variable and context dependent. We hypothesized that, in the real world: (1) individuals will tend to select a walking speed that minimizes cost of transport (net or gross), and (2) the use of a walking speed that minimizes cost of transport is independent of context. To test these hypotheses, we combined in-lab experiments to establish the subject-specific relationships between cost of transport and walking speed and long-term data collection to capture real-world walking speed and contextual factors. The results of this study provide insight into the energetic cost of walking in the real world, and how contextual information can be effectively used to understand human locomotion. This study also highlights the benefits of ecologically relevant experimental designs for the study of human movement, health and overall behavior.

Data and results from 17 subjects recruited from a healthy population are presented in this work (11 females, 6 males, 26±6 years, 168±10 cm, 65±9 kg). Participants were excluded if they had health issues that would limit their ability to walk or breathe, such as severe cardiac disease or asthma. Participants signed an electronic consent form prior to the first visit, and this study was approved by the Institutional Review Board at the University of Michigan.

Movement and activity data were first collected over the course of a week from the subjects during their daily life. During an initial visit to the lab, participants were given an accelerometer (activPAL^TM, PAL Technologies Ltd, Glasgow, UK) and an IMU (Opal, APDM, Portland, OR, USA) to wear during the 7 days of monitoring (see Table S1). The activPAL was chosen for its small size and ability to log data continuously for the week-long trial. Additionally, activity classification algorithms developed by PAL Technologies were combined with custom algorithms to isolate walking (Wu et al., 2022; Ryan et al., 2006). Wu et al. (2022) reported that several studies have found high agreement (98%) between the activPAL and other validated devices in the detection of stepping time (Wu et al., 2022). The activPAL, being a single-point accelerometer, does not allow for direct measurement of walking speed. As such, we complemented this sensor with the IMU to obtain accurate measurements of walking speed (detailed in ‘Data processing’, ‘Walking speed estimation for a walking period’, below). Wear time for each sensor can be found in the Appendix, ‘Sensor wear time’.

During the same visit, the Ethica app (Ethica Data, Toronto, ON, Canada) was installed on each participant's phone. The app logged GPS data from the phone throughout the week. The sampling rate of the GPS data was variable, averaging a measurement every 90 s. The resolution of the measurements depended on the participant's phone and whether they were inside or outside. We asked participants to keep the app open in their phone background and to allow the app to access their location. As GPS data can be sensitive, participants were able to turn off the app for periods of time at their discretion (Fig. 1A).

Participants were instructed to go on a daily walk of at least 10 min. We specifically prompted participants to take a ‘pleasure walk’ or ‘stroll’, described as ‘a walk for the purpose of walking, with no particular purpose nor destination’. This prompt was used to increase context diversity in the data, and ensure that there would be long walking bouts for analysis.

To facilitate labeling and classification, the participants kept an activity log detailing when they were walking, the purpose of the walk and where they were (e.g. home, work, etc.). A log template and a detailed explanation about how to fill out the log were provided to the participants, along with a set of instructions that included information on how to charge and wear the sensors. Participants could also opt-in to receive daily text reminders to charge and wear the sensors, and to take their daily walk.

Following the week of real-world data collection, the participants returned the sensors and scheduled the in-lab visit. At the start of the second visit, an exit interview was conducted with the participant to clarify information from the log with the activPAL and GPS data. During the interview, participants were asked to provide supplementary information if the logs were incomplete (e.g. a walk was logged but the purpose was missing). The participants were also asked to recall the context of recorded activities that were not logged (e.g. a walk is classified from the sensor data but absent from the log). This interview ensured that the contextual information for the real-world walking data was complete and accurate.

An experimental investigation of energetic cost during a range of walking speeds was then conducted with each participant. Sixteen reflective markers were first placed on the participant's lower body to measure walking kinematics using a 26-camera Vicon Motion Capture system (Vicon, Oxford, UK) collecting data at 100 Hz. Markers were placed on the following locations on both the right and left leg: anterior superior iliac, posterior superior iliac, thigh, knee, tibia, toe, ankle, heel. A COSMED K5 system (COSMED, Rome, Italy) was used to measure metabolic cost. This system uses a mask worn around the subject's mouth and nose, and a small backpack that carries the portable measurement unit with the battery. Oxygen and carbon dioxide volumetric flow rate were measured breath by breath. To prevent measurement bias, participants were asked to refrain from eating, drinking caffeine and exercising 5 h prior to this second visit. Once the participants felt comfortable, they were instructed to perform a 5 min period of quiet standing to obtain resting metabolic rate. Walking trials were conducted on an instrumented split-belt treadmill (Bertec, Columbus, OH, USA) (Fig. 1A). Ground reaction force data were sampled at 1000 Hz from both belts.

Participants were given time to familiarize themselves with the split-belt treadmill before the experiment was conducted. During the experiment, the participants were asked to walk on the treadmill at six different speeds for 6 min each. Data from the week-long data collection were used to determine the range of speeds used for this task. We separated equally across the six speeds the interval between the maximum and minimum speeds observed in the real world. Often, the fastest speed originally chosen had to be reduced to accommodate the treadmill discomfort that participants felt. The order of the speeds was randomized and a 2 min seated resting period was allowed between each 6 min trial.

We grouped the real-world walking data into walking periods following the method outlined in Baroudi et al. (2022) (Fig. 1B). Briefly, we used the proprietary algorithm from the activPAL, which identifies stepping (Wu et al., 2022; Ryan et al., 2006). Then, we grouped consecutive stepping bouts into stepping periods if the individual was standing (based on the activPAL classification) for less than 1 min in between two stepping bouts. The objective of this grouping was to capture the discontinuous nature of real-world walking. For instance, if an individual stops at a pedestrian light before crossing, the walk bouts before and after that stop were grouped together in a stepping period. Lastly, the activPAL algorithm does not distinguish between running and walking within stepping. Thus, we developed a classification algorithm to extract walking periods from all stepping periods.

Once we extracted walking periods for each participant, we used the foot-worn IMU data to estimate stride speed (Fig. 1B). Heel strike events in a stride create high peaks in angular velocity that allow for stride detection. The x-axis signal, around which the foot flexes, was smoothed using a locally weighted scatterplot smoothing (LOWESS) method. A peak detection method was applied to isolate strides. Walking periods with fewer than 5 strides were discarded to reduce errors in gait parameter estimation. To estimate stride speed, we used the zero-velocity update (ZUPT) algorithm (Ojeda and Borenstein, 2007; Potter et al., 2019; Rebula et al., 2013). This algorithm leverages the assumption that the velocity of the foot on the ground is close to zero when a human is walking to integrate the acceleration while correcting for the IMU drift. The velocity and position of the foot were subsequently obtained. We followed the implementation formulated by Rebula et al. (2013) using the same hardware. From the foot position, we extracted stride length and calculated stride speed by dividing stride length by stride time.

A custom algorithm (detailed in the Appendix, ‘Steady-state walking in the real world’) was used to identify steady-state strides within a walking bout (Fig. 2). Briefly, we considered a stride to be at steady state when the individual was walking straight (i.e. not turning), with a constant velocity (i.e. not accelerating or decelerating). We started by creating rolling windows of 3 strides in a walking bout with a 2-stride overlap. The second stride of each window was classified as steady state or non-steady state using the foot-worn IMU data. The first and last strides of a bout were discarded. Then, for each window, we created a vector with the three stride speeds and stride lengths calculated using the method outlined in the previous sub-section (‘Walking speed estimation for a walking period’). From these vectors, we calculated the coefficients of variation (CV_speed and CV_length) to measure whether stride length and stride speed varied, indicating a possible acceleration or deceleration. If both of these coefficients were above 7%, we classified the stride as non-steady state. In addition, we calculated cosine similarity between the direction of each pair of consecutive strides. Cosine similarity measures the similarity between two vectors and is bounded between 0 and 1. If the cosine similarity was under 0.7 (e.g. the stride directions are separated by a 45 deg angle), the stride was classified as non-steady state. Otherwise, the stride was classified as steady state. The thresholds for the different parameters were determined by conducting a sensitivity analysis as detailed in the Appendix. We evaluated this algorithm using a controlled experiment.

We manually labeled each walking period using a combination of the manual log given by the participant, the exit interview, and the GPS data (Fig. 1B). For each walking period, we visualized the log entry with a satellite view of the GPS data to isolate the location and purpose of a walk. This process allowed us to isolate repeated locations for a participant, such as their home and workplace. Once all participants' data were labeled, we isolated six common contexts: Work, Commute (i.e. repeated trajectories between home and work), Pleasure (i.e. from the pleasure walk that participants were specifically requested to do and labeled as such), Shopping, Home and Other Outdoor (i.e. any outdoor walk that was not classified as pleasure or commute). Two participants carried out a small number (<5) of walks they labeled as Exercise that we included in Other Outdoor as well. Other walks such as church, amusement park or dog walks were labeled as Other Outdoor as they were rare and often specific to a given participant. The few walking periods (<1%) that had missing labels were also labeled as Other Outdoor.

We used the force plates from the instrumented treadmill to detect gait events. We discarded strides where the participants did not correctly place their foot on the corresponding belt. The heel marker was used to extract stride length as it moved the least throughout the trials (as opposed to the toe marker, for instance, that was scrunched during plantar flexion) and never got obstructed from our camera setup. To calculate stride length, we multiplied stride time by the speed of the treadmill belt (assumed constant), and we added the distance between two consecutive foot strikes from the same foot to account for back and forth movement of the participant on the treadmill. Stride speed was then calculated by dividing stride length by stride time.

To obtain metabolic rate at steady state, we used the last 2 min of each 6 min trial. The breath-by-breath measurements from the indirect calorimetry system were averaged; then, the Brockway equation was used to estimate whole-body gross metabolic rate (Brockway, 1987). Finally, we subtracted the resting metabolic rate measured during the quiet standing period to obtain net metabolic cost. To ensure the validity of the derivation, we made sure the respiratory quotient never exceeded 1. We calculated cost of transport by dividing the metabolic rate by stride speed and normalizing by body mass. Lastly, we identified the coefficients of a 2nd order polynomial curve mapping both gross and net cost of transport to stride speed using the MATLAB curve-fitting toolbox. To identify the energetically optimal speed range, we looked at the minimum cost of transport value and added 10%. This resulted in two points on the cost of transport curves, one on the left and one on the right side of the minimum (Fig. 1Ciii shows an example with the net cost of transport curve). The associated speeds with these two values of cost of transport were used to define the lower and upper bound of the energetically optimal speed range for both gross and net cost of transport. Specifically, the speed corresponding to the point on the left side of the minimum cost of transport represents the lower bound, while the speed corresponding to the point on the right side represents the upper bound. By considering the range of speeds between these two points, we can identify an energetically optimal speed range where the cost of transport is minimal. This approach was used to obtain a cost of transport range that was within 10% of the minimum for all participants. This range is influenced by the steepness of the curve. As such, an individual with a shallow cost of transport curve would have a larger energetically optimal speed range. The value of 10% was chosen heuristically as there was no prior to use as a baseline for determining a reasonable energetically optimal range. To quantify whether humans used a walking speed within the energetically optimal range, we evaluated the proportion of steady-state strides for each context within the identified ranges.

For three participants, the measurements of metabolic rate failed for different reasons. One participant's respiratory quotient was consistently over one. Another did not have proper placement of the mask so only a limited number of breaths were registered, which did not allow for a sufficiently accurate estimate of metabolic rate. Finally, many participants reported that the mask irritated their eyes and caused nose congestion; one participant could not complete the trial for this reason. We suspect this particular discomfort came from the solution (cidex) used to disinfect the mask between participants.

Paired t-tests were conducted to evaluate whether participants selected walking speeds that minimized their gross and net cost of transport. Specifically, we tested whether the differences between the observed distribution of steady-state stride speeds estimated during daily life and the energetically optimal speeds measured in the lab for both gross and net costs were significantly different from 0. To test whether walking speeds that minimize cost of transport were independent of context, we calculated the percentage of real-world steady-state stride speeds within the energetically optimal speed range for each context and participant for both gross and net costs. We chose to use linear mixed models to assess the effects of both gross and net cost of transport on the selection of walking speeds. Each model included random effects for individual participants to accommodate intra-subject variability and the nested structure of the data (context was classified for identified walking periods for each participant) (Field and Wright, 2011). We compared different model complexities (with and without random effects) using the Akaike information criterion (AIC) (Field and Wright, 2011; Akaike, 1998) and selected the models that explained the most variance in the data. Significance of the tests was evaluated at the α=0.05 level. All statistical analyses were conducted in R.

We found 1731 walking periods across all participants that met our criteria for steady state (Fig. 2 and the Appendix, ‘Steady-state walking in the real world’), with a total of 304,309 strides (Table 1). The majority (64%) of walking periods were under 5 min, with 15% under 1 min (Fig. 3). The context Pleasure contained the most strides (steady state and non-steady state) across participants and for almost all individual participants, although S4 and S9 did not take any pleasure walks. The context Commute also gathered around 7% of all strides even though only 8 participants had walks in this context (only 45 walking periods total). Gait observed during Work contained 25% of the total identified walking periods, but the average duration of these walks was the smallest (2.7 min) and represented a little less than 5% of the total identified strides. It is important to note that the proportion of strides within each context is influenced by subject compliance. As such, contexts such as Home may be underrepresented if participants remove their shoes (and consequently the foot-worn IMU) when at home.

We mapped net and gross cost of transport to walking speed using data collected during the in-lab treadmill walking task (Fig. 1C). We verified that there was no correlation between goodness of fit, R² and root mean squared error (RMSE). For instance, R² and RMSE using net cost of transport for subject S2, who had an energetically optimal speed of 0.86 m s⁻¹, was 0.86 and 0.082 m s⁻¹. In contrast, R² and RMSE for S4, who had an energetically optimal speed of 1.37 m s⁻¹, was 0.87 and 0.434 m s⁻¹. The differences in energetically optimal speed also motivated the use of the +10% range. It was not possible to use 95% confidence intervals (CI) around the minimum because the fits only use 6 data points, resulting in very large CI. Overall, the net and gross cost of transport models had an average R² of 0.78 and 0.85 and RMSE of 0.20 and 0.22 J kg⁻¹ m⁻¹, respectively. Energetically optimal speeds that minimized cost of transport varied between individuals (Table S2), ranging from 0.82 m s⁻¹ for subject S8 to 1.37 m s⁻¹ for S4, with an average minimum cost of 1.83 J kg⁻¹ m⁻¹ for net cost of transport. For gross cost of transport, the range was from 1.18 m s⁻¹ for S2 to 1.44 m s⁻¹ for S7, with an average minimum cost of 3.53 J kg⁻¹ m⁻¹. Overall, energetically optimal speeds for gross cost of transport were on average 0.24 m s⁻¹ higher than those for net cost of transport (Fig. 4; Table S2).

Overall, an average of 51.7% of the identified strides within a walking period were classified as steady state, but the percentage of steady-state strides varied by context. When looking at the ensemble of strides across all walking periods, we found 75.8% of steady-state strides. Around 37% of all strides identified during walking at home were steady state, while 86% of the strides during a commute were steady state (Fig. 3). We observed high variability in the proportion of steady-state strides during walking in indoor contexts (e.g. Home, Shopping and Work) (Fig. 3). In contrast, these particular contexts had a low variability in walking period duration, with averages between 2.7 min for Work and 5.1 min for Shopping. We found that contexts containing longer duration walking periods, such as Commute or Pleasure, also contained a higher percentage of steady-state strides (32.7% and 31.6% of all steady-state strides, respectively).

We tested whether our participants walked in the real world at speeds comparable to the energetically optimal speeds identified in the lab using net and gross cost of transport. Fig. 5Ai,Bi shows the distribution of the difference between real-world and energetically optimal stride speed for all participants using gross and net cost of transport. Fig. 5Aii,Bii shows the proportion of all steady-state strides within the energetically optimal speed range determined using gross and net cost of transport.

We found that, across all participants and contexts, participants walked at a stride speed significantly higher than the energetically optimal speed when using net cost of transport (P<0.05), with a mean difference of 0.32 m s⁻¹ (30% increase). However, there was no significant difference between real-world walking speed and optimal speed determined using gross cost of transport (P=0.11), with a mean difference of 0.06 m s⁻¹. Overall, participants walked within the net energetically optimal range for 45.6±33.0% of their strides compared with 81.6±16.1% within the gross energetically optimal range (see Table S2). In other words, 45.6% of all participants’ steady-state stride speeds were within their respective net energetically optimal speed range compared with 81.6% when looking at the optimal speed range calculated using gross cost of transport. Next, we tested whether there was a dependence between the use of an energetically optimal walking speed and context. We found a significant relationship between the proportion of energetically optimal speeds determined using net cost of transport (e.g. real-world stride speeds within the energetically optimal speed range) and contexts across participants (s.d.=0.29, 95% CI: 0.19, 0.42). All contexts, apart from Other Outdoor, significantly predicted the proportion of strides at energetically optimal speeds. Commute was arbitrarily chosen as the baseline for the model. The coefficients indicate that participants were more likely to use energetically optimal speeds in all contexts when compared with Commute (Fig. 5). In contrast, the model built using gross cost of transport (s.d.=0.20, 95% CI: 0.16, 0.24) only showed a significant contribution of the context Commute. All of the coefficients are reported in Table 2. Individuals walked much faster when commuting relative to both the other contexts (net: ∼+0.14 m s⁻¹; gross: ∼+0.09 m s⁻¹) and to the energetically optimal speed range (net: ∼+0.36 m s⁻¹; gross: ∼+0.17 m s⁻¹).

The values and the variability of walking speed changed from one context to another for the same participant (see Table S2). Participants appeared to walk faster than the energetically optimal speed when commuting. This was also the context that exhibited the least variability with longer walks (Fig. 3). However, when shopping or at work, variability in real-world walking speeds was larger, with a greater overlap with energetically optimal speed ranges (Fig. 5).

Laboratory-based studies have found that individuals tend to use walking speeds that minimize cost of transport. Building on these results, the work presented here investigated walking economy in the real world by testing two hypotheses: (1) on average, individuals will self-select energetically optimal walking speeds (determined using net or gross cost of transport) and (2) the use of energetically optimal walking speeds is independent of context. We found that: (1) participants typically walked faster than the speeds that minimized their net cost of transport, aligning more closely with the speeds that minimized their gross cost of transport, and (2) the proportion of walking speeds within the energetically optimal range differed by context, with greater variation observed for net cost of transport. This suggests that individuals have multiple competing objectives when walking in the real world, including minimizing cost, which influences walking strategy.

Various in-lab studies have observed that many self-selected kinematic parameters optimize energetic cost (Abram et al., 2019; Wong et al., 2019; Selinger et al., 2015). These studies used either gross cost of transport or net cost of transport. Most of these studies were conducted in the lab, during steady-state walking, where participants walked for bouts shorter than 20 min. As such, we expected to see a similar relationship in the real world, particularly during long walks at steady state. There is also evidence in the literature that indicates individuals may be minimizing gross cost of transport when walking (Ralston, 1958; Elftman, 1966; Molen et al., 1972). Our data show that humans tend to minimize gross cost of transport when walking in the real world (Figs 4 and 5), suggesting that participants select movement strategies that minimize cost for both lab and real-world walking. First, we observed that individuals walked within their energetically optimal speed, as determined by gross cost of transport, approximately 82% of the time across various contexts in the real world. In contrast, they walked within the optimal speed range defined by net cost of transport about 46% of the time. Second, while preferred walking speeds varied by context among participants, our results indicate that only the Commute context significantly influenced the proportion of walking speeds within the energetically optimal range as defined by gross cost of transport. Conversely, using net cost of transport revealed that participants were more likely to walk at energetically optimal speeds in all contexts compared with Commute.

We observed that the predominantly indoor contexts (Shopping, Work, Home) contained the most energetically optimal strides. In these contexts, physical constraints such as halls, doors, rooms and furniture may affect how individuals are able to move in the environment. While only around 12% of all steady-state strides were observed during these contexts, these constraints (e.g. with many starts/stops and turns) might have led participants to slow down and walk at a stride speed closer to the speed that minimized net cost of transport (Figs 5 and 3). These contexts also resulted in a high variability in walking speed, which might have led to a bigger overlap with the energetically optimal speed range (Fig. 5 and Table 2). We expected participants to select energetically optimal speeds in the contexts Other Outdoor, Pleasure and Commute, as they contained longer walking periods with more steady-state behavior (Fig. 3). These three contexts contained around 74% of all data. We found that almost 90% of the steady-state walking speeds during a Pleasure walk were energetically optimal, compared with 83% and 73% for Other Outdoor and Commute, respectively. It is important to note that we specifically asked participants to take ‘pleasure walks’ to elicit a walk without any particular destination or objective other than walking. Therefore, participants likely went for a type of walk they would not have necessarily selected otherwise. These walks, although rare (approximately one a day), were long and thus contained many strides. The higher proportion of energetically optimal strides within this context may reflect the results from laboratory-based studies as there were no other competing objectives. However, it is important to note that the presence of researchers during laboratory-based studies can itself impact an individual's motion (Friesen et al., 2020). In contrast, the Other Outdoor and Commute walks often have fixed destinations and time constraints (e.g. getting to work on time), which could explain the use of faster walking speeds that have a higher energetic cost. This difference was particularly clear for commuting, where the highest walking speeds were measured (Table 2).

These findings can provide insight into research aiming to develop technological advancements based on human energetics, such as research in lower-body assistive devices, where control strategies for the assistance are designed to minimize energetic cost. Srinivasan (2009) (see also Carlisle and Kuo, 2023) detailed that the preference of using a speed that minimizes gross cost of transport when walking can be explained by the evolutionary legacy from our ancestors, who needed to use a ‘maximum range speed’ to cover the greatest distance for a given energy budget (that included the resting metabolic rate). Although human lifestyle has evolved from those hunter gatherers, Srinivasan (2009) posits that humans have retained the artifact of minimizing gross cost of transport when walking. Our results suggest that, depending on the context in which someone is walking, it may be more relevant to use gross cost of transport when analyzing the energetics of walking. While daily-life contexts exhibit variations that sometimes misalign with energetic optimality, our findings indicate that these differences are not substantial. However, it is possible that, given the many constraints of our real-world environment, individuals may not always select energetically optimal movement strategies. As such, experimental designs should evolve to take into account context within the real-world scenarios in order to ensure the ecological relevance of technological innovations. Slade et al. (2022) carried out a subject-specific optimization of a lower-body exoskeleton in the real world by recreating a realistic real-world scenario where participants walked short bouts in an uncontrolled environment, using ‘ecologically relevant audio prompts’ that elicited variability in the walking speed used by the participants. Such experimental design ensures that the technology (here an exoskeleton) can be used by individuals across different contexts and walking behaviors.

It is difficult to quantify the potential energetic consequences or penalties on the metabolism that someone experiences or perceives when deviating from their energetically optimal walking patterns. Across all individuals, we observed deviations in stride speed from the energetic optimum up to 0.48 m s⁻¹ (e.g. 40% more from minimum cost of transport for subject S5 in the context Pleasure). Medrano et al. (2022) estimated the ‘just noticeable difference’ in metabolic rate that individuals perceived with the assistance of a lower-body exoskeleton when walking on a treadmill. They found that participants (N=10) were able to perceive changes of around 20±5% with an accuracy of 75%. Thus, individuals may be mostly unable to perceive the deviations we observed from the energetically optimal walking speed. Even if participants could perceive the deviation, the energetic penalty could potentially be negligible given that most walks were relatively short in distance and duration (Fig. 3).

In the animal kingdom, the best locomotion strategy depends on context and might not always involve steady state. A prey evading a predator utilizes transient states with high acceleration that prioritize maneuverability over energetic consumption (Moore et al., 2017). In this work, a large portion of the observed movements occurred during non-steady-state/transient behavior (48.3% of all strides were classified as non-steady state). The proportion of steady-state strides was dependent on context. As expected, walks in more spatially constrained contexts (e.g. at home) contained more non-steady-state behavior (Fig. 3) (Glaister et al., 2007). Although fewer strides were identified in these contexts (compared with Commute or Other Outdoor, for instance), they contained more walking periods. In other words, when an individual stood up to walk, they were more often inside, in contexts such as Work or Home (22.2% and 14.4% of walking periods, respectively). This prevalence of transient behavior highlights the importance of studying all types of human movement that can be observed in the real world, particularly for health and mobility. For example, the work of King et al. (2022) was focused on the importance of turns and the potential associated risks for people with Parkinson's Disease when turning.

Preferred walking speed is a clinically important parameter used to quantify health and well-being (Fritz and Lusardi, 2009; Graham et al., 2008). We observed large variability within the identified steady-state strides between and within individuals. Between individuals, we noted a large variability in the overlap between the energetically optimal speed range determined using both the gross and net cost of transport and the real-world speed distribution within the same context (Table S2). Overall, there did not seem to be a way to predict the overlap size for a given context for all participants. For instance, in the context Pleasure, the overlap ranged from 0% to 100% when using net cost of transport and from 3.4% to 100% when using gross cost of transport. This suggests that other variables could potentially explain the variability between individuals, such as fitness level. Within individuals, we observed a large variability in the walking speed used for different contexts (Table S2). For instance, both Commute and Other Outdoor contained long walking periods with a large proportion of steady-state strides (Fig. 3). However, we measured differences in walking speed up to 0.24 m s⁻¹. The variability observed in our data makes it challenging to estimate a single preferred walking speed in the real world for all observed contexts. The speeds measured during pleasure walks are the least likely to be influenced by other factors such as destination or time constraints, and may be the most comparable to data collected in the lab. However, future work should investigate whether leveraging the ensemble of the data and deriving a usable range of speeds to characterize preferred walking behavior could be a stronger health indicator. Taken together, these variabilities in walking strategy confirm that researchers should consider designing experiments that allow participants to display the range of behavior they use during daily life. Additionally, the development of subject-specific models to capture a representative movement profile that reflects daily life could lead to a more representative metric for assessing an individual's health and well-being.

Our experimental design combined in-lab and real-world measurements. We built subject-specific energetically optimal speed ranges using in-lab measurements on the treadmill, and compared these ranges with real-world estimates of speed. To mitigate the effect of the differences between the laboratory and the real world, we: (1) enforced the relationship between stride speed and stride length found in the real world on the treadmill (Appendix, ‘Enforcing real-world walking strategy on the treadmill’), and (2) used a large uncertainty interval of +10% around the minimum cost of transport (which creates a range of speeds that correspond to the minimum of the cost of transport curve). We recognize that enforcing a movement pattern measured from unconstrained gait during treadmill walking will not replicate real-world conditions, and that the resulting metabolic cost during these conditions will likely differ from what would be measured through direct measurement during daily live. However, we believe this choice resulted in a better representation of the real-world metabolic cost than measurements made during unconstrained steady-state treadmill walking. Further research should investigate the cost of walking with and without these additional constraints on a treadmill. The different cutoffs needed to determine the energetically optimal speed range should also be further investigated.

In our protocol, we chose to elicit periods when the participants were walking without any other objective than the walk itself (‘pleasure walks’), with the goal of collecting data from gait at steady state for comparison to the data collected in the lab. This choice allowed us to diversify the contextual factors observed and better understand the differences between the laboratory and the real world. But as a consequence, the data for some subjects might not represent the behavior they would have naturally exhibited (Brinkerhoff et al., 2022). Additionally, future research should broaden the population diversity and increase the sample size. The methods and insights from this study could potentially be relevant for clinical populations.

Finally, we defined context as a combination of location and purpose; however, there are many external contextual factors that we did not include, such as terrain type or topography. Researchers have also found that walking with another individual can affect the speed at which people prefer to walk, and that the gender and nature of the relationship between the individuals walking together play a role in this effect (Wagnild and Wall-Scheffler, 2013; Bornstein and Bornstein, 1976). In our attempt to measure parts of these effects, we requested participants to note whether they were walking with other people in their self-reports. However, the exit interviews revealed considerable discrepancies in the participants’ accounts, undermining our confidence in the reliability of this contextual factor. Consequently, we opted to exclude it from our analytical considerations. Future studies should also consider internal contexts, such as an individual's mood or fatigue, as they may play a role in someone's movement in the real world.

Researchers now have the ability to measure human movement in the real world. Persistent monitoring is a powerful tool that can create rich datasets and provide a unique understanding of natural human behavior. In this work, we found that humans walk in a variety of contexts and exhibit a wide range of walking strategies and behavior. Consequently, individuals do not necessarily use a walking speed that minimizes their cost of transport in the real world. Overall, we recommend that researchers take into account the possible discrepancies between in-lab and real-world behavior when studying walking biomechanics. For instance, in-lab experiments can be designed to simulate real-world conditions to fully represent an individual's movement profile and capabilities. Moreover, it is essential to carefully choose between gross and net cost of transport when conducting analyses. We believe the findings of this work can provide insight for improvements in the study of human mobility for health, but also in robotics for the design of lower-body assistive devices.

Participants were instructed to wear the activPAL during the whole week but were allowed to remove it overnight if they wished. As such, the compliance for this sensor was high. We had an average of 6 h of non-wear time for the week across all participants. Subject S1 accumulated the most non-wear time over the week (36.4 h). They removed the sensor for an entire day and one night for personal reasons; 13 participants had less than 5 h of non-wear time over the week.

The IMU was attached on participants' shoes using a pouch secured with their laces. As such, participants were instructed to wear the IMU whenever they went out and were wearing their shoes. On average, participants wore the sensor for 9.2 h per day. The average daily wear time ranged from 6.9 h for S3, to 13.2 h for S12. Many participants were able to recharge the sensor during the day, which explains high daily wear time. Sundays were the days with the least wear time (8.4 h). Some participants did not wear the sensor for an entire day, because they forgot to place the sensor in their shoe, or they did not wear that specific pair of shoes, or they did not leave their home on that day.

We found less than 10% difference in parameter a, except for subjects S12 and S15 between real-world and treadmill walking. There was more difference in parameter b, with an average difference of 23%. For 10 participants, the difference in parameter b was an increase. For 15 participants, the difference in parameter a was a decrease. This reflects the tendency of participants to lower their stride length for a given stride speed, and particularly for faster speeds. In fact, when b increases, stride length decreases for a higher stride speed, and when a decreases, stride length decreases for all given stride speeds. Fig. A1 shows an example with two different participants in real-world versus treadmill power models. S10 adopted a consistently lower stride length for a given stride speed when walking on the treadmill, whereas S15 successfully matched their in-lab walking to the real world.

The notion of steady state can be used to describe any type of dynamic process that reaches an unvarying condition. For human movement, steady-state walking is the convergence of specific parameters to a point of stability. The most common characterizations of steady-state walking use either physiological parameters (e.g. heart rate, oxygen consumption) (Parvataneni et al., 2009) or mechanical parameters (e.g. stride speed, stride frequency) (Macfarlane and Looney, 2008; Strutzenberger et al., 2021; Lindemann et al., 2008), or a combination of the two. In the real world, the large variability of contexts can lead to a range of walking behavior involving a combination of steady-state and non-steady-state walking. Slowing down, stopping, starting or turning are all motions that can lead to non-steady-state gait. In our study, we wanted to extract steady-state walking from real-world data using our set of sensors. Because a validated steady-state classification algorithm for real-world walking is lacking in the literature, we created an unsupervised algorithm using mechanical parameters to characterize and differentiate steady-state and non-steady-state walking. We used data from a controlled experiment to verify of our algorithm.

The algorithm (detailed below) was applied to all walking bouts (within walking periods) for a specific subject. We iterated through all strides (N) within a bout and discarded the first and last strides. We started by creating vectors of stride speeds and stride lengths using three consecutive strides (s_i−1, s_i and s_i+1). The coefficient of variation (CV) was calculated for each of these vectors (CV_length and CV_speed). A high CV is indicative of large variations from the mean in a given vector. In our case, it would indicate a change of stride speed or stride length within the three selected strides. Then, we calculated the direction of strides s_i−1 and s_i using the foot position derived from the integration of the IMU data as explained in Materials and Methods (‘Data processing’, ‘Walking speed estimation for a walking period’). Cosine similarity (cosθ) was calculated, with θ being the angle between the direction of s_i−1 and s_i. Cosine similarity was chosen to evaluate the alignment in the direction of the two consecutive strides. If cosθ is close to 1, it means the vectors are almost aligned. Finally, we compared CV_length, CV_speed and cosθ against thresholds to classify stride s_i. The choice of thresholds is explained in the next section.

To determine the thresholds for the three parameters we selected, we conducted a sensitivity analysis following the leave-one-out method. We varied one parameter while fixing the two others to explore how sensitive our outputs were to each variable. The outputs we monitored were: (1) the distribution of steady-state stride speed for each participant, and (2) the percentage of strides identified as steady state across all participants. We fixed CV_speed and CV_length to 0.07 and 0.07, respectively, which were derived from Macfarlane and Looney (2008). We fixed cosθ to 0.7, which translates to a maximum of 45 deg between the direction of two consecutive strides.

We did not observe a large sensitivity of the mean and standard deviation of steady-state stride speed when varying the different parameters. Thus, we did not use this output to select the thresholds for each parameter.

We observed that the variation of both CV_speed and CV_length influenced the percentage of identified steady-state strides following a first-order response trend, with a convergence to a value close to 80% for a representative subject. In contrast, the variation cosθ did not influence the percentage of identified steady-state strides apart from very large values (e.g. cosθ>0.97) (Fig. S1). Humans generally vary their stride speed and stride length when they are about to turn. Thus, this result indicates that most turns in the real world are likely captured by a change of CV_speed and/or CV_length. We used the results from the sensitivity analysis on this output to determine thresholds for each parameter. As cosθ did not influence either outputs in a meaningful way, we kept a threshold of 0.7. For CV_speed and CV_length, we picked the value at which the percentage of identified steady-state strides crossed the ±2% boundary around the value this output converged to (Fig. S1). This resulted in a choice of 0.07 for both CV_speed and CV_length.

To confirm the validity of the thresholds we chose, we used a controlled in-lab experiment in which participants walked back and forth on a hallway. We reconstructed the track of each participant and observed the identified steady-state strides using our selected thresholds. Fig. A2 shows a representative subject's track with the associated changes in parameters CV_length, CV_speed and cosθ. Steps around a turn to walk back in the hallway were identified as non-steady state. We also notice that the second stride and the second to last stride were classified as non-steady state. This corresponds to the transition between walking and stopping. As a reminder, the first and last strides were discarded to be able to run the designed algorithm. Each parameter shows how the accelerations and decelerations as well as the turns are captured by the different chosen thresholds (Fig. A2B).

The authors thank the Neurobionics Lab and the Locomotor Control Systems Lab of the University of Michigan for sharing their space with us for this study. The authors also thank the Precision Health Initiative for funding parts of this work and facilitating the collaboration of this multi-disciplinary team.