A self-paced walk test for individual calibration of heart rate to energy expenditure

Introduction: Estimating free-living physical activity (PA) with continuous heart rate (HR) monitoring is challenging due to individual variation in the relationship between HR and energy expenditure. This variation can be captured through individual calibration with graded exercise tests, but structured tests with prescribed load requires medical screening and are not always feasible in population settings. We present and evaluate an individual calibration method using HR response to a less demanding self-paced walk test. Methods: 643 participants from the Fenland Study (Cambridgeshire, UK) completed a 200-meter self-paced walk test, a treadmill test, and one week of continuous HR and accelerometry monitoring. Mixed effects regression was used to derive a walk test calibration model from HR response to the walk using treadmill-based parameters as criterion. Free-living PA estimates from the calibration model were compared with treadmill-calibrated as well as non-exercise calibrated estimates. Results: The walk calibration model captured 57% of the variance in the HR-energy expenditure relationship determined by the treadmill test. Applying the walk calibration method to data from free-living yielded similar PA estimates to those using treadmill calibration (52.7 vs 52.0 kJ {middle dot} kg-1 {middle dot} day-1; mean difference: 0.7 kJ {middle dot} kg-1 {middle dot} day-1, 95% CI: -0.0, 1.5) and high correlation (r=0.89). Individual differences were observed (RMSE: 10.0 kJ {middle dot} kg-1 {middle dot} day-1; 95% limits of agreement: -20.6, 19.1 kJ {middle dot} kg-1 {middle dot} day-1). Compared to using a non-exercise group calibration model (RMSE: 14.0 kJ {middle dot} kg-1 {middle dot} day-1; 95% limits of agreement: -30.4, 24.5 kJ {middle dot} kg-1 {middle dot} day-1), the walk calibration improved precision by 29%. Conclusions: A 200-meter self-paced walk test captures a significant proportion of the between-individual variation in the HR-energy expenditure relationship and facilitates estimation of free-living PA in population settings.

Estimating physical activity (PA) in free-living conditions using continuous heart rate (HR) monitoring is challenging due to substantial between-individual variation in the relationship between HR and energy expenditure (Hilloskorpi et al., 1999;Li et al., 1993).If unaccounted for, this variation leads to imprecise PA estimates when applied in populations settings (Brage et al., 2015).Various techniques have been proposed to address this issue (Andrews, 1971;Brage et al., 2007;Ceesay et al., 1989;Payne et al., 1971;Rennie et al., 2001;Strath et al., 2000).Individual calibration via graded exercise testing, which characterizes the HR-energy expenditure relationship across a wide range of intensities, can produce precise PA estimates and has emerged as a preferred approach.Nonetheless, the implementation of graded exercise tests with prescribed workloads may cause selection bias in population settings, as pre exercise test medical screening procedures may exclude certain at-risk individuals (Fentem et al., 1994).Risk-stratified test procedures can partially address the issue of selection bias but introduce additional complexities, such as the need for multiple exercise testing protocols to accommodate diverse fitness levels, and still require some degree of pretest screening (Gonzales et al., 2021).
An alternative method is the use of self-paced exercise testing, such as walk tests, for individual calibration of the HR-energy expenditure relationship.Self-paced tests require minimal or no pretest screening and are more accessible (Williams, 2008), but they typically cover only a narrow intensity range.As such, they only partially capture the HR-energy expenditure relationship, which could lead to inaccuracies when estimating PA in free-living conditions.To address this limitation (Brage et al., 2007), a calibration model based on a reference exercise test with known energetic cost could extend the relationship established through self-paced testing across a broader range of intensities.Doing so could yield PA estimates comparable to those attained from individual calibration via graded exercise testing, but with less precision.
Here, we develop and evaluate a novel calibration method that uses HR response to a self-paced walk test.We compare estimates of free-living PA energy expenditure (PAEE) derived from this method to those obtained from a standardized treadmill test and nonexercise calibration.We also compare estimates of cardiorespiratory fitness from the two exercise calibration methods.Our study offers insights into the potential of a self-paced walk test as a practical and inclusive alternative to established individual calibration techniques.

Methods Calibration Model Framework
The relationship between exercise HR response and energy expenditure (intensity) for an individual can be described using a simple linear model: where HR l and I l i are HR (in beats per minute) and exercise intensity (in Joules per minute per kilogram) measurements at several levels (l) of a graded exercise test.The intercept, β 0 i (in Joules per minute per kilogram), and slope, β 1 i (in Joules per beat per kilogram) that define the linear HR-to-exercise intensity relationship can be individually determined using regression analysis.
After individually determining the linear HR-to-exercise intensity relationship in a participant sample with a broad range of exercise capacity, the individual estimates of β 0 i and β 1 i can be aggregated and used as a tool for calibrating exercise intensity in other exercise testing modalities involving large muscle groups.This approach is particularly useful in exercise testing situations where direct measurement of exercise intensity is not feasible, or the test spans a narrow intensity range, but other predictive factors that influence the HR-to-exercise intensity relationship may be measurable or already known.Using these factors, we can equate the individual linear HR-to-exercise intensity relationships, defined by β 0 i and β 1 i for each participant, to a mixed-effects regression model that estimates the same relationships: In this model, I estimated i represents exercise intensity values computed from the ith individual-specific β 0 i and β 1 i coefficients at several defined HR levels (HR l ).The intercept and slope coefficients b 0 i and b 1 i vary with each individual and converge to the individual-specific values of β 0 i and β 1 i through their linkage with I estimated i .A set of n parameters, denoted as P x i , which are associated with corresponding sets of fixed regression coefficients γ 0x and γ 1x , are nested within both b 0 i and b 1 i .These parameters are features that capture individual-level characteristics known to influence exercise capacity, such as age, sex, or features derived from the exercise test being calibrated.The nesting of these parameters within b 0 i and b 1 i allows the model to account for betweenindividual variation when estimating the relationship between HR and exercise intensity.The fixed intercept and slope coefficients are estimated as γ 00 and γ 10 , which represent the expected baseline exercise intensity and the average rate of change in exercise intensity with HR, respectively, across all individuals in the sample.Finally, r i is a random intercept to account for clustering of I estimated i values within individuals.

Application of Calibration Model for Self-Paced Walk Test
We used the described exercise test calibration framework to develop a self-paced walk test calibration model.For each individual in a participant sample, we first derived the intercept and slope coefficients defining the HR-energy expenditure relationship (β 0 i and β 1 i ) using a standardized treadmill test (Gonzales et al., 2023), with intensity at each time point previously established using indirect calorimetry (Brage et al., 2007), as the reference exercise test.We then constructed parameter set P x i consisting of features derived from both the walk test and participant-level characteristics known to influence exercise capacity.We then used β 0 i , β 1 i , and P x i to construct the calibration model.Our approach is described in detail below.

Study Participants
A subsample of 643 participants from the population-based Fenland Study of 12,435 individuals in the East of England (Lindsay et al., 2019) were included in the present analysis.
Participants provided informed written consent, and the study was approved by the local research ethics committee.Participants arrived at a clinical testing facility to complete exercise testing following an overnight fast and abstention from smoking and vigorous PA on the morning of their visit.Participants in this substudy performed two exercise tests-a standardized submaximal treadmill test and a self-paced 200-m walk test-and 1 week of free-living monitoring.Most (96%) participants performed the exercise tests on the same day, but 25 participants performed the treadmill test up to 3 months later.Participants on beta-blocker doses ≤50% of maximal daily allowance were included (n = 120).Those on higher doses or who were otherwise contraindicated for exercise testing with prescribed load only performed the self-paced walk test but not the treadmill test and were thus excluded from the present comparison study.

Clinical Exercise Testing
The treadmill test was performed using standardized procedures as described in detail elsewhere (Gonzales et al., 2023).Briefly, the test consisted of several stages of progressively faster walking and increasing incline levels for 15 min, followed by 5 min of running.
For the self-paced walk test, two markers were placed 20 m apart in a flat, indoor corridor.Participants then walked at a self-determined pace from one marker to the other and back, completing five laps for a total distance of 200 m.If participants could not complete the total distance, they were instructed to stop walking.After completing the test, participants were provided a chair and asked to sit quietly.Recovery HR was monitored for 1 min.Both the time spent and total distance covered during the test were recorded.

HR Measurement During Clinical Exercise Testing
HR response to walk and treadmill tests was measured using combined HR and movement sensors positioned on the chest.An interbeat interval logger and uniaxial accelerometer were used (Actiheart, CamNtech) in 453 participants.In this device, the ECG waveform is sampled at 128 Hz and a standard peak detection algorithm is applied in firmware to identify the QRS complex and record resulting interbeat intervals (Brage et al., 2005;Pan & Tompkins, 1985).For the remaining 190 participants, an ECG signal recorder (sampling at 256 Hz) and triaxial accelerometer were used (CardioWave, CamNtech).The peak detection algorithm from the Actiheart device was applied to the ECG signal recorded with the CardioWave device, allowing interbeat interval data across both devices to be harmonized.Interbeat interval data were converted to HR data and expressed as HR above sleeping HR (HRaS, see below).An 11-beat running median filter was applied to HRaS data.For the treadmill test, exercise HR response data were continuously recorded and then compiled into 10-s intervals, excluding the initial 2.5 min.We then estimated β 0 i and β 1 i for each participant using linear regression of exercise HR response against the known energetic cost of the treadmill test (Brage et al., 2007).

HR Measurement During Free-Living
Following their visit to the clinical testing facility, participants wore an Actiheart sensor continuously for 6-8 days and nights to quantify PA during free-living.Sleeping HR was derived from these data as the average robust minimum daily HR.This was defined as the HR below which at least 30 min per day were accumulated (the second percentile).For HR data from free-living, we used a robust Gaussian process regression method to infer the true HR from the potentially noisy sensor measurements and aid in the classification of nonwear (Brage et al., 2015;Stegle et al., 2008).

Walk Calibration Model Derivation
To build a walk calibration model, we extracted features from the walk test that could be used to capture variation in the HR-energy expenditure relationship (Figure 1, left panel).The walk test's energetic cost was estimated for each participant by applying a published metabolic cost equation for walking (Ludlow & Weyand, 2016) to their average walking speed.This method was chosen because energetic cost values estimated in this way closely aligned with those directly measured from the treadmill test at similar walk speeds and a 0% incline (Brage et al., 2007).We computed two features from walk test HR response: (a) average Energy Pulse (EP ave ), defined as the average HRaS during the final minute of walking divided by the estimated energetic cost of walking, and (b) the HRaS at 45 s into recovery (RecHRaS 45s ), which was estimated using quadratic regression of the first 60 s of recovery HR data and solving for 45 s.These two derived walk test features, along with participant age, sex, and beta-blocker usage (binary yes/no), were combined to construct the parameter set P x i , inclusive of all these terms and their two-way interactions.
Upon deriving β 0 i , β 1 i , and P x i , we next constructed the walk test calibration model using mixed-effects regression.We first estimated I estimated i from the treadmill-based β 0 i and β 1 i at several simulated HR values (HR simulated ).These HR values were selected to evenly cover the submaximal exercise intensity range (0-100 bpm above HRaS) and were incremented by steps of 10 bpm.We then regressed I estimated i against terms defined by b 0 i (intercept terms) and the interaction of b 1 i with HR simulated (slope terms).Terms from b 0 i included a fixed effect parameter and the parameter set P x i .For b 1 i , these terms interacted with the values in HR simulated .We simplified the model by applying several heuristics for removing redundant terms, including statistical significance of parameters, variance inflation factor analysis for multicollinearity, and expert judgment of coefficient estimates.

Flex HR Estimation From Exercise Tests
An additional individual calibration parameter, flex HR (Ceesay et al., 1989;Spurr et al., 1988), is needed for applying exercise testbased calibration equations to HR data from free-living.The linear HR-exercise intensity relationship is not valid at low HR levels, so the regression line established by individual calibration is only extrapolated down to a flex HR point, below which we interpolated to resting HR (Figure 1, right panel).
Individual's flex HR was determined from the treadmill test as the HR midway between the lowest treadmill walking HR and resting HR determined as 10 bpm above their sleeping HR (awake rest is approximately 10 bpm above sleep).The energy cost of the slowest walking speed for the treadmill protocol is approximately 160 J•min −1 •kg −1 (8 ml O 2 •min −1 •kg −1 ) above rest, so lowest exercise HR will reflect this standardized level of exertion.For the self-paced walk test, the estimation of the lowest HR during exercise will depend on the chosen walk speed.In order to standardize flex HR estimation from self-paced walk test performance, we therefore used the walk-calibrated linear relationship between HR and intensity from above and solved it by setting I estimated i to 160 J•min −1 •kg −1 to estimate HR at this intensity, and then computing the average between this value and a HRaS value of 10 bpm (awake rest): If this estimate was lower than 0.25 × HRaS for any of the calibration methods, it was truncated to that value.

Estimation of Cardiorespiratory Fitness
Maximal oxygen consumption (VO 2 max) was estimated by extrapolating the linear HR-energy expenditure relationship established by both the walk test and the treadmill test to age-predicted maximal HR (Tanaka et al., 2001).

Estimation of PA Energy Expenditure During Free-Living
We applied both the standard treadmill-based equation and the derived walk test equation for calibrating HR to energy

SELF-PACED WALK TEST AND HEART RATE
expenditure to data from free-living.Both equations were applied as derived when observed HR was above the respective flex HR points.Below flex HR, the relationship was estimated as the straight line between the activity intensity at the flex HR point and 0 J•min −1 •kg −1 at HRaS = 10 bpm (and 0 J•min −1 •kg −1 below 10 bpm).HR estimates of intensity were combined with nonindividualized estimates of intensity based on device-measured trunk acceleration in a branched model to estimate activity intensity time series.(Rennie et al., 2001) Both the treadmilland the walk-based estimates of intensity were summarized as the total volume of PA, or PAEE as well as time spent in moderate-tovigorous PA (MVPA), here defined as intensity above 4 METs.
We compared the walk and treadmill calibration methods at the level of generating estimates of daily PA using the treadmillcalibrated estimates as criterion.We used Pearson's correlation analysis for relative agreement, paired t test to assess significance of mean absolute differences, and Bland-Altman analysis for evaluating absolute agreement and exploration of the pattern of individual-level differences.Root mean square error of individual differences was used to quantify precision.As an additional comparison, we included group-calibrated estimates of PAEE and MVPA from a model that does not utilize any dynamic calibration information unique to the individual but is based on the average HRaS-to-activity intensity relationship from 11,000 participants from the Fenland Study but including terms for sex and beta blockage (and implicitly sleeping HR; Lindsay et al., 2019).

Statistical Software
All analyses were performed using Stata/SE (version 17.0).Statistical significance was set at p < .05.

Development of Calibration Model
A total of 313 women and 330 men participated in the study (Table 1).Men had a higher body mass index than women and a higher proportion of men were on beta-blockers; otherwise, characteristics between men and women were generally similar.
Summary statistics of measured and derived parameters from the treadmill and self-paced walk exercise tests are shown in Table 2.The ratio of walk energy cost over HR response (EP ave ) was skewed, hence was natural log-transformed before further analysis.The derived calibration equation using only self-paced walk test parameters (and sleeping HR) captured 57% of the variance in the treadmill-calibrated HR to energy expenditure relationship in the derivation data set; this compares to 23% for a model for HRaS without walk parameters but including terms for sex and beta blockage (model not shown).The walk calibration equation had a root mean square error of 76 J•min −1 •kg −1 and was estimated as: Solving the walk test calibration model for 160 J•min −1 •kg −1 and averaging this with resting HR yielded a mean flex HRaS value of 20.2 bpm, which was similar to the mean value from the treadmill test of 19.1 bpm.The difference was not statistically significant, but the standard deviation of the walk test estimate was only about a third of that observed for the treadmill test.
We used scatter plots and Bland-Altman analysis to assess agreement between individual-level intercept and slope parameters estimated from the walk test calibration model (b 0 i and b 1 i ) with their corresponding parameters (β 0 i and β 1 i ) from the treadmill test (Figure 2).Mean differences for both parameter pairs were not significantly different from zero.A negative proportional bias was observed, where lower parameter estimates from the walk test model tended to be positively biased, and higher estimates negatively biased, compared with their corresponding treadmill parameters.Proportional bias was more pronounced for b 1 i (slope) compared with b 0 i (intercept).VO 2 max estimated from the walk test was similar to estimates from the treadmill test but also had negative proportional bias.Walk test calibration model parameters had less dispersion than those from the treadmill test (Table 2).
We examined differential bias of individual-level intercept b 0 i and slope b 1 i by sex and beta-blocker use (Supplementary Table S1 [available online]).The walk-based slope b 1 i was significantly greater than treadmill-based slope β 1 i in women and beta-blocked participants, but was significantly smaller in men.No significant difference was found between walk-based intercept b 0 i and treadmill-based intercept β 0 i by sex, but b 0 i was significantly lower than β 0 i in betablocker users.In women, VO 2 max estimated from the walk test was significantly greater than VO 2 max estimated from the treadmill test, but in men walk-based estimates were significantly lower.There was no differential bias in VO 2 max by beta-blocker use.
An alternative and more complex calibration equation was derived that included additional terms for sex and beta-blocker status.This equation explained 62% of the variance and had a root mean square error of 73 J•min −1 •kg −1 : The resulting slope, intercept, and fitness estimates from this equation are shown against the corresponding treadmill-based estimates in Supplementary Figure S1 (available online).Including these additional terms and interactions resulted in the appearance of two clusters for b 1 i , the difference between which was of similar magnitude as the mean sex difference in treadmill-based slope.

PA During Free-Living
Calibration equations from the walk and treadmill test methods were applied to free-living observations of HR and combined with accelerometry to estimate habitual PA.A total of 609 participants had sufficient valid data from free-living to be included in this analysis, providing a median (interquartile range) of 149  hr of data.Table 3 shows PAEE and MVPA during free-living, as estimated by combined HR and movement sensing using either treadmill calibration or walk calibration of the HR signal, as well as group-calibrated PAEE (no dynamic calibration information), and Figure 3 shows the agreement between PA estimates.Walk-calibrated PAEE values using the simple walk calibration were highly correlated (r = .89)with and not significantly different from treadmill-calibrated estimates (mean [95% confidence interval; CI] difference was 0.7 [−0.0, 1.5] kJ•kg −1 •day −1 ).Individual differences were observed, with root mean square error of 10.0 kJ•kg −1 •day −1 and 95% limits of agreement being −19.1 to 20.6 kJ•kg −1 •day −1 .In terms of the error variation pattern, there was a small tendency for the walk-based estimates to overestimate at lower levels of PAEE and underestimate at higher levels of PAEE, which is also reflected in the lower standard deviation for walk-based estimates of PAEE.Results for the alternative more complex walk calibration equation were similar (r = .90,no mean difference, root mean square error of 9.4 kJ•kg −1 •day −1 , and 95% limits of agreement −18.0 to 19.4 kJ•kg −1 •day −1 ) at the whole-sample level.Subgroup analyses did, however, show differential bias by beta-blocker status for the simple walk calibration model but not for the alternative more complex model.By comparison, the agreement between groupcalibrated (average of all treadmill tests in the Fenland Study) and treadmill-calibrated PAEE results was less tight; correlation was weaker but still significant at r = .77,and in this subsample, there was a significant underestimation of 2.9 kJ•kg −1 •day −1 (95% CI [−4.0, 1.8]) compared with the treadmill-calibrated results; 95% limits of agreement were also wider at −30.4 to 24.5 kJ•kg −1 •day −1 , root mean square error being 14.0 kJ•kg −1 •day −1 .With regard to MVPA (Table 3 and Figure 4), walk-calibrated estimates using the simple model were strongly correlated (r = .85)with, and not significantly different from, treadmill-calibrated results (mean difference of 0.9 min/day, 95% CI [−0.5, 2.3] min/day) but with some individual variation (root mean square error of 17.3 min/day and 95% limits of agreement −33.7 to 35.5 min/day); there was, however, less tendency for individual errors to depend on MVPA level.The alternative more complex walk calibration model again performed similarly (r = .86,no significant mean difference, root mean square error of 16.3 min/ day and 95% limits of agreement −31.9 to 33.3 min/day) but the group-calibrated model showed poorer agreement with treadmillcalibrated estimates of MVPA (r = .73,significant mean [95% CI] bias of −5.7 [−7.3, 4.0] min/day, and substantial individual differences with root mean square error of 21.6 min/day and 95% limits of agreement of −47.5 to 36.1 min/day) and a tendency for errors to covary with MVPA level.Again, subgroup analyses revealed differential bias by beta-blocker status for the simple walk calibration model but not for the alternative more complex walk calibration model.

Discussion
We present an individual calibration method of HR to energy expenditure using a self-paced walk test.A mixed-effects regression model was used to relate walk test HR response to that from a standardized treadmill test with known energetic cost.Fitness and free-living PA estimates from the walk test were strongly correlated with and comparable to estimates using treadmill calibration.The variability between walk-calibrated and treadmill-calibrated activity estimates was less than that between group-calibrated and treadmill-calibrated estimates.
The walk test calibration model captured 57% of the variance in the HR-energy expenditure relationship determined by the treadmill test, which is comparable to another study that used a structured walk test (Brage et al., 2007).Estimated VO 2 max agreed between both tests, extending more focused work on fitness estimation using self-paced exercise (Petrella et al., 2001).
The flex HR from the walk test was similar to the mean flex value from the treadmill test, but the variance of walk-based flex values was substantially reduced.Small differences in flex HR often result in large differences in PA estimates if using the flex HR technique during free-living (Ceesay et al., 1989;Leonard, 2003;Spurr et al., 1988); however, this parameter is less influential when modeling PAEE from combined HR and movement sensing (Brage et al., 2015).Walk test-calibrated PAEE estimates from combined HR and movement sensing were highly correlated with, and not significantly different from, estimates obtained through calibration by treadmill testing.In contrast, group-calibrated estimates of habitual PA from combined HR and movement sensing had a small negative bias of 2.9 kJ•kg −1 •day −1 and a root mean square  (Brage et al., 2004), walk-calibrated estimates were closer and in tighter agreement with treadmill values than group-calibrated estimates, eliminating the bias and reducing error by about 20% for the simple calibration model and 25% for the complex calibration model.
These results underscore the utility of our calibration approach, particularly in population studies where structured exercise testing might be impractical or introduce selection bias through medical screening procedures.We have previously used a selfpaced walk test to account for differences in cardiorespiratory fitness when examining PA levels of tuberculosis patients (Faurholt-Jepsen et al., 2014) and in pregnant women (Hjorth et al., 2012).Those studies used exercise HR response to selfpaced walking to account for variance in cardiorespiratory fitness by including it as a covariate alongside group-calibrated PA variables in epidemiological analyses.However, this statistical approach to accounting for between-individual variance in HR to energy expenditure relationships will not directly reduce the error for the PA variable in the association analysis and does not allow examination of dose-response relationships between PA and health outcomes without adjustment for fitness which may be considered to be on the causal pathway; this could result in an underappreciation of the importance of PA.We have implemented the self-paced walk test and the method described herein in the second phase of the Fenland cohort study to capture dynamic HR response to exercise.Out of 7,831 individuals who attended, 243 were contraindicated to exercise for various reasons (high betablocker dose, ECG abnormalities, etc.) but performed the selfpaced walk test and subsequent free-living monitoring of PA.
Our approach presents possibilities for more personalized and accurate assessments of habitual PA, with potential implications for interventions.Self-paced walking tests are commonly used in specific population groups-including older adults, children, and patients with low exercise tolerance-to assess fitness, musculoskeletal function, and chronic disease risk (Bennell et al., 2011).While several of these tests provide information about muscular fitness, many are too short to provide information about cardiorespiratory fitness.Our calibration method uses a 200-m self-paced walk test, which can readily interface with these existing practices and be used for health monitoring.For example, accurately assessing habitual PA in older adults can enhance our understanding of the relationship between PA and age-associated diseases like cardiovascular disease and dementia (Harridge & Lazarus, 2017).Improved PA estimates in children could enhance our ability to investigate early-life determinants of obesity and Type 2 diabetes (Hannon et al., 2005).Additional work to assess the validity and applicability of both self-paced walk tests and our individual calibration approach within each distinct population group would be required.Further, it should be noted that any individual calibration test should be repeated if there has been changes in fitness, either from deconditioning or as a result of starting a new exercise regime.
Our study has limitations.The walk test calibration procedure described here includes the necessity to estimate energy cost of walking; while this could be directly measured using portable respiratory gas analysis, this would severely impact feasibility of the test.We used the cost equation by Ludlow et al. (Ludlow & Weyand, 2016) which also matched our internal directly measured energy cost of walking at similar speeds on the treadmill.Other prediction equations have been published, for example, by American College of Sports Medicine (Pescatello et al., 2014) and also from the Fitness Registry and the Importance of Exercise National Database (FRIEND; Kokkinos et al., 2017).The American College of Sports Medicine equation produces lower and the FRIEND equation produces higher estimates of energy cost, compared to estimates produced by the Ludlow equation (Ludlow & Weyand, 2016).Gold-standard measures, specifically the doubly labeled water method for PAEE and maximal exercise testing with direct VO 2 measurement for cardiorespiratory fitness, were not used in this study.Implementing both techniques in a large population study, however, would pose logistical and practical challenges to research personal and study participants.Finally, the presence of proportional bias in our approach suggests that calibration values for individuals at the margins may be closer to the sample mean.This could cause estimates from these individuals to appear more similar than they truly are.

Conclusions
HR response to self-paced walking captures a substantial proportion of the between-individual variability in the HR-energy   expenditure relationship and allows estimation of cardiorespiratory fitness and habitual PA when coupled with HR monitoring during free-living.Self-paced walking is safe for most people and could be used to reduce error in derived estimates from continuous HR monitoring in settings where a wider range structured exercise calibration test is not feasible.

Figure 1 -
Figure 1 -Example HR response to self-paced walk test and depiction of derived test features (left panel) for individual calibration of the HR to energy expenditure linear relationship (right panel).PAEE = physical activity energy expenditure; HR = heart rate; HRaS = heart rate above sleep; VO 2 = oxygen consumption.

Figure 3 -
Figure 3-Estimates of habitual PAEE from combined sensing using individual calibration of HR from self-paced walk test (simple and alt.) or static (group) versus calibration using treadmill test for 296 women (light gray) and 313 men (dark gray).Scatter plots (upper panels) include lines of unity.Bland-Altman plots (lower panels) show difference between methods against the treadmill estimate.HR = heart rate; PAEE = physical activity energy expenditure; alt.= alternative; Acc = device-measured trunk acceleration.

Figure 4 -
Figure 4-Estimates of habitual MVPA from combined sensing using individual calibration of HR from self-paced walk test (simple and alt.) or static (group) versus calibration using treadmill test for 295 women (light gray) and 312 men (dark gray).Scatter plots (upper panels) include lines of unity, and Bland-Altman plots (lower panels) show difference between methods against the treadmill estimate.Note that plots exclude one woman and one man with MVPA > 180 min/day to preserve resolution for the remaining data points.Acc = device-measured trunk acceleration;

Table 2
Exercise Parameters and Estimates From Walk and Treadmill Tests Note.Values are mean (SD).Fenland walk calibration substudy (n = 643).HRaS = heart rate above sleep; RecHRaS 45s = heart rate above sleep at 45 s of recovery after walk test; EP ave = average energy pulse (walk energy over HRaS ratio); VO 2 max = maximal oxygen consumption.Calibration parameters (slope and intercept) and cardiorespiratory fitness estimates from self-paced walk test versus treadmill test for 313 women (light gray) and 330 men (dark gray).Scatter plots (upper panels) include lines of unity.Lower panels are Bland-Altman plots.VO error of 14 kJ•kg −1 •day −1 , when compared with treadmill-calibrated estimates.The self-paced walk test eliminated the mean bias in this sample and reduced the root mean square error in PAEE from group calibration by 29%.Similarly for time spent in MVPA, which utilizes more of the HR information in the branched framework

Table 3
Estimates of Habitual Physical Activity During Free-Living Using Different Methods of Individual Calibration for the Heart Rate-Energy Expenditure Relationship N PAEE (kJ•kg −1 •day −1 ) MVPA (min/day) Values are mean (SD) unless specified.Fenland walk calibration substudy.PAEE = physical activity energy expenditure; MVPA = moderate-to-vigorous physical activity; alt.= alternative.Walk-calibrated estimates use either the simple equation or the alt.more complex equation with additional demographic terms.* p < .05for difference to treadmill-based estimates. *Note.