Physical activity is difficult to assess accurately, particularly in children. Objective methods may be necessary for accurately assessing physical activity energy expenditure (PAEE), because recall ability is limited and patterns of physical activity in children are typically sporadic, especially in those under the age of 10 (²⁷). Gold standard methods of measurement such as doubly labeled water, indirect calorimetry, and direct observation are not feasible for the free-living assessment of PAEE in large, epidemiological studies. Consequently, there is a need for accurate and discreet objective methods that are easy to use, with low participant and investigator burden.

Many objective methods have been validated to measure PAEE in children, including both accelerometry (ACC) and heart rate monitoring (HR). The Actigraph uniaxial accelerometer is probably the most commonly used accelerometer out of the many available for physical activity research. The Actigraph has been validated as a measure of physical activity in children, both in a controlled laboratory environment and during free-living (^14,15). Heart rate monitoring has also been validated for use in children, both in controlled and free-living situations (^15,22).

HR and ACC each have limitations for the estimation of PAEE; HR can increase because of environmental conditions, without an increase in PAEE. Accelerometry counts display a nonlinear relationship with PAEE for activities other than walking. These limitations can affect the accuracy of the methods, because measurement errors are mainly activity and intensity dependent (⁷).

The combination of HR and ACC is more likely to accurately assess PAEE than either method used alone, because the two methods have uncorrelated error (⁶). Despite the limitations of both HR and accelerometry, few studies have used combined HR and ACC (HR+ACC), and they rarely have been combined in a single device with inherent time synchronization. The combined heart rate monitor and accelerometer (Actiheart) has been validated to assess the PAEE of treadmill walking, graded walking, and running in 12-yr-old children (¹⁰). The validity of HR+ACC remains to be determined for predicting PAEE during a range of free-living activities in children.

The purpose of this study was to compare the accuracy of four models using uniaxial ACC and four models using combined HR+ACC to predict PAEE (estimated from oxygen uptake) during six common activities in children. Three PAEE-prediction models derived using the current data (one using ACC and two using HR+ACC) and five previously published prediction models (three using ACC and two using HR+ACC) were cross-validated to estimate PAEE in this sample. All ACC models were multiple linear regression models. The first was derived with the current data, and the three published models were derived either during a ramped treadmill test (¹⁰), three speeds of flat treadmill walking (²⁹), or various lifestyle activities (²⁵). For HR+ACC, two multiple linear regression models were derived using the current data, one including a step test. Two previously published HR+ACC models were also used-one linear and one branched model, coefficients and parameters for both of which were derived during a ramped treadmill test (^6,10).

METHODS

Participants and methods.

Children were recruited from the Avon Longitudinal Study of Parents and Children (ALSPAC), described in detail elsewhere (¹⁷). Ethical approval for this study was obtained from the ALSPAC law and ethics committee and from local research ethics committees. The present study was performed between June 2004 and July 2005. Children aged 11 yr who agreed to wear an Actigraph for 7 d between January 2003 and January 2005 were invited for further study (they were, however, age 12 by the time of this study) (²³). The children were asked not to eat or drink for at least 1 h before their visit and to wear clothing appropriate for exercise. Children were accompanied by a parent and were asked to respond verbally to questions from a modified physical activity readiness questionnaire (PAR-Q) to confirm their suitability to participate in the study (¹). The test protocol was explained; parents gave written informed consent, children gave written assent.

Anthropometric measures.

Height was measured to the nearest 0.1 cm (Leicester Height Metre, Invicta Plastics, Leicester, UK) and weight to the nearest 0.1 kg (Seca 770, Hamburg, Germany).

Protocol.

Children were fitted with an Actigraph, an Actiheart, and a portable metabolic unit (Cosmed K4b²; Cosmed, Rome, Italy) and were given approximately 5 min to become familiar with wearing the equipment. The Actigraph was attached to the mid-line of the right hip with a tight elastic belt, and the Actiheart was attached to the chest with two standard ECG electrodes; one electrode was placed at the base of the child's sternum and the other horizontally to the child's left side, with the Actiheart spaced so that the wire between the two clips of the Actiheart was straight but not taut. Both monitors were time synchronized with the Cosmed metabolic system. The Actiheart was set to record in 15-s epochs, and the Actigraph was set to record in 10-s epochs.

The exercise tests were performed indoors. Children were asked to perform six activities, each of which lasted for 5 min. Table 1 describes these activities in the order they were carried out. The activities were selected to provide graded increases in intensity and to reflect the type of locomotor activities that comprise the majority of children's activity (²⁸). Hopscotch was included to simulate a sporadic jumping, bending, and stretching type of activity. Apart from lying and sitting, all activities were self-paced to better reflect free-living conditions. Walking and jogging activities took place around an indoor jogging track. Lying and sitting were on a bench with an exercise mat to lie on at the side of the jogging track. Children progressed through the activities without stopping, apart from a short break while walking to the hopscotch activity. Walking and jogging speeds were calculated by using markers every 5 m on the jogging track and calculating speed from distance traveled and duration.

Step test calibration.

To further calibrate the HR+ACC method, an incremental 8-min step test was carried out to account for some of the variance in individual HR-PAEE relationships. A detailed description of the step test can be found elsewhere (⁵), but, briefly, the step test required children to step up and down on a 0.205-m aerobic step, beginning at 60 steps per minute (15 body lifts per minute) and increasing to 132 steps per minute for 8 min, followed by 2 min of seated rest. The speed of the step test was controlled by a drum beat, included in the Actiheart software, to ensure time synchronization. The step test was carried out by each child after completion of the six activities and after a rest of about 5 min.

Combined HR+ACC (Actiheart).

Detailed descriptions of the Actiheart and Actigraph are available elsewhere (^5,16); these devices are just examples of those available. Briefly, the Actiheart (Cambridge Neurotechnology, Cambridge, UK) is a combined heart rate monitor and accelerometer (HR+ACC). The Actiheart weighs approximately 8 g and is able to measure acceleration, HR, HR variability, and ECG magnitude for epoch settings of 15, 30, and 60 s. Memory capacity is 128 kb, which allows 11 d of recording with an epoch of 60 s. Data on interbeat intervals and ECG waveforms can be recorded for approximately 24 h and 13 min, respectively. Acceleration is measured by a piezoelectric element within the Actiheart, with a frequency response of 1-7 Hz (3 dB) and stored as counts that relate linearly to acceleration by a factor of 0.003 m·s⁻² per count per minute (⁵).

ACC (Actigraph).

The Actigraph Model 7164 (Actigraph LLC, Fort Walton Beach, FL) is sensitive to movements between 0.51 and 3.6 Hz (⁹). The acceleration signal is represented by an analog voltage that is sampled and digitized by an eight-bit analog-to-digital converter at a rate of 10 times per second. The Actigraph has 64-kb, nonvolatile, random-access memory and is initialized and downloaded via a serial port interface.

Indirect calorimetry (Cosmed).

The Cosmed K4b² measures breath-by-breath ventilation (V_E), concentration of expired oxygen (F_EO₂), and carbon dioxide (F_ECO₂). The unit weighs 1.5 kg and is held in a chest harness. Expired air was collected via a face mask. The instrument was calibrated in accordance with the manufacturer's instructions, as described elsewhere (⁵). The Cosmed K4b² has been validated in children, with small, positive biases in V˙O₂ of less than 6% during walking and running being observed (¹⁹).

Data reduction.

All data were pooled into a database (Microsoft Access) and then transferred to Stata 8.2 (Statacorp, College Station, TX) for analysis. The average of data between minutes 3.5 and 4.5 of each activity was used for analysis. Energy expenditure (J·min⁻¹·kg⁻¹) was calculated from V˙O₂ using the de Weir formula (¹²). Resting energy expenditure was assumed to be equal to the lowest recorded energy expenditure.

PAEE was predicted using eight PAEE-prediction equations (a-h) listed in Tables 2 and 3. Of these equations, five were previously published (b-d, g, and h) (absolute validity), and three were linear regression models derived using the current data (a, e, and f) (criterion-related validity):

• Previously published models:
• Model b. Corder ACC model (¹⁰)
• Model c. Puyau ACC model (²⁵)
• Model d. Trost ACC model (²⁹)
• Model g. Corder HR+ACC model (¹⁰)
• Model h. Branched HR+ACC model (^6,10)
• Models derived using the current data:
• Model a. ACC (measured with Actigraph) and height.
• Model e. HR+ACC using heart rate above sleep (HRaS) and ACC (measured with Actiheart), gender, and an HRaS-gender interaction term
• Model f. HR+ACC, as model e but including step test parameters (Actiheart).

The previously published PAEE-prediction equations were modified so that all were expressed as joules per minute per kilogram or joules per minute. All results are presented in joules per minute per kilogram; the equation output in joules per minute (²⁹) was divided by body weight before statistical analysis. Model b (¹⁰) was expressed using counts per minute, and not counts per 15-s epoch as in the original publication. Models c (²⁵) and d (²⁹) were transferred from kilocalories to joules (multiplication by 4186). Models g (¹⁰) and h (^6,10) were rederived using heart rate above sleep (HRaS) rather than heart rate above rest as in the original publication, to aid comparability with Model f, requiring the use of HRaS when deriving the step test-calibration parameters.

Resting heart rate (RHR) was measured as the lowest steady-state heart rate during minutes 3.5-4.5 of lying or sitting for each individual. Sleeping heart rate (SHR) was estimated from measured RHR in this sample, using SHR = 0.4195RHR + 27.4 (r = 0.56, SEE = 5.2). This equation was derived from measured SHR and RHR in 30, 12- to 13-yr-old children (unpublished data). All heart rate values are expressed in beats per minute above sleep (HRaS), and all accelerometry count values are expressed in counts per minute.

The step test allows individual HR-PAEE calibration to be carried out without indirect calorimetry and has been described previously (⁵). The step test lasts for 8 min with stepping frequency ramping up linearly from 15 step cycles per minute (one step cycle is "up, up, down, down") to 33 per minute after 8 min. The mechanical lift work rate from the step test, PAEE_step (J·min⁻¹·kg⁻¹), is calculated as 9.81 m·s⁻² × step height (m) × number of step cycles per minute. Linear regression analysis was then used to model PAEE_step against HRaS from the step test, to derive individual calibration parameters. The slope and intercept from these equations, denoted β_step and α_step, were then included as additional terms in model f (HR+ACC) in the form of an interaction term (β_step × HRaS) and a singular term (α_step), respectively.

The branched model was derived according to Brage et al. (⁶) but by replacing the accelerometry and HR equations by ones derived in children (¹⁰). The branched model approach uses both HR and ACC equations, extrapolated to go through the origin (RMR and SHR, or 0 counts per minute, respectively). The HR and ACC equations are weighted in varying proportions to predict PAEE. The proportions always sum up to 1, but they depend on the level of heart rate (bpm) and activity counts per minute. Figure 1 shows a flow chart summarizing this branched approach, including the thresholds used. All branching thresholds were derived a priori using data from 39, 12- to 13-yr-old children carrying out a ramped treadmill test (¹⁰). The first branch uses a threshold value of 25 counts per minute. The y and z parameters are used as y = y₁SHR + y₂ and z = z₁SHR + z₂; y values were derived by linear regression of SHR on average HRaS between the fastest walking (5.8 km·h⁻¹) and slowest running speeds (9 km·h⁻¹) to denote a transition HR, and z values were derived by linear regression of SHR on the average HRaS between resting and the slowest walking speed (3.2 km·h⁻¹) to denote a flex HR (¹⁰).

A well-recognized problem with PAEE equations is the bias from positive intercepts (^6,11). To avoid this bias, all eight prediction models were replaced with estimates from two wall functions; PAEE = 200 × ACC counts or PAEE = 200 HRaS, for values of acceleration < 5 counts per minute or HRaS < 5 bpm, respectively, however, only in cases where the original equation estimate was larger than the wall function estimate. Also, when negative estimates of PAEE were generated from the a priori equations, these estimates were replaced with PAEE (J·kg⁻¹·min⁻¹) = 0.1 HRaS + 0.1ACC_AH for the HR+ACC models and PAEE (J·kg⁻¹·min⁻¹) = 0.1ACC_MTI for the ACC models. The wall and floor functions represent very conservative safeguards against spurious PAEE predictions.

Statistical Analyses.

For derivation of equations, we used repeated-measures ANOVA with random intercepts. The three PAEE models derived using current data (a, e, and f) were cross-validated using the Student's jackknife approach ("leave-one-out"); that is, calculating predictions of PAEE from n permutations of the equations derived on the whole sample except data from the individual for whom the equation prediction was intended (n − 1) and then comparing this prediction against the observed (¹⁸).

PAEE predicted from each model was compared against the criterion or measured value, calculated from indirect calorimetry. A modified Bland-Altman method was used to determine whether there was any systematic or activity-dependent error in the PAEE predictions (⁴). The difference (estimation error) between predicted and measured PAEE was calculated (predicted − measured) for all models, and this was determined for each activity separately and for all activities combined. Limits of agreement and ratio limits of agreement were calculated to assess the difference between predictions over the different activities (²).

RESULTS

Participant characteristics are shown in Table 4. Boys had 3% higher weight and BMI and 8.5% higher resting energy expenditure than the girls in the sample, and resting heart rate was 8.8% higher in the girls. The average speeds (mean ± SD) for the self-paced slow walking, brisk walking, and jogging were 4.4 ± 0.7, 5.8 ± 0.8, and 9.2 ± 1.5 km·h⁻¹, respectively.

PAEE predicted using ACC and HR+ACC models derived in the current study were all highly correlated with measured values and explained a substantial amount of the variance in measured PAEE with relatively low RMSE (R² = 0.87-0.91; RMSE 97.3-118.0 J·min⁻¹·kg⁻¹); these models are displayed in Tables 2 and 3.

ACC data also explained a substantial amount of the variance in overall PAEE for all previously published models (R² = 0.81-0.87), but most had a higher RMSE than those derived in the current study (118.0-245.3 J·min⁻¹·kg⁻¹). The mean difference (predicted − measured PAEE) and 95% confidence intervals for all models are displayed in Table 5. For four of the eight models assessed, PAEE predictions were different from the measured values; these were two HR+ACC models, one linear and a branched model (^6,10), and the ACC models derived by Puyau (²⁵) and Corder (¹⁰).

Figures 2 and 3 show the spread of prediction error for all eight models, for activities separately and combined; the mean differences between the PAEE predictions and the measured values (predicted − measured PAEE) are shown with 5th and 95th percentiles. The mean bias for activities separately and combined for each model are shown in Table 6. Because of the presence of heteroscedasticity, ratio limits of agreement were calculated using log-transformed data and presented as dimensionless ratios (Table 7). The average differences between measured and predicted values on a ratio scale were −35 to +13% for the ACC models and −24 to −5% for the HR+ACC models. The 95% ratio limits of agreement indicate the level to which PAEE values predicted from all equations may differ substantially from measured values for any individual in the population.

Overall, the HR+ACC models show less activity-dependent error than the ACC models; however, most models overestimated PAEE during sedentary activities, and all four ACC models underestimated PAEE during vigorous activity (i.e., jogging).

DISCUSSION

The primary aim was to determine the validity of ACC and HR+ACC to assess PAEE during six common activities in children. The predictions from a priori and post hoc derived ACC and HR+ACC models were compared against the criterion (indirect calorimetry). PAEE predicted from the three post hoc derived models agreed well with measured values for all activities combined; however, when each activity was examined separately, some systematic error was present in all three predictions. As the post hoc models were derived on the current data, they would be expected to perform more accurately when cross-validated on the same activity mix, although the jackknife cross-validation approach circumvents autocorrelation tied to the individual. Consequently, further studies would be required to establish the validity of these models for use in other situations and for other age groups in which movement economy and style could well differ from this sample (^21,24). The large range of the 95% ratio limits of agreement for all models suggests that these equations are only accurate for the assessment of group-level PAEE.

The five previously published PAEE-prediction models all seem to provide reasonable predictions of overall PAEE for all activities combined. However, after examining the accuracy of the models over the different activities, there is systematic error present for all models; this is indicated by negative correlations between the measured value from indirect calorimetry and the difference (predicted − measured PAEE). Correlation coefficients of between 0.18 and −0.64 for the errors of HR+ACC models and −0.34 to −0.95 for errors of Actigraph models indicate that the HR+ACC models' error is more random in nature than error for the ACC models and, therefore, predicted PAEE more accurately over a wider range of activities. This suggests that ACC models are more dependent on the activities tested and less dependent on participant characteristics, whereas the opposite may be the case for HR-based models. It is worth noting that the Trost equation was the most accurate, with the lowest RMSE (126.0 J·min⁻¹·kg⁻¹), of the a priori ACC models, but the RMSE was higher than for both a priori HR+ACC models (115.6 and 118.0 J·min⁻¹·kg⁻¹).

The ACC models (a-d) all underestimate PAEE for higher-intensity activities, to the greatest extent during jogging; this is likely to be because uniaxial accelerometry in general cannot accurately account for the increased stride length (^9,20). Actigraph counts have been shown to level off at approximately 8000 counts per minute and 9 km·h⁻¹ during running in 9- to 11-yr-old children (⁸)-similar values to the average 7531 counts per minute and 9.2 km·h⁻¹ during jogging in this study. However, Actigraph counts have been shown to increase by 4.7% (8692 to 9118 counts per minute) between slow running (10 km·h⁻¹) and faster running (12.8 km·h⁻¹) in 13-yr-old children, although the corresponding V˙O₂ (mL·kg⁻¹·min⁻¹) increase was 14.6% (³⁰). Other possible explanations for this underestimation include the differences between treadmill running and overground running (³¹) and the use of equations derived using lifestyle activities leading to overestimation of low-intensity activities and underestimation of vigorous activities (^3,30). Additional underestimation may arise from frequency-based filtering, particular to the Actigraph; however, it is likely that biomechanical changes during running are a more important cause of this underestimation (⁷). This, along with the overestimation of the ACC predictions during sedentary activities (lying and sitting), probably caused by fidgeting, generating movement counts without the expected increase in PAEE, suggests that these ACC models may be less accurate if used with free-living data, unless combined with inactivity thresholds (¹¹). These models may underpredict PAEE to a greater extent in more active children and falsely enhance PAEE of less active children, thereby reducing between-individual variance in physical activity levels. This could be a considerable concern for studies using accelerometry to determine PAEE or examining relationships between physical activity and disease outcomes (¹³).

Less activity-dependent (intensity dependent) error was present in PAEE predicted using the HR+ACC models. The inclusion of heart rate in these models may have improved the prediction of PAEE for higher-intensity activities. The use of branched modeling slightly improved the estimation accuracy of PAEE, with a lower RMSE than the linear a priori HR+ACC model (RMSE; 115.6 vs 118.0 J·min⁻¹·kg⁻¹); the benefits of branched modeling are likely to increase when a wider range of activities are carried out, such as during free-living. In addition, sleeping HR was only estimated from a short, clinical measure of resting HR in this study, and the branched model relies on sleeping HR to both anchor the HR-PAEE equation in the origin and to direct the observations to the correct branches (weightings). The addition of step test-derived variables to the HR+ACC model did improve the prediction by lowering RMSE (97.3 vs 100.1 J·min⁻¹·kg⁻¹). Despite this, the additional predictive power of adding a step test to the HR+ACC model may not be worthwhile in this situation, considering the additional time required to carry out the test and the improvement in accuracy achieved. It is possible that by expressing heart rate as HRaS and also including gender in the HR+ACC models, most of the between-individual variation in the HR-PAEE relationships that one would hope to capture by an individual calibration test has already been captured in the original equation.

The six activities carried out include sedentary activities (lying and sitting) and nonsedentary activities with a significant vertical acceleration component (slow walking, brisk walking, jogging, and hopscotch). Consequently, all six activities are expected to be well measured by accelerometry because all activities mainly result in vertical accelerations; these activities may not fully test the predictive ability of both monitors. It is likely that the accuracy of the HR+ACC predictions would not be much affected if higher intensity and activities with limited vertical movement such as cycling were included, because of the benefits of heart rate monitoring during these activities. The importance of this will, however, depend on the activity patterns of the population studied. Known limitations of accelerometry for assessing these types of activities may significantly affect the accuracy of these ACC models if applied to nonambulatory activities. ACC is commonly used for the assessment of time spent at different intensities of physical activity using cut points; however, for estimating physiological energy expenditure, the limitations discussed above may make it less useful than HR+ACC for estimating PAEE in varied situations. This highlights the need for validation studies of physical activity-measurement devices to carefully examine error over different activity intensities and not just as an overall measure to gain a better understanding of the overall predictive ability of the monitors.

PAEE was overestimated during low-intensity or sedentary activities by all models, and this could, to some extent, be attributable to the protocol. The children only carried out lying and sitting for 5 min each at the start of the study visit, and they may have been excited or anxious, consequently increasing their heart rate without an associated increase in energy expenditure. However, there is evidence that 6 min of supine rest is enough to provide useful estimates of resting energy expenditure (REE) (¹⁰). The lowest heart rate of all those recorded during the 3.5th to 4.5th minutes of the activities was used as the resting heart rate. For a minority of volunteers, the heart rate during sitting was lower than that for lying, indicating that the volunteers were not completely relaxed during supine rest. Because these values agree with published resting values (¹⁹) this should not be too much of a concern for the REE. Even so, the resting heart rate measured in this study may have been overestimated because of the short measurement period and a less-than-ideal resting environment. Consequently, the predicted SHR values may be slightly overestimated and the HRaS values subsequently underestimated, which would lower PAEE predictions from a priori HR models. Weight, BMI, and resting energy expenditure were slightly higher in boys, and resting heart rate was higher in girls; these are physiological differences that have been documented previously (²⁶).

The eight models assessed were derived in different situations-using walking, graded walking, and running data (^6,10); treadmill walking and jogging data (²⁹); and multiple lifestyle activities for the current study and the study by Puyau et al. (²⁵). The accuracy of ACC models varies depending on the situation (i.e., the activities performed) where they were derived and then applied. However, the situation where a combined HR+ACC model is derived does not seem to affect the accuracy of PAEE prediction to the same extent as those models using only ACC. Both ACC and HR+ACC provide valid predictions of overall PAEE; on the basis of the activities in this study, HR+ACC assessments exhibit less activity-dependent error than accelerometry alone and, therefore, may be more accurate and widely applicable to predict PAEE than methods based on accelerometry alone.

SUMMARY

ACC and HR+ACC can both be used to provide valid predictions of overall PAEE during these six activities in children on a group level. However, systematic error was present for all models, highlighting the need for validation studies of physical activity-measurement devices to carefully examine error over different activity intensities and not just as an overall measure. ACC models showed more systematic error than the HR+ACC models, and their accuracy is more dependent on the activities tested and less dependent on participant characteristics, whereas the opposite may be the case for HR-based models. Systematic error may be unavoidable when using linear models to predict PAEE, especially those based on ACC alone. Both ACC and HR+ACC provide valid predictions of overall PAEE, but on the basis of the activities in this study, PAEE-prediction models using combined heart rate and accelerometry may be more accurate and widely applicable than those based on accelerometry alone, even if they are derived in a different situation from where they are applied-particularly in populations where nonambulatory activities are common.

We are grateful to all the families who took part in this study, the midwives for their help in recruiting them, and the whole ALSPAC team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, volunteers, managers, receptionists, and nurses. The UK Medical Research Council, the Wellcome Trust, and the University of Bristol provide core support for ALSPAC. This research was specifically funded by the U.S. National Heart, Lung and Blood Institute (R01 HL071248-01A).