Ethical approval was obtained from the Regional Ethical Review Board in Umeå, Sweden, and from the Cambridgeshire research ethics committee, Cambridge, UK.

One hundred and eight healthy women (aged 20–35 yrs) residing in the eastern area of the county of Västerbotten, Sweden were recruited through local media advertising and with the assistance of midwives working in local antenatal clinics. Thirty-five of these women were studied during weeks 28–32 of pregnancy, whereas the remainder were non-pregnant. Non-pregnant and pregnant women were of a similar socio-demographic background. The vast majority of non-pregnant women had maintained a stable relationship for at least a year prior to recruitment and reported that they anticipated becoming pregnant in the future. The outcome of the 35 pregnancies (all occurring after the current investigation) was 34 successful deliveries at term (31 vaginal deliveries, 1 planned and 2 acute caesarean sections) and 1 premature birth (including offspring health complications).

Ninety-nine healthy women and men (aged 22–65 yrs) from Cambridgeshire in the UK were recruited through local media advertising to a study aimed at evaluating the validity of a physical fitness test.

Participants in both studies were initially interviewed by telephone and asked to complete a modified version of the Rose Angina Questionnaire to identify major contraindications to exercise [14]. Exclusion criteria included recent major cardiovascular events, recent physically debilitating surgical procedures, serious unmanaged psychiatric disorders, illicit drug dependency, and an inability to commit fully to the study procedures. The objectives and procedures of the study were explained in detail to the participants, after which they provided written and verbal informed consent.

In the Swedish study centre, the accelerometer was worn on the wrist continuously for 10 days of free-living and total energy expenditure (TEE) was simultaneously measured using the doubly labelled water (DLW) method. Additionally, resting energy expenditure (REE) and anthropometric characteristics were measured [15].

In the British study centre, participants were asked to wear one hip and one wrist accelerometer for 7 days of free-living. At the end of the monitoring period, participants were asked to indicate the acceptability of each monitor on a 10 level ordinal rating scale, where 1 represented a very low level of acceptability and 10 represented a very high level of acceptability.

The accelerometer (GENEA, Unilever Discover, Sharnbrook Bedfordshire, UK) comprised a tri-axial STMicroelectronics accelerometer (LIS3LV02DL) with a dynamic range of ±6 g (1 g = 9.81 m·s⁻²), as described elsewhere [13]. The acceleration was sampled at 40 Hz (Sweden) and 80 Hz (UK) and data were stored in g units for offline analyses. The accelerometer (12×29×37 mm) was attached to the wrist with a nylon weave strap (both groups) and to the hip with an elastic belt (UK sample only). In order to ensure an even balance of left and right wrist positioning in the Swedish study, every second participant entering the study was asked to wear the accelerometer on the left wrist and every other to wear it on their right wrist, irrespective of hand dominancy. In the British study, both accelerometers were worn on the non-dominant body side. Participants were instructed to wear the accelerometer on the wrist continuously but to remove the hip-placed accelerometer during water-based activities and sleeping. A diary was provided to assess monitor non-wear time.

Accelerometer non-wear time was estimated on the basis of the standard deviation and the value range of each accelerometer axis, calculated for consecutive blocks of 30 minutes. A block was classified as non-wear time if the standard deviation was less than 3.0 mg (1 mg = 0.00981 m·s⁻²) for at least two out of the three axes or if the value range, for at least two out of three axes, was less than 50 mg. Thresholds were based on lab experiments in which thirty GENEA accelerometers were left motionless on a flat, stable surface for 30 minutes, showing that the standard deviation of an acceleration signal (which has some inherent noise) is 2.6 mg during non-motion. Therefore, the 3.0 mg threshold will allow a maximal increase of 0.4 mg in the standard deviation, which when expressed in angular orientation of the acceleration sensor corresponds to a standard deviation of 1.6 degrees []. Phan et al. showed that the acceleration of the chest in a resting person resulting from the breathing movement alone has an amplitude of 10 mg, while the vibrations resulting from the heart beat have a peak-to-peak amplitude of 80 mg [16]. Therefore, even the tiniest wrist movements are likely to be picked up by the method as described above.

Participants for whom more than 50% of the wrist data was classified as non-wear were excluded from further analyses (two pregnant women from the Swedish study). For the remainder of the participants, non-wear time segments were labelled as missing.

Next, a simple summary measure was derived from the raw acceleration signals, involving a filtering stage to extract the accelerations related to body movement using a fourth-order Butterworth band pass filter (ω₀: 0.2–15 Hz), followed by the calculation of the vector magnitude (). The resulting signal was then averaged over intervals of one second. Three basic approaches for the imputation of movement during non-wear segments were evaluated: i) no imputation, with non-wear time regarded as no movement (Acc₀); ii) imputation of non-wear time by the average movement during wear time for that participant (Acc₁); and iii) imputation of non-wear time using the available wear time data at similar times on other days for each participant (Acc₂). Here, Acc₂ is assumed to be best capable of dealing with large periods of missing data as it takes into account the 24-hour cycle of human behaviour. Finally, the average was calculated for each participant. All signal processing was done in R (http://cran.r-project.org) using package Signal.

Participants visited the Clinical Research Center at Umeå University Hospital the morning after a 10-hour fast on day 1 of the study. Height was measured using a wall-mounted stadiometer to the nearest 0.5 cm, body weight was measured using a calibrated digital scale (Tanita Corporation, Tokyo, Japan) to the nearest 0.1 kg, and arm length, defined as the distance between the lateral edge of the acromion and the processes styloidius of the ulna, was measured using a non-stretchable measurement tape to the nearest 0.5 cm. Arm length was included as it may explain variation in wrist acceleration, because of the mechanical relationship between radius (arm length) and acceleration of a rotating object (accelerometer). REE was measured under thermoneutral conditions for 30 minutes using indirect calorimetry with a ventilated hood (Deltatrac II, Datex-Ohmeda, Inc., WI, USA) placed over participants who were lying still and quietly on a bed without sleeping for 30 minutes. The accelerometer was thereafter fitted to the wrist. Prior to the completion of the testing session, each participant was given an accurately weighed oral dose of DLW stable isotopes (0.07 g ²H₂O and 0.174 g H₂¹⁸O per kg body weight). In addition to a pre-dose urine sample, 10 additional urine samples were collected, one for each of the 10 days that followed the day of dosing. The time of each sample was noted by the participant in a log. Urine samples were stored in plastic urine vials at +4°C until collection by the research team. Samples were subsequently frozen at −20°C pending analysis. Isotopic enrichments of dose and urine samples were analyzed at MRC Human Nutrition Research, Cambridge, UK [17]. PAEE was calculated as 0.9× TEE – REE [17].

Linear regression analysis was applied to develop prediction models for PAEE. A priori, separate models for pregnant and non-pregnant women were evaluated, including the following variables: wrist acceleration, body weight, age, body height, body side (dominant wrist vs. non-dominant wrist), and arm length. To determine whether the relationship between wrist acceleration and PAEE was affected by body side (dominant or non-dominant wrist attachment) an interaction analysis was performed using a multiplicative term (acceleration×body side) plus the marginal effects for this term. Finally, a leave-one-out cross validation analysis was applied to estimate model performance outside the training dataset [18], which was evaluated by modified Bland-Altman plots using criterion PAEE on the horizontal axis [19]. All models are expressed in MJ day⁻¹ as this is regarded to be the most appropriate way to evaluate the contribution of wrist acceleration independent of body weight to the total explained variation in PAEE (MJ day⁻¹) from a statistical point of view [9]. However, we acknowledge the preference for other normalisation approaches from a biological perspective [20], so regression models for PAEE expressed in Joules min⁻¹ kg⁻¹ are reported in the appendix S1 (table A) to facilitate a more complimentary interpretation of our results.

Acceptability scores (UK study) for wrist and hip accelerometer placements are summarised as median (inter-quartile range) for wrist and hip attachments and stratified by sex. The equality in acceptability between wrist and hip sites was tested using a two-sided Wilcoxon paired signed-rank test and a non-paired signed-rank test for male vs. female comparisons.

All analyses were carried out in the open-source tool R (http://www.r-project.org). An alpha level of p<.05 was regarded as statistically significant.

No accelerometer data was retrieved from 9 participants due to failure to wear the monitor or technical errors. Three of these participants also failed to collect urine samples, resulting in 99 participants with a complete set of data. Owing to suboptimal power management in the monitor firmware (a problem that appears to affect measurement duration in this version of the GENEA monitor), the data collection period was curtailed for some participants in the Swedish study. On average, 8.2 days of data were collected (median: 9.6, 25^th percentile: 7.6 days). In 97 out of these 99 participants, at least one day worth of data was collected. These figures relate to the length of the raw data and may partially represent periods of non-wear. According to the diaries, all participants wore the wrist accelerometers for the entire duration of the 10 day monitoring period. However, the non-wear detection classified two participants out of the 97 as having worn the monitor for less than 50% of the measurement duration; these individuals were thus excluded from further analyses. An example of the acceleration (Acc2) and the non-wear detection over time in one Swedish participant is shown in Figure 1. Next, regression analysis was done in two groups separately: i) for all participants in whom more than 7 days of data were collected (N = 74, 26 pregnant and 48 non-pregnant women) and ii) for the first three days of data in all participants for whom one or more days of data was collected (N = 95; 30 pregnant and 65 non-pregnant women).

The average space ratios (Ko/Kd) for non-pregnant and pregnant women were 1.034 and 1.030, respectively. Significant correlations were found between accelerometer output and PAEE (table 2 and 3). A graphical evaluation of Acc₂ as a function of PAEE is shown in figure 2. In non-pregnant women, Acc₂ explained 24% (1–3 days of data. SE: 1.00 MJ) and 21% (>7 days of data. SE: 0.98 MJ) of the variation in PAEE. Introducing body weight to the model increased the explained variation for the 1–3 days of data model and the >7 days of data model to 31% (SE: 0.95 MJ) and 31% (SE: 0.92 MJ), respectively (table 2). No significant correlation was found between PAEE and body weight (p = 0.21), nor between PAEE and arm length (p = 0.12) (table 2). Further, no interaction was found between body side and Acc₂ in non-pregnant women (p = 0.62), (table 3). Acc₂ and body weight were not significantly correlated to each other in non-pregnant women: r −0.16, p = 0.20 (1–3 day of data), r −0.27, p = 0.07 (>7 day of data). In pregnant women, Acc₂ over the first three days explained 11% (SE: 0.71 MJ) of the variation in PAEE, and after addition of body side to the model this increased to 27% (SE: 0.65 MJ). None of the models significantly explained variation in PAEE during pregnancy when >7 days of data was used. In pregnant women, there was also no significant correlation between body weight and PAEE (p = 0.95). Acc₂ and body weight were not significantly correlated to each other in pregnant women: r −0.01, p = 0.94 (1–3 day of data), r −0.17, p = 0.42 (>7days of data). In both pregnant and non-pregnant women, squared wrist acceleration did not significantly contribute to the explained variation by wrist acceleration alone, thus providing support for a linear model analysis of the data (models not shown).

In the cross-validation based on the leave-one-out approach, PAEE estimates based on Acc₂ remained significantly correlated to measured PAEE in non-pregnant women, but this correlation was not statistically significant in pregnant women (table 4). In pregnant women, the interaction between body side and Acc₂ was weaker in the cross-validation analysis although still statistically significant in the shorter measurement period and larger sample size (see table 4). A graphical evaluation (modified Bland & Altman plot) of the PAEE estimation error against measured PAEE (cross-validation) is shown in figure 3 for models based on Acc₂ and body weight (non-pregnant women) and Acc₂ with body side (pregnant women).

Fourteen UK participants were excluded, as acceptability scores were not collected, and two additional participants were excluded, as no acceleration was recorded for either the wrist or the hip, resulting in 83 participants with data available for analysis. The acceptability score for wrist attachment was 0.47 higher than hip attachment (p<.001). The median (IQR) score for wrist attachment was 9 (8–10), and the corresponding value for hip attachment was 9 (7–10) as shown in figure 4. When stratified by sex, men scored the wrist placement on average 0.51 higher (IQR: 0–1) compared to the hip placement (p = 0.02). Women scored the wrist placement 0.43 higher (IQR: 0–1), a difference which was not statistically significant. No significant difference was found between sexes for the wrist scores (p = 0.57) or for the hip scores (p = 0.89). The estimated percentage of wear time was higher for wrist attachment (median: 99%) compared with hip attachment (median: 65%) in the UK sample (t = −14.6, p<.001). Sixty five percent wear time represents 97.5% of waking hours (assuming 16 waking hours per day). Wrist acceleration explained 45.3% of the variation in hip acceleration (p<.001), which was not improved by addition of BMI (p = 0.68), age (p = 0.07), or body weight (p = 0.68) to the regression model.