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Reexamination of Validity and Reliability of the CSA Monitor in Walking and Running


Medicine & Science in Sports & Exercise: August 2003 - Volume 35 - Issue 8 - pp 1447-1454
APPLIED SCIENCES: Physical Fitness and Performance

BRAGE, S., N. WEDDERKOPP, P. W. FRANKS, L. B. ANDERSEN, and K. FROBERG. Reexamination of Validity and Reliability of the CSA Monitor in Walking and Running. Med. Sci. Sports Exerc., Vol. 35, No. 8, pp. 1447–1454, 2003.

Purpose: To evaluate the reliability and validity of the CSA (model 7164) accelerometer (MTI) in a wide walking-running speed range in laboratory and field.

Method: Twelve male subjects performed three treadmill walking/running sessions and one field trial with the same continuous protocol involving progressively increasing velocities at 5 min per interval from 3 to 6 km·h−1 (walking) and 8 to 20 km·h−1 (running). In the field trial, this protocol was terminated after 35 min (14 km·h−1), but the trial then extended with 5-km running at a freely chosen velocity. In both scenarios, two CSAs were mounted on each hip and the step frequency measured at each velocity. Oxygen uptake (V̇O2·kg−1) was measured on the last two treadmill sessions. Correlation analyses were performed for mean CSA output relationship with speed, V̇O2 per kilogram, and step frequency.

Results: In all trials, CSA output rose linearly (R2 = 0.92, P < 0.001) with increasing speed until 9 km·h−1 but remained at ∼10,000 counts·min−1 during running, thus underestimating V̇O2 per kilogram at speeds > 9 km·h−1. Estimation errors increased with speed from 11% (P < 0.01) at 10 km·h−1 to 48% (P < 0.001) at 16 km·h−1, when assuming a linear relationship. Freely chosen velocities in the field trial ranged from 10.9 to 16.3 km·h−1. No difference in the CSA-speed relationship was observed between the two scenarios. Differences in CSA output between subjects could partially be attributed to differences in step frequency (R = −0.34 (P = 0.02) for walking and R = −0.63 (P < 0.001) for running).

Conclusion: CSA output increases linearly with speed in the walking range but not in running, presumably due to relatively constant vertical acceleration in running. Between-subject reliability was related to step frequency because CSA data are filtered most at higher movement frequencies. Epidemiological CSA data should thus be interpreted with these limitations in mind.

The volume of evidence that physical activity is protective against various morbidities and premature mortality is increasing. However, physical activity is a difficult behavior to characterize because it involves several important dimensions, such as intensity, frequency, duration of activity bouts, and total energy expenditure. To understand how these components relate to morbidity, the continuous and precise measurement of intensity is needed. Accelerometry has been proposed as an objective method for this purpose.

The Computer Science and Applications (CSA) Model 7164 (now also known as the MTI accelerometer; Manufacturing Technology Inc., Fort Walton Beach, FL) is a uniaxial piezo-electric accelerometer with a dynamic range of ± 2.13 g and a frequency-dependent bandwidth filter, which can be regarded as a mathematical weighting function. Validity, expressed as linear correlation with average acceleration, was shown to be dependent on movement frequency in a mechanical setup (6). The CSA has also been validated against mass-specific oxygen consumption rate (V̇O2·kg−1) during walking and running but only at moderate running speeds (17,25,29). Furthermore, although the CSA exhibits good intra-instrument reliability (low coefficient of variation) in mechanical setups constructed to produce sinusoidal accelerations, inter-instrument differences have been reported (6,22). These differences were found to be heteroschedastic with some CSA units differing by 20–40% in the acceleration range 1–10 m·s−2 (6), which corresponds to a range typical of walking and running. However, inter-instrument reliability during walking and running has not been explored by a Bland-Altman (4) approach. Additionally, between-subject reliability has not been linked to the effect of frequency-dependent filtering. Therefore, the purpose of this study was to investigate aspects of reliability and validity within a wider speed range during both laboratory and field conditions. It was hypothesized that validity to some extent would be compromised during moderate to fast running because of the dependency on frequency, and that this dependency may explain possible differences between subjects and between laboratory and field observations.

1Institute of Sport Science & Clinical Biomechanics, University of Southern Denmark, Main Campus: Odense University, Odense, DENMARK;

2Institute of Public Health, University of Cambridge, Cambridge, UNITED KINGDOM;

3University Hospital of Odense, University of Southern Denmark, Odense, DENMARK; and

4Institute of Sport Science, University of Copenhagen, DENMARK

Address for correspondence: Søren Brage, Department of Public Health, Cambridge University, University Forvie Site, Robinson Way, Cambridge CB2 2SR, UK, England; E-mail:

Submitted for publication November 2002.

Accepted for publication April 2003.

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Twelve male subjects (22.7–30.0 yr, 63.9–91.2 kg, 169–199 cm) performed three treadmill trials (trials A, B, and C) and one field trial (trial F) with similar protocols. Trials were separated by at least 2 d. All subjects were healthy and well trained with a mean peak V̇O2 per kilogram (fitness) of 61.5 mL·min−1·kg−1 (range: 51.0–71.5 mL·min−1·kg−1). The subjects gave their informed written consent on entry to the study, which was approved by the local research ethics committee (Denmark).

The protocol consisted of 5-min intervals (continuous) at the following treadmill velocities: 3 and 6 km·h−1 of walking and 8, 9, 10, 12, 14, 16, 18, and 20 km·h−1 of running until voluntary exhaustion. Walking (i.e., “constant ground contact”) was compulsory during the first two velocities, as was running (i.e., visible ‘flight phase’) at 8–20 km·h−1. Mass-specific oxygen consumption rate (V̇O2·kg−1 measured in mL·min−1·kg−1) was measured continuously every 30 s (15-s sampling period, 15-s pause) during trials B and C, with expired air collected using a face mask and analyzed by an open-circuit system (EO Sprint, Erich Jaeger GmbH). The output of this equipment agrees well with that obtained using the Douglas bag technique (pair wise steady state values of the two methods were within ± 2%, measured during walking and running at 3, 6, 10, and 16 km·h−1 on the treadmill). The ventilation and gas analyzers were calibrated before each test. Body mass was measured on a calibrated digital scale before each of the treadmill trials.

The progressive protocol used during the treadmill trials was also used for the field trial but terminated after 35 min, covering the speed range 3–14 km·h−1. After a 5-min break, subjects were instructed to run back to the lab (home trip distance about 5.14 km) at their usual training intensity. To control and monitor the speed of the subject, and to measure interval distance (Distinterval), an investigator cycled alongside the subject. The bicycle on which the investigator rode was equipped with a computerized speedometer (Specialized, Morgan Hill, CA) calibrated for speed and distance using the same treadmill described earlier. The field trial was carried out on flat terrain, on small roads with little traffic, and on nonwindy and dry days (air temperatures 15–20°C).

In both experimental set-ups, two CSA units were mounted on each hip (units 10523, 10526, 10564, and 10580) at the same position for all subjects and in all trials. Heart rate (HR) was measured with a Polar Vantage NV heart rate monitor (Polar Electro Oy, Kempele, Finland). At each velocity, the time for 20 steps was recorded twice, because of expected variations in this parameter (3). The final incomplete intervals (duration < 5 min) in trials A, B, and C were included in the analysis if their duration was ≥ 2 min 30 s.

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For each velocity, steady state V̇O2 per kilogram (trial B and C only) and HR (beats per minute, bpm) were calculated as the mean of minutes 3.30–5.00 after change of speed. In the final incomplete intervals, V̇O2 per kilogram and HR were expressed as the mean of the two highest values, respectively. Fitness (peak V̇O2·kg−1) was determined as the maximal observed value in any of the trials B and C. Step frequency (SF) was calculated as the mean of the two assessments on each velocity. The home trip in the field trial was analyzed in 5-min data intervals, e.g., four data points for a 20-min run. Actual field speed was calculated as Distinterval/5 min and expressed in kilometers per hour (km·h−1).

CSA output (counts·min−1) was calculated for each CSA unit and expressed as the mean of 4 min on each velocity in each trial, allowing 1 min for speed change and/or adaptation. The calculated mean of all four CSA units was denoted CSA_All.

Inter-instrument reliability was explored by plotting the CSA unit-specific differences relative to CSA_All against speed (modified Bland-Altman (4) plot) as done previously (6) and further addressed by the intraclass correlation coefficient (ICC) of absolute agreement (24) using the two-way mixed Cronbach’s alpha model. All analyses on reliability were restricted to the speed range 3–14 km·h−1. Effect of step frequency on between-subject reliability was assessed with partial correlations, adjusted for speed or V̇O2 per kilogram.

A customized frequency-corrected variable (CFC_CSA) was created from CSA_All, according to observations on sinusoid accelerations in a mechanical setup (6). The equation CFC_CSA = CSA_All/[0.0576·f2 −0.559·f + 1.45] yielded an estimate with a linear response to average acceleration for movement frequencies (f) between 0.95 and 4 Hz in the mechanical setup. This also allowed CSA unit-specific predictions of average acceleration (Ac_10523, Ac_10526, Ac_10564, and Ac_10580) and their mean (Ac_CSA) to be calculated by equations from the mechanical setup.

The relationships between the outcome variables (speed or V̇O2·kg−1) and the predicting variables (CSA_All or CFC_CSA) were analyzed with multiple linear regression. The models were adjusted for fitness when V̇O2 per kilogram was the outcome measure. A subanalysis was performed to yield a prediction equation of V̇O2 per kilogram for the 3–9 km·h−1 speed range to compare with previous validation studies (17,25,29). Prediction models of V̇O2 per kilogram for the entire speed range were also explored using multiple linear regression, adding HR as an independent variable, as combinations such as this are known to improve estimates of V̇O2 per kilogram (20,26). ANOVA post hoc tests (Bonferroni) were performed to assess significance level of differences between velocities. Differences attributed to experimental setting (laboratory or field) were explored using multiple linear regression. Normality of regression residuals was explored by agreement of their frequency distributions with the superimposed normality curve. The software package SPSS, version 11.0 (SPSS, Inc., Chicago, IL) was used for all statistical analyses.

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Speed relations of V̇O2, HR, and step frequency.

All subjects completed the 3- to 14-km·h−1 intervals in all trials. At 16 km·h−1, all subjects met the inclusion criteria in trials A and C, but only nine subjects did so in trial B. Two subjects completed the 18-km·h−1 intervals in all treadmill trials. At this speed, five, four, and, five subjects met the inclusion criteria for trials A, B, and C, respectively. Walking speeds in trial F were significantly different (P < 0.001) from the prescribed speed, with means (±SD) of 3.46 km·h−1 (±0.20) and 5.77 (±0.15) km·h−1, respectively. The measured speed in the 8- to 10-km·h−1 intervals coincided with the prescribed speed (±0.26) but averaged 3% lower (P < 0.001) than prescribed (±0.22) in the 12- to 14-km·h−1 intervals. The mean speed chosen by the subjects for the home trip was 13.97 km·h−1 (range 10.9–16.3 km·h−1).

Increases in treadmill speed were associated with a linear increase (R2 = 0.97, individual R2 range 0.96–0.99) in V̇O2 per kilogram levels in trials B and C; the relationship being V̇O2 per kilogram = 3.78·speed + 0.06·Fitness −6.9 (standard error of the estimate (SEE) = 2.8 mL·min−1·kg−1). HR levels also increased linearly with speed (R2 = 0.88, individual R2 range 0.93–0.99 for treadmill trials). HR from the field trial were significantly lower than the laboratory trials, as determined by multiple linear regression, which produced significant (P < 0.001) coefficients for speed, experimental setting (SETT = 1 for laboratory, 0 for field), and fitness. This model (R2 = 0.89, SEE = 11.3 bpm) was HR = 9.36·speed + 6.2·SETT −1.0·Fitness + 98.0. The relationship between V̇O2 per kilogram and HR was also linear (R2 = 0.95, P < 0.001, SEE = 3.3 mL·min−1·kg−1) according to the model V̇O2 per kilogram = 0.398·HR + 0.535·Fitness −51.9.

The step frequency (SF) increased (ANOVA, P < 0.001) with treadmill speed (Fig. 1). Bonferroni post hoc tests revealed significant CSA output differences between walking speeds and between walking and 8-km·h−1 running. Further increments in running speed were associated with much smaller increases in SF with significance reached only with ≥ 3-km·h−1 differences. The same pattern was observed in the field, although SF averaged 0.07 Hz (P = 0.016) higher in the field, as determined by multiple linear regression. Between-subject differences in SF were negatively correlated with body weight (R = −0.16, P = 0.003) and height (R = −0.12, P = 0.019).

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CSA relations to speed.

Mean CSA outputs (CSA_All) are shown in Table 1 for each velocity in all four trials. Accelerometer output rose approximately linearly with speed until 8 or 9 km·h−1, but further increments in running speed did not significantly affect the CSA output; it leveled off at approximately 10,000 counts·min−1 and showed a tendency toward a decrease at highest speeds (Fig. 2).

ANOVA post hoc test revealed significant differences between consecutive velocities in the 3–8 km·h−1 range. All running values were significantly different from the 6-km·h−1 values. In trial F, post hoc tests performed on both CSA_All and CSA_All adjusted for speed deviations from the prescribed protocol produced results similar to those from the treadmill trials. No significant differences were found between any of the trials, and no difference (P = 0.565) in the speed-CSA output relationship could be attributed to experimental setting (trials A, B, and C pooled) when tested using multiple linear regression on the 3–14 km·h−1 speed range.

The filter corrected CSA output (CFC_CSA) is shown against treadmill speed in Figure 3. This variable exhibited a relationship with speed comparable with the uncorrected CSA_All, although individual relationships showed a weaker tendency to decrease on the highest velocities. The leveling-off for CFC_CSA around 27,000 CFC_counts·min−1 corresponds to an acceleration of 9 m·s−2 (6).

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Inter-instrument reliability, expressed as CSA unit-differences relative to the common mean CSA_All (from treadmill trials 3–14 km·h−1), is illustrated in Figure 4, upper panels. The majority of the CSA unit-differences (all trials) were within ± 30%. Linear relationships between CSA unit-differences and speed were found for all CSA units, although the relationship was weak for 10580. The calculated single measure intra-class correlation coefficient (ICC) was 0.91 (95% CI: 0.88–0.93), and the average measure ICC was 0.98 (95% CI: 0.97–0.98). Both ICC were significant at the 0.001 level. CSA unit-differences remained after calibration, (Fig. 4, lower panels). Relative CFC_CSA unit-differences showed linear relationships with speed, being negative for unit 10580 but positive for the other three units.

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Between-subject reliability.

Partial correlations of CSA_All and SF, adjusted for speed and stratified by walking and running, were inverse and significant (R = −0.34, P = 0.02 for walking and R = −0.63, P < 0.001 for running). Partial correlations of CFC_CSA and SF, adjusted for speed and stratified by walking and running, were nonsignificant (R = −0.02, P = 0.873 for walking and R = 0.11, P = 0.187 for running).

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V̇O2 prediction models.

The relationships between CSA outputs and V̇O2 per kilogram were nonlinear (linear R2 = 0.59, SEE = 9.69 mL·min−1·kg−1 for CSA_All, and R2 = 0.78, SEE = 7.06 mL·min−1·kg−1 for CFC_CSA. Residuals from these two regressions had distributions with abnormal skewness/kurtosis). Actual regression models are thus only presented for the subanalysis in the 3–9 km·h−1 speed range. This yielded an R2-value of 0.89 (P < 0.001) and an SEE of 3.22 mL·min−1·kg−1 for the following model:EQUATION

Regression residuals were normally distributed. For the same speed range, a similar model was derived for CFC_CSA with an R2 value of 0.95 (P < 0.001). The corresponding SEE was 2.26 mL·min−1·kg−1. EQUATION

Distributions of residuals from this model were also normal. The CSA coefficients of models 1 and 2 were virtually unaltered by the adjustment for fitness. Step frequency could enter model 1 at the 0.001 significance level but was rejected in model 2 (P = 0.805). Both prediction models significantly underestimated V̇O2 per kilogram at higher running velocities (P < 0.001), with linearly increasing prediction error. From 10 km·h−1 to 16 km·h−1, the mean error increased from 11% to 48% for model 1. For model 2, the mean error increased from 5% at 10 km·h−1 to 36% at 16 km·h−1. V̇O2 per kilogram was also modeled by multiple linear regression over the 3–16 km·h−1 speed range, adding HR as a predictor. The derived models for CSA_All+HR and CFC_CSA+HR (R2 = 0.95, SEE = 3.29 mL·min−1·kg−1 and R2 = 0.95, SEE = 3.28 mL·min−1·kg−1, respectively) were significant at the 0.001 level and had normal distributed residuals:EQUATION EQUATION

The model-specific CSA coefficients were not significant (P = 0.089 and P = 0.055 for models 3 and 4, respectively). All other coefficients were significant at the 0.001 level.

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Speed relations of V̇O2, HR, and step frequency.

Walking and running were investigated over a wide speed range. The observed relationships between steady state V̇O2 per kilogram, HR levels, and speed are approximately linear, which is consistent with the findings reported elsewhere (1,2,7). The absolute coefficients and values depend on movement economy/efficiency, training history, physical maturity, gender, genetics, and other factors. Our study population is a select group of trained individuals. Although we have adjusted our analyses for fitness level, absolute coefficients of the equations may not generalize precisely to other populations.

Speed is a proxy measure for the mass-specific mechanical intensity or power in joules per minute per kilogram (30), which is not completely linear in the walking range (10). Total mechanical power can be divided into external and internal components (30). The latter is proportional to both speed and step frequency, thus constituting an increasingly larger proportion of the total mechanical intensity with increasing speed (23). However, the calculation of total mechanical power in this manner has received some criticism, as it depends largely on assumptions of energy transfer between body segments (30). V̇O2 per kilogram (aerobic intensity) during steady state exercise is a proxy measure for mass-specific metabolic energy turnover (total intensity) and could also be converted into the unit joules per minute per kilogram. The error incumbent in this measure depends on the degree of anaerobic metabolism, which plays a progressively greater role as speed increases (7,19).

The observed step frequency pattern, which is similar to that reported elsewhere (8,9,11,12), describes a relatively steeper linear relationship with speed in the walking range, than in the running range. Step frequencies in the field test were 0.07 Hz higher (P = 0.016) compared with treadmill trials. This may be due to the different surface compliance (∼ surface stiffness) of asphalt versus the treadmill rubber belt (16) and air resistance (14).

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CSA relations to speed.

The CSA output rose linearly with speed over the walking/jogging range (3–9 km·h−1). However, at higher running velocities CSA output leveled off and showed a tendency to drop at the highest velocities. The frequency-corrected values (CFC_CSA) with known linear response to acceleration (6) showed generally the same pattern, although without the decrease in accelerometer output. This variable virtually paralleled the step frequency pattern.

The absolute CSA readings are comparable to the findings of other validation studies (17,25,29). In children, however, CSA output during running have been shown to be lower (29). In this present study, we observed a negative correlation between CSA output and step frequency when adjusted for speed, which may explain why CSA output is lower in children. The leveling-off in CSA output during running reported here is consistent with the findings of Nichols and coworkers (25). This was particularly evident in two of their subjects, where running speed exceeded 16 km·h−1, but where CSA output was approximately 10,000 counts·min−1. Nichols et al. attributed this observation to experimental setting. Results from our study, however, indicate that the CSA-speed relationship during walking and running does not differ much between settings. Moreover, this relationship was also unaffected by the V̇O2 measurement equipment, as CSA outputs in trial A versus B and C were similar.

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Biomechanical issues.

The pattern of the predicted average accelerations of the present study is similar to those predicted by biomechanical theory (8,9,11). This pattern also indicates that there are substantial biomechanical differences between walking and running. Walking can be modeled as an inverted pendulum with potential and kinetic energy constantly interchanging. Running, on the other hand, is characterized by simultaneous increments (and decrements) of the potential and kinetic energy, and can be modeled as a bouncing system with a natural frequency in steps per second of (k/m)0.5/π, where m is the body mass and k is the vertical stiffness constant (8). This assumption holds true until about 11 km·h−1 because the average acceleration during the contact phase of the stride is equal to the average acceleration in the aerial phase, which is always 1 g (8). As speed increases above 11 km·h−1, the relative duration of the contact phase of the stride decreases and the rebound becomes asymmetric. To restore the vertical momentum (constant across running speeds), average contact phase acceleration must increase with shorter contact duration. It is possible that at this point the CSA reaches the upper limit of its dynamic range (±2.13 g), which could then explain some of the leveling-off. In 17 endurance runners, force plate measured peak acceleration increased from about 2.8 to 2.9 g when running speed was increased from 11.7 to 18 km·h−1 (19). This indicates that the dynamic range of the CSA is compromised during running in general. However, this is not likely to be the cause of leveling-off, as peak acceleration increased less than 5% in that speed range. Moreover, average acceleration varies even less due to the difference in contact time. Dividing total work rate into vertical and horizontal components stresses the limitations of vertical uniaxial accelerometry as a predictor of total mechanical power (work rate), especially in running (15). The CSA mounted on the hip (measuring along the longitudinal axis) is a marker of average vertical mechanical power, which is the largest component of total power below 4-km·h−1 walking. At faster speeds, horizontal power predominates, whereas vertical power increases only until the subject starts to run. In fact, horizontal power increases by a factor >10 from 7 to 32 km·h−1 of running, whereas vertical power is almost constant in this interval (11). This precludes the prediction of total mechanical power from vertical acceleration. Hence, generating horizontal forces constitutes a significant and increasingly larger proportion of total power (13). Therefore, it seems most likely that the observed leveling-off in the CSA output during running is mainly due to the biomechanical characteristics of running, i.e., that average vertical acceleration is relatively constant across running speed. Any residual suppression may be attributed to frequency-based filtering, as CFC_CSA did not drop as much as CSA_All on the fastest speeds. The filter-corrected variable leveled off at an output, corresponding to 9 m·s−2 (6). In retrospect, we had expected a value of 9.8 m·s−2 (1 g). This discrepancy may be explained by the fact that the dynamic range of the CSA is exceeded in running. Additionally, the conversion of counts to acceleration is based on sinusoidal movement, and as the CSA only measures time-varying accelerations, zeros would be recorded during the aerial phase of a running stride if the CSA was attached exactly to the body’s center of gravity. In practice, however, the acceleration of the hip may vary during the aerial phase, due to tilting of the pelvis when the left and right side of the body move in opposite directions.

The biomechanical explanation for the leveling-off, as opposed to the reason being limitations in the CSA itself, is supported by validation studies of other accelerometers. For example, Haymes and Byrnes (18) reported failure to detect changes in (uniaxial) Caltrac output during treadmill running from 8 to 12.8 km·h−1, and a triaxial accelerometer, described by Meijer and coworkers (21), had the highest sensitivity of its piezo-electric element in the vertical direction and was found to systematically underestimate running intensity. Bouten and colleagues (5) reported for the triaxial Tracmor that V̇O2 was better predicted from registrations in the anterior-posterior direction, despite the major acceleration component occurring along the longitudinal axis. These findings indicate that additional measurement along the anterior-posterior axis may be required to differentiate intensity in the running range with accelerometry.

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As reported by others (25,29), inter-instrument reliability (difference between units worn on left and right hip) was poorer at slow walking speed than during faster walking speeds. These findings are consistent with those of our study. It could partially be attributed to differences in sensitivity of the CSA units, and partially to real contralateral and/or anteroposterior variability on the slower speeds of walking, presumably because biomechanics at these locations are more variable on slower walking speeds (10). Subjects did seem to focus on maintaining balance to a greater degree in the 3-km·h−1 intervals and subconsciously kept pacing at this speed in the field trial. In running, reliability was generally better than in walking, which is in contrast to previous observations (25). Individual characteristics such as body size, hip geometry, and the amount of soft tissue deposition on the hip may explain differences between accelerations along the anterlateral, the posterolateral, and the mediolateral lines.

The intraclass correlation coefficients were high (ICC > 0.91, P < 0.001), but this statistic does not reveal absolute differences specific to each speed. CSA unit-specific relative differences to the common mean, CSA_All, were found to be high, the majority of which were within ± 30%. Linear relations of relative errors to speed were found in all units, although this was weak for CSA unit 10580. The CSA unit-specific error pattern coincided with observations from the mechanical setup (6), which supports these findings. Because poor inter-instrument reliability results in regression dilution when applying the method in population studies, CSA unit-specific calibration before and maybe during field measurement may increase the statistical power to detect clinically significant effects. Alternatively, postmeasurement statistical adjustments can be employed, which is possible for CSA data that has already been collected, because the raw data output files are stamped with the serial number of the CSA. Differences between CSA units did, however, persist after calibration, as illustrated in lower panels of Figure 4, although three of the CSA units aligned. As our calibration assumes that filtering follows the same pattern in all CSA units, the residual difference in the calibrated values could partially be due to a violation of this assumption. If so, much more sophisticated calibration procedures are required. Real contralateral and/or anteroposterior variability, however, is also a plausible explanation for the remaining differences.

The effect of step frequency on between-subject reliability is relatively large; differences in step frequency explain about 11% and 40% of the (speed-adjusted) variance in CSA output in walking and running, respectively. This is supported by the ability of step frequency to enter the V̇O2 prediction model with CSA_All. Applying equations to eliminate the frequency dependency could potentially enhance this dimension of the reliability, as CFC_CSA models were generally more precise and did not allow entry of step frequency into the prediction model of V̇O2 per kilogram.

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V̇O2 prediction models.

The relationship between CSA output and V̇O2 per kilogram for the 3–9 km·h−1 speed range (model 1) is relatively consistent with the estimates of other investigators (17,25,29). Interestingly, our regression slopes remained largely unaltered by adjustment for fitness, suggesting that the relationship between an increase in CSA output and increase in energy expenditure is independent of fitness. However, our models and those of other investigators, all significantly underestimate V̇O2 per kilogram in moderate- to high-intensity running, with estimation errors increasing with speed, which approach 50% at 16 km·h−1. The error in predicting total metabolic energy turnover is even greater, due to the progressively greater contribution of anaerobic metabolism at higher exercise intensities (7,19). Walking/running speed may be an equally, or even a better estimate of the total metabolic energy turnover. For the 5-km home trip in the field trial, the subjects chose velocities that would all be significantly underestimated by walking/jogging derived CSA equations. Because these are not uncommon running speeds and running is common to many sports (1), the prevalence of this intensity prediction error is likely to be high in people who engage in structured exercise. This phenomenon may well explain, why the CSA underestimated vigorous activity in a field evaluation when compared with an activity log (27). However, the CSA is likely to provide a reasonably valid estimate of the total energy expenditure of daily physical activity over longer periods of time (i.e., several days) at population level, because for most people, daytime activity is predominantly at low intensity (27).

The multiple regression models, where HR is a co-predictor, explain the most of the variation in V̇O2 per kilogram and the model-specific CSA coefficients were only borderline significant. Therefore, HR appears to be the most powerful predictor of V̇O2 per kilogram during treadmill walking and running when the entire speed range is considered. This may question the utility of (uniaxial) accelerometry over HR monitoring (28), when considering the appropriateness of a physical activity assessment technique in epidemiology. However, HR shows variation with variables other than physical activity, such as mental stress, temperature, level of dehydration, etc. (28). Furthermore, most of the errors resulting from these factors would not be positively correlated with the estimation error incumbent in CSA assessment of physical activity. The CSA may therefore be used to quantify relatively low-intensity activity, and once above a certain intensity threshold, activity may be estimated from HR recordings. The appropriate threshold could be the CSA output value corresponding to the transition between walking and running. Averaging the CSA readings for 6 and 8 km·h−1 would correspond to 6683 counts·min−1 (or 14,459 CFC_counts·min−1 for CFC_CSA) in our study sample; other populations, however, are likely to have different thresholds. In a recent study (26), a combined HR and movement sensor utilized movement data (at chest level) to determine which one of two HR based equations (slope and intercept for the V̇O2-HR relationship) should be applied to predict intensity of activities performed in a respiration chamber. Total energy expenditure was accurately predicted on a group level (±0.0%, range −22% to +19%). The CSA thresholds may also be used for interpretation of epidemiological data, i.e., values beneath this point can be treated as a continuous variable with a linear association with intensity, whereas values above the threshold could be considered to be categorical, i.e., coding activity into “at least moderate intensity.” By analyzing the data this way, corrections for dependency on movement frequency may be less important, although correction would still improve precision of the estimates, especially for comparisons between individuals with different step frequency patterns. For the analysis of combined data, thresholds could also be based on HR, e.g., the HR at the walking-running transition. This would correspond to 101 bpm (range 91–125 bpm) for this study sample. As a third alternative, accelerometer and HR predicted energy expenditure could be averaged within a certain intensity range, i.e., above a certain number of counts per minute and below transition HR, using the accelerometer predictions and HR predictions exclusively below and above this range, respectively. The precision of such combinations remains to be determined.

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Linearity between CSA output and mass-specific aerobic intensity cannot be assumed at moderate to high running velocities. The CSA discriminates intensity within the walking range, between walking and running, but not within the running range. This is mainly due to different biomechanics of the two activities. Mean estimation error of V̇O2 per kilogram was 48% in 16-km·h−1 running. If intensity relations are among the research objectives, other measurement directions or inclusion of a HR monitor should be considered. Between-subject reliability relates to step frequency because CSA data are filtered more the higher the movement frequency. This dimension of reliability can be improved by applying equations to off set the filter weight. Inter-instrument differences are significant and suggest that unit-specific calibration may improve data quality and study power. The conclusions drawn from this study are based solely on the activities of walking and running; other activities are likely to relate differently to energy expenditure. It may, however, be advisable when interpreting accelerometer data from population-based research to consider the limitations described in this study.

The study received financial support from the Danish Medical Research Council. All experiments comply with current Danish law.

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