Figure 1.
Estimation of resting metabolic rate in experimental and simulated data.
Mouse metabolic chamber datasets were simulated, consisting of the total energy expenditure (TEE), resting metabolic rate (RMR) and physical activity (PA) (A). The simulated data shows to be similar to the experimental data (B), exhibiting a diurnal rhythm in activity patterns and RMR, and high frequency time variations in the TEE that are due to PA. Simulated datasets were used to evaluate the accuracy of the estimated RMR time series (RMR est) by means of penalised spline regression. For details regarding the simulation procedure, see the Methods section and Supplementary Text 4.
Figure 2.
The time variations in the RMR that are estimated by the penalised spline model depend on the number of knots used in the spline function: 4 knots/day are sufficient to capture the diurnal rhythm in the RMR, whereas more knots are needed to estimate faster time variations (A). Calculating the root mean square estimation error (RMSE) for a range of frequency components in the RMR shows that more accurate estimates of high frequency components are obtained when the knot number is increased (B). Roughly, are needed to estimate frequency components in the RMR of up to
. However, higher frequency components are estimated with a relatively larger error.
Figure 3.
Estimation accuracy of the penalised spline model and dependency on the sample rate.
The accuracy of the penalised spline model in estimating the average and time-dependent RMR deteriorates when TEE and PA are sampled at a lower rate (A). This effect is less strong if TEE has been sampled at a low rate but PA at a high rate. The effect of sampling PA at a low rate is that fast transitions between active and inactive periods are not rendered faithfully (B). These inaccuracies result in a larger unexplained variance of the fitted penalised spline model on both the simulated and experimental data (C). The effect of sampling TEE at a low rate on the time-dependent RMR estimates is illustrated by transforming a single high resolution dataset into N low resolution datasets, and superimposing the N different RMR estimates (D). When the TEE time series are downsampled by a factor N = 120, corresponding to a sample time of , there is considerably more variation in the RMR estimates than with a downsampling factor of N = 45 (
). The variability in the RMR estimates (the downsampling induced variability; DIV) showed a linear dependency on
for simulated and experimental data (E).
Figure 4.
Dependency of estimation accuracy on chamber size to flow rate ratio.
Increasing the chamber size to flow rate ratio (the washout time ), the high frequency variations in TEE that are caused by PA are attenuated by the filtering effect of gas diffusion through the metabolic chamber (A). Consequently, accurate TEE decomposition becomes more difficult, as demonstrated by the increase in estimation error of the average and time-dependent RMR for larger
(B).
Figure 5.
Performance comparison of estimation methods.
Estimated RMR time series by means of linear regression, TEE averaging for zero activity, Kalman filtering and penalised spline modelling are shown for a typical simulated (A) and experimental (B) dataset. The overall estimation accuracy in average RMR (C) and time-dependent RMR (D) was calculated based on 500 simulated datasets (expressed as Root Mean Square Error). For the estimation error in the average RMR the bias-variance decomposition was calculated to gain more insight in the origin of the error (E). Error bars indicate half the standard deviation.
Table 1.
Comparison of metabolic parameters of male and female C57Bl/6J mice after a 10 week high fat diet.
Figure 6.
Case study: energy expenditure and activity of male and female mice after a 10 week high fat diet.
Time-dependent group averages are shown of TEE and RMR (A) and AEE (B) for male and female mice. Lines indicate group averages and gray bands represent standard error of the mean; black-white bars indicate the dark-light periods. The P-spline model contained 15 knots/day. The TEE of male mice was higher during most of the day, except for the start of the dark period. The RMR of male mice was higher than that of female mice during each period of the day, whereas AEE was overall similar, except for the start of the dark period. Group differences were also present in average daily TEE and RMR, whereas no differences were found in average daily AEE (C). Time-dependent group averages of spontaneous PA show that female mice were more active, especially during the first phase of the dark period (D). The reason that the higher activity of female mice did not engender a difference in energy expenditure is that the caloric cost of activity (CCA) was lower in this group (E). (error bars represent standard error of the mean; *P<0.05, **P<0.001).
Table 2.
Correlation of metabolic parameters with body weight (n = 15).