Our mathematical model of infant macronutrient balance presents a continuous dynamic picture of the complex interactions of macronutrient intake, oxidation, and body composition that occur during normal growth. The model was used to integrate a variety of experimental data from the longitudinal study of Butte et al (5
), and, for the first time, calculated the dynamic changes in macronutrient oxidation rates and the changes in 24-h RQ that would be required to consistently integrate the body composition, diet composition, and daily average
data obtained by Butte et al.
Our model predicted that breastfed boys undergo significant dynamic adaptations of fuel selection over the first 2 y of life. Despite a very high initial percentage of dietary fat, oxidation of fat is greatly suppressed and only gradually increases after birth, whereas nonfat oxidation closely follows intake over the entire period. These substrate oxidation dynamics are reflected in the time course of the calculated 24-h RQ, where the low initial level of fat oxidation is manifested as a high initial RQ that is followed by a drop over time as relatively more fat is burned.
The physiologic mechanisms underlying these changes in substrate utilization are not specified by our model and deserve further investigation. Because the nutritional environment of the developing fetus is determined primarily by a high rate of glucose transfer across the placenta (14
), it is possible that the gestational period has endowed the newborn with a low capacity for fat oxidation and a high capacity for de novo lipogenesis (which can appear as a low fat oxidation via indirect calorimetry). Alternatively, the magnitude of positive energy balance during postnatal development may itself regulate substrate utilization, suppressing fat oxidation through an insulin-related mechanism. Indeed, whereas insulin concentrations have been observed to dramatically fall over the first 48 h after birth (15
), insulin remains 2.5-fold higher 48 h after birth than 1 y after birth (16
Because the rate of weight gain is driven by an imbalance between energy intake and expenditure, it is necessary to know the time course of total energy expenditure to use the body-composition changes to calculate energy intake. The doubly labeled water method is the gold standard method for assessing free-living energy expenditure, but this method requires an estimate of the 24-h RQ to translate the measured
rate into total energy expenditure (17
). Butte et al previously assumed that the RQ could be estimated on the basis of diet composition along with corrections for body-composition change determined from previous cross-sectional data (2
). However, the assumed cross-sectional body-composition data (2
) had previously been shown to significantly differ from Butte et al’s longitudinal measurements, especially during the first year of life (5
). Therefore, the previous assumptions used to estimate the 24-h RQ, and thereby determine the total energy expenditure, were not self-consistent.
Our model, on the other hand, calculated the 24-h RQ that was required to be consistent with the body-composition, diet composition, and
data obtained by Butte et al, thereby bypassing the need to provide RQ estimates to calculate total energy expenditure. The model predicted energy intake requirements that were slightly lower than the previous estimates of Butte et al (6
) as well as the 2004 FAO/WHO/UNU recommendations for growing infants (13
) and were significantly lower than previous estimates (12
). Nevertheless, the fact that our new estimates for the energy intake requirements are similar to those of Butte et al suggests that the assumed RQ values used in that study, although different from our calculated values, had little effect on the calculated total energy expenditure (18
It should be noted that there is a paucity of longitudinal data on 24-h RQs for growing infants. Much of the available RQ data relates to very-low-birth-weight and preterm infants (20
), with only limited data available for full-term infants (26
). Although the lack of available data precludes a direct comparison between simulation and experiment, our simulations provide experimentally testable predictions for how RQ would be expected to vary during infancy. Furthermore, the ability of our model to extract information about RQ exemplifies how mathematical modeling may be used to obtain information from experimental data that would otherwise be missed.
The experimental data obtained by Butte et al was reported in the literature as mean values and corresponding SDs because the data resulted from measurements of 76 different infants (5
). Given that the model uses these data as inputs, we investigated whether the variability of the data influenced the model outputs. We calculated energy intake, total energy expenditure, and 24-h RQ dynamics in response to variations in the time courses of
, percentage fat content of the diet, body weight, and body-composition curves compared with their mean values.
We found that fairly large changes in the percentage fat content of the diet, body weight, or body-composition curves had little effect on the calculated energy intake or the total energy expenditure. Changing the percentage fat content of the diet did, however, markedly alter the 24-h RQ dynamics, whereas shifting the body weight and body-composition curves had practically no effect on the RQ dynamics. Shifting the
rate curve generated a significant change in the energy dynamics and in the initial dynamics of the calculated 24-h RQ.
In summary, our study demonstrates the utility of integrating experimental data through a mathematical model to extract physiologic information that would otherwise not be available. As we have shown, the model can be used to determine how variability in the experimental measurements (ie, the model inputs) influences the calculated values of interest (ie, the model outputs)—a task that would be prohibitively tedious without the aid of a mathematical model.