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Keywords:

  • weight gain;
  • energy intake;
  • energy expenditure;
  • physical activity

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Objective: To develop a model based on empirical data and human energetics to predict the total energy cost of weight gain and obligatory increase in energy intake and/or decrease in physical activity level associated with weight gain in children and adolescents.

Research Methods and Procedures: One-year changes in weight and body composition and basal metabolic rate (BMR) were measured in 488 Hispanic children and adolescents. Fat-free mass (FFM) and fat mass (FM) were measured by DXA and BMR by calorimetry. Model specifications include the following: body mass (BM) = FFM + FM, each with a specific energy content, cff (1.07 kcal/g FFM) and cf (9.25 kcal/g FM), basal energy expenditure (EE), kff and kf, and energetic conversion efficiency, eff (0.42) for FFM and ef (0.85) for FM. Total energy cost of weight gain is equal to the sum of energy storage, EE associated with increased BM, conversion energy (CE), and diet-induced EE (DIEE).

Results: Sex- and Tanner stage–specific values are indicated for the basal EE of FFM (kff) and the fat fraction in added tissue (fr). Total energy cost of weight gain is partitioned into energy storage (24% to 36%), increase in EE (40% to 57%), CE (8% to 13%), and DIEE (10%). Observed median (10th to 90th percentile) weight gain of 6.1 kg/yr (2.4 to 11.4 kg/yr) corresponds at physical activity level (PAL) = 1.5, 1.75, and 2.0 to a total energy cost of weight gain of 244 (93 to 448 kcal/d), 267 (101 to 485 kcal/d), and 290 kcal/d (110 to 527 kcal/d), respectively, and to a total energy intake of 2695 (1890 to 3730), 3127 (2191 to 4335), and 3551 (2487 to 4930) kcal/d, respectively. If weight gain is caused by a change in PAL alone and PAL0 = 1.5 at baseline t = 0, the model indicates a drop in PAL of 0.22 (0.08 to 0.34) units, which is equivalent to 60 (18 to 105) min/d of walking at 2.5 mph.

Discussion: Halting the development or progression of childhood obesity, as observed in these Hispanic children and adolescents, by counteracting its total energy costs will require a sizable decrease in energy intake and/or reciprocal increase in physical activity.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Childhood obesity arises from long-term dysregulation of energy balance; however, the energetics for the development of childhood obesity are poorly delineated. The energy imbalance required for weight gain from increased energy intake and/or decreased physical activity in children remains uncertain. A model was developed in normal adults to predict weight gain based on the First Law of Thermodynamics, which dictates that the change in stored energy in the body equals energy intake minus energy expenditure (EE),1 and the Second Law of Thermodynamics, which states that the conversion of excess energy into new tissue requires energy (1)(2). The basic principle underlying the model is that any given sustained long-term change in energy intake or EE will produce changes in body weight and composition until a new steady state is established.

Energy requirements for storing energy in body tissues may differ in growing children given the strong anabolic drive to deposit not only fat but also lean tissue. At a minimum, the basic assumptions of the adult model would have to be modified to reflect the energy partitioning into fat and lean tissue during the growth process, energetic efficiency for tissue synthesis, and higher basal EE in children. Previous estimations of the energy cost of growth (3)(4)(5)(6) were not based on a dynamic model that integrated the increasing energy requirements required to sustain normal, or in the case of obesity, excessive growth. Swinburn et al. (7) derived a regression equation to predict changes in body weight from perturbations in energy intake or EE based on a cross-sectional relationship between body weight and total EE (TEE). The predicted energy imbalance associated with weight gain was higher than previous estimates because the energy required to sustain the higher body mass was considered. Here we develop a model detailing the processes and energetic components of weight gain in children and adolescents.

The VIVA LA FAMILIA Study offers a unique opportunity to derive a model for the development of childhood obesity in a large sample of non-overweight and overweight children in whom 1-year changes in weight and body composition and basal metabolic rate (BMR) were measured. The mathematical model is based on empiric data and current understanding of human energetics to predict the obligatory increase in energy intake or, conversely, decrease in physical activity associated with weight gain in children and adolescents. We developed and applied a pediatric model to answer the following questions: 1) Do the specific basal EEs for fat mass (FM) and fat-free mass (FFM) vary as a function of age, sex, or Tanner stage? 2) Does the fraction of fat in new tissue (fr) vary as a function of age, sex, Tanner stage, body mass, or amount of weight gain? 3) What is the energy imbalance required to produce observed 1-year weight gains varying from 1 to 22.5 kg/yr in children and adolescents? 4) What is the total energy cost of weight gain relative to the combustible energy stored? 5) If physical activity is constant, what must the incremental change in energy intake be to result in these weight gains? 6) If energy intake (EI) is constant, what must the decrease in physical activity be to result in these weight gains?

Research Methods and Procedures

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Study Design and Subjects

Subjects were participants in the VIVA LA FAMILIA Study, which was designed to identify genetic and environmental factors affecting childhood obesity in the Hispanic population. The study design and baseline phenotyping are described elsewhere (8). As part of the study design, children returned after 1 year for repeat anthropometric and body composition measurements. Subjects with incomplete data were excluded from the modeling. Also, because the aim of this study was to model weight gain, subjects who lost weight or who were weight-stable (±1.0 kg/yr) were excluded. Although the dynamics of energy turnover during weight loss is of interest to us, our sample size was insufficient for modeling purposes. Mathematical modeling of the total energy cost of weight gain was performed on 488 children (260 boys and 228 girls). Mean age was 11.4 ± 2.9 years (range, 5 to 19 years). All children and their parents gave written informed consent or assent. The protocol was approved by the Institutional Review Board for Human Subject Research for Baylor College of Medicine and Affiliated Hospitals and the Southwest Foundation for Biomedical Research.

Anthropometry and Body Composition

Body weight to the nearest 0.1 kg was measured with a digital balance, and height to the nearest 1 mm was measured with a stadiometer. Total body estimates of FFM, the sum of lean tissue and bone mineral content, and FM were measured by DXA using a Hologic Delphi-A whole body scanner (Delphi-A; Hologic, Waltham, MA). Overweight was defined as BMI ≥95th percentile (9) and FM ≥85th percentile (10)(11).

Sexual Maturation

Tanner stages of sexual maturation based on pubic hair and breast and penile development illustrated with drawings were by self-report (12)(13).

BMR

Oxygen consumption (Vo2) and carbon dioxide production (Vco2) were measured continuously in an 18- or 30-m3 room calorimeter for 24 hours. The performance of the room respiration calorimeters has been described in detail previously (14). Errors from 24-hour infusions of N2 and CO2 were −0.34 ± 1.24% for Vo2 and 0.11 ± 0.98% for Vco2. BMR was measured under thermoneutral conditions on awakening after a 12-hour fast. The children were asked to remain still, but awake, for 30 minutes. The children were monitored both visually and by a motion sensor to confirm that they were lying still (<50 activity counts/min) for the entire measurement. BMR was computed according to Weir (15).

Mathematical Model for Weight Gain

In this model, each parameter has a physiological interpretation, e.g., specific energy content and basal EE of FM and FFM, fraction of fat in added tissue, etc. The model is a modification of the model developed in normal adults (2). The modifications reflect the differences in basal EE and composition of synthesized tissues between children and adults. To account for developmental changes, we found it necessary and instructive to adjust the parameters based on the data for each sex and Tanner stage group. In this dataset, age and Tanner stage are highly correlated (r = 0.84; p = 0.001) and interchangeable. For mathematical modeling of weight gain, it was more convenient to use categorical rather than continuous variables.

We assume that BMR is given by the expression

  • image

In Christiansen et al. (2), the basal EE of FM (kf) and basal EE of FFM (kff) are assumed to be constants common to all adults. However, these data make it possible and necessary to estimate values in each sex and Tanner stage group. In the literature, the physical activity level (PAL) has frequently been defined as the ratio between total EE and basal metabolic rate: PAL = TEE/BMR. However, some of the EE does not depend on physical activity; therefore, we use a more complex equation for total EE during weight gain accounting for conversion energy (CE) and diet-induced EE (DIEE). CE is the energy used to convert dietary energy intake into combustible energy in new tissue. We assume that DIEE = 0.1 EI. In Christiansen et al. (2), this term was ignored, with the argument that it can be included in the definition of EI (replace EI by 0.9 EI). However, this is not adequate when the estimation of energy requirements is a key issue.

  • image

The efficiency of the conversion from EI into new tissue depends on the composition of the tissue. We model this effect by the two efficiency coefficients ef (efficiency in the conversion of energy to FM) (0.85) and eff (efficiency in the conversion of energy to FFM) (0.42) for the formation of FM and FFM, respectively. If fr denotes the fat fraction in new tissue (fr), this is partitioned as:

  • image

The following relationship between energy imbalance and rate of increase in body mass (BM) is derived in the adult model (2):

  • image

where the constant c is given by

  • image

By inserting Equations 1 and 2 into 3, we get the following equation, which shows how BM is controlled by EI and PAL:

  • image

Body weight accretion is controlled by both EI and PAL. Because there are no EI or PAL data available in this dataset, extra assumptions are required. We shall consider the cases where PAL or EI is constant. We also assume that the rate of weight gain is constant during the period and normalize the weight gain ΔBM to 1 year for every subject.

We first compute the energy cost of weight gain for each subject based on two time-points, 1 year apart. The energy stored in added tissue is

  • image

Energy used for conversion, normalized to 1 year, is

  • image

For reference, we compute the steady-state EE, i.e., the EE in 1 year assuming no change in BM and excluding DIEE:

  • image

As BM increases, EE = PAL × BMR changes during the period, so the accumulated EE is an integral. Assuming that PAL is constant we get

  • image

The total energy intake in 1 year with weight increase ΔBM is

  • image

Hence, the energy cost of weight gain ΔBM in 1 year is

  • image

The energy cost per kilogram weight gain is

  • image

This value is constant within each sex and Tanner stage group.

In the above, we assume that PAL is constant during weight increase. Alternatively, we may assume that EI = EI0 is constant and that a constant rate of weight gain is obtained by variation of PAL = PAL(t) alone. For reference, let PAL0 be defined by the steady-state equation at time t = 0, i.e., by Equation 3, PAL0 × BMR(0) = 0.9 × EI0. PAL(t) can then be computed from Equation 3:

  • image

By combining Equations 1 and 2, we get

  • image

Inserting this into Equation 12 yields

  • image

Note that PAL(0) < PAL0 because the person is not in steady state at time t = 0.

Specification of the Model

Here we summarize the simplifications and assumptions made in the model.

  • 1
    . BM can be partitioned into FM and FFM. These are determined by the data for each child.
  • 2
    . FM and FFM each has a specific energy content, cf and cff, and a specific basal EE, kf and kff.
  • 3
    . The conversion of surplus energy intake into FM and FFM requires specific amounts of energy, given by the efficiencies ef and eff, which are independent of energy imbalance and composition of food intake.
    Total EE is given by TEE = CE + DIEE + PAL × BMR. TEE is the sum of conversion energy used in the synthesis of new tissues, DIEE, and energy expended in physical activity estimated as a multiple of BMR.
  • 4
    . fr is independent of BM or weight gain.
  • 5
    . fr is determined as the median for each sex–Tanner stage group.
  • 6
    . BM increases at a constant rate during the period.

Coefficients and Constants Used in the Formulas

Energy stored per kilogram of FFM (cff) equals 4.48 kJ/g (1.07 kcal/g) based on the assumptions that FFM is comprised, on average, of 0.19 g protein/g FFM (16), and the heat of combustion of protein is equal to 5.65 kcal/g (17). Energy stored per kilogram of FM (cf) equals 9.25 kcal/g based on the heat of combustion of fat (17); eff equals 42% for protein (5); and ef equals 85% for fat (5).

For the application of the model, empirical values of BM, ΔBM, BMR, FM, FFM, and fr are used. Assumed values for DIEE and PAL are used for modeling. Computations are performed at PAL = 1.5, 1.75, or 2.0, which correspond to low-active, active, and very active levels of physical activity, respectively. kf and kff are determined as part of the results.

Statistical Methods

ACCESS (version 9; Microsoft Corp., Seattle, WA) was used for database management. STATA (version 8.2; StataCorp LP., College Station, TX) was used for statistical analyses. Data are summarized as median (10th to 90th percentile). Descriptive statistics and general least squares regression were performed. Statistical significance was set at p < 0.05.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Derivation of Coefficients from Empirical Data in Children and Adolescents

Application of the adult model using Equation 1 with basal EE values for FM and FFM of kf = 6.45 kcal/kg/d and kff = 27.7 kcal/kg/d, respectively, to compute BMR for each subject in the VIVA LA FAMILIA Study clearly showed the need for adjustment of these parameters in children. BMR computed using adult constants was equal to 0.64, 0.75, 0.84, 0.92, and 0.97 of actual BMR at Tanner stages 1 to 5, respectively. Generalized least squares regression applied to Equation 1 was, therefore, used to derive the coefficients for basal EE of FFM and FM in children (Question 1: Do the specific basal EEs for FM and FFM vary as a function of age, sex, or Tanner stage?). FFM accounts for 75% of the variance in BMR, and FM accounts for an additional 6% of the variance in children. A strong effect of Tanner stage (p = 0.001) on the coefficient for basal EE of FFM (kff) was observed (Figure 1), with a smaller but significant effect of sex (p = 0.001). The coefficient for FFM (kff) decreased significantly with Tanner stage from 44.6, 37.9, 33.8, 30.9, to 28.9 kcal/kg FFM/d in boys and 48.2, 40.2, 34.7, 31.4, to 31.0 kcal/kg FFM/d in girls, approaching the adult value of 27.7 kcal/kg FFM/d (18) in late adolescence. The coefficient for FM (6.13 ± 1.36 SE kcal/kg FM/d) did not differ systematically by Tanner stage or sex, nor did it differ from the adult value of 6.45 kcal/kg FM/d (18). We, therefore, used the adult value kf = 6.45 kcal/kg FM/d in all groups, and the best fit for kff, given kf = 6.45, within each sex and Tanner stage group. This corresponds to the implicit assumption that FM composition is similar for children and adults, whereas FFM changes composition with sex and Tanner stage group.

image

Figure 1. : Basal EE (kff) of FFM as a function of Tanner stage.

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The changes in FFM and FM and associated energy storage in the non-overweight and overweight boys and girls are shown in Figure 2. The fr was computed for each child (Question 2: Does the fr vary as a function of age, sex, Tanner stage, body mass, or amount of weight gain?). fr was found to be a function of sex and Tanner stage (i.e., a significant interaction between sex and Tanner stage, p = 0.001; Figure 3). For boys, fr first decreased and then increased. For girls, fr increased gradually with Tanner stage. Median fr was equal to 0.45, 0.26, 0.06, 0.35, and 0.47 in boys and 0.42, 0.41, 0.50, 0.58, and 0.67 in girls for Tanner stages 1 to 5, respectively. fr was independent of BM, overweight status, and rate of weight gain.

image

Figure 2. : One-year changes in weight, FM, and FFM and associated energy storage in non-overweight and overweight boys and girls.

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image

Figure 3. : fr in newly synthesized tissues in non-overweight and overweight boys and girls.

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Application of the Theory

We apply the above equations to the observed 1-year weight gains of 488 Hispanic children and adolescents (Table 1). Median (10th to 90th percentile) weight gain is 6.1 kg/yr (2.4 to 11.4 kg/yr), equivalent to a 13.3% (4.4% to 24.6%) increase in BM. Weight gain increases with age, peaking at ∼11 years of age, at which time it decreases. Adjusted for age (p = 0.03) and Tanner stage (p = 0.001), weight gain is significantly higher in overweight compared with non-overweight subjects (p = 0.001) and in boys vs. girls (p = 0.007). It follows that energy storage [ΔC (combustible energy in BM)] is greater in overweight subjects (p = 0.001) and boys (p = 0.02).

Table 1. . Computation of the total energy cost of weight gain in non-overweight and overweight Hispanic boys and girls
 BoysGirlsAll
 Non-overweightOverweightNon-overweightOverweight 
  1. BM, body mass; C, combustible energy; CE, conversion energy; EE, energy expenditure; EEss, energy expenditure steady state; PAL, physical activity level. Median (10th to 90th percentile).

N112148111117488
BM (BM0, kg)42.0 (27.5 to 70.1)70.2 (39.9 to 101.4)41.4 (25.1 to 61.5)64.4 (37.7 to 91.1)53.0 (29.8 to 86.6)
Change in BM (ΔBM, kg/yr)5.0 (2.4 to 8.4)8.4 (4.0 to 13.4)4.0 (1.6 to 7.9)7.2 (2.5 to 11.6)6.1 (2.4 to 11.4)
C stored (ΔC, kcal/yr)17,680 (7,652 to 34,171)30,393 (11,740 to 53,225)19,376 (8,465 to 37,743)33,971 (12,822 to 59,602)24,850 (9,231 to 47,854)
CE (kcal/yr)7,560 (3,728 to 12,739)12,924 (6,188 to 20,574)6,296 (2,571 to 12,230)11,104 (3,855 to 17,828)9,364 (3,728 to 17,397)
Increase in EE (EE − EEss; PAL = 1, kcal/yr)24,446 (12,049 to 42,858)41,418 (18,970 to 68,860)16,901 (6,707 to 38,045)33,884 (8,477 to 55,055)30,334 (9,532 to 56,232)
Total energy cost of weight gain (PAL = 1.5, kcal/yr)71,924 (33,288 to 122,461)120,886 (58,153 to 194,572)58,266 (24,678 to 113,130)105,184 (35,543 to 167,730)89,032 (33,842 to 163,656)
Total energy cost of weight gain (PAL = 1.75, kcal/yr)78,694 (37,108 to 133,235)131,840 (62,500 to 212,758)62,604 (26,554 to 124,086)114,781 (38,492 to 181,933)97,408 (36,720 to 176,917)
Total energy cost of weight gain (PAL = 2.0, kcal/yr)85,231 (41,196 to 145,114)142,793 (66,746 to 233,065)67,127 (28,430 to 135,041)124,450 (41,212 to 197,145)105,784 (40,091 to 192,537)

First, we assume that the constant rate of weight gain is caused by variation in EI alone. The increment in EE associated with the increase in BM is computed from the difference in EE during steady-state and non–steady-state conditions at the base PAL = 1.0. The total energy cost of weight gain is computed from the sum of the energy stored, conversion energy, and the increment in EE at PAL = 1.5, 1.75, and 2.0.

For modeling, ΔBM, ΔC, and CE are constant in time and, therefore, can be scaled to 1 day. ΔEE and, thus, the total energy cost of weight gain, increase with increasing BM throughout the year. Dividing ΔEE or the total energy cost of weight gain by 365 days yields the average value for the 1-year period, which is not the same as ΔEE or the total energy cost of weight gain for a 1-day increase in BM, except if the 1 day is mid-year. The total energy cost of weight gain is presented on a daily basis to contextualize it relative to daily energy requirements (Figure 4). The median total energy cost of weight gain computed at mid-year is 244 (93 to 448 kcal/d), 267 (101 to 485 kcal/d), and 290 kcal/d (110 to 527 kcal/d) for PAL = 1.5, 1.75, and 2.0, respectively (Question 3: What is the energy imbalance required to produce observed 1-year weight gains varying from 1 to 22.5 kg/yr in children and adolescents?).

image

Figure 4. : Total energy cost of weight gain computed for PALs of 1.5, 1.75, and 2.0.

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The relative contribution of ΔC, CE, ΔEE, and DIEE to the total energy cost of weight gain is a function of PAL (Question 4: What is the total energy cost of weight gain relative to the combustible energy stored?). Total energy cost of weight gain is partitioned into energy storage (24% to 36%), conversion energy (8% to 13%), increase in EE (40% to 57%), and DIEE (10%). In Figure 5, the partitioning of the total energy cost of weight gain is shown for non-overweight and overweight boys and girls at PAL = 1.5 and 1.75.

image

Figure 5. : Partitioning of the total energy cost of weight gain into ΔC, CE, increase in EE over steady-state EE, and DIEE computed for PALs of 1.5 and 1.75 in non-overweight and overweight children.

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The obligatory total EI to support the observed rates of weight gain is computed at PAL = 1.5, 1.75, and 2.0 and normalized to 1 year (Table 2) and 1 day (Figure 6; Question 5: If physical activity is constant, what must the incremental change in energy intake be to result in these weight gains?). The total energy intake is 2695 (1890 to 3730), 3127 (2191 to 4335), and 3551 (2487 to 4930) kcal/d at PAL = 1.5, 1.75, and 2.0, respectively. Total EI is significantly higher in overweight compared with non-overweight subjects and in boys vs. girls to support not only the higher weight gains but also higher basal and activity-related EE.

Table 2. . Obligatory total EIs to support the observed rates of weight gain in non-overweight and overweight Hispanic boys and girls assuming a constant rate of weight gain caused by variation in EI alone
 BoysGirlsAll
 Non-overweightOverweightNon-overweightOverweight 
  1. EI, energy intake; TEI, total energy intake; PAL, physical activity level. Median (10th to 90th percentile).

N112148111117488
TEI at PAL = 1.5 (kcal/yr)869,668 (674,527 to 1,162,252)1,184,891 (846,225 to 1,541,513)788,740 (607,605 to 962,096)1,054,442 (818,705 to 1,348,890)983,520 (689,899 to 1,361,306)
TEI at PAL = 1.75 (kcal/yr)1,010,682 (783,497 to 1,346,324)1,373,594 (977,101 to 1,786,663)916,706 (706,168 to 1,121,065)1,220,418 (952,536 to 1,558,504)1,141,420 (799,697 to 1,582,443)
TEI at PAL = 2.0 (kcal/yr)1,152,024 (892,466 to 1,530,396)1,562,298 (1,111,540 to 2,031,813)1,044,248 (804,731 to 1,280,033)1,390,770 (1,086,368 to 1,769,520)1,296,096 (907,874 to 1,799,613
image

Figure 6. : Total daily energy intake as a function of weight gain computed for PALs of 1.5, 1.75, and 2.0.

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Second, we assume that a progressive decline in PAL alone accounts for the constant rate of weight gain, i.e., EI is constant (Table 3; Question 6: If EI is constant, what must the decrease in physical activity be to result in these weight gains?). We choose PAL0 = 1.5 and fix EI0 by the (hypothetical) steady-state equation PAL0 × BMR(0) = 0.9 × EI0. Because we assume a constant dBM/dt, the person is not in steady state at time t = 0. There is already an energy imbalance at t = 0; therefore, PAL(0) < PAL0. The time-course for PAL(t) is computed from Equation 13 at t = 0, 0.25, 0.50, and 1.0 year. Our model shows that PAL(0) = 1.43. By the end of the 1-year interval, PAL gradually drops 0.22 units (0.08 to 0.34 units) to account for the observed changes in BM. The fall in PAL units is higher in the overweight (0.25 units) than in the non-overweight (0.18 units) children. The continuous change in PAL during the year is larger than the initial energy imbalance.

Table 3. . PALs throughout the 1-year period to support the observed rates of weight gain in non-overweight and overweight Hispanic boys and girls assuming a constant rate of weight gain caused by variation in physical activity alone
 BoysGirlsAll
 Non-overweightOverweightNon-overweightOverweight 
  • PAL, physical activity level.

  • *

    Median (10th to 90th percentile).

N112148111117488
PAL (t = 0 years)1.431.411.441.411.43
 (1.39 to 1.47)*(1.37 to 1.46)(1.39 to 1.47)(1.36 to 1.48)(1.37 to 1.47)
PAL (t = 0.25 years)1.411.381.411.371.39
 (1.34 to 1.46)(1.32 to 1.45)(1.33 to 1.46)(1.30 to 1.46)(1.32 to 1.46)
PAL (t = 0.50 years)1.371.331.381.341.35
 (1.28 to 1.45)(1.25 to 1.43)(1.28 to 1.45)(1.24 to 1.45)(1.26 to 1.45)
PAL (t = 1.0 years)1.301.251.331.271.28
 (1.19 to 1.42)(1.15 to 1.41)(1.17 to 1.43)(1.13 to 1.43)(1.16 to 1.42)

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

We modified a model developed in normal adults (2) to predict the energy imbalance associated with weight gain in children and adolescents based on empirical EE and body composition data and human energetics (17). In the pediatric model, the total energy cost of weight gain is equal to the sum of energy storage, EE associated with increased body mass, conversion energy, and DIEE. The pediatric model is applied to predict the obligatory increase in EI or, conversely, decrease in EE required to produce weight gain in children and adolescents. Relative to the adult model (2), two modifications were made. The specific basal EE for FFM, kff, and the fraction of fat in added tissue, fr, depend on sex and Tanner stage group.

In the pediatric model, the total energy cost of weight gain includes the ΔEE associated with increasing ΔBM, which is computed as a multiple of BMR, estimated from FFM and FM using basal EE coefficients, kff and kf. Our finding that the coefficient for FFM (kff) decreased significantly with Tanner stage is consistent with dynamic changes in the composition and metabolic activity of FFM that occur as children mature. In contrast, basal EE per kilogram FM (kf) was similar to values for adults, as expected from the minor, but invariable, contribution of adipose tissue to basal metabolism. The decline in BMR relative to weight or FFM seen during childhood is caused by the slower growth of organs with high metabolic rates (i.e., brain, liver, heart, and kidney) and the steady increase in less metabolically active tissues (i.e., muscle, bone, and adipose tissue) (19), as well as the probable decrease in the metabolic rate of specific organs and tissues (20)(21).

The pediatric model also requires an estimate of energy storage (ΔC) based on the fractional composition of the weight gain. We observed differential changes in fat fraction in new tissue (fr) in boys and girls as they progressed through puberty because of the pronounced sexual dimorphism in FFM and FM deposition (22). In boys, the rapid rise in FFM and fall in the percent FM are caused largely by the rise in serum testosterone. In girls, the increase in FM is attributed to the rise in serum estradiol. Young organisms possess the ability to lay down significant amounts of FFM as they gain weight in response to surfeit energy, whereas adults deposit more fat. In the adult model (2), constant fat fraction values, fr = 0.67 and fr = 0.76, were used for men and women, respectively. Forbes (22) estimated that the composition of weight gain induced by overfeeding in adults was ∼38% FFM and 62% FM, and the energy cost of weight gain averaged 8 kcal/g, ignoring ΔEE and DIEE. Our estimated total energy cost of weight gain (14.5, 15.8, and 17.1 kcal/g at PAL = 1.5, 1.75, and 2.0, respectively) is higher because it includes ΔEE and DIEE. For comparison purposes, if ΔEE and DIEE are ignored, the average cost of weight gain is 5.9 kcal/g, with considerable variation caused by sexual maturation. In boys, the values are 6.3, 4.7, 3.0, 5.5, and 6.4 kcal/g, and in girls, they are 6.0, 6.0, 6.7, 7.4, and 8.1 kcal/g at Tanner stages 1 to 5, respectively.

This model was applied to this cohort of non-overweight and overweight Hispanic children and adolescents in whom weight gain varied tremendously from a minimum of 1.0 kg/yr to a maximum of 22.5 kg/yr. Median (10th–90th percentile) weight gain was equal to 6.1 kg/yr (2.4 to 11.4 kg/yr), or 13.3% (4.4% to 24.6%) increase in body mass. The excessive weight gains in overweight subjects, further exacerbating their obesity, are notable. Naturally, it follows that the total energy cost of weight gain is greater in overweight subjects, but it is also higher in boys and younger, less mature children.

In the pediatric model, energy stored (ΔC) and conversion energy (CE) are directly proportional to weight gain, whereas the increment in EE (ΔEE) is a multiplicative function of PAL and ΔBM. Consequently, the relative contributions of ΔC (0.24 to 0.36), CE (0.08 to 0.13), ΔEE (0.40 to 0.57), and DIEE (0.1 EI by definition) to the total energy cost of weight gain vary with PAL. Former estimations of the energy cost of growth ignored the substantial contribution of ΔEE caused by increasing BM and the lesser DIEE requirement (3)(4)(5)(6). The median total energy cost of weight gain computed at midyear (i.e., 244, 267, and 290 kcal/d) does not reveal the substantial range (10th–90th percentile) of values for individuals (93 to 448, 101 to 485, and 110 to 527 kcal/d for PAL = 1.5, 1.75, and 2.0, respectively).

The substantial contribution of ΔEE because of increasing BM was recognized by Swinburn et al. (7), who estimated the effects of energy imbalance on changes in weight in children using a model derived from the relationship between TEE, measured by doubly labeled water, and body weight. In our model, TEE was estimated factorially from CE, DIEE, and a multiple of BMR. Basic assumptions underlying Swinburn et al.'s prediction equation included steady-state conditions (i.e., TEE = energy intake = energy flux) and negligible energy cost of growth. The coefficient in their regression equation was derived statistically from their dataset, which possibly limits its applicability to other populations. Their conclusion, however, regarding the probable changes in EI required for a given weight gain is consistent with ours.

Our computations have important implications for estimated energy requirements of children and adolescents during normal and excessive growth. The total EIs required to support the observed rates of weight gain are substantially higher than estimated energy requirements that do not integrate energy needs over a time interval and, thus, ignore the energy required to support the increasing BM (23)(24). For modeling purposes, computations are performed at PAL = 1.5, 1.75, or 2.0. PAL has been shown to be a valid index of TEE adjusted for BMR (25). Based on available doubly labeled water studies (23), most U.S. children and adolescents probably fall into the low active (PAL = 1.5) to active (PAL = 1.75) categories of physical activity. The obligatory total energy intakes at PAL = 1.5 and 1.75 are substantially higher than mean energy intakes reported in food surveys, such as the U.S. Continuing Survey of Food Intakes by Individuals (23), which substantiates the likely underestimation by existing diet assessment methodology (26).

Alternatively, weight gain can result from a progressive decline in physical activity. The mandatory fall in PAL is computed at 0, 0.25, 0.50, and 1.0 year to show the magnitude of change required to account for the observed rates of weight gain in our cohort. Over the 1-year interval, PAL gradually drops an average of 0.22 units; again, the central tendency does not reflect individual variation (0.08 to 0.34 units). For the mean age and weight of the children in the VIVA LA FAMILIA Study, this would translate into ∼60 min/d (18 to 105 min/d) of walking at 2.5 mph (0.07 kcal/kg/min).

The development of childhood obesity most likely occurs from a combination of surfeit of EI and decline in physical activity; however, the plasticity of dietary intake is greater than that of physical activity. Given the mandatory physical activities required for daily living, weight gain in sedentary children and adolescents whose PALs are at the physiological minimum is attributable to excess dietary EI.

This model predicted the total energy cost of weight gain based on energy storage, energetic efficiency of tissue synthesis, DIEE, and EE to support the increased BM. The total energy cost of weight gain is substantially higher than estimates that do not integrate energy needs over time and, thus, ignore the energy required to support the increased BM. The obligatory total energy intake or decline in physical activity required for weight gain is also substantially greater than estimated energy requirements for the development of childhood obesity. Halting the progression of childhood obesity, as observed in this cohort of Hispanic children and adolescents, will require a sizable decrease in EI and/or reciprocal increase in physical activity. Ideally, the development of obesity should be prevented by blocking the positive energy balance that initially leads to excessive growth in children.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

This project was funded with federal funds from NIH Grant R01 DK59264 and from the United States Department of Agriculture–Agricultural Research Service under Cooperative Agreement 58-6250-51000-037.

Footnotes
  • 1

    Nonstandard abbreviations: EE, energy expenditure; TEE, total EE; BMR, basal metabolic rate; FM, fat mass; FFM, fat-free mass; fr, fat fraction in new tissue; EI, energy intake; Vo2, oxygen consumption; Vco2, carbon dioxide production; kf, basal EE per kilogram FM; kff, basal EE per kilogram FFM; PAL, physical activity level; CE, conversion energy; DIEE, diet-induced EE; ef, efficiency in the conversion of energy to FM; eff, efficiency in the conversion of energy to FFM; BM, body mass; cff, energy stored per kilogram of FFM; cf, energy stored per kilogram of FM; C, combustible energy in BM.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Research Methods and Procedures
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
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