Short and Long-Term Energy Intake Patterns and Their Implications for 2 Human Body Weight Regulation

PHB-10312; No of Pages 6 Physiology & Behavior xxx (2014) xxx–xxx

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Physiology & Behavior

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1 Short and long-term energy intake patterns and their implications for 2 human body weight regulation

3Q1 Carson C. Chow, Kevin D. Hall ⁎

4Q2 Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, MD, United States 5

6 HIGHLIGHTS 7 8 • Body weight is relatively stable despite large daily variations in food intake. 9 • Over the years, millions of kilocalories are consumed but only thousands are stored. 10 • Mathematical models show that body weight regulation may not require precise control of day-to-day food intake. 11 • We describe promising new methods to monitor diet adherence and control body weight. 12 13

15 article info abstract 14 16 Article history: Adults consume millions of kilocalories over the course of a few years, but the typical weight gain amounts to 28 17 Received 31 December 2013 only a few thousand kilocalories of stored energy. Furthermore, food intake is highly variable from day to day 29 18 Received in revised form 17 February 2014 and yet body weight is remarkably stable. These facts have been used as evidence to support the hypothesis 30 19 Accepted 18 February 2014 that human body weight is regulated by active control of food intake operating on both short and long time 31 20 Available online xxxx scales. Here, we demonstrate that active control of human food intake on short time scales is not required for 32 body weight stability and that the current evidence for long term control of food intake is equivocal. To provide 33 21 Keywords: 34 22 Energy balance more data on this issue, we emphasize the urgent need for developing new methods for accurately measuring 23 Food intake energy intake changes over long time scales. We propose that repeated body weight measurements can be 35 24 Energy intake used along with mathematical modeling to calculate long-term changes in energy intake and thereby quantify 36 25 Body weight regulation adherence to a diet intervention and provide dynamic feedback to individuals that seek to control their body 37 26 Feedback control weight. 38 27 39 Mathematical model © 2014 Published by Elsevier Inc. 404143 42

44 1. Introduction human energy balance is many months and that body weight is remark- 57 ably stable despite large random daily ﬂuctuations in food intake. How- 58 45 Humans consume food episodically in the form of meals and snacks. ever, relatively small persistent changes in energy intake can have a 59 46 In contrast, a continuous supply of energy is required to maintain life substantial effect on body weight over long time scales, although not 60 47 and perform physical work. Therefore, even weight-stable humans are as large as was previously believed. We show how the sensitivity of 61 48 practically always in a state of energy imbalance. When we discuss body weight to long-term changes in energy intake can be harnessed 62 49 human body weight regulation as a problem of energy balance [1], to provide accurate estimates of changes in free-living energy intake 63 50 there is an implicit assumption of time averaging. What is the relevant using repeated body weight measurements. Furthermore, such 64 51 time scale over which energy is balanced in weight stable people? methods allow for monitoring adherence to a lifestyle intervention 65 52 This basic question has been neglected despite its fundamental role in and the possibility of dynamic model-based feedback control of body 66 53 understanding humanUNCORRECTED body weight regulation. weight. PROOF 67 54 Here, we explore the question of how short and long-term patterns 55 of energy intake affect body weight using mathematical modeling of 2. Short-term energy intake ﬂuctuations have little effect on 68 56 human metabolism. We demonstrate that the relevant time scale of body weight 69

In his classic 1927 metabolism textbook, Eugene Dubois states that 70 ⁎ Corresponding author at: National Institute of Diabetes & Digestive & Kidney Diseases, “there is no stranger phenomenon than the maintenance of a constant 71 Q3 12A South Drive, Room 4007, Bethesda, MD 20892, United States. Tel.: +1 301 402 8248; 72 fax: +1 301 402 0535. body weight under marked variation in bodily activity and food con- E-mail address: [email protected] (K.D. Hall). sumption” [2]. For example, free-living energy intake is known to vary 73

Please cite this article as: Chow CC, Hall KD, Short and long-term energy intake patterns and their implications for human body weight regulation, Physiol Behav (2014), http://dx.doi.org/10.1016/j.physbeh.2014.02.044 2 C.C. Chow, K.D. Hall / Physiology & Behavior xxx (2014) xxx–xxx

74 from day to day by 20–30% while body weight fluctuates relatively little standard deviation in the body weight is reduced by a factor proportion- 107 75 [3]. al to the square root of the averaging time in comparison to the standard 108 76 Mathematical models of human energy balance and body weight dy- deviation of the energy intake. Note that if the energy intake time course 109 77 namics have demonstrated that small body weight fluctuations are ex- exhibits significant autocorrelations, the fluctuations of body weight 110 78 pected even with relatively large random day-to-day variations of will become more prominent. 111 79 energy intake [4–7]. For example, the gray curve in Fig. 1A illustrates 80 the large fluctuations in energy intake of a subject who participated in 3. Is human energy balance actively regulated through control of 112 81 the Beltsville one year dietary intake study [8]. The black curve in food intake? 113 82 Fig. 1A illustrates the estimated energy expenditure in this subject 83 using a computational model of human macronutrient metabolism Weight stability despite large food intake fluctuations might be 114 84 and body composition dynamics [9]. Despite repeated daily energy im- misinterpreted to imply the existence of a highly sensitive feedback 115 85 balances amounting to several hundred kilocalories, Fig. 1B shows that control system whereby each day's food intake is adjusted to compen- 116 86 the measured and simulated body weight fluctuations were small. sate for previous energy imbalances. However, mathematical models 117 87 In Appendix A, we use a simplified mathematical model of human demonstrate that active control of food intake is not necessary to ex- 118 88 body weight dynamics to show that the standard deviation of the plain the stability of body weight in the face of large, uncorrelated, 119 89 body weight fluctuations is a decreasing function of a parameter ε day-to-day energy intake fluctuations. Rather, the long term average 120 90 representing how energy expenditure varies with body weight. Greater energy intake will be stable if fluctuations are uncorrelated such that in- 121 91 body weight fluctuations are expected when the energy expenditure take on one day is not significantly influenced by the intake on the day 122 92 versus body weight curve is shallower. We previously estimated that before. In other words, body weight regulation does not require active 123 93 the average adult has ε ≈ 22 kcal/kg/day [10] and we show in control of food intake operating on a short time scale. 124 94 Appendix A that weight variations on the order of 1 kg correspond to Another argument for active control of food intake emphasizes the 125 95 random, uncorrelated, daily energy intake variations on the order of long-term stability of body weight in comparison to the cumulative en- 126 96 630 kcal/day. Even for a conceivably low value of ε = 10 kcal/kg/day ergy consumed and was articulated by eminent obesity researcher 127 97 for an extremely sedentary person, day-to-day food intake variations Jeffery Friedman: “The average human consumes one million or more 128 98 of ~400 kcal/day are required to result in body weight fluctuations of calories per year, yet weight changes very little in most people. These 129 99 1 kg. Therefore, body weight is remarkably stable in the face of random, facts lead to the conclusion that energy balance is regulated with a pre- 130 100 uncorrelated fluctuations in energy intake. cision of greater than 99.5%” [11]. This example compares the energy 131 101 The reason why body weight fluctuations are small in comparison to content of typical yearly weight gain (about 0.5 kg or 4000 kcal) with 132 102 variations in energy intake and physical activity is that the slope of the the cumulative energy consumed in a year (about 1 million kcal). Un- 133 103 relationship between energy expenditure and body weight causes fortunately, this calculation ignores the dynamic adaptations of energy 134 104 human weight change to operate on a very slow characteristic time expenditure as body weight is gained that act to counter a persistent in- 135 105 scale. Therefore, the day-to-day fluctuations in food intake are effective- crement in energy intake [12]. As has been previously demonstrated 136 106 ly averaged over a long time. By the law of large numbers, the expected [13], without properly accounting for energy expenditure changes, 137 very small persistent increases in energy intake have been erroneously 138 A calculated to generate unrealistically huge weight gains over extended 139 4000 time periods. Since such enormous weight gain clearly does not typical- 140 3500 ly occur, this may be mistaken as evidence in support of active control of 141 142 3000 human energy intake. When correctly accounting for energy expenditure adaptations, 143 2500 what is the expected long-term weight gain for a persistent change in 144 2000 energy intake? For a person maintaining their average body weight, 145 1500 the long-term mean energy intake equals the long-term mean energy 146 1000 expenditure which is proportional to the body weight. Hence, long- 147 Intake Data Energy Rate (kcal/d) 500 term changes in body weight are related to persistent changes in energy 148 Expenditure Model Δ εΔ 149 0 intake by the relation I = W and the new equilibrium weight takes 0 4 8 12 16 20 24 28 32 36 40 44 48 52 several years to be achieved [12]. Hence, to maintain weight within 1 kg 150 Time (weeks) over several years requires that the long-term average energy intake 151 must be accurate to within about ε = 22 kcal/day. 152 B Active control of food intake may be required to limit the long-term 153 100 drift in energy intake — especially in the face of a dramatic change in the 154 food environment. Is there evidence for such active control of long-term 155 80 food intake in humans? A decade-long natural experiment provides 156 equivocal evidence. Since the 1970s, U.S. per capita food availability in- 157 60 UNCORRECTEDcreased by roughly PROOF 750 kcal per day whereas average adult increased 158 their energy intake by only about 250 kcal/day over this time period 159 40 [10]. In other words, the dramatic increase in availability and marketing 160 of highly palatable, convenient, inexpensive, and energy-dense foods 161 Body Weight (kg) 20 Data Model may have been actively resisted since only about one third of the in- 162 0 creased food available was actually eaten. Thus, these data might be 163 0 4 8 12 16 20 24 28 32 36 40 44 48 52 interpreted as evidence that there is active control of human food in- 164 Time (weeks) take. However, it is unclear exactly how much of an increase in average 165 energy intake would have been expected if there was no active control. 166 Fig. 1. Large daily fluctuations of energy intake and energy balance lead to little variation of Following periods of experimental overfeeding in humans, ad libitum 167 body weight. (A) Daily energy intake data and computer simulated energy expenditure of energy intake generally returns to baseline without an appreciable un- 168 a participant in the Beltsville one year dietary intake study [8]. (B) Weekly body weight 169 data and computational model simulations illustrating the relative stability of body dershoot as might be expected if food intake was actively controlled weight. [14–17]. However, a substantial degree of hyperphagia was observed 170

Please cite this article as: Chow CC, Hall KD, Short and long-term energy intake patterns and their implications for human body weight regulation, Physiol Behav (2014), http://dx.doi.org/10.1016/j.physbeh.2014.02.044 C.C. Chow, K.D. Hall / Physiology & Behavior xxx (2014) xxx–xxx 3

171 following the prolonged period semi-starvation in the Minnesota exper- inaccurate [21,22]. New technologies are currently being developed to 200 172 iment [18] which may indicate that food intake is actively controlled. improve the accuracy of food intake measurements. For example, 201 173 Another example that may provide support for the long-term active con- much progress has been achieved developing remote food photography 202 174 trol of human food intake is that energy intake has been estimated to re- [23,24] as well as devices that count bites [25] or measure chewing and 203 175 turn to baseline shortly after instituting a diet intervention resulting in swallowing [26]. However, these technologies remain somewhat bur- 204 176 weight loss [9,12] as illustrated in the computational model simulations densome for subjects to maintain over the long time periods that are re- 205 177 depicted in Fig. 2 where a 100 kg individual was prescribed a reduced quired to investigate the role of energy intake changes in human body 206 178 calorie diet of 750 kcal/day that was predicted to lead to weight loss fall- weight regulation. An alternative method involves repeated measure- 207 179 ing within the green curves over the subsequent 2 years. This example ments of energy expenditure using the doubly labeled water method 208 180 shown in Fig. 2A simulates the ubiquitous weight loss plateau that typi- along with repeated body composition assessments to measure changes 209 181 cally occurs after 6–8 months and the subsequent slow weight regain in body energy stores [27]. While this method is theoretically sound and 210 182 [19]. Fig. 2B illustrates the corresponding energy intake changes (gray provides accurate measurements of human energy intake over extend- 211 183 curve) and indicates that the weight loss plateau occurred as a result of ed time periods, it is prohibitively expensive and involves specialized 212 184 waning adherence to the prescribed caloric restriction. The red curve in training and equipment. 213 185 Fig. 2B is the 28 day moving average energy intake change showing It has recently been proposed that validated mathematical models of 214 186 that at the time of maximum weight loss after 8 months, this simulated human body weight dynamics can be used to estimate energy intake 215 187 individual had an average caloric restriction of only about 250 kcal/day changes using repeated body weight measurements [9,28,29]. These 216 188 and the average caloric restriction was nil by 10 months. This response simple and inexpensive methods for measuring energy intake changes 217 189 might be interpreted as the result of active control of long-term food in- exploit the fact that long-term body weight change is a sensitive predic- 218 190 take despite intentional caloric restriction. However, it is also possible tor of small persistent changes in energy intake. For example, using only 219 191 that food intake is driven primarily by habits that are not subject to ac- the body weight data from Fig. 2A, the data points in Fig. 2Barethecal- 220 192 tive homeostatic control. More data on the long-term response of food culated average change in energy intake and the blue curves represent 221 193 intake to environmental perturbations and weight loss interventions the 95% conﬁdence interval [28]. Thus, repeated measurements of 222 194 are clearly needed. Unfortunately, the largest impediment to collecting body weight can be translated into the average change in energy intake 223 195 such data is the difﬁculty of obtaining accurate and precise measure- over extended time periods. Concurrent measurement of physical activ- 224 196 ments of human food intake over extended time periods [20]. ity changes (e.g., using accelerometery and/or heart rate monitoring) 225 can also be incorporated in the mathematical model to account for the 226 197 4. Measuring energy intake changes over long time scales separate contributions of diet and exercise on body weight change. 227

198 Self-reported measurements of human energy intake (e.g., 24 hour 5. Adherence monitoring and model-based feedback control of 228 199 recall, food frequency questionnaire, and diet records) are notoriously body weight 229

A Given the typically large day to day energy intake ﬂuctuations and 230 100 the difﬁculty with accurately self-tracking energy intake, how would 231 232 95 an individual know that they are adhering to a target level of caloric restriction during a weight loss program? As illustrated in Fig. 2B, repeat- 233 90 ed body weight measurements can be used to inexpensively estimate 234 85 average changes in energy intake in near real-time that can be com- 235 pared to the prescribed diet to monitor diet adherence. In this example, 236 80 loss of adherence to the prescribed 750 kcal/day diet restriction could 237

Body Weight (kg) 75 have been recognized well before the weight loss plateau. 238 Fig. 3 illustrates a schematic of how adherence monitoring using re- 239 70 peated body weight measurements might be used to adjust the weight 240 0 3 6 9 12 15 18 21 24 loss intervention parameters via model-based feedback control to 241 Time (months) achieve a desired weight loss target [30]. At the outset of the interven- 242 B tion, a personalized mathematical model is generated based on baseline 243 1000 demographics and anthropometrics as well as any direct physiological 244 500 measurements such as resting energy expenditure, body composition, 245 and physical activity level. Such a personalized mathematical model 246 0 can be used to calculate the diet and physical activity changes required 247 -500 to achieve and maintain a specified weight loss target [12]. After the 248 weight management intervention is specified and initiated, monitoring 249 -1000 body weight (and possibly physical activity) for several weeks can be 250 -1500 used to calculate actual change in diet and physical activity. This infor- 251 Energy Intake (kcal/d) UNCORRECTED PROOF Δ mation can be used to update the mathematical model parameters 252 -2000 and generate a prediction of the future body weight trajectory given 253 0 3 6 9 12 15 18 21 24 the calculated level of adherence to the prescribed intervention. The 254 Time (months) body weight goal can then be modified and/or the intervention param- 255 eters can be adjusted to achieve the weight goal. Thus, repeated body 256 Fig. 2. Simulated weight loss plateau and regain as a result of loss of diet adherence. (A) A 257 prescribed 750 kcal/day reduction in baseline energy intake was predicted to result in a weight measurements along with mathematical model simulations re- body weight trajectory falling within the green curves. However, weight loss typically pla- sult in an iterative adjustment of the body weight goal and prescribed 258 teaus after 6–8 months and is often followed by slow regain. (B) The gray curve shows the intervention [30]. 259 simulated daily energy intake changes underlying the body weight trajectory. The red Fig. 4 illustrates a hypothetical example where such a model-based 260 curve is the 28 day moving average and the filled black circles and blue curves are the es- feedback control intervention was initiated in the simulated individual 261 timated average energy intake and its 95% confidence interval calculated using only the 262 body weight data. (For interpretation of the references to color in this figure legend, the shown in Fig. 2 beginning at 6 months (arrow). Practical implementa- reader is referred to the web version of this article.) tion of such a model-based feedback control methodology in real 263

Please cite this article as: Chow CC, Hall KD, Short and long-term energy intake patterns and their implications for human body weight regulation, Physiol Behav (2014), http://dx.doi.org/10.1016/j.physbeh.2014.02.044 4 C.C. Chow, K.D. Hall / Physiology & Behavior xxx (2014) xxx–xxx

Baseline 6. Conclusions 271 Demographics & Anthropometrics Mathematical modeling of human metabolism and body weight dy- 272 namics suggests that the large day to day variations in energy intake are 273 irrelevant for body weight regulation. Rather, persistent changes in en- 274 Prescribed Diet & Mathematical Model Predicted ergy intake can lead to substantial weight changes over long time scales. 275 Physical Activity Body Weight of Human Metabolism Long-term weight gain resulting from a persistent increase in energy in- 276 take is not as large as previously supposed and body weight eventually 277 + plateaus due to increased energy expenditure and the reestablishment 278 Intervention Σ of long term energy balance. Nevertheless, relatively small persistent 279 Feedback changes in energy intake will lead to an appreciable increase in the 280 - Control steady state body weight. 281 More data are required to better understand whether human food 282 Monitor Weight 283 Calculate intake is under active control or is primarily habitual and follows the & Activity Adherence changing environment. Unfortunately, it is extraordinarily difﬁcult to 284 (e.g., accelerometer) directly measure human food intake over extended time periods with 285 accuracy and precision. New devices and technologies are being devel- 286 Fig. 3. Schematic of a method for personalized model-based feedback control of body oped to address these issues [23–26]. Mathematical modeling currently 287 weight. Using individual anthropometric and demographic data, a personalized mathe- 288 matical model of metabolism is created to plan a lifestyle intervention to achieve a goal provides the most inexpensive and simplest way to translate repeated body weight in a speciﬁed time frame. By monitoring body weight and physical activity re- measures of body weight into accurate estimates of energy intake 289 peatedly, adherence to the intervention can be calculated and used iteratively to provide changes [28]. These methods will be useful for calculating how energy 290 quantitative feedback regarding revised body weight predictions or changes in the pre- intake responds following experimental perturbations as well as natu- 291 scribed intervention required to achieve the body weight goal. rally over the course of time. Furthermore, these new methods have 292 practical implications for weight management interventions since 293 they can be used to monitor adherence to a prescribed lifestyle inter- 294 264 patients could be facilitated using mHealth technologies that allow for vention and provide quantitative dynamic feedback on how to achieve 295 265 frequent remote monitoring of body weight and physical activity weight goals [30]. 296 266 along with electronic delivery of feedback messages describing adher- 267 ence metrics and adjustments to the prescribed intervention. Future re- Acknowledgments 297 268 search is required to investigate the optimal timing of feedback 269 messages and goal adjustments as well as the overall effectiveness of This research was supported by the Intramural Research Program of 298 270 such a model-based feedback control method of weight management. the National Institutes of Health, National Institute of Diabetes & Diges- 299 tive & Kidney Diseases. 300

Appendix A 301 A 302 100 A.1. The energy balance equation 303

95 We begin our analysis with the energy balance equation where the 304 90 rate of change in stored body energy is given by the difference between 305 the metabolizable energy intake rate I and the energy expenditure rate. 306 85 We previously developed and validated a mathematical model of 307 80 human energy expenditure that included resting metabolic rate, ther- 308 309

Body Weight (kg) mic effect of feeding, tissue deposition and turnover costs, and adaptive 75 changes of energy expenditure with over and underfeeding [10,31,32]. 310 70 Using our model of energy expenditure, we demonstrated that the ener- 311 0 3 6 9 1215182124 gy balance equation is [10]: 312 Time (months)

B 1000 η þ ρ þ αη þ αρ γ þ αγ F F L L dW ¼ − 1 F L þ δ − ðÞ−β ðÞþ α I ðÞ−β ðÞþ α W b 500 1 1 dt 1 1

-500 UNCORRECTED PROOF where W is the body weight, I is the energy intake rate, γL and γF are the 314 -1000 regression coefﬁcients relating resting metabolic rate versus lean mass (L) and fat mass (F), respectively [33]. Physical activity energy expendi- 315 -1500 Energy Intake (kcal/d) ture is proportional to body weight for most activities [34] and δ repre- 316 Δ -2000 sents the level of physical activity. The parameter β accounts for thermic 317 0 3 6 9 1215182124 effect of feeding as well as adaptation of energy expenditure during a 318 Time (months) diet perturbation, and ηF and ηL account for the biochemical cost of tis- 319 sue turnover and deposition [35] assuming that the change of L is pri- 320 Fig. 4. Hypothetical implementation of model-based feedback control of body weight. marily accounted for by body protein and its associated water [36]. 321 (A) After weight loss plateaued at 6 months, the control method was implemented to pro- The parameter α represents the relationship between changes of lean 322 vide feedback on the loss of diet adherence and the revised diet prescription required to α ≡ ﬁ 323 achieve the weight loss goal. (B) Continued monitoring of body weight allows for and fat mass: dL/dF [37] and b is a constant that de nes the steady sustained monitoring of adherence to the prescribed intervention. state body weight. 324

Please cite this article as: Chow CC, Hall KD, Short and long-term energy intake patterns and their implications for human body weight regulation, Physiol Behav (2014), http://dx.doi.org/10.1016/j.physbeh.2014.02.044 C.C. Chow, K.D. Hall / Physiology & Behavior xxx (2014) xxx–xxx 5

325 Assuming that α is approximately constant for modest weight chang- where ζ is a stochastic white noise source. The standard deviation of the 366 326 es [38], we simplify the above equation by introducing parameters ρ and ε body weight can then be calculated to yield: 327 to rewrite the above equation as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ! ! u 2 2 2 2 t σ σ ðÞI−b cσ σ ðÞI−b σ σ ¼ I þ a − I a = 1− a : dW w 2ερ ε3ρ3 ε2ρ2 ε3ρ2 ρ ¼ I−εW−b: ð1Þ 2 2 2 dt 368 Hence, increased negative correlations between activity and energy 329 intake will increase body weight fluctuations whereas positive correla- 369 For the average sedentary adult in the U.S., we have previously tions will decrease fluctuations. This is expected because energy intake 370 330 estimated that ρ = 9100 kcal/kg and ε =22kcal/kg/day[10] and and physical activity have opposing effects on energy balance. 371 331 b ~ 600 kcal/day. This simple linear differential equation has an ex- The third moment of the body weight distribution is: 372 332 ponential as its solution and the time constant τ = ρ/ε defines the 333 characteristic time scale of weight change. For typical values of the "# 3σ 4 σ 2σ 2 σ 3σ 2σ 2σ 2 2 σ σ 3 334 parameters, τ ~ 410 days indicating that body weight changes are !1 !I a þ I I a − c I a þ 2c I a − 3I c I a : 2 2 ε5 3 2 3 4 335 very slow. σ σ ε ε ε ε 1− a 1− a ε 2ε 336 A.2. Fluctuations of body weight with variable energy intake 374 Hence, there is positive skewness if physical activity fluctuations are 337 Our goal is to calculate the standard deviation of the body weight present. However, the extent of the fluctuations can be reduced or pos- 375 338 as a function of the standard deviation of the food intake. Consider sibly reversed if the correlations are negative between physical activity 376 339 the energy intake rate in Eq. (1) to be stochastic and written in the and intake. 377 340 form: I ¼ I þ ξ, where I is a mean intake rate and ξ is a normallyp distrib-ffiffiffiffiffi 341 uted fluctuation with zero mean and standard deviation σ = dt. The I References 378 342 convention of stochastic calculus is to scale the standardpffiffiffiffiffi deviation of 379 343 the fluctuation by the square root of the time step dt so σI has units [1] Hill JO. Understanding and addressing the epidemic of obesity: an energy balance – 380 344 of kcal/(square root day). This scaling does not affect the result. Using perspective. Endocr Rev 2006;27:750 61. [2] Du. Bios EF. Basal metabolism in health and disease. 2nd ed. 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Please cite this article as: Chow CC, Hall KD, Short and long-term energy intake patterns and their implications for human body weight regulation, Physiol Behav (2014), http://dx.doi.org/10.1016/j.physbeh.2014.02.044 6 C.C. Chow, K.D. Hall / Physiology & Behavior xxx (2014) xxx–xxx

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