BYU ScholarsArchive. Brigham Young University. Saori Sakita Brigham Young University - Provo. All Theses and Dissertations

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1 Brigham Young University BYU ScholarsArchive All Theses and Dissertations Development and Use of a Physiologically Based Mathematical Model Describing the Relationships and Contributions of Macronutrients to Weight and Body Composition Changes Saori Sakita Brigham Young University - Provo Follow this and additional works at: Part of the Food Science Commons, and the Nutrition Commons BYU ScholarsArchive Citation Sakita, Saori, "Development and Use of a Physiologically Based Mathematical Model Describing the Relationships and Contributions of Macronutrients to Weight and Body Composition Changes" (00). All Theses and Dissertations This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu, ellen_amatangelo@byu.edu.

2 Development and Use of a Physiologically-based Mathematical Model Describing the Relationships and Contributions of Macronutrients to Weight and Body Composition Changes Saori Sakita A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Nutritional Science Robert T. Davidson, Chair N. Paul Johnston Tory L. Parker Department of Nutrition, Dietetics, and Food Science Brigham Young University August 00 Copyright 00 Saori Sakita All Rights Reserved

3 ABSTRACT Development and Use of a Physiologically-based Mathematical Model Describing the Relationships and Contributions of Macronutrients to Weight and Body Composition Changes Saori Sakita Department of Nutrition, Dietetics, and Food Science Master of Nutritional Science The effect of the dietary macronutrient composition on weight loss has been a controversial issue for decades. During that time, a high-protein, high-fat, and lowcarbohydrate diet has been one of the more popular weight loss diets with the public. We hypothesized that a computer simulation model using STELLA software could help to better understanding the effect of the dietary macronutrient composition on weight loss. We calculated daily total oxidation instead of total energy expenditure as others have done based on the facts that carbohydrate, fat, and protein intake influence carbohydrate, fat, and protein oxidation. In order to create a simple and accurate model comparing dietary macronutrient composition effects, we eliminated exercise as a factor and focused on a sedentary population. The model was validated by five sets of published human data. Following model validation, simulations were carried out to compare the traditional highcarbohydrate diet recommended by the American Dietetic Association and two wellknown high-protein diets (Atkins and the Zone diet). The results of computer simulation suggested that the lean tissue retention effect of a high-protein diet, especially with a lower-fat diet, compared with a traditional high carbohydrate diet over 6 months. Keywords: computer model, body weight change, body composition change, dietary macronutrient composition, macronutrient oxidation, high-protein diet

4 ACKNOWLEDGEMENTS I appreciate Dr. Davidson for his amazing generosity, endless patience, and unbelievable positive thinking. Without his trust, I could not have done this research. I also want to thank Dr. Johnston for his friendly support; Dr. Franz for her experienced advice; and Dr. Parker for his flexible help. Thanks to Mrs. Melanie Peine for her friendliness, guidance, and understanding as a mother. I deeply appreciate all of the faculty members I associated with for their acceptance and patience with my international background. Lastly, I really want to express appreciation for my husband who encouraged me to apply to graduate school and daughter who was born in the middle of my graduate study years.

5 TABLE OF CONTENTS Title Page.i Abstract...ii Acknowledgments..iii Table of Contents....iv List of Tables and Figures..... vii BACKGROUND. METHODS..5. Software Model Development Required Initial Model Parameters Calculated Model Parameters a. Initial Body Weight b. Macronutrient Metabolism 8 --c. Energy Intake d. Total Energy Expenditure e. Future Body Composition Note 3. Model Validation Model Application. 5 RESULTS..6. Model Validation Overfeeding 6 iv

6 --a. Comparison to Jebb (993, 996) b. Comparison to Horton (995) Energy Balance a. Comparison to Abbott (995) Underfeeding..8-3-a. Comparison to Jebb (993, 996) b. Comparison to Berlin (96) c. Comparison to van Gemert (000) Model Application. 0 DISCUSSION. Model Validation Individual Evaluation Data < Strengths and Problems > Overfeeding <Validity and Limitations > Energy Balance <Validity and Limitations > Underfeeding <Validity and Limitations > 7-5. Overall <Validity and Limitations > Model Application Summary (Benefits)...3 REFERENCES..33 TABLES AND FIGURES.40 APPENDICES Appendix A. STELLA model for people with BMI<30..4 Appendix B. STELLA model for people with BMI>30..9 v

7 Appendix C. A list of abbreviations vi

8 LISTS OF TABLE AND FIGURES Table -a. Jebb (993) Overfeeding (Subject ) Figure -a. Jebb (993) Overfeeding (Subject ) Table -b. Jebb (993) Overfeeding (Subject 5) Figure -b. Jebb (993) Overfeeding (Subject 5)..46 Table -c. Jebb (993) Overfeeding (Subject 6)...48 Figure -c. Jebb (993) Overfeeding (Subject 6)..50 Table -d. Jebb (993) Overfeeding (Mean, n=3).5 Figure -d. Jebb (993) Overfeeding (Mean, n=3) 54 Table -e. Jebb (996) Overfeeding (Mean, n=3).56 Figure -e. Jebb (996) Overfeeding (Mean, n=3) 57 Table -a. Horton (995) HC Overfeeding (Lean Subject Mean, n=9).58 Figure -a. Horton (995) HC Overfeeding (Lean Subject Mean, n=9)...59 Table -b. Horton (995) HF Overfeeding (Lean Subject Mean, n=9).60 Figure -b. Horton (995) HF Overfeeding (Lean Subject Mean, n=9) 6 Table -c. Horton (995) HC Overfeeding (Obese Subject Mean, n=7)...6 Figure -c. Horton (995) HC Overfeeding (Obese Subject Mean, n=7).63 Table -d. Horton (995) HF Overfeeding (Obese Subject Mean, n=7) Figure -d. Horton (995) HF Overfeeding (Obese Subject Mean, n=7)..65 Table -e. Horton (995) HC Overfeeding (All Subject Mean, n=6)..66 Figure -e. Horton (995) HC Overfeeding (All Subject Mean, n=6) 68 Table -f. Horton (995) HF Overfeeding (All Subject Mean, n=6)..70 Figure -f. Horton (995) HF Overfeeding (All Subject Mean, n=6). 7 vii

9 Table 3-a. Abbott (995) Energy Balance (Male Subject Mean, n=7) 74 Figure 3-a. Abbott (995) Energy Balance (Male Subject Mean, n=7)..75 Table 3-b. Abbott (995) Energy Balance (Female Subject Mean, n=7) 76 Figure 3-b. Abbott (995) Energy Balance (Female Subject Mean, n=7)...77 Table 4-a. Jebb (993) Underfeeding (Subject )..78 Figure 4-a. Jebb (993) Underfeeding (Subject ) 80 Table 4-b. Jebb (993) Underfeeding (Subject 3 ) 8 Figure 4-b. Jebb (993) Underfeeding (Subject 3 )...84 Table 4-c. Jebb (993) Underfeeding (Subject 4).. 86 Figure 4-c. Jebb (993) Underfeeding (Subject 4) 88 Table 4-d. Jebb (993) Underfeeding (Mean, n=3)...90 Figure 4-d. Jebb (993) Underfeeding (Mean, n=3)..9 Table 4-e. Jebb (996) Underfeeding (Mean, n=3)...94 Figure 4-e. Jebb (996) Underfeeding (Mean, n=3)..95 Table 5-a. Berlin (96) Underfeeding (Subject W.T.) Figure 5-a. Berlin (96) Underfeeding (Subject W.T.)...97 Table 5-b. Berlin (96) Underfeeding (Subject E.C.)..98 Figure 5-b. Berlin (96) Underfeeding (Subject E.C.) Table 5-c. Berlin (96) Underfeeding 0-57 Days (Subject A.I.) Figure 5-c. Berlin (96) Underfeeding 0-57 Days (Subject A.I.).. 0 Table 5-d. Berlin (96) Underfeeding Days (Subject A.I.)...0 Figure 5-d. Berlin (96) Underfeeding Days (Subject A.I.)..03 Table 6-a. van Gemert (000) 0-90 Days after Surgery (Mean, n=8). 04 viii

10 Figure 6-a. van Gemert (000) 0-90 Days after Surgery (Mean, n=8)...06 Table 6-b. van Gemert (000) Days after Surgery (Mean, n=8). 08 Figure 6-b. van Gemert (000) Days after Surgery (Mean, n=8)....0 Table 7-a. Application ADA vs. HP diet at Underfeeding (80 days).... Figure 7-a. Application at Underfeeding (80 days)...4 Table 7-b. Application ADA vs. HP diet at Energy Balance (80 days) Figure 7-b. Application at Energy Balance (80 days) 8 Table 7-c. Application ADA vs. HP diet at Overfeeding (80 days)..0 Figure 7-c. Application at Overfeeding (80 days). ix

11 BACKGROUND The effect of dietary macronutrient composition on weight loss has been a controversial issue for decades (Noble and Kushner, 006). Lately, several studies have suggested that a high-protein, low-carbohydrate diet is more effective to lose body weight and fat mass (Labayen et al., 003; Meckling and Sherfey, 007) or other positive effects, such as a positive nitrogen balance, higher satisfaction, and a lean body mass retention effect with/without exercise (Noakes et al., 005; Parker et al., 00; Johnston et al., 004; Layman et al., 003; Layman et al., 005), in healthy individuals compared to a high-carbohydrate diet. Those effects were observed even in long-term interventions up to one year (Gardner et al., 007; Clifton et al., 008). However, there are other studies showing that the macronutrient composition does not have an effect on weight loss, but weight loss only depends on the total calorie intake (Luscombe et al., 00; Luscombe et al., 003; Brinkworth et al., 004). In spite of the fact that the results are inconsistent, a high-protein, low-carbohydrate diet has been one of the popular weight loss diets with the public. Blanck et al. (006) indicates that.5% of Americans have used a high-protein, low-carbohydrate diet, and 3.4% of them were currently using it. Also, the mean weight loss was 8.3 pounds, and more than 90% of users reported some weight-loss with a high-protein, low-carbohydrate diet. In addition, about 40% of men and 30% of women used a high-protein, low-carbohydrate diet for more than months. However, it is unclear if the weight loss is truly induced by macronutrient composition (highprotein in this case) or by other factors. In fact, it is difficult for experimental research to prove the effect because of the many factors to be considered (e.g. variation of high-protein diet, subjects body type, gender, age, disease, etc). "!!

12 One possible way to understand the dietary macronutrient contribution to energy balance and weight change is by using a dynamic computer simulation model. In fact, many investigators have worked to create computer models which reflect human physiology. Several models exist, which estimate body weight change (Antonetii, 973; Kozusko, 00; Christiansen et al., 00) or body composition change (Alpert, 979; Westerterp et al., 995; Novotny and Rumpler, 998; Caloin, 004; Alpert, 005; Christiansen, 005) based on energy balance. Only a few models were created to investigate how the dietary macronutrient composition affects body composition change. Abdel-hamid (003) simulated the effectiveness of a high-carbohydrate diet with moderate and high intensity physical activity on weight loss. However, only the results of the model s simulations were reported; the model algorithms were not published. Therefore, this model is not available for use or validity evaluation. About the same time, Flatt (004) established a twocompartment model that explained the relationship between body fat content under a variety of physiological conditions, including dietary fat intake, physical activity level, glycogen level, etc. His model showed not only that high dietary fat intake but also a high glycogen level was correlated with steady-state body fat contents. He hypothesized that lowered physical activity level and higher availability of snacking in recent society were reducing glycogen depletion between meals. Therefore, he concluded that a high glycogen level might be one of the contributions to the recent obesity prevalence in the United States, even though the dietary fat content of the nation has slightly decreased since 970 s (Willett, 998). However, in this model, he did not include total body weight change. Rather, he focused on body fat percent. Recently, Hall (006) introduced a model, partly physiologically-based, with parameters fitted to match human data. He created this model based on in vivo human data from the famous Minnesota #!!

13 Starvation Studies by Ancel Keyes (950), and considered the human body composition with dietary macronutrient intake changes. The result fits nicely with several other published shortterm studies, and demonstrated validity. However, many equations in this model were based on estimations rather than being based on actual physiological measurements, and mathematical calculations in his model were very complicated to understand and use for non-engineeringtrained biological scientists or the lay public. More recently, Hall (00) introduced another model, similar to his previous one (006). This new model included ketone body metabolism and took into account macronutrient utilization under different situations. However, this new model continued to use estimations. The above models have suggested valuable results about the macronutrient effect on weight change, and took the first steps toward a future complete human body model. However, a major challenge was that a mathematical model could not be easily completed because of the vast number of factors to be considered. It would continuously require improvements. In 007, Ritchie (007) showed that a computer model using STELLA software could reasonably estimate future weight of healthy adults who consistently reported calorie intake. Based on his research, we hypothesized that a computer model could be developed to show the effect of macronutrients on energy balance. Therefore, the purpose of this study was to develop a mathematical model that was based on published physiological data, and describe the relationships and contributions of macronutrients on weight and body composition change. One of the basic principles of modeling is that a model should be as simple as possible. However, at the same time, it should adequately describe what is happening in human bodies. To create such a model, we decided to eliminate the physical activity and energy balance factor because there were not enough data available yet. Rather, we focused on the energy oxidation of $!!

14 dietary macronutrients on the sedentary human body. In order to accomplish this, we did not calculate total energy expenditure as a sum of resting energy expenditure, thermic effect of food, and physical activity. Instead, we calculated daily total oxidation, which was the sum of carbohydrate, fat, and protein oxidations. Some studies suggested that high carbohydrate intake induced carbohydrate oxidation and suppressed fat oxidation (Acheson et al., 98; Sherry et al., 994; Horton et al., 995; Jebb et al., 996). Contrarily, high fat intake did not tend to lead to increased fat oxidation (Horton et al., 995; Schwarz et al., 995). In addition, protein oxidation seems not to be highly related with carbohydrate and fat intake, but with protein intake (Bingham and Cummings, 985; Young et al., 000). Based on this information, we created a physiological-based simple model, which simulates human body weight and composition change affected by differing macronutrient composition and intake, and evaluated it by comparing to published human data. Through this model, we examined the difference between a traditional high-carbohydrate diet and high-protein diet during underfed, energy balanced, and overfed situations. %!!

15 METHODS. Software The STELLA software (isee systems, inc., Lebanon, NH, USA, provides a graphical modeling environment where quantitative amounts of material may be transferred (via Flows ) into or out of reservoirs (called Stocks ). The flow into or out of the stock can be envisioned as a pipeline controlled by a valve which can be opened to start or increase the flow or closed to decrease or stop a flow, resulting in a decrease or increase of material in the stock. The rate of flow is user-defined as to units and timescale and can be as simple as a numerical constant or be a mathematical equation with a value that changes over time. Processes or components that may affect the flow rate can be embedded in Convertors and be connected to the flow rate from which the software forms mathematical rate equations. There are four unique interface levels available in the STELLA software. The top level allows a user interface to be constructed with several selectable parameter-changing input devices and data output options. The model may be set up to run with limited or no access available to the actual model interface levels. The second interface level, the MAP level allows the modeler to graphically design the model by placing stocks, flows, converters and connectors. The third interface level, the Model level, allows the stocks, flows and converters to be populated with parameter values and equations. The fourth interface level, the Equations level shows the mathematical equations and differential equations that the software automatically derives for solving when the model is run.. Model Development We identified a small set of published reports relating macronutrient oxidation to carbohydrate and protein intake (described below). A multi-compartment model was envisioned with one &!!

16 compartment for each of the macronutrients describing dietary intake, oxidation, and conversion to other macronutrient forms and storage entities as appropriate. Other ancillary parameters and calculations were made based as described below. -. Required Initial Model Parameters. Gender. The user enters a numerical value of 0,, or for a male, premenopausal female, or postmenopausal female, respectively. This value is used in an IF-THEN statement to calculate bone mineral mass (described below). Initial Body Weight (Initial BW). The user enters a numerical value in kilograms. This value is used along with initial percent body fat to calculate initial fat and lean body mass, and liver mass. Initial Percent Body Fat. The user enters a numerical value in percentage. This value is used along with initial body weight to calculate initial fat mass and initial lean mass. Energy Intake. The user enters a numerical value in grams of dietary carbohydrate, dietary protein, and dietary fat, respectively. These values are used to calculate carbohydrate, protein and fat levels, and total energy intake. -. Calculated Model Parameters. --a. Initial Body Composition Initial Fat Mass (Initial FM). Initial FM (kg) = Initial BW (kg) * [Initial % body fat / 00]. Initial Lean Body Mass (Initial LBM). Initial LBM (kg) = Initial BW (kg) Initial FM (kg). Bone Mass. Following regression equations are used to calculate bone mass (Ferretti, 998). When gender is male, Bone mass (g) = [ [0.050 * Initial LBM (kg) * 000]] (n = 905, r = 0.887). When gender is premenopausal female, Bone mass (g) = [ [0.053 * Initial LBM (kg) * 000]] (n = 330, r = 0.45). When gender is postmenopausal female, Bone mass (g) = '!!

17 [ [0.043 * Initial LBM (kg) * 000]] (n = 399, r = 0.6). Age limitations are from 3 to 83 years old for male and from to 87 years old for female. Liver Weight. Liver weight (kg) = 0.06 * Initial BW (kg). Liver weight is approximately.6% of total BW (Brown et al., 997). Initial Body Water. Initial body water (kg) = 0.73 * Initial LBM. This equation is based on LBM being 73.% water and FM having essentially no water (Sheng and Huggins, 979). Extracellular Water. Extracellular water (g) = [ [0.464 * Initial body water (kg)]] * 000. This regression equation is calculated from data contained in Ritz (006). Age limit for this equation is from 5 to 63 years old. We hypothesized that extracellular water would not change for the short-term weight change. Therefore, this model does not account for water change, such as edema, during severe starvation (Hall, 006) Initial Intracellular Water. Initial intracellular water (g) = [ [ * Initial body water (kg)]] * 000. This regression equation calculated from data in Ritz (006). Age limit for this equation is also from 5 to 63 years old. Initial Body Cell Mass. Initial body cell mass (g) = [Initial LBM (kg) * 000] Extracellular water (g) Bone mass (g) (Hall, 006). Initial Liver Glycogen. Initial liver glycogen (g) = Liver weight (kg) * 43.7 (g/kg wet liver tissue). Liver glycogen varies from 4.3 to 80. grams glycogen/kg wet liver tissue, mean 43.7 (n = 58, Nilsson 973). We used the mean value, 43.7 g/kg wet liver tissue, for the calculation. Initial Protein. Initial protein (g) = Initial body cell mass * Body cell mass is approximately 8% protein (Albert, 989). Non-Bound Intracellular Water. Non-bound intracellular water (g) = Initial intracellular water (g) [ * Initial protein (g)] [.4 * Initial liver glycogen (g)]. There is a theory that each gram of (!!

18 protein has about grams of water associated with it (MacKay and Bergman 934, McBride et al. 94). Also, several theories estimate that each gram of glycogen has from.4 to 3.8 grams water associated with it (.4 g: Puckett and Wiley, 93;.4 g: Nilsson, 973;.7 g: McBride et al., 94; 3 g: MacKay and Bergman, 93; 3.8 g: Mackay and Bergman, 934). We chose.4 grams as a water weight associated with glycogen storage because that was from the most recent study based on human subjects (n = 58). Initial Intracellular Solids. Initial intracellular solids (g) = Initial body cell mass (g) Initial protein (g) Initial liver glycogen (g) Initial intracellular water (g). This equation is based on equation of Hall, b. Macronutrient Metabolisms Carbohydrate Oxidation (Cox). Two carbohydrate oxidation equations were used in this model based on subject s body mass index (BMI). Cox (g) for BMI>30 = [ [0.035 * [Dietary carbohydrate (g) / Eucaloric CHO (g) * 00]]] * BW (kg). The regression equation is based on data from Schwarz (995). Cox (g) for BMI<30 = [[ * [Dietary carbohydrate (g) / Body weight (kg))] * BW (kg) (Shetty, 994). Fat Oxidation (Fox). Two carbohydrate oxidation equations are used in this model based on subject s BMI. Fox (g) for BMI>30 = [.034 [0.009* Dietary carbohydrate (g) / Eucaloric CHO (g) * 00]] * BW (kg). The egression equation is based on data from Schwarz (995). Fos (g) for BMI<30 = [[ [-0.43] * [Dietary carbohydrate (g) / BW (kg)] * BW (kg). The regression equation is based on data from Shetty (994). Protein Oxidation (Pox). Pox (g) = [ [-0.05] * [Dietary carbohydrate / BW (kg)] * [Dietary protein (g) / BW (kg)]] * BW (kg). The regression equation is based on data from Young (000) and Shetty (994). )!!

19 Max Liver Glycogen. Max liver glycogen (g) = liver weight (kg) * 80. (Nilsson, 973). Glycogen Synthesis. Glycogen synthesis (g) = 0.55 * [Max liver glycogen (g) Liver glycogen (g)]. The equation is based on linear regression slope of 0.55 of remaining glycogen storage capacity versus glycogen synthesis rate (Acheson et al., 988). Glycogenolysis. Glycogenolysis (g) = [.44 [ * Dietary carbohydrate (g) / Body weight (kg)]] * BW (kg). The regression equation is based on data from Selz (003). Gluconeogenesis from Glycerol (Gluconeogenesis F ). Gluconeogenesis F (g) = Fox (g) * Molecular weights of triglyceride, fat free acids, and glycogen are about 860, 37, and 9, respectively (Hall, 006). Therefore, glycerol mass is approximately 0% of triglyceride molecule mass (MTG = 860 g/mol, MFFA = 37 g/mol, MGLY = 9 g/mol, 9/860 = 0.070). As a triglyceride molecule is mobilized for fatty acid oxidation, the released glycerol is converted to glucose in the liver. Gluconeogenesis from Protein (Gluconeogenesis P ). Gluconeogenesis P (g) = * Pox (g). One gram of dietary protein has carbon equivalent of g glucose (van Milgen, 00; Institute of Medicine of the National Academies, 005). Lipogenesis of Glucose. Lipogenesis glucose (g) = Dietary carbohydrate (g) + Gluconeogenesis P (g) + Glycogenolysis (g) + Gluconeogenesis F (g) Cox (g) Glycogen synthesis (g). This equation describes the amount of glucose that is converted to fat. This is not the amount of fat that is produced from the glucose that is given in the next equation. Lipogenesis to Fat. Lipogenesis fat (g) = Lipogenesis glucose (g) *0.357 *.070. One gram of glucose equals about /3 g fat (0.357: table 3 in Schwarz et al., 995) and added 0% for glycerol backbone of triglyceride. Total Oxidation. Total oxidation (kcal) = [Cox (g) * 4.8] + [Fox (g) * 9.44] + Pox (g) * 4.704]. *!!

20 --c. Energy Intake Total Energy Intake (TEI). TEI (kcal/day) = Dietary carbohydrate (kcal) + Dietary protein (kcal) + Dietary fat (kcal). Total energy intake is the sum of dietary macronutrient energy intake. Carbohydrate Energy Percent. Carbohydrate energy % = [Dietary carbohydrate (g) * 4.8 * 00] / TEI. The percent of carbohydrate in the diet is equal to the kcal of carbohydrate in the diet divided by the total energy intake (in kcal) multiplied by 00%. The energy density of carbohydrate is taken to be 4.8 kcal/g (Table 6 in Livesey and Elia, 988). Fat Energy Percent. Fat energy % = [Dietary protein (g) * 9.44 * 00] / TEI. The percent of fat in the diet is equal to the kcal of fat in the diet divided by the total energy intake (in kcal) multiplied by 00%. The energy density of carbohydrate is taken to be 9.44 kcal/g (Table 6 in Livesey and Elia, 988). Protein Energy Percent. Protein energy % = [Dietary protein (g) * * 00] / TEI. The percent of protein in the diet is equal to the kcal of protein in the diet divided by the total energy intake (in kcal) multiplied by 00%. The energy density of carbohydrate is taken to be kcal/g (Table 6 in Livesey and Elia, 988). --d. Total Energy Expenditure (Eucaloric Carbohydrate Calculation) Total Energy Expenditure (TEE). TEE (kcal/day) = [PAL * RMR (kcal)] + TEF (kcal/day). TEE is the total energy expended from physical activity, basal metabolism, and food thermogenesis. In this model the physical activity level (PAL) is a factor increase over resting metabolism and therefore includes resting metabolism. TEE is estimated only for calculating eucaloric CHO intake which is used for carbohydrate and fat oxidation calculation equations. We chose.3 for PAl because this model only simulated for sedentary people. "+!

21 Thermic Effect of Food (TEF). TEF (kcal) = [0.05 * Dietary fat (kcal)] + [05 * Dietary protein (kcal)] + [0.075 * Dietary carbohydrate (kcal)]. TEF, also called diet induced thermogenesis, represents the energy expended for food digestion, transport and storage; Values for TEF range from 0 to 5% of TEI (Miles et al. 993). Body fat has the lowest processing cost of the macronutrients at 0 to 5%. Carbohydrate processing costs are 5 to 0% and protein processing cost is equivalent to 0 to 30% (Institute of Medicine of the National Academies, 005). Therefore, we took the median value for TEF of fat, carbohydrate, and protein;.5, 7.5, and 5%, respectively. Resting Metabolic Rate (RMR). RMR (kcal) = [.5 * LBM (kg)] The regression equation is from Wang et al. (000). Physical Activity Level (PAL). This is a numerical value corresponding to the physical activity levels as listed in the Dietary Reference Intakes manual for Energy, Carbohydrate, etc. (Institute of Medicine of the National Academies, 005): Sedentary =.0.3, low active =.4.5, active =.6.8, very active =.9.5. Model equations for macronutrient oxidations are only based on sedentary people data. Therefore, we decided to use.3 for PAL. This value is used to calculate total energy expenditure (described below). Eucaloric Carbohydrarte Intake (Eucaloric CHO). Eucaloric CHO (g) = [TEE * 0.47] / 4.. Eucaloric CHO level is about 47% of TEI when a person is weight stable (Schwarz, 995). When a person is weight stable (in energy balance) then TEE = TEI so we used TEE in this calculation. --e. Future Body Composition Intracellular Water. Intracellular water (g) = Non-bound intracellular water (g) + [Liver glycogen (g) *.4] + [Protein (g) * ]. Glycogen binds.4 g water per gram, protein binds g water per gram (Nilsson, 973). ""!

22 Body Water. Body water (kg) = [Extracellular water (g) + Intracellular water (g)] / 000. Lean Body Mass (LBM). LBM (kg) = [Body cell mass (g) + Bone mass (g) + Extracellular water (g)] / 000. Fat Mass (FM). FM (kg) = FM (g) / 000. Body Weight (BW). BW (kg) = FM (kg) + LBM (kg). Percent Body Fat. % body fat (%) = FM (kg) / BW (kg) * Notes This model does not show the metabolism change of a human body during a single day. Rather, it shows longer-term expectation of body weight and composition change. This model is created only for healthy adults, who do not require any energy for growth. Therefore, it is not applicable to children or adolescents. The equations used for carbohydrate, fat, and protein oxidations were based predominantly on the results of non-obese healthy males with data from one female. Therefore, the model might apply best to males. More detailed quantitative data needed to determine gender specificity. The gender input parameter is only used for bone mass calculation. We assumed that extracellular water, non-bound intracellular water, intracellular solid (cell mass minus protein, liver glycogen, and intracellular water), and bone mass would not change with short-term weight change. Therefore, this model does not account for edema seen with severe starvation (Hall, 006). 3. Model Validation In order to test the validity of the model, we simulated five published human studies by Jebb (993, 996), Horton (995), Abbott (988), Berlin (96), and van Gemert (000). No model "#!

23 parameters were altered for this validation. The calculation methods of input data of each study were as follow: Jebb et al. (993, 996) measured body weight and composition change, and macronutrient oxidation rate of five healthy men (from 9 to 4 years of age) during over and underfeeding for days (Subject during overfeeding and subject 3 during underfeeding are the same person). They reported macronutrient intake, fecal loss, and macronutrient oxidation as a total amount for the entire experimental period. Therefore, we divided the total by days and used them as an average daily macronutrient intake input. We compared the simulated oxidation rates with the reported oxidation rates. We also compared it with the sum of reported oxidation and fecal loss amount in order to investigate the effect of fecal loss (a measure of absorption rate). Because the initial body fat percentage was not directly shown on the paper, we estimated it by the equation % Fat =.8 * BMI 0.3, which was an equation recommended in their paper (Jebb et al. 993). We compared the body weight and composition change and macronutrient oxidation rates between the published data and simulation results for days. Horton et al. (995) also measured body weight, body composition changes, and macronutrient oxidation rates of 6 healthy men (8-46 years old) after carbohydrate or fat overfeeding (HC and HF diet) for 4 days. They reported body weight and composition changes of both lean (n=9) and obese (n=7) participants separately. However, they reported only one macronutrient oxidation rate for all participants. Therefore, for the validation of the oxidation rate, we took the average of all participants age, body weight, and body fat rate as input parameters. Because they did not report the energy intake and macronutrient composition directly, we calculated this from the baseline energy requirement and baseline % fat intake, based on the following information; ) excess energy was set at 50% above baseline (Horton et al., 995), ) excess energy was "$!

24 provided entirely as fat during one period and as carbohydrate during another (Horton et al., 995). We assumed that the baseline protein intake was 5% of baseline total energy intake. Then, we compared the published data and the simulation results of the body weight and composition changes for lean and obese subjects separately, and macronutrient oxidation rate for all subjects for 4 days. Abbot et al. (988) measured macronutrient intake and oxidation rate of 7 male and 7 female subjects for 4 hours at energy balance. They did not report the data of each subject, but mean values. Therefore, we input the mean values for subjects age, body weight, and fat rate to the model and simulated them. We included the loss of protein as a part of protein oxidation. We compared the simulated protein oxidation rate with the reported oxidation rate. We also compared it with the sum of reported oxidation and other loss of protein in order to investigate the effect of other loss (e.g. absorption rate, etc.). Berlin et al. (96) measured body weight and composition change of three obese patients (BMI: , body fat %: ) during underfeeding for a relatively longer term (55-00 days). Total calorie intake was controlled. They reported total energy intake and nitrogen intake over 6 day period. Therefore, we calculated the daily protein intake, using the well-known equation: nitrogen intake * 6.5 = protein intake. Also, we assumed that total carbohydrate intake was 50% of total calorie intake, and calculated fat intake as the remainder of total calorie intake. We compared the body weight and composition change between the data and simulation results for 55 to 00 days. Van Gemert et al. (000) measured the body weight and composition changes, and macronutrient oxidation rates of 8 subjects ( male and 7 female) after vertical banded gastroplasty. All of the participants were obese (initial BMI: ), and lost body weight "%!

25 and fat mass dramatically after the surgery. The body composition and macronutrient oxidation measurements were done at 3 and months after the surgery. Dietary intakes were based on dietary records that patients kept for 48 hours before measuring body composition and macronutrient oxidation. We assumed that subjects consumed the same number of calories for 3 or months after the surgery based on the dietary records as no other information was collected between the dates. Then, we compared the body weight and composition change, and macronutrient oxidation rate between the data and the simulation results for months. 4. Model Application After the validations, we compared the traditional diet recommended by the American Dietetic Association (ADA diet) and two well-known high-protein diets (Atkins and the Zone diet) with our model. We chose a 40-year-old male with weight 00 kg and body fat 30% as a test subject by means of simulation. We did not show a female subject simulation because the results were similar and we expected that there would not be a big difference between genders. We ran the model for 80 days because the first body weight change usually happens in the first six months (Sacks et al., 009). We chose the following dietary macronutrient compositions, carbohydrate: 55%, fat: 30%, protein: 5% for ADA diet, 0%, 60%, 30% respectively for Atkins diet, and 40%, 30%, 30% respectively for the Zone diet (Gardner, 007). "&!

26 RESULTS. Model Validation -. Overfeeding --a. Comparison to Jebb (993, 996) Table -a, b, c, d and figure -a, b, c, d reports the difference between Jebb s overfeeding data (993) and the simulation results during overfeeding. The simulated carbohydrate oxidation was slightly lower than Jebb s data (mean oxidation of days). The mean difference was -7% (range: - to -%). When including a mathematical correction for fecal loss with the oxidation, the mean difference became higher, -% (range: -6 to 7%). Conversely, our simulated fat oxidation was slightly higher than Jebb s data. The mean difference was 5% (range: to 6%). Adding the fecal loss to the oxidation did not change the mean difference much (-3%, range: 0 to -5%). Compared to carbohydrate and fat, the difference between the simulated protein oxidation and published oxidation (Jebb et al., 993) was higher (mean: 8%, range: 7 to 5%). However, the difference became much smaller when adding the fecal loss to the oxidation equation (mean: 3%, range: - to 8%). Table -e and figure -e compared the simulated oxidation and measured mean oxidation of each day for days (Jebb et al., 996). The published values of oxidation of carbohydrate and fat matched closely with the simulation results around the second day. However, after the second day, the simulation results of oxidation values crossed the actual results; the Cox was higher than the simulated value and the Fox was lower than the simulated value. Compared to Cox and Fox, Pox did not change through the entire period. The mean FM gain of the Jebb s data (996) was.0 kg, compared with the simulated FM gain,.49 kg (difference: 46%). The mean LBM gain of the data was.88 kg, compared with the "'!

27 simulated FM gain, 0.95 (difference: -49%). In sum, the mean BW gain of the data was.90 kg, compared with the simulation FM gain,.44 (difference: -6%). The mean BW difference was comparably close to the simulation result. However, the body composition changes (BM and LBM) did not match the published data. Lower Cox and higher Pox with the model caused more FM and less LBM accumulation compared with the published data results. --b. Comparison to Horton (995) Table and figure reported the difference between Horton s data (995) and the simulated results during the overfeeding. The simulated BW gain of both lean and obese subjects closely matched the published data within about 0% (0 to -4%, table -a, b, c, d). However, the body composition changes did not match the data. The model tended to accumulate more FM and less LBM compared with the real data (table -a, b, c, d). The % difference was highest in LBM of obese subjects with HF diet (-03%, table -d). The simulated FM accumulation of all subjects matched the data especially with HF diet (% difference: %) and moderately with HC diet (% difference: 9%). However, LBM accumulations were much lower with the model simulation compared with the published data (% difference in HC diet: 54%, HF diet: 8%). As a result, the simulated BW gains were much higher than the real BW gains (% difference in HC diet: 36%, HF diet: 34%). The Cox with HC diet started from g and reached g at the end of the intervention. Conversely, the Fox with HC diet was reduced from 4.78 g to g for 4 days. With HF diet, the Cox was decreased (from to 08.7 g), and the Fox was increased (from 50.3 to g) decently. The Fox of the model simulation and published data were fitted within 0% differences. The model simulation overestimated the Cox rates, and the differences were getting smaller toward the end of the intervention. That implied that the results might have "(!

28 matched if the intervention period had been longer. The model simulation overestimated the Pox with both HC and HF diets. That resulted in a LBM difference between the simulation and the published results. -. Energy Balance --a. Comparison to Abbott (995) Table 3 and figure 3 showed the difference between the published data and simulation results, when energy balance food was supplied. Abbott et al. did not report the weight and body composition change because it was only a 4 hour experiment. Rather, they reported the oxidation rate of a single day. The simulated Cox fitted with experimental data within 0% differences (Male: -6%, Female -9%). Also, the simulated Pox matched the published data, when other losses were combined with Pox amounts. In addition, the male data fitted with the simulation result well (% difference: 8%), although the model overestimated the Fox (about 39%) for female subjects. A higher body fat % of female subjects (Male: 3%, Female: 35%) might cause this result because Fox was calculated based on BW, not LBM. If we had access to the data based on LBM, we might have obtained better results. -3. Underfeeding Table 4-6 and figure 4-6 reported the difference between the published data and simulation result during underfeeding. -3-a. Comparison to Jebb (993, 996) With Jebb s data (996), our model underestimated each of the macronutrients oxidation, except the 3 rd and 4 th day with Cox and the st day of Fox (table 4-e and figure 4-e). However, the differences were moderate toward the end of the intervention period (% difference Cox: -0%, Fox: -9%, and Pox: -3%, table 4-e). When we compared the simulated oxidations with the ")!

29 average oxidation rate of days, the difference between the simulation and published data became slightly smaller, but the simulated Pox still exceeded the published data by more than 0% (% difference Cox: 9%, Fox: -7%, and Pox: -3%, table 4-e). As a result, the simulated FM loss was closely fitted with the real FM loss (table 4-d and figure 4-d). However, the simulated LBM loss did not reach the level of real LBM loss (table 4-d and figure 4-d). That reflected the total BW loss (table 4-d and figure 4-d). We calculated not only the mean data but also the individual data (tables 4-a, b, c and figures 4- a, b, c). With subject, the simulated oxidations were higher with carbohydrate and lower with fat and protein compared with Jebb s data (993) (table 4-a and figure 4-a). Those results were the same as the mean results. However, % differences were larger with Cox and Fox, and smaller with Pox (table 4-a and figure 4-a) compared with the mean oxidation (table 4-d and figure 4-d). That ended up the better fit between the simulated and published body composition changes (table 4-a) because the higher Cox and lower Fox cancelled each other. With subject 3, the simulated Fox and Pox were reasonably matched with the published data, while the model overestimated Cox 4% (table4-b). With these oxidation rates, we expected the model simulation might lose more LBM. However, the result was opposite. Subject 3 lost more LBM than the simulation result. With subject 4, the model underestimated Cox moderately and Pox apparently, while it estimated Fox well (table 4-c and figure 4-c). As a result, the model simulated FM loss fairly good but overly underestimated LBM loss (table 4-c and figure 4-c). -3-b. Comparison to Berlin (96) With Berlin s data (96), simulated FM losses were fitted with the real data for the first month with subject W.T. (figure 5-a) and E.C. (figure 5-b), also for months with subject A.I. (figures 5-c, d). W.T., E.C., and A.I. are name initials of each subject. After the first or second months, "*!

30 the model suggested greater FM loss than the published data. The longer the intervention would be, the bigger the differences might be, based on the curve indications (figures 5-a, b, c, d). On the other hand, the simulated LBM losses were smaller than the data with subject W.T. (figure 5- a), but bigger than the data with subject E.C. and A.I. through the intervention (figures 5-c, d). As a result, the simulated BW losses were smaller than the data with subject W.T., and bigger than the data with E.C. and A.I. (figures 5-a, b, c, d). -3-c. Comparison to van Gemert (000) With van Gemert s data (000), the model overestimated Cox (3%) and underestimated Pox (- 3%) at the point of 3 months after the surgery (table 6-a and figure 6-a). However, the simulated Fox was closely matched with the published data toward the end of the 3 months intervention (%, table 6-a and figure 6-a). As a result, although the simulated BW and FM were a little higher than the published data, LBM loss was matched with the published data within 0% (-7%, table 6-a). Twelve months after the surgery, the simulated Cox and Pox were matched with data with 0% differences (Cox: -0%, Pox: 0%, table 6-b). However, simulated Fox was 38% below the actual value (table 6-b). Nevertheless, the simulated FM loss was a close fit to the data, while simulated LBM loss was clearly overestimated compared to the published data. From 3 to months after the surgery, subjects from the van Gemert study did not lose much LBM (- 0.6 kg, table 6). However, the simulated person lost nearly kg of LBM.. Model Application With our model simulation, the Atkins diet induced the most BW loss during underfeeding (ADA: kg, Atkins: -0.7 kg, Zone: -0.5 kg, table 7-a). Also, Atkins diet led to less BW gain during energy balance (ADA: 3.5 kg, Atkins:.44 kg, Zone: 3.6 kg, table 7-b) and overfeeding (ADA: 6.86 kg, Atkins: 5.60 kg, Zone: 7.38 kg, table 7-c). However, the #+!

31 differences were slight. Body composition changes suggested different results. During underfeeding, FM loss was the biggest with the Zone diet, and followed by Atkins and ADA diet (ADA: -.7 kg, Atkins: kg, Zone: kg, table 7-a). Also, FM gain with the Zone diet was the smallest during overfeeding (ADA:.96 kg, Atkins: 3.55 kg, Zone: 0.94 kg, table 7-c). Even with an energy balanced diet, the ADA diet induced FM gain and LBM loss (FM: 5.05 kg, LBM: -.8 kg, table 7-b). On contrary, HP diet induced FM loss and LBM gain (Atkins, FM: -.6 kg, LBM: 3.59 kg; Zone, FM: -.86 kg, LBM: 6.47 kg; table 7-b). #"!

32 DISCUSSION There have been several efforts to create mathematical models, which might be used to estimate macronutrient effects on BW and body composition change. However, there is no consensus. Our model was created in order to take another step toward understanding the macronutrient effect on BW change. Most equations that we used in the model were based on published literature. The difference was that we calculated TEE only based on the macronutrient intake, not based on RMR, TEF, and exercise as other researchers have done. More specifically, the carbohydrate and fat oxidation rates were based on the daily carbohydrate intake, and protein oxidation was calculated from daily carbohydrate and protein intake. In this way, we investigated the effect of daily macronutrients intake and oxidation on weight and body composition change.. Model Validation For the model validation, we used five published human studies because we were not able to find one complete data set which could evaluate the model well enough. The first reason why we could not find one appropriate data set was that we needed to test our model at least under the three situations; overfeeding, underfeeding, and at energy balance. If our model simulated the human body well under those three situations, we could tell that the model was well developed. No published data, which we found, measured human BW and body composition change under all three situations. Therefore, we simulated multiple data; two overfeeding (Jebb et al., 993 & 996; Horton et al., 995), one at energy balance (Abbott et al., 995), and four underfeeding (Jebb et al., 993 & 996; Berlin et al., 96; van Gemert et al., 000). The second reason why we evaluated our model with several studies was that each study had a different superior point. For example, we chose overfeeding studies by Jebb and Horton. Jebb s study was superior for measuring macronutrient oxidation and fecal loss continuously throughout ##!

33 the experiment period although the duration of the experiment is comparatively short, days (993, 996). Compared with Jebb and his colleagues, Horton et al. measured body weight and composition change only at days 0,, 7, and 4 (995). However, they compared carbohydrate overfeeding and fat overfeeding with the same total calorie intake. Therefore, we could use this study to test if our model could simulate differences in macronutrient composition. Finally, everyone has a different body type. We attempted to create a model for an individual to input his/her data and acquire his/her future BW and composition change. In order to validate our model, we should test not only the average of group-based data but also several individual-based data. -. Individual Evaluation Data < Strengths and Problems > Jebb s data (993, 996): Jebb s study was superior for measuring macronutrient intake and oxidation continuously throughout the experiment period both at under and overfeeding. They also measure the total macronutrient intake, oxidation, and fecal loss for days. Because of the data, we could see the effect of fecal loss on the body composition change. However, the duration was short, and the number of subjects was small. Also, some reported outcomes from the articles published in 993 and 996 had minor differences. Therefore, we simulated the data from 993 and 996, separately. Horton s data (995): Horton s study was superior for comparing lean and obese subjects with both HC and HF diets. They also measured body composition change and macronutrient oxidation rate. The subject number was larger than Jebb s study, although the duration was short. However, they did not report direct macronutrient intake, so that we had to estimate them. This process decreased the accuracy of our results. Also, they did not report the macronutrient oxidation rates for lean and obese subjects separately, which might give different results. #$!

34 Abbot s data (995): The duration of this study is short (4 hours) yet the number of subjects is larger than the other studies, and included both males and females. This study was useful to validate if our model was working at energy balance, especially for macronutrient oxidation rates. Berlin s data (96): This study was outstanding because the energy and nitrogen intake were controlled and body composition changes were measured (including BW, FM, body water, lean tissue solid) every six day period for a relatively longer term (from 55 days to 00 days). The problem was that because this study was relatively old, some data might not be reliable. For example, subject A.I. lost very little LBM while she lost about kg FM for 96 days of the experimental period. Unless she worked out excessively a lot (that was not mentioned), she would have been expected to lose some LBM along with the fat loss. Also, she had diabetes and severe edema, which is not accounted by our model. This might affect the difference between the data and the simulation results. Another problem was the accuracy of macronutrient intake. Because they only reported TEI and nitrogen intake, we had to estimate carbohydrate and fat intake. Therefore, the accuracy of carbohydrate and fat intake was likely low. Van Gemert s data (000): This study was suitable for the validation of our model because subjects lost considerable BW, and also the study period was comparatively long. However, the energy intake was only measured at the three points, before and 3 and months after the surgery. We adapted them for the entire experiment. Therefore, the difference between the data and simulation results might be caused by the low accuracy of energy intake. -. Overfeeding <Validity and Limitations > As we evaluated our model with several published data sets, we noticed that the results of body composition changes were different between lean subjects and obese subjects. Based on Horton s #%!

35 data (995), obese subjects tended to gain more FM (HC diet:.06 kg, HF diet:.90 kg) compared with lean subjects (HC diet:.09 kg, HF diet:. kg) both with HC and HF diet (table -a, b, c, d), while LBM gains are similar (Obese HC diet:.4 kg, HF diet:.08 kg vs. Lean HC diet:.38 kg, HF diet:.0 kg). Therefore, we applied two different equations for Cox and Fox calculations based on BMI (obese BMI > 30), so that our model simulation would better fit with the real data. Unfortunately, we could not obtain the macronutrient oxidation rate for lean and obese subjects separately with Horton s study. Therefore, we only compared body composition change between lean and obese subjects. Our decision to apply two different equations based on BMI was successful. The simulated BW changes were fairly matched with the published data. Besides, with Jebb s data (993, 996), the simulated Cox, Fox, and Pox (when including fecal loss) matched closely with the published mean oxidation values (table and figure 4-9). Therefore, we concluded that our model could estimate Total BW change during overfeeding reasonably well. However, body composition changes did not match exactly. Specially, LBM gain was apparently underestimated by the model simulation, while FM gain was slightly overestimated. Attempts to optimize composition changes during underfeeding led to gross overestimations during overfeeding conditions, and vice versa. The best fit under all conditions was obtained with the equations reported herein. Perhaps, if we could have found enough data to calculate Pox equations based on BMI, we might have developed a better LBM gain estimation. Also, all macronutrient oxidation equations were calculated based on oxidation (g) per BW (kg). In the future, access to data to calculate oxidation equations based on LBM might lead to more accurate model simulation results. Jebb (993, 996) and Horton (995) reported macronutrient oxidation rate change through the intervention periods. The published Cox and Fox matched with the simulation results around the #&!

36 nd to 5 th day. However, after a few days passed, the published oxidations crossed the simulation results and were different from the simulation results. The human body adjusts Cox and Fox based on the carbohydrate intake (Horton et al., 995; Schwart et al., 995; Shetty et al., 994; Young et al., 000). Our model does not account for this adjustment. The simulated Cox and Fox values matched the published results between 3 rd and 5 th day the most because the equations are based on 3 to 5 days of macronutrient oxidation rates. In order to improve our model, we need access to a longer intervention. Compared to Cox and Fox, Pox did not change much through the entire period. This was because high carbohydrate intake did not affect Pox compared to Cox and Fox (Jebb et al., 996). Also, Jebb (993, 996) and Horton (995) focused more on HC and HF diets effect on oxidation changes. In fact, in both Jebb s (993, 996) and Horton s (995) studies, protein intakes were kept about 5% of TEI. Data available were limited to short-term overfed interventions, involving a - or 4- day intervention. Obviously, it is difficult to find long-term overfeeding data because a long-term weight-gain program is seldom carried out experimentally in this time period when obesity is the prevalent social problem. The human body usually needs transition time to adjust itself to changed energy intake, usually 4-7 days (Acheson et al., 988). Even though our model simulations fit with those published values in some levels, the results could be applied for shortterm simulations. Also, Jebb (993, 996) used different macronutrient energy density values especially for carbohydrate (carbohydrate; kcal/g, fat; kcal/g, protein; kcal/g) from our model (carbohydrate; 4. kcal/g, fat; 9.4 kcal/g, protein; 4.7 kcal/g). Based on Liversey and Elia (988), energy density of carbohydrate depends on the composition. For example, polysaccharides including starch and glycogen produce almost 4. kcal/g of energy. On the other #'!

37 hand, monosaccharides, such as glucose, galactose, or fructose, produce about 3.7 kcal/g of energy. While Jebb (993, 996) used monosaccharides energy density for carbohydrate, we chose polysaccharides as the representative of dietary carbohydrate. That might affect the results, slightly reducing the calorie effect of carbohydrate. -3. Energy Balance <Validity and Limitations > During energy balance, except female fat oxidation, macronutrient oxidation values from the model simulation matched with experimental data reasonably well. This result showed the validity of our model, at least at the energy balance. One of the possible reasons why Fox values for women subjects did not match the simulation results was because the equations that we used for macronutrient oxidation were based on male data. This result implied that the female fat oxidation rate might be lower than for males. This lower Fox rate might be due to the higher body fat % (men vs women; 3% vs 35%) because the Fox equation was not based on LBM, but total BW. However, the exact reason cannot be determined until additional female data is available. Other gender factors might be affected. We need further data to improve our model equations. -4. Underfeeding <Validity and Limitations > For the short-term intervention (Jebb et al., 996), the simulated FM change fit the published data (table 4-d). Also, the simulated Cox, Fox, and Pox matched with the published data fairly well (table and figure 4-d). In sum, we concluded that our model could estimate FM changes for short-term during underfeeding reasonably well. However, underestimated Pox caused a slight difference between the simulated and published LBM losses. Also, if we added protein absorption rate (fecal loss effect) in our model as Jebb did (996), the difference might have been smaller. However, we did not have access to adequate data to do this. #(!

38 For the longer-term interventions, the results were more varied. One thing we could say was that simulated FM changes fairly fit the published data with all subjects. However, LBM changes were not matched with the published data, except at the earlier period of Berlin s data. Several reasons could be considered. The first possible reason was the accuracy of the LBM data. Because Berlin et al. did not report LBM changes we calculated it by subtracting FM from BW. Therefore, if one of these values (FM and BW) was not measured accurately, it leads to incorrect LBM data. Based on table and figure 5-c, d, subject A.I. barely lost any LBM while she lost 3 kg of FM for 00 days. Usually, people lose LBM with FM loss (Westerterp et al., 995). Therefore, this result indicated the possible inaccuracy of LBM data. The second reason was the accuracy of TEI. As we mentioned for Berlin (96), they only reported TEI and nitrogen intake. Therefore, we had to assume carbohydrate and fat intake proportions. Also, in the van Gemert (000) study, TEE was only measured at the three points, before and 3 and months after the surgery. We adapted them for the entire period of the experiment. Therefore, the difference between the data and simulation results might be caused by the low accuracy of macronutrient or energy intake. Lastly, gender could be another possible reason. As mentioned in the methods section, macronutrient oxidation equations were calculated based on male data. Conversely, the majority of subjects in Berlin (96) and van Gemert (000) were women ( : 9). Therefore, this gender difference may have affected the results. -5. Overall <Validity and Limitations > Based on the results of the validations, our current model could simulate accurately the following situations;. Estimating BW, Cox, Fox, and Pox for weeks during overfeeding. (Note: Fecal loss included in Pox) #)!

39 . Estimating Cox, Fox, and Pox of men and Cox and Pox of women for 4 hours at energy balance. (Note: Other loss included for Pox) 3. Estimating FM, Cox, Fox, and Pox for weeks during underfeeding. (Note, fecal loss not included for Pox) 4. Estimating FM for year during underfeeding. The limitations of our current model were as followed;. Limited duration. Human body tends to adjust TEE to changed TEI. For example, at the overfeeding, TEE is gradually increased due to the increase of RMR, and vice versa. However, our model did not account for the adjustment. It only estimates the early increase/decrease of BW, FW, and LBM.. Limited subjects. Macronutrient oxidation equations in our model were calculated from data with small subject numbers. Also, all subjects were healthy young males. Therefore, our model might not be age or gender specific. 3. Limited available data. Macronutrient oxidation equations in our model were calculated as oxidation (g) per BW (kg). If we could access data showing macronutrient oxidation rate per LBM, our model might estimate the oxidation rate more correctly. 4. Limited application. As we mentioned in the introduction, we eliminated physical activity energy utilization from our model in order to avoid the complication. Therefore, we can apply this result only for sedentary people because all the data were based on the results of sedentary people. 5. Body type. Each person has a different body type. This current model could not account for the calculation of the different body types. #*!

40 6. Absorption rate. Fecal loss (or absorption rate) was not accounted for. This is needed in future models. While we created the model, we encountered several problems. First of all, data were very limited because these experiments needed were not available. Obtaining body composition change and macronutrient oxidation rate for each gender, age, or BMI seemed improbable. Also, it was hard to find long-term data during overfeeding because it might not be ethical to conduct long-term overfeeding experiments. Besides, long-term studies usually come with lower accuracy of data. Therefore, although we believe that our current model suggested some important information, further investigations are definitely required.. Model Application The results from the model simulation suggested that Atkins diet would induce the most BW loss during underfeeding, the least BW gain at energy balance and with overfeeding. The ADA diet comes after Atkins diet, and the Zone diet resulted in the worst BW loss and gain. However, the Zone diet induced the most preferable body composition change compared with ADA and Atkins diet, losing more FM and retaining LBM. Although our model is not yet perfect, this result implied that the muscle sparing effect of a high-protein diet might be preferable compared with a traditional high-carbohydrate diet. This result is consistent with the conclusions of a recent review (Clifton, 009). In his review, Clifton stated that high protein diets may minimize lean tissue loss during energy restriction. Based on our model, a low carbohydrate intake induced lower Cox and higher Fox. This resulted in higher FM loss or lower FM gain. Also, with our model, as the dietary protein intake exceeds Pox, the simulated person tends to gain LBM, and vice versa. Because of this system, FM and LBM changes conflicted with each other using a balanced diet (Novotny and Rumpler, 998; $+!

41 Westerterp et al., 995). This is one of our model s limitations. In order to improve our model, we need data which shows the relationship between energy balance and Pox. 3. Summary (Benefits) Although our model did not match with the published human data completely, our model still quantitatively showed the possible effects of macronutrient composition on BW and composition changes for 6 months of a dietary intervention specifically during an underfeeding situation. Our model did not suggest that high-protein diets induced more BW loss compared with traditional high-carbohydrate diet. Rather, a high-protein diet led to extra FM loss and conserved LBM. This conclusion, that a high-protein diet may improve LBM retention, also matched with the result of a previous report (Krienger, 006). In spite of the fact that our model was created by using very simple equations based on simple linear or multiple regressions calculated from published human data, our model outcomes matched published data at energy balance and underfeeding situation under limited situations. This implies the possibility that computer simulations can imitate the human body in the future, even though some limitations may exist. In fact, as more data is published showing the relationship between energy balance and Pox, we can improve our model more elaborately and precisely. According to a telephone survey of US adults conducted from September 00 to December 00 (Blanck et al., 006), 3790 people out of 9300 are currently trying to lose weight. If those dieters can predict their future weight loss accurately with a computer simulated model, it may be easier for them to persist on the diet. This may lead overweight or obese people to lose weight successfully. The simulation model could help people with weight problems to choose a more effective diet and stick with it. Also, the computer model might be an effective tool for diet $"!

42 counselors. It may show results of diet manipulation of single macronutrients, for example, consuming only carbohydrate, protein, or fat that could not be done experimentally. In addition, computer simulation does not require any complicated instruments and high cost, so that anyone can use it easily. After the model s accuracy has been shown to be useful, it could be used as a clinical device to show the patients their future weight change with their daily macronutrient intakes. $#!

43 REFERENCES Abbott WGH, Lillioja BV, Christin L, Freymond D, Lillioja S, Boyce VL, Anderson TE, Bogardus C, and Ravussin E. Short-term energy balance: relationship with protein, carbohydrate, and fat balance. Am J Physiol 55: E33-E337, 988. Abdel-hamid TK. Exercise and diet in obesity treatment: an integrative system dynamics perspective. Med Sci Sports Exerc 36: , 003. Acheson KJ, Flatt JP, and Jequier E. Glycogen synthesis versus lipogenesis after a 500 gram carbohydrate meal in man. Metabolism 3(): 34-40, 98. Acheson KJ, Schutz Y, Bessard T, Anantharaman K, Flatt JP, and Jequier E. Glycogen storage capacity and de novo lipogenesis during massive carbohydrate overfeeding in man. Am J Clin Nutr 48: 40-47, 988. Alberts B, Bray D, Lewis J, Raff M, Roberts K, and Watson JD. Molecular Biology of the Cell (3 rd ed.). New York: Garland, 989. Alpert SS. A limit on the energy transfer rate from the human fat store in hypophagia. Journal of Theoretical Biology 33: -3, 005. Alpert SS. A two-reservoir energy model of the human body. Am J Clin Nutr 3: 70-78, 979. Antonetti VW. The equations governing weight change in human beings. Am J Clin Nutr 6: 64-7, 973. Berlin NI, Watkin DM, and Gevirtz NR. Measurement of changes in gross body composition during controlled weight reduction in obesity by metabolic balance and body density body water technics. Metabolims : 30-34, 96. $$!

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45 Ferretti JL, Capozza RF, Cointry GR, Garcia SL, Plotkin H, Alvarez Filgueira ML, and Zanchetta JR. Gender-related differences in the relationship between densitometric values of whole-body bone mineral content and lean body mass in humans between and 87 years of age. Bone : , 998. Flatt JP. Carbohydrate-fat interactions and obesity examined by a two-compartment computer model. Obesity Research (): 03-0, 004 Gardner CD, Kiazand A, Alhassan S, Kim S, Stafford RS, Balise RR, Kraemer HC, and King Ac. Comparison of the Atkins, Zone, Ornish, and LEARN diets for change in weight and related risk factors among overweight premenopausal women. JAMA 97(9): , 007. Hall KD. Computational model of in vivo human energy metabolism during semistarvation and refeeding. Am J Physiol Endocrinol Metab 9: E3-E37, 006. Hall KD. Predicting metabolic adaptation, body weight change, and energy intake in humans. Am J Physiol Endocrinol Metab 98: E449-E466, 00. Horton TJ, Drougas H, Brachey A, Reed GW, Peters JC, and Hill JO. Fat and carbohydrate overfeeding in humans: different effects on energy storage. Am J Clin Nutr 6: 9-9, 995. Institute of Medicine of the National Academies. Dietary reference intakes for energy, carbohydrate, fiber, fat, fatty acids, cholesterol, protein, and amino acid Jebb SA, Murgartoyd PR, Goldberg GR, Prentice AM, and Coward WA. In vivo measurement of changes in body composition: description of methods and their validation against -d continuous whole-body calorimetry. Am J Clin Nutr 58: 455-6, 993. Jebb SA, Prentice AM, Goldberg GR, Murgatroyd PR, Black AE, and Coward WA. Changes in macronutrient balance during over- and underfeeding assessed by -d continuous whole-body calorimetry. Am J Clin Nutr 64: 59-66, 996. $&!

46 Johnston CS, Tjonn SL, and Swan PD. High-protein, low-fat diets are effective for weight loss and favorably alter biomarkers in healthy adults. J Ntri 34: , 004. Kays A. The Biology of Human Starvation. Minneapolis, MN: University of Minnesota, 950. Kozusko FP. Body weight setpoint, metabolic adaption and human starvation. Bulletin of Mathematical Biology 63: , 00. Krienger JW, Sitren HS, Daniels MJ, and Langkamp-Henken B. Effects of variation in protein and carbohydrate intake on body mass and composition during energy restriction: a metaregression. Am J Clin Nutr 83: 60-74, 006. Labayen I, Diez N, Gonzalez A, Parra D, and Martinez JA. Effects of protein vs. carbohydrate-rich diets on fuel utilization in obese women during weight loss. Forum Nutr 56: 68-70, 003. Layman DK, Boileau RA, Erickson DJ, Painter JE, Shiue H, Sather C, and Christou DD. A reduced ratio of dietary carbohydrate to protein improves body composition and blood lipid profiles during weight loss in adult women. J Ntri 33: 4-47, 003. Layman DK, Evans E, Baum JI, Seyler J, Erickson DJ, and Boileau RA. Dietary protein and exercise have additive effects on body composition during weight loss in adult women. J Ntri 35: , 005. Livesey G and Elia M. Estimation of energy expenditure, net carbohydrate utilization, and net fat oxidation and synthesis by indirect calorimetry: evaluation of errors with special reference to the detailed composition of fuels. Am J Clin Nutr 47: , 988. Luscombe ND, Clifton PM, Noakes M, Farnsworth E, and Wittert G. Effect of a highprotein, energy-restricted diet on weight loss and energy expenditure after weight stabilization in hyperinsulinemic subjects. Int J Obes Relat Metab Disord 7(5): ,

47 Luscombe ND, Parker B, Clifton PM, Wittert G, and Noakes M. Effects of energy-restricted diets containing increased protein on weight loss, resting energy expenditure, and the thermic effect of feeding in type diabetes. Diabetes Care 5(4): , 00. MacKay EM and Bergman HC. The amount of water stored with glycogen in the liver. J Biol Chem 05: 59-6, 934. MacKay EM and Bergman HC. The relation between glycogen and water storage in the liver. J Biol Chem 96: , 93. McBride JJ, Guest MM, and Scott EL. The storage or the major liver components; emphasizing the relationship of glycogen to water in the liver and the hydration of glycogen. J Biol Chem 39: , 94. Meckling KA and Sherfey R. A randomized trial of a hypocaloric high-protein diet, with and without exercise, on weight loss, fitness, and markers of the Metabolic Syndrome in overweight and obeses women. Appl Physiol Nutr Metab 3: , 007. Nilsson LH. Liver glycogen content in man in the postabsorptive state. Scand J Clin Lab Invest 3: 37-33, 973. Noakes M, Keogh JB, Foster PR, and Clifton PM. Effect of an energy-restricted, high-protein, low-fat diet relative to a conventional high-carbohydrate, low-fat diet on weight loss, body composition, nutritional status, and markers of cardiovascular health in obese women. Am J Clin Nutr 8: , 005. Novotny JA and Rumpler WV. Modeling of energy expenditure and resting metabolic rate during weight loss in humans. Advances in Experimental Medicine and Biology 445: 93-30, 998. $(!

48 Parker B, Luscombe N, Noakes M, and Clifton P. Effect of a high-protein, highmonounsaturated fat weight loss diet on glycemic control and lipid levels in type diabetes. Diabetes Care 5: , 00. Puckett HL and Wiley FH. The relation of glycogen to water storage in the liver. J Biol Chem 96: , 93. Ritchie CB. Estimations and simulations of regional body composition. A thesis of department of Nutiriton, Dietetics, and Food Science in Brigham Young University Ritz P. Body water spaces and cellular hydration during healthy aging. Ann N Y Acad Sci 904: , 006. Sacks FM, Bray GA, Carey VJ, Smith SR, Ryan DH, Anton SD, McManus K, Champagne CM, Bishop LM, Laranjo N, Leboff MS, Rood JC, de Jonge L, Greenway FL, Loria CM, Obarzanek E, and Williamson DA. Comparison of weight-loss diets with different composition of fat, protein, and carbohydrates. N Engl J Med 360: , 009. Schwarz JM, Neese RA, Turner S, Dare D, and Hellerstein MK. Short-term alterations in carbohydrate energy intake in humans. J Clin Invest 96: , 995. Selz R, Theintz G, Tappy L, and Schneiter P. Evaluation of hepatic and whole body glycogen metabolism in humans during repeated administrations of small loads of C glucose. Diabetes Metab 9: , 003. Sheng HP and Huggins RA. A review of body composition studies with emphasis on total body water and fat. Am J Clin Nutr 3: , 979. Shetty PS, Prentice AM, Goldberg GR, Murgatroyd PR, McKenna APM, Stubbs RJ, and Vouschenk PA. Alterations in fuel selection and voluntary food intake in response to isoenergetic manipulation of glycogen stores in human. Am J Clin Nutr 60: , 994. $)!

49 van Gemert WG, Westerterp KR, van Acker BAC, Wagenmakers AJM, Halliday D, Greve JM, and Soeters PB. Energy, substrate and protein metabolism in morbid obesity before, during and after massive weight loss. Int J Obes 4: 7-78, 000. van Milgen J. Modeling biochemical aspects of energy metabolism in mammals. J Nutr 3: , 00. Wang Z, Heshka S, Gallagher D, Boozer CN, Kotler DP, and Heymsfield SB. Resting energy expenditure-fat-free mass relationship: new insights provide by body composition modeling. Am J Physiol Endocrinol Metab 79: E539-E545, 000. Westerterp KR, Donkers JHHLM, Fredrix EXHM, and Boekhoudt P. Energy intake, physical activity and body weight: a simulation model. British Journal of Nutrition 73: , 995. Willett WC. Is dietary fat a major determinant of body fat? Am J Clin Nutr 67(3 Suppl): 556S- 56S, 998. Young VR, El-Khoury AE, Raguso CA, Forslund AH, and Hambraeus L. Rates of urea production and hydrolysis and leucine oxidation change linearly over widely varying protein intakes in healthy adults. J Nutr 30: , 000. $*!

50 TABLES AND FIGURES Table -a. Comparison of Jebb s data (subject *, 993) vs. model simulation results during overfeeding. Overfeeding (Duration: days) Data Sim. ** Dif. *** % Dif. **** Subject ' Gender Male Age 4.00 Height (m).77 Initial Body Composition Weight (kg) BMI 3.87 Body Fat (%) ***** 0.45 Fat Mass (kg) 5.9 Lean Body Mass Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) ***** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Fat Free Mass (kg/days) * Subject (overfeeding) and subject 3 (underfeeding) are the same individual. ** Simulation results. *** Differences between published data and simulation results. **** %Differences = difference / data. ***** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures.estimation. Differences more than 0%. 40

51 Table -a. Comparison of Jebb s data (subject *, 993) vs. model simulation results during overfeeding. (Cont.) Overfeeding (Duration: days) Data Sim. ** Dif. *** % Dif. **** Subject ' Macronutrient Balance Carbohydrate Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) 5.50 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Fat Intake (g/days) 73.0 (g/day) 4.77 Fecal Losses (g/days) (g/day) 7.3 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Protein Intake (g/days) (g/day) 3.60 Fecal Losses (g/days) (g/day) 0.05 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) 9.9 * Subject (overfeeding) and subject 3 (underfeeding) are the same individual. ** Simulation results. *** Differences between published data and simulation results. **** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 4

52 i) 80 BW (kg) ii) 0 FM (kg) iii) 65 LBM (kg) Figure -a. Comparison of Jebb s data (subject *, 993) vs. model simulation results during overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 4

53 iv) 800 Cox (g/day) 400 v) Fox (g/day) 400 vi) Pox (g/day) Figure -a. Comparison of Jebb s data (subject *, 993) vs. model simulation results during overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 43

54 Table -b. Comparison of Jebb s data (subject 5, 993) vs. model simulation results during overfeeding. Overfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects 5 Gender Male Age.00 Height (m).98 Weight (kg) 80. BMI 0.43 Body Fat (%) **** 6.05 Fat Mass (kg).85 Lean Body Mass 67.6 Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Fat Free Mass (kg/days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures.estimation. Differences more than 0%. 44

55 Table -b. Comparison of Jebb s data (subject 5, 993) vs. model simulation results during overfeeding. (Cont.) Overfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects 5 Macronutrient Balance Carbohydrate Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Fat Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) 4.6 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) 0.44 Protein Intake (g/days) 4.00 (g/day) Fecal Losses (g/days) (g/day) 4.80 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day).49 * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 45

56 i) 85 BW (kg) 80 ii) FM (kg) D 34 00??0? iii) 75 LBM (kg) Figure -b. Comparison of Jebb s data (subject 5, 993) vs. model simulation results during overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 46

57 iv) 800 Cox (g/day) 400 v) Fox (g/day) D 58 00??9? vi) 800 Pox (g/day) Figure -b. Comparison of Jebb s data (subject 5, 993) vs. model simulation results during overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 47

58 Table -c. Jebb (993) Overfeeding (Subject 6) Overfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects 6 Gender Male Age 6.00 Height (m).6 Weight (kg) BMI 3.34 Body Fat (%) **** 9.77 Fat Mass (kg).96 Lean Body Mass Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Fat Free Mass (kg/days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures.estimation. Differences more than 0%. 48

59 Table -c. Comparison of Jebb s data (subject 6, 993) vs. model simulation results during overfeeding. (Cont.) Overfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects 6 Macronutrient Balance Carbohydrate Intake (g/days) (g/day) 5.8 Fecal Losses (g/days) (g/day) 3.83 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) 7.90 (g/day) 4.4 Fat Intake (g/days) (g/day) 4.90 Fecal Losses (g/days) (g/day) 3.9 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) 89.5 Protein Intake (g/days) (g/day) 3.40 Fecal Losses (g/days) (g/day) 9.55 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) 7.3 * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 49

60 i) 65 BW(kg) 60 ii) D 00??9? 0 FM(kg) iii) 55 LBM(kg) D 35 00??0? Figure -c. Comparison of Jebb s data (subject 6, 993) vs. model simulation results during overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 50

61 iv) 800 Cox (g/day) 400 v) D 3 00??9? 800 Fox (g/day) 400 vi) Pox (g/day) D 3 00??9? Figure -c. Comparison of Jebb s data (subject 6, 993) vs. model simulation results during overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 5

62 Table -d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during overfeeding. Overfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects Mean Gender Male Age 9.67 Height (m).79 Weight (kg) 7.80 BMI.55 Body Fat (%) **** 8.75 Fat Mass (kg) 3.46 Lean Body Mass Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Fat Free Mass (kg/days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 5

63 Table -d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during overfeeding. (Cont.) Overfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects Mean Macronutrient Balance Carbohydrate Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) 3.3 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) 47.0 (g/day) Fat Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) 5.07 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) 84.7 Protein Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) 4.80 Oxidation (g/days) 87.7 (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) 75.3 (g/day).94 * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 53

64 i) 80 BW (kg) ii) 0 FM (kg) iii) 65 LBM (kg) Figure -d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 54

65 iv) 800 Cox (g/day) 400 v) D 4 00??9? 800 Fox (g/day) vi) ox 800 : Published PRO Oxi g per day Pox (g/day) D 4 00??9? Figure -d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 55

66 Table -e. Comparison of Jebb s data (mean, n=3, 996) vs. model simulation results during overfeeding. Cabohydrate Intake (g/d) Oxidation (g/d) Day Data Data Sim. * Dif. ** % Dif. *** Fat Intake (g/d) Oxidation (g/d) Day Data Data Sim. * Dif. ** % Dif. *** Protein Intake (g/d) Oxidation (g/d) Day Data Data Sim. * Dif. ** % Dif. *** * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Differences more than 0%. 56

67 i) 800 Cox (g/day) ii) Fox (g/day) 400 iii) Pox (g/day) Figure -e. Comparison of Jebb s data (mean, n=3, 996) vs. model simulation results during overfeeding. (Cont.) i) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. ii) Fat Oxidation Rate and Dietary Fat Intake. iii) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 57

68 Table -a. Comparison of Horton s data (lean subject mean, n=9, 995) vs. model simulation results during high-carbohydrate overfeeding. HC Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** Lean Subjects (n=9) Mean Gender Male Age 8.60 Height (m).79 Initial Body Compositon Weight (kg) BMI (kg/m^).35 Body Fat (%).40 Fat Mass (kg) 4.70 Lean Body Mass (kg) Baseline Energy Requirement (MJ/d). (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) 5.00 (kcal) Overfeeding Energy Intake (MJ/d) 6.68 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) (kcal) Macronutrient Intake Carbohydrate Intake (g/day) 67.7 Fat Intake (g/day) 0.38 Protein Intake (g/day) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. 58

69 i) 75 BW (kg) D ??5? ii) 0 FM (kg) D ??5? iii) 60 LBM (kg) Figure -a. Comparison of Horton s data (lean subject mean, n=9, 995) vs. model simulation results during high-carbohydrate overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 59

70 Table -b. Comparison of Horton s data (lean subject mean, n=9, 995) vs. model simulation results during high-fat overfeeding. HF Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** Lean Subjects (n=9) Mean Gender Male Age 8.60 Height (m).79 Initial Body Compositon Weight (kg) BMI (kg/m^).35 Body Fat (%).40 Fat Mass (kg) 4.70 Fat Free Mass (kg) Baseline Energy Requirement (MJ/d). (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) 5.00 (kcal) Overfeeding Energy Intake (MJ/d) 6.68 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 86. Protein (%) (kcal) Macronutrient Balance Carbohydrate Intake (g/day) Fat Intake (g/day) 4.8 Protein Intake (g/day) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. 60

71 i) 75 BW (kg) D 5 00??5? ii) 0 FM (kg) D 5 00??5? iii) 60 LBM (kg) Figure -b. Comparison of Horton s data (lean subject mean, n=9, 995) vs. model simulation results during high-fat overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 6

72 Table -c. Comparison of Horton s data (obese subject mean, n=7, 995) vs. model simulation results during high-carbohydrate overfeeding. HC Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** Obese Subjects (n=7) Mean Gender Male Age Height (m).79 Initial Body Compositon Weight (kg) BMI 3.43 Body Fat (%) 35.6 Fat Mass (kg) Fat Free Mass (kg) Baseline Energy Requirement (MJ/d) 3.97 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 0.4 Protein (%) 5.00 (kcal) Overfeeding Energy Intake (MJ/d) 0.95 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 0.4 Protein (%) (kcal) Macronutrient Intake Carbohydrate Intake (g/day) Fat Intake (g/day) 6.68 Protein Intake (g/day) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. 6

73 i) 0 BW (kg) ii) 40 FM (kg) D ??5? iii) 70 LBM (kg) Figure -c. Comparison of Horton s data (obese subject mean, n=7, 995) vs. model simulation results during high-carbohydrate overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 63

74 Table -d. Comparison of Horton s data (obese subject mean, n=7, 995) vs. model simulation results during high-fat overfeeding. HF Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** Obese Subjects (n=7) Mean Gender Male Age Height (m).79 Initial Body Compositon Weight (kg) BMI 3.43 Body Fat (%) 35.6 Fat Mass (kg) Fat Free Mass (kg) Baseline Energy Requirement (MJ/d) 3.97 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 0.4 Protein (%) 5.00 (kcal) Overfeeding Energy Intake (MJ/d) 0.95 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) (kcal) Macronutrient Balance Carbohydrate Intake (g/day) Fat Intake (g/day) Protein Intake (g/day) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. 64

75 i) 0 BW (kg) D ??5? ii) 45 FM (kg) D ??5 iii) 70 LBM (kg) Figure -d. Comparison of Horton s data (obese subject mean, n=7, 995) vs. model simulation results during high-fat overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 65

76 Table -e. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-carbohydrate overfeeding. HC Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** All Subjects (n=6) Mean Gender Male Age 3.54 Height (m).79 Initial Body Compositon Weight (kg) BMI (kg/m^) 6.9 Body Fat (%) 9.4 Fat Mass (kg) 4.46 Lean Body Mass (kg) Baseline Energy Requirement (MJ/d).37 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 00.0 Protein (%) 5.00 (kcal) Overfeeding Energy Intake (MJ/d) 8.55 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) 97.4 Fat (%) (kcal) 00.0 Protein (%) (kcal) Total Oxidation (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. 66

77 Table -e. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-carbohydrate overfeeding. (Cont.) HC Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** Macronutrient Balance Carbohydrate Intake (g/day) Oxidation day 0 (MJ/day) 5.30 (g/day) Oxidation day (MJ/day) 8.0 (g/day) Oxidation day 7 (MJ/day) 0.50 (g/day) Oxidation day 4 (MJ/day) 0.60 (g/day) Fat Intake (g/day) Oxidation day 0 (MJ/day) 5.60 (g/day) Oxidation day (MJ/day) 3.0 (g/day) Oxidation day 7 (MJ/day).90 (g/day) Oxidation day 4 (MJ/day).0 (g/day) Protein Intake (g/day) 94.5 Oxidation day 0 (MJ/day).70 (g/day) Oxidation day (MJ/day).30 (g/day) Oxidation day 7 (MJ/day).0 (g/day) Oxidation day 4 (MJ/day).0 (g/day) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. Estimated by figures. 67

78 i) 90 BW (kg) D ??5? ii) 30 FM (kg) iii) 65 LBM (kg) Figure -e. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-carbohydrate overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 68

79 iv) Cox (g/day) 400 v) D ??5? 800 Fox (g/day) 400 vi) D ??5? 800 Pox (g/day) Figure -e. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-carbohydrate overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. v) Fat Oxidation Rate and Dietary Fat Intake. vi) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 69

80 Table -f. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-fat overfeeding. HF Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** All Subjects (n=6) Mean Gender Male Age 3.54 Height (m).79 Initial Body Compositon Weight (kg) BMI (kg/m^) 6.9 Body Fat (%) 9.4 Fat Mass (kg) 4.46 Lean Body Mass (kg) Baseline Energy Requirement (MJ/d).37 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 00.0 Protein (%) 5.00 (kcal) Overfeeding Energy Intake (MJ/d) 8.55 (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) (kcal) Total Oxidation (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. 70

81 Table -f. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-fat overfeeding. (Cont.) HF Overfeeding (Duration: 4 days) Data Sim. * Dif. ** % Dif. *** Macronutrient Balance Carbohydrate Intake (g/day) Oxidation day 0 (MJ/day) 5.30 (g/day) Oxidation day (MJ/day) 4.40 (g/day) Oxidation day 7 (MJ/day) 4.70 (g/day) Oxidation day 4 (MJ/day) 4.90 (g/day) Fat Intake (g/day) 64.6 Oxidation day 0 (MJ/day) 4.30 (g/day) Oxidation day (MJ/day) 6.50 (g/day) Oxidation day 7 (MJ/day) 6.30 (g/day) Oxidation day 4 (MJ/day) 6.50 (g/day) Protein Intake (g/day) 94.5 Oxidation day 0 (MJ/day).50 (g/day) Oxidation day (MJ/day).40 (g/day) Oxidation day 7 (MJ/day).0 (g/day) Oxidation day 4 (MJ/day).30 (g/day) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Differences more than 0%. Estimated by figures. 7

82 i) 90 BW (kg) D ??5? ii) 30 FM (kg) iii) 65 LBM (kg) Figure -f. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high-fat overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 7

83 iv) 800 Cox (g/day) v) D ??5? 800 Fox (g/day) vi) Pox (g/day) Figure -f. Comparison of Horton s data (all subject mean, n=6, 995) vs. model simulation results during high- fat overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. v) Fat Oxidation Rate and Dietary Fat Intake. vi) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 73

84 Table 3-a. Comparison of Abbott s data (male subject mean, n=7, 995) vs. model simulation results at energy balance. Energy Balance (Duration: 4 hours) Data Sim. * Dif. ** % Dif. *** All Subjects (n=7 each) Mean Gender Male Age 7.00 Height (m).80 Initial Body Compositon Weight (kg) BMI (kg/m^) 30.5 Body Fat (%) 3.00 Fat Mass (kg).54 Fat Free Mass (kg) Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Energy Expenditure (kcal/d) Total Oxidation (kcal/d) Macronutrient Balance Carbohydrate Intake (kcal) 9.00 (g/day) 85.7 Oxidation (kcal/day) (g/day) Fat Intake (kcal) (g/day) Oxidation (kcal/day) (g/day) Protein Intake (kcal) (g/day) 0.40 Oxidation (kcal/day) (g/day) Other Losses (kcal/day) (g/day).6 Oxidation+Other Losses (g/day) * Oxidation ** Simulation results. *** Differences between published data and simulation results. **** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 74

85 i) 800 Cox (g/day) ii) H 3 00??5? ox : Published FAT Oxi g per day 3: Diet Fat 800 Fox (g/day) 400 iii) H 3 00??5? ox : Published PRO Oxi g per day 3: Diet Protein 800 Pox (g/day) H 3 00??5? Figure 3-a. Comparison of Abbott s data (male subject mean, n=7, 995) vs. model simulation results at energy balance. i) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. ii) Fat Oxidation Rate and Dietary Fat Intake. iii) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 75

86 Table 3-b. Comparison of Abbott s data (female subject mean, n=7, 995) vs. model simulation results at energy balance. Energy Balance (Duration: 4 hours) Data Sim. * Dif. ** % Dif. *** All Subjects (n=7 each) Mean Gender Female Age 5.00 Height (m).63 Weight (kg) BMI (kg/m^) Body Fat (%) Fat Mass (kg) 3.55 Fat Free Mass (kg) Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Energy Expenditure (kcal/d) Total Oxidation (kcal/d) Macronutrient Balance Carbohydrate (kcal) Intake (g/day) Oxidation (kcal/day) (g/day) Fat (kcal) Intake (g/day) Oxidation (kcal/day) 7.00 (g/day) Protein (kcal) Intake (g/day) Oxidation (kcal/day) (g/day) Other Losses (kcal/day) (g/day).6 Oxidation+Other Losses (g/day) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 76

87 i) 800 Cox (g/day) ii) H 38 00??5? 800 Fox (g/day) 400 iii) Pox (g/day) H 38 00??5? Figure 3-b. Comparison of Abbott s data (female subject mean, n=7, 995) vs. model simulation results at energy balance. i) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. ii) Fat Oxidation Rate and Dietary Fat Intake. iii) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 77

88 Table 4-a. Comparison of Jebb s data (subject, 993) vs. model simulation results during underfeeding. Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects Gender Male Age Height (m).73 Weight (kg) 67.7 BMI.63 Body Fat (%) **** 8.86 Fat Mass (kg).77 Lean Body Mass (kg) Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 78

89 Table 4-a. Comparison of Jebb s data (subject, 993) vs. model simulation results during underfeeding. (Cont.) Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects Macronutrient Balance Carbohydrate Intake (g/days) 7.60 (g/day) Fecal Losses (g/days) (g/day) 3.08 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Fat Intake (g/days) 79.0 (g/day) 3.7 Fecal Losses (g/days) (g/day) 3.88 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) -77. Protein Intake (g/days) (g/day) 64.7 Fecal Losses (g/days) (g/day) 6.95 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 79

90 i) 70 BW (kg) D ??4? ii) Mass kg 0 : Published Data Fat Mass kg FM (kg) iii) Body Mass kg 60 : Published Data Lean Body Mass kg LBM (kg) Figure 4-a. Comparison of Jebb s data (subject, 993) vs. model simulation results during highfat overfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 80

91 iv) 400 Cox (g/day) 00 v) D ??4? 400 Fox (g/day) D ??4? vi) 400 g p y Pox (g/day) D ??4? Figure 4-a. Comparison of Jebb s data (subject, 993) vs. model simulation results during overfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 8

92 Table 4-b. Comparison of Jebb s data (subject3 *, 993) vs. model simulation results during underfeeding. Underfeeding (Duration: days) Data Sim. ** Dif. *** % Dif. **** Subjects 3' Gender Male Age 4.00 Height (m).77 Weight (kg) BMI 4.57 Body Fat (%) *****.35 Fat Mass (kg) 6.44 Lean Body Mass (kg) Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) ***** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * Subject (overfeeding) and subject 3 (underfeeding) are the same individual. ** Simulation results. *** Differences between published data and simulation results. **** %Differences = difference / data. ***** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 8

93 Table 4-b. Comparison of Jebb s data (subject 3 *, 993) vs. model simulation results during underfeeding. (Cont.) Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects 3 Macronutrient Balance Carbohydrate Intake (g/days) 7.60 (g/day) Fecal Losses (g/days) (g/day) 5.4 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Fat Intake (g/days) (g/day) 3.7 Fecal Losses (g/days) 4.50 (g/day).04 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) -6.3 Protein Intake (g/days) (g/day) 64.7 Fecal Losses (g/days) 0.0 (g/day) 7.5 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) -3.9 * Subject (overfeeding) and subject 3 (underfeeding) are the same individual. ** Simulation results. *** Differences between published data and simulation results. **** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 83

94 i) 80 BW (kg) ii) 0 FM (kg) iii) 65 LBM (kg) D ??4? Figure 4-b. Comparison of Jebb s data (subject 3, 993) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 84

95 iv) 400 Cox (g/day) 00 v) Fox (g/day) 00 vi) Pox (g/day) Figure 4-b. Comparison of Jebb s data (subject 3, 993) vs. model simulation results during underfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 85

96 Table 4-c. Comparison of Jebb s data (subject 4, 993) vs. model simulation results during underfeeding. Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects 4 Gender Male Age 9.00 Height (m).87 Weight (kg) 76.3 BMI.83 Body Fat (%) **** 7.83 Fat Mass (kg) 3.6 Lean Body Mass (kg) 6.7 Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 86

97 Table 4-c. Comparison of Jebb s data (subject 4, 993) vs. model simulation results during underfeeding. (Cont.) Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects Macronutrient Balance Carbohydrate Intake (g/days) (g/day) Fecal Losses (g/days) (g/day) 4. Oxidation (g/days) 7.60 (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Fat Intake (g/days) 77.0 (g/day) 3.0 Fecal Losses (g/days) (g/day).96 Oxidation (g/days).30 (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Protein Intake (g/days) (g/day) 64.7 Fecal Losses (g/days).00 (g/day) 7.58 Oxidation (g/days) 6.30 (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 87

98 i) 80 BW (kg) ii) 0 FM (kg) 5 iii) D ??4? Body Mass kg 65 : Published Data Lean Body Mass kg LBM (kg) D ??4? Figure 4-c. Comparison of Jebb s data (subject 4, 993) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 88

99 iv) 400 Cox (g/day) 00 v) Fox (g/day) 00 vi) Pox (g/day) Figure 4-c. Comparison of Jebb s data (subject 4, 993) vs. model simulation results during underfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 89

100 Table 4-d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during underfeeding. Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects (n=3) Mean Gender Male Age 3.33 Height (m).79 Weight (kg) BMI 3.0 Body Fat (%) 9.34 Fat Mass (kg) 4.5 Lean Body Mass (kg) 59.4 Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) Total Oxidation + Fecal Loss (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Estimation. Differences more than 0%. 90

101 Table 4-d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during underfeeding. (Cont.) Underfeeding (Duration: days) Data Sim. * Dif. ** % Dif. *** Subjects (n=3) Mean Macronutrient Balance Carbohydrate Intake (g/days) 83.7 (g/day) Fecal Losses (g/days) (g/day) 4. Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Fat Intake (g/days) 78.3 (g/day) 3.8 Fecal Losses (g/days) (g/day).96 Oxidation (g/days) 8.77 (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Protein Intake (g/days) (g/day) 64.7 Fecal Losses (g/days) 08.7 (g/day) 7.35 Oxidation (g/days) (g/day) Oxidation + Fecal Loss (g/day) Balance (g/days) (g/day) Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 9

102 i) 80 BW (kg) ii) 0 FM (kg) iii) 65 LBM (kg) Figure 4-d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 9

103 iv) 400 Cox (g/day) v) 400 Fox (g/day) 00 vi) D ??4? 400 Pox (g/day) D ??4 Figure 4-d. Comparison of Jebb s data (mean, n=3, 993) vs. model simulation results during underfeeding. (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate Simulation Published Data. 93

104 Table 4-e. Comparison of Jebb s data (mean, n=3, 996) vs. model simulation results during underfeeding. Carbohydrate Intake (g/d) Oxidation (g/d) Day Data Data Sim. * Dif. ** % Dif. *** Fat Intake (g/d) Oxidation (g/d) Day Data Data Sim. * Dif. ** % Dif. *** Protein Intake (g/d) Oxidation (g/d) Day Data Data Sim. * Dif. ** % Dif. *** * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Differences more than 0%. 94

105 i) 400 Cox (g/day) ii) D 59 00??4? 400 Fox (g/day) 00 iii) Pox (g/day) Figure 4-e. Comparison of Jebb s data (mean, n=3, 996) vs. model simulation results during underfeeding. (Cont.) i) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. ii) Fat Oxidation Rate and Dietary Fat Intake. iii) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 95

106 Table 5-a. Comparison of Berlin s data (subject W.T., 96) vs. model simulation results during underfeeding. Underfeeding (Duration: 55 days) Data Sim. * Dif. ** % Dif. *** Subject W.T. Gender Male Age Height (m).8 Initial Body Compositon Weight (kg) BMI 60.6 Body Fat (%) **** 58.6 Fat Mass (kg) 5.50 Lean Body Mass (kg) 83.0 Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) (kcal) 49.6 Macronutrient Intake Carbohydrate (g/day) 97.5 Fat (g/day) 6.58 Protein (g/day) End Body Composition Weight (kg) BMI Body Fat (%) * Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/period) Fat Weight (kg/period) Lean Body Mass (kg/period) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. Estimated by figures. 96

107 i) 00 BW (kg) ii) 0 FM (kg) 00 iii) D ??6? 00 LBM (kg) Figure 5-a. Comparison of Berlin s data (subject W.T., 96) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 97

108 Table 5-b. Comparison of Berlin s data (subject E.C., 96) vs. model simulation results during underfeeding. Underfeeding (Duration: 70 days) Data Sim. * Dif. ** % Dif. *** Subject E.C. Gender Female Age Height (m).74 Initial Body Compositon Weight (kg) 8.00 BMI 4.8 Body Fat (%) **** Fat Mass (kg) Lean Body Mass (kg) Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) 00.6 Protein (%) (kcal) Macronutrient Intake Carbohydrate (g/day) 97.5 Fat (g/day).5 Protein (g/day) End Body Composition Weight (kg) BMI Body Fat (%) * Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/period) Fat Weight (kg/period) Lean Body Mass (kg/period) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. Estimated by figures. 98

109 i) 30 BW (kg) D ??6? ii) 80 FM (kg) D ??6? iii) 55 LBM (kg) Figure 5-b. Comparison of Berlin s data (subject E.C., 96) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 99

110 Table 5-c. Comparison of Berlin s data (subject A.I., 0-57 days, 96) vs. model simulation results during underfeeding. Underfeeding (Duration: 57 days) Data Sim. * Dif. ** % Dif. *** Subject A.I. Gender Female Age Height (m).57 Initial Body Compositon Weight (kg) 0.00 BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass (kg) Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) (kcal) 39.3 Macronutrient Intake Carbohydrate (g/day) 93.3 Fat (g/day) 5.97 Protein (g/day) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/period) Fat Weight (kg/period) Lean Body Mass (kg/period) #DIV/0! * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. Estimated by figures. 00

111 i) 05 BW (kg) D ??6? ii) 70 FM (kg) D ??6? iii) 50 LBM (kg) Figure 5-c. Comparison of Berlin s data (subject A.I., 0-57 days, 96) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 0

112 Table 5-d. Comparison of Berlin s data (subject A.I., days, 96) vs. model simulation results during underfeeding. Underfeeding (Duration: 55 days) Data Sim. * Dif. ** % Dif. *** Subject A.I. Gender Female Age Height (m).57 Initial Body Compositon Weight (kg) BMI Body Fat (%) **** 60. Fat Mass (kg) Lean Body Mass (kg) Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) (kcal) Fat (%) (kcal) Protein (%) (kcal) Macronutrient Intake Carbohydrate (g/day) Fat (g/day) 0.5 Protein (g/day) End Body Composition Weight (kg) BMI Body Fat (%) **** Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/period) Fat Weight (kg/period) Lean Body Mass (kg/period) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. **** Body Fat =.8 (Wt/Ht^)-0.3 Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Estimation. Differences more than 0%. Estimated by figures. 0

113 i) 95 BW (kg) D ??6? ii) 60 FM (kg) D ??6? iii) 45 LBM (kg) Figure 5-d. Comparison of Berlin s data (subject A.I., days, 96) vs. model simulation results during underfeeding. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 03

114 Table 6-a. Comparison of van Gemert s data (mean, n=8, 000) vs. model simulation results 0-90 days after surgery. After Surgery (0-90 days) Data Sim. * Dif. ** % Dif. *** Obese Subjects (n=8) Mean Gender (male, female), 7 Age Height (m).69 Weight (kg) 30.0 BMI Body Fat (%) 5.50 Fat Mass (kg) Lean Body Mass (kg) 6.80 Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Energy Expenditure (MJ/d) (kcal/d) Total Oxidation (kj/d) (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Differences more than 0%. 04

115 Table 6-a. Comparison of van Gemert s data (mean, n=8, 000) vs. model simulation results 0-90 days after surgery. (Cont.) After Surgery (0-90 days) Data Sim. * Dif. ** % Dif. *** Macronutrient Balance Carbohydrate Intake (kj) (kcal) (g) 8.65 Oxidation (kj/day) (kcal/day) (g/day) Fat Intake (kj) (kcal) (g) 4.79 Oxidation (kj/day) (kcal/day) 5.9 (g/day) Protein Intake (kj) (kcal) 3.45 (g) 7.94 Oxidation (kj/day) (kcal/day) (g/day) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Differences more than 0%. 05

116 i) 35 BW (kg) D 5 00??6? ii) 75 FM (kg) D 5 00??6? iii) 75 LBM (kg) Figure 6-a. Comparison of van Gemert s data (obese subject mean, n=8, 000) vs. model simulation results 0-90 days after surgery. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 06

117 iv) 400 Cox (g/day) v) D 7 00??6? 400 Fox (g/day) vi) Pox (g/day) Figure 6-a. Comparison of van Gemert s data (obese subject mean, n=8, 000) vs. model simulation results 0-90 days after surgery. (Cont.) iv) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. v) Fat Oxidation Rate and Dietary Fat Intake. vi) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake. 07

118 Table 6-b. Comparison of van Gemert s data (obese subject mean, n=8, 000) vs. model simulation results days after surgery. After Surgery (9-360 days) Data Sim. * Dif. ** % Dif. *** Obese Subjects (n=8) Mean Gender (male, female), 7 Age Height (m).69 Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass (kg) Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Energy Expenditure (MJ/d) (kcal/d) Total Oxidation (kj/d) (kcal/d) End Body Composition Weight (kg) BMI 9.43 Body Fat (%) * Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/4days) Fat Weight (kg/4days) Fat Free Mass (kg/4days) * Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Fecal loss included. Data compared in following figures. Differences more than 0%. 08

119 Table 6-b. Comparison of van Gemert s data (obese subject mean, n=8, 000) vs. model simulation results days after surgery. (Cont.) After Surgery (9-360 days) Data Sim. * Dif. ** % Dif. *** Macronutrient Balance Carbohydrate Intake (kj) (kcal) (g) Oxidation (kj/day) (kcal/day) 8.8 (g/day) Fat Intake (kj) (kcal) (g) Oxidation (kj/day) (kcal/day) (g/day) Protein Intake (kj) (kcal) 03.5 (g) 43.9 Oxidation (kj/day) (kcal/day) 9.45 (g/day) Simulation results. ** Differences between published data and simulation results. *** %Differences = difference / data. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. Differences more than 0%. 09

120 i) 0 BW (kg) D 34 00??6? ii) 60 FM (kg) D 34 00??6 iii) 60 LBM (kg) Figure 6-b. Comparison of van Gemert s data (obese subject mean, n=8, 000) vs. model simulation results days after surgery. i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change Simulation Published Data. 0

121 iv) 400 Cox (g/day) v) D 40 00??6? 400 Fox (g/day) vi) Pox (g/day) D 40 00??6? Figure 6-b. Comparison of van Gemert s data (obese subject mean, n=8, 000) vs. model simulation results days after surgery. (Cont.) iv) Carbohydrate Oxidation Rate and Dietary Carbohydrate Intake. v) Fat Oxidation Rate and Dietary Fat Intake. vi) Protein Oxidation Rate and Dietary Protein Intake Simulation Published Data Dietary Intake.

122 Table 7-a. Application: Comparison of ADA * diet vs. high-protein diets during underfeeding (80 days). Underfeeding (Duration: 80 days) ADA * Sim. ** Atkins Sim. Zone Sim. Subjects Gender Male Male Male Age Height (m) Initial Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass (kg) Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * American Dietetics Association. ** Simulation results. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures.

123 Table 7-a. Application: Comparison of ADA * diet vs. high-protein diets during underfeeding (80 days). (Cont.) Underfeeding (Duration: 80 days) ADA * Sim. ** Atkins Sim. Zone Sim. Macronutrient Balance Carbohydrate Intake (kcal) (g/day) Oxidation (g/day) Fat Intake (kcal) (g/day) Oxidation (g/day) Protein Intake (kcal) (g/day) Oxidation (g/day) * American Dietetics Association. ** Simulation results. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. 3

124 i) BW (kg) ii) FM (kg) D ?3?8? iii) LBM (kg) Figure 7-a. Application: Comparison of ADA * diet vs. high-protein diets during underfeeding (80 days). i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change ADA diet Atkins diet The Zone diet. 4

125 iv) 600 Cox (g/day) v) Fox (g/day) vi) Pox (g/day) Figure 7-a. Application: Comparison of ADA * diet vs. high-protein diets during underfeeding (80 days). (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate ADA diet Atkins diet The Zone diet. 5

126 Table 7-b. Application: Comparison of ADA * diet vs. high-protein diets at energy balance (80 days). Energy Balance (Duration: 80 days) ADA * Sim. ** Atkins Sim. Zone Sim. Subjects Gender Male Male Male Age Height (m) Initial Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass (kg) Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * American Dietetics Association. ** Simulation results. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. 6

127 Table 7-b. Application: Comparison of ADA * diet vs. high-protein diets at energy balance (80 days). (Cont.) Energy Balance (Duration: 80 days) ADA * Sim. ** Atkins Sim. Zone Sim. Macronutrient Balance Carbohydrate Intake (kcal) (g/day) Oxidation (g/day) Fat Intake (kcal) (g/day) Oxidation (g/day) Protein Intake (kcal) (g/day) Oxidation (g/day) * American Dietetics Association. ** Simulation results. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. 7

128 i) 0 BW (kg) ii) D ?3?8? Mass kg ADA : Fat Mass kg Atkins 3: Fat Mass kg Zone 50 FM (kg) iii) 90 LBM (kg) D ?3?8? Figure 7-b. Application: Comparison of ADA * diet vs. high-protein diets at energy balance (80 days). i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change ADA diet Atkins diet The Zone diet. 8

129 iv) 600 Cox (g/day) v) Fox (g/day) vi) Pox (g/day) Figure 7-b. Application: Comparison of ADA * diet vs. high-protein diets at energy balance (80 days). (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate ADA diet Atkins diet The Zone diet. 9

130 Table 7-c. Application: Comparison of ADA * diet vs. high-protein diets during overfeeding (80 days). Overfeeding (Duration: 80 days) ADA * Sim. ** Atkins Sim. Zone Sim. Subjects Gender Male Male Male Age Height (m) Initial Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass (kg) Total Energy Intake (kcal/d) Macronutrient Composition Carbohydrate (%) Fat (%) Protein (%) Total Oxidation (kcal/d) End Body Composition Weight (kg) BMI Body Fat (%) Fat Mass (kg) Lean Body Mass Body Composition Change Body Weight (kg/days) Fat Weight (kg/days) Lean Body Mass (kg/days) * American Dietetics Association. ** Simulation results. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures. 0

131 Table 7-c. Application: Comparison of ADA * diet vs. high-protein diets during overfeeding (80 days). (Cont.) Overfeeding (Duration: 80 days) ADA * Sim. ** HP Sim. HP Sim. Macronutrient Balance Carbohydrate Intake (kcal) (g/day) Oxidation (g/day) Fat Intake (kcal) (g/day) Oxidation (g/day) Protein Intake (kcal) (g/day) Oxidation (g/day) * American Dietetics Association. ** Simulation results. Color & highlight distinction: Model inputs. Simulation results. Data compared in following figures.

132 i) BW (kg) D ?3?8? ii) 60 FM (kg) iii) LBM (kg) D ?3?8? Figure 7-c. Application: Comparison of ADA * diet vs. high-protein diets during overfeeding (80 days). i) Body Weight Change. ii) Fat Mass Change. iii) Lean Body Mass Change ADA diet Atkins diet The Zone diet.

133 iv) 600 Cox (g/day) v) Fox (g/day) 300 vi) Pox (g/day) Figure 7-c. Application: Comparison of ADA * diet vs. high-protein diets during overfeeding (80 days). (Cont.) iv) Carbohydrate Oxidation Rate. v) Fat Oxidation Rate. vi) Protein Oxidation Rate ADA diet Atkins diet The Zone diet. 3

134 APPENDICES Appendix A: STELLA model for people with BMI<30 A-. Interface 4

135 A-. Model 5

136 A-3. Equations Body Composition Change delta_body_water_kg = Body_Water_kg - Initial_Body_Water_kg delta_body_weight_kg = Body_Weight_kg - Initial_Body_Weight_kg delta_fat_mass_kg = Fat_Mass_kg - Initial_Fat_Mass_kg delta_lbm_kg = LBM_kg - Initial_LBM_kg Future Body Composition Body_Cell_Mass_g = Intracellular_Water_g + Protein_g + Liver_Glycogen_g + Intracellular_Solids_g {Equation from Kevin D. Hall (006)} Body_Water_% = (Body_Water_kg / Body_Weight_kg) * 00 Body_Water_kg = (Extracellular_Water_g + Intracellular_Water_g) / 000 Body_Weight_kg = Fat_Mass_kg + LBM_kg Fat_Mass_kg = Fat_g / 000 Fat_Rate_% = (Fat_Mass_kg / Body_Weight_kg) * 00 Intracellular_Water_g = Non_Bound_Intracellular_Water_g + Liver_Glycogen_g *.4 + Protein_g * {Protein binds with g of water. Data from MacKay and Bergman (934), McBride et al. (94) Glycogen binds with.4g of water. Data from Puckett and Wiley (93), Nilsson (973)} LBM_kg = (Body_Cell_Mass_g + Bone_Mass_g + Extracellular_Water_g) / 000 {Equation from Hall (006)} Initial Body Composition Bone_Mass_g = IF (Gender = 0) THEN (( * Initial_LBM_kg) * 000) ELSE IF (Gender = ) THEN (( * Initial_LBM_kg) * 000) ELSE (( * Initial_LBM_kg) * 000) {Equations from Ferretti (998), Figure. Age limitations are from 3 to 83 years old for male and from to 87 years old for female.} Extracellular_Water_g = ( * Initial_Body_Water_kg) * 000 {Data from Ritz (000). Age limit is 5~63yrs} Gender = 0 {A user has to imput this data. Males: 0, Premenopausal females:, Postmenopausal females:. Note: Age limitations are from yrs to 87 yrs.} Initial_Body_Cell_Mass_g = (Initial_LBM_kg * 000) - Extracellular_Water_g - Bone_Mass_g {Equation from Hall (006)} Initial_Body_Water_kg = Initial_LBM_kg * 0.73 {Data from Sheng and Huggins (979)} Initial_Body_Weight_kg = 0 {A user has to input this data.} Initial_Fat_Mass_kg = Initial_Body_Weight_kg * Initial_Fat_Rate_% * 0.0 Initial_Fat_Rate_% = 0 {A user has to imput this data} Initial_Intracellular_Water_g = ( * Initial_Body_Water_kg) * 000 {Data from Ritz (000). Age limit is 5~63yrs} Initial_LBM_kg = Initial_Body_Weight_kg - Initial_Fat_Mass_kg Initial_Liver_Glycogen_g = Liver_Weight_kg * 43.7 {Data from Nilsson (973)} Initial_Protein_g = Initial_Body_Cell_Mass_g * 0.8 {Lean cell mass is approximately 8% protein. Data from Albert (989)} Intracellular_Solids_g = Initial_Body_Cell_Mass_g-Initial_Protein_g-Initial_Liver_Glycogen_g- Initial_Intracellular_Water_g {Equation from Kevin D. Hall 006} Liver_Weight_kg = Initial_Body_Weight_kg * 0.06 {Liver weight is.6% of total Body Weight. Data from Brown et al. (997)} 6

137 Non_Bound_Intracellular_Water_g = Initial_Intracellular_Water_g - (Initial_Protein_g * ) - (Initial_Liver_Glycogen_g *.4) {Protein binds with g of water. Data from MacKay and Bergman (934), McBride et al. (94) Glycogen binds with.4g of water. Data from Puckett and Wiley (93), Nilsson (973)} Macronutrient Metabolism Carb_g(t) = Carb_g(t - dt) + (Glycogenolysis + Gluconeogenesis_f + Diet_CHO + Gluconeogenesis_p - Glycogen_Synthesis - Lipogenesis_glu - CHO_plus_PRO_ox) * dt INIT Carb_g = 0 INFLOWS: Glycogenolysis = (.44 + ( ) * (Diet_CHO / Body_Weight_kg)) * Body_Weight_kg {Data from Selz (003)} Gluconeogenesis_f = FAT_ox * {Glycerol is about0% of total TG} Diet_CHO = 0 {A user has to input this info.} Gluconeogenesis_p = Gluconeogenesis_p' * {Glucose equivalent to g of US intake protein is g. Data from DRI and Milgen (00)} OUTFLOWS: Glycogen_Synthesis = (Max_Liver_Glycogen_g - Liver_Glycogen_g) * 0.55 {In g/day. Linear regression slope of 0.55 of remaining glycogen storage capacity versus glycogen synthesis rate. Data from Acheson et al. (988)} Lipogenesis_glu = Diet_CHO + Gluconeogenesis_p + Glycogenolysis + Gluconeogenesis_f - CHO_plus_PRO_ox - Glycogen_Synthesis CHO_plus_PRO_ox = (( * (Diet_CHO / Body_Weight_kg) ) * Body_Weight_kg) + (PRO_ox * 0.9) {Data from Shetty (994)} Fat_g(t) = Fat_g(t - dt) + (Diet_Fat + Lipogenesis_fat - FAT_ox - Gluconeogenesis_f) * dt INIT Fat_g = Initial_Fat_Mass_kg * 000 INFLOWS: Diet_Fat = 0 {A user has to input this info.} Lipogenesis_fat = (Lipogenesis_glu * 0.357) *.070 {Absolute DNL is about one third of the amount of the glucose converted to fat. Data from Schwarz (995), Table 3. Adding 0% to account for glycerol.} OUTFLOWS: FAT_ox = ( ((-0.43) *( Diet_CHO / Body_Weight_kg))) * Body_Weight_kg {Data from Shetty (994)} Gluconeogenesis_f = FAT_ox * {Glycerol is about0% of total TG} Liver_Glycogen_g(t) = Liver_Glycogen_g(t - dt) + (Glycogen_Synthesis - Glycogenolysis) * dt INIT Liver_Glycogen_g = Initial_Liver_Glycogen_g {in grams typical storage level in liver} INFLOWS: Glycogen_Synthesis = (Max_Liver_Glycogen_g - Liver_Glycogen_g) * 0.55 {In g/day. Linear regression slope of 0.55 of remaining glycogen storage capacity versus glycogen synthesis rate. Data from Acheson et al. (988)} OUTFLOWS: Glycogenolysis = (.44 + ( ) * (Diet_CHO / Body_Weight_kg)) * Body_Weight_kg {Data from Selz (003)} Protein_g(t) = Protein_g(t - dt) + (Diet_Protein - Gluconeogenesis_p') * dt INIT Protein_g = Initial_Protein_g INFLOWS: Diet_Protein = 0 {A user has to input this info.} 7

138 OUTFLOWS: Gluconeogenesis_p' = PRO_ox UNATTACHED: PRO_ox = ( (-0.05) * (Diet_CHO / Body_Weight_kg) * (Diet_Protein / Body_Weight_kg)) * Body_Weight_kg {Data from Young (000) and Shetty (994)} Max_Liver_Glycogen_g = Liver_Weight_kg * 80. {Data from Nilsson (973)} Oxidation Rate CHO_oxi_per_kg = CHO_oxi / Body_Weight_kg Fat_ox_per_kg = FAT_ox / Body_Weight_kg Protein_ox_per_kg = PRO_ox / Body_Weight_kg Total Energy Intake Carbohydrate_en% = (Diet_CHO * 4.8 * 00) / TEI {Energy Density of CHO: 4.8. Data from Livesey and Elia (988), table 6} Fat_en% = (Diet_Fat * 9.44 * 00) / TEI {Energy Density of FAT: Data from Livesey and Elia (988), table 6} Protein_en% = (Diet_Protein * * 00) / TEI {Energy Density of PRO: Data from Livesey and Elia (988), table 6} TEI = Diet_CHO * 4. + Diet_Protein * Diet_Fat * 9.4 {TEI:Total Energy Intake (kcal/day), Energy Density of CHO: 4.8, FAT: 9.44, PRO: Data from Livesey and Elia (988), table 6} Total Oxidation CHO_oxi = CHO_plus_PRO_ox - (PRO_ox * 0.905) Total_Oxidation_kcal = CHO_oxi * FAT_ox * PRO_ox * {Energy Density of CHO: 4.8, FAT: 9.44, PRO: Data from Livesey and Elia (988), table 6} Not in a sector 8

139 Appendix B: STELLA model for people with BMI>30 B-. Interface 9

140 B-. Model 30