The Calculus of Calories Quantifying Human Body Weight Dynamics

Transcription

1 The Calculus of Calories Quantifying Human Body Weight Dynamics Kevin D. Hall, Ph.D. NIDDK May 2, 2013

2 The Old Math of Weight Loss 3500 kcal per pound Practical Guide to the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults. NHLBI Obesity Education Initiative (2000).

3 Soda Taxes & Obesity Reversal? Body Weight (kg) kcal per lb rule Time (years) TA Smith, BH Lin, HY Lee. USDA ERS Research Report 100 (2010)

4 Human Macronutrient Metabolism Food Intake Carbohydrate Intake Fat Intake Protein Intake Physical Activity Fuel Selection Carbohydrate Oxidation Fat Oxidation Nitrogen Excretion Mathematical Model of Human Metabolism Energy Expenditure Resting Metabolic Rate Total Energy Expenditure Body Weight Lean Mass Fat Mass Body Water Body Composition Glucose Turnover Gluconeogenesis Lipolysis Ketogenesis Lipogenesis Metabolic Fluxes

5 Model Equations dg ρc = CI DNL + GNG P + GNG F G 3 P CarbOx dt DNL = df ρf = 3M FFAFI MTG + εd DNL KUexcr ( 1 εk ) KTG FatOx dt ρ dp PI GNG ProtOx P = P dt FFM = BM + ECF + ECP + LCM = BM + ECF + ECP + ICW + P + G + ICS = BM + ECF + ECP + ICW ˆ + P(1 + h ) + G(1 + h ) + ICS decf 1 = Na ECF ECF CI CI + ECF dt τ d ECF dt ( diet ξna ( init ) ξci ( 1 b )) [ Na] ( ) = ξ BW BW ECF BW BW init P G TEE = TEF + PAE + RMR D ˆ F D F PI G KTG = ρkdf AK exp exp RMR = Ec + γbm B + γ FFM FFM M B G ( 1+ hg ) ( ECF ECFinit ) + γf F ˆ kp kg KK + DF DF PIb Ginit + (1 εd) DNL + (1 εg)( GNGF + GNGP) + ( 1 εk) KTG 0, if KTG ρk < KTGthresh dp df dg KUexcr = ρk KUmax ( KTG ρk KTGthresh ) + ηn Nexcr + ( ηp + εp ) DP + ηp + ηf DF + ηf + ηgdg + η, else G dt dt dt ( KTGmax KTGthresh ) dt τt dt ˆ γ FFM TEF = α FI + α PI + α CI F ( b) ( EI EI ) λ EI EI T, if EI < EI 1 b = λ2 b T, else dm i = γi dffm i ( ) ( 1 ) γ = ˆ γ 1+ 1 σ FFM FFM T PAE = δ + σt BW + υbw P C CarbOx = GNG + GNG G3P + f TEE f p C FatOx = KetOx + ff TEE ProtOx = f TEE P CI ( G Ginit ) d d ( GG ) + K f f init C F ( ˆ ) { ( )} ( min ) w ( ˆ G DG DG) + wcmax 0, 1+ SC CI CIb G G + G = Z w D D = Z F F F ˆ G DG = DG G init { 0, ( 1+ )} + ( ˆ ) exp ( ( δ + υ) ( δ + υ )) w MAX P D D S k fp = Z dpsig τ PI = SP PI PIb Psig dt [ ] P sig P P A A b b 2 3 ˆ F D = D L + L F Keys F F diet PA ( ) ( ) SL dl KL 1 + AL BL exp k diet LCI CIb + BL τ L = L dt SL K + MAX F F ρcm G M G GNGF = FI + DFρC ρfmtg MTG GNG d DNL L D P ˆ P PI = DP + χ P Keys PIb SL { 0, ( Keys 1) } L PA diet δ + υ = ψ 1 δ init + υ init ˆ P CI PI = GNG Γ + ( Γ + χ ) P Keys CIb PIb P P C P

6 Model Validation Compare model predictions with data from independent experiments only changing the initial conditions of the model to match the study & no parameter fitting! KD Hall. Am J Physiol 291: E23 E37 (2006). KD Hall. Am J Physiol. 298(3): E (2010).

7 Weight Loss during Fasting 65 Body Weight (kg) BW data BW model Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012). Data from F. Benedict A study of prolonged fasting (1915)

8 Fasting & Body Composition Mass Change (kg) Fat-free Mass Fat Mass Fat Mass Fat-free Mass Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012).

9 Fasting & Fuel Mobilization Metabolic Flux (g/d) Lipolysis Proteolysis Glycogenolysis Days of Fasting Glycogenolysis Lipolysis Proteolysis KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012).

10 Fasting & Fuel Utilization Oxidation Rate (kcal/d) Carbohydrate Oxidation Carbohydrate Fat + Ketones Protein Fat + Ketone Oxidation Protein Oxidation Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012).

11 Fasting & Respiratory Quotient Burning Carbs Respiratory Quotient Burning Fat Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012). Data from F. Benedict A study of prolonged fasting (1915)

12 Fasting & Energy Expenditure Energy Rate (kcal/d) TEE model TEE data Total Energy Expenditure RMR model RMR data Resting Metabolic Rate Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012). Data from F. Benedict A study of prolonged fasting (1915)

13 Fasting & Ketone Excretion 8 Ketone Excretion (g/d) Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012). Data from F. Benedict A study of prolonged fasting (1915)

14 Fasting & Nitrogen Excretion N excretion (g/d) Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012). Data from F. Benedict A study of prolonged fasting (1915)

15 3500 Leibel et al. NEJM 1995 Energy Rate (kcal/d) % Weight Loss 20% Weight Loss Energy Intake Time (weeks)

16 140 Leibel et al. NEJM Body Weight Mass (kg) Fat-Free Mass 40 Fat Mass Time (weeks)

17 3500 Leibel et al. NEJM Energy Rate (kcal/d) Physical Activity Total Energy Expenditure Resting Metabolic Rate Time (weeks)

18 The Biggest Loser Competition Johannsen, Knuth, Huizenga, Ravussin, Hall. JCEM (2012) K.D. Hall. Obesity (2013)

19 Biggest Loser Model Simulations 20 Isolated on Ranch At Home Mass Change (kg) Fat Mass Body Weight Time (weeks) K.D. Hall. Obesity (2013)

20 Biggest Loser Model Simulations Energy Rate (kcal/d) Total Energy Expenditure Resting Metabolic Rate Energy Intake Exercise Time (weeks) K.D. Hall. Obesity (2013)

21 Inverse Problem: Estimating Intake Baseline Demographics & Anthropometrics Body Weight Mathematical Model of Human Metabolism Energy Intake KD Hall. Am J Physiol. 298(3): E (2010) KD Hall, CC Chow. AJCN 94:66-74 (2011)

22 Weight Plateau and Regain 10 5 Weight Change (kg) Time (months) Data from LP Svetky et al. JAMA. 299: (2008)

23 Energy Balance Interpretation 2500 Energy Intake Energy Rate (kcal/d) Total Energy Expenditure Progressive Loss of Diet Adherence! Time (months) KD Hall. Am J Physiol. 298(3): E (2010).

24 Weight Loss Maintenance 0-2 Mass Change (kg) Fat Mass Change Body Weight Change Time (months) KD Hall. Am J Physiol. 298(3): E (2010).

25 Energy Intake for Maintenance 2500 Energy Rate (kcal/d) Energy Intake Total Energy Expenditure ~200 kcal/d Time (months) KD Hall. Am J Physiol. 298(3): E (2010).

26 5% Weight Loss vs. Maintenance 5% Weight Loss in 6 months Maintenance of 5% Weight Loss BMI = 35 kg/m kcal/d -90 kcal/d BMI = 50 kg/m kcal/d -100 kcal/d

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28 Soda Taxes & Obesity Reversal? Body Weight (kg) kcal per lb rule Dynamic Model Time (years) KD Hall et al. The Lancet (2011)

29 Prevalence BMI > Predicted Change in Obesity Prevalence N = 4293 Dynamic Model 3500 kcal per lb rule Time (years) BH Lin, TA Smith, HY Lee, KD Hall. Econ Hum Biol (2011)

30 Modeling the Rise of Adult Obesity 82 Average Body Weight (kg) Ave. Body Weight Year Data from National Health and Nutrition Examination Survey (NHANES)

31 U.S. Food Supply 3900 Per Capita Food Energy (kcal/d) FAO Food Supply USDA Loss Adjusted Food Availability Food Intake (model) Year KD Hall, J Guo, M Dore, CC Chow. PLoS ONE (2009)

32 If we had eaten all of the 100 USDA Food Available Average Body Weight (kg) Simulated Body Weight NHANES Body Weight Year

33 Food Supply, Intake, and Waste 3900 Per Capita Food Energy (kcal/d) FAO Food Supply Wasted Food! Food Intake (model) Year KD Hall, J Guo, M Dore, CC Chow. PLoS ONE (2009)

34 Progressive Increase of 1800 Food Waste Per Capita Food Waste (kcal/d) Food Waste (model) Food Loss (USDA) Year KD Hall, J Guo, M Dore, CC Chow. PLoS ONE (2009)

35 Progressive Increase of 1800 Food Waste 120 Per Capita Food Waste (kcal/d) Food Waste (model) Solid Food Waste (EPA) Per Capita Solid Food Waste (kg/yr) Year KD Hall, J Guo, M Dore, CC Chow. PLoS ONE (2009)

36 The Push Hypothesis Agriculture Research, Subsidies, & Policy Obesity Increased production Increased food waste More Cheap food KD Hall, J Guo, M Dore, CC Chow. PLoS ONE (2009)

37 Intramural NIH Amber Courville (CC) Peter Herscovitch (CC) John Ingeholm (NIMH) Seth Kallman (NIMH) Alex Martin (NIMH) Lydia Milbury (NIMH) Kristina Rapuano (NIMH) Nancy Sebring (CC) W. Kyle Simmons (NIMH) Nora Volkow (NIDA) Intramural NIDDK Thomas Bemis Dhruva Chandramohan Kong Chen I-Ling Chen Helen Cheung Carson Chow Stephanie Goodwin Juen Guo Gail Hall Peter Jordan Nick Knuth Bernard Miller Laura Musse Vipul Periwal Carla Prado Arjun Sanghvi Mario Siervo Monica Skarulis Wayne Staton Terri Wakefield Extramural Collaborators Graham Finlayson (Leeds) Dympna Gallagher (Columbia) Steve Gortmaker (Harvard) Robert Huizenga (UCLA) Darcy Johannsen (Pennington) Biing Lin (USDA) Peter Murgatroyd (MRC Cambridge) Eric Ravussin (Pennington) Leanne Redman (Pennington) Boyd Swinburn (Deakin) Steven R. Smith (Sanford Burnham) Special Thanks Nursing Staff at the NIH MCRU Volunteer Study Subjects