Body Weight Dynamics Kevin D. Hall, Ph.D. NIDDK May 2, 2013 The - PowerPoint PPT Presentation

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

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).

Soda Taxes & Obesity Reversal? 82 80 Body Weight (kg) 78 76 3500 kcal per lb rule 74 72 70 0 1 2 3 4 5 Time (years) TA Smith, BH Lin, HY Lee. USDA ERS Research Report 100 (2010)

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

Model Equations      ∆  P PI = + χ ˆ       D D dG   ρ = − + + − − P P ( )   P  PI  CI DNL GNG GNG G P 3 CarbOx ×   d     CI G G C P F G Keys b dt = = init ˆ DNL   D D ( ) d + G G d  G  2 G G K dF ( ) ρ = + ε − − − ε −   init DNL init 3 M FI M DNL KU 1 KTG FatOx 3 F [ ] = + F FFA TG d excr k ˆ   dt D D L L   F F diet PA F   dP Keys ρ = − − PI GNG ProtOx ( ) ( ) P P  + − × − +  dt S K  1 A B exp k CI CI B  L dL τ = − L L L L b L { } diet L = + + + ( ) FFM BM ECF ECP LCM L diet S dt + − S L K MAX 0, F F 1 L = + + + + + + L Keys BM ECF ECP ICW P G ICS       ρ δ + υ = + + + ˆ + + + + + BM ECF ECP ICW P (1 h ) G (1 h ) ICS M M = + ρ = ψ −       P G C G G GNG FI D L 1 ρ δ + υ F F C PA  M   M    dECF 1 ( ) ( ) ( ) F TG TG init init = ∆ − ξ − − ξ − + ∆ Na ECF ECF 1 CI CI ECF [ ] diet Na init CI b dt Na         ∆ ∆ P CI PI ( ) = − Γ + Γ + χ ˆ         ∆ GNG GNG   d ECF ( ) P P C P τ = ξ − − ∆   P  CI   PI    BW BW ECF   Keys b b BW BW init dt         ˆ = + + D D PI G TEE TEF PAE RMR = ρ − −     F F     KTG D A exp k exp k ( ) ( )   = + γ + γ − − ∆ + − − + γ + K F K ˆ P G      PI   G  RMR E M FFM M G 1 h ECF ECF F  K D D    b init c B B FFM B g init F K F F ( ) ρ <   + − ε + − ε + + − ε 0, if KTG KTG (1 ) DNL (1 )( GNG GNG ) 1 KTG K thresh   d g F P K ( ) = ρ ρ −   KU KU KTG KTG dP dF dG excr + η + η + ε + η + η + η + η + η K max K thresh , else N ( ) D D D   ( ) − N excr P P P P F F F G G G  KTG KTG  dt dt dt max thresh { } ( ) ( ) ( )   + + ∆ + λ ∆ − < ˆ   EI EI T , if EI EI w ( D D ) w MAX 0, 1 S CI CI G G G dT τ =  = 1 b b G G G C C b min  f ( ) λ ∆ − T   C EI EI T , else dt   Z 2 b ( ) ˆ w D D = ∑ dM = F F F γ γ f i ˆ F FFM i Z dFFM  = + − + × i { } ( ) CarbOx GNG GNG G P 3 f TEE ( ) ( ) ( ) ( ) + + − δ + υ δ + υ ( ) ˆ f p C γ = γ  + − σ  w MAX 0, 1 P D D S exp k ˆ  1 1 T   P sig P P A A b b = = + × FFM FFM f FatOx KetOx f TEE P ( ) F Z = δ + σ + υ PAE 1 T BW BW  = × ProtOx f TEE dP P τ = ∆ − sig = α + α + α S PI PI P TEF FI PI CI PI P b sig F P C dt  

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): E449-66 (2010).

Weight Loss during Fasting 65 BW data Body Weight (kg) 60 BW model 55 50 45 -5 0 5 10 15 20 25 30 35 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)

Fasting & Body Composition 2 Fat Mass 0 Fat Mass Mass Change (kg) Fat-free Mass -2 -4 -6 Fat-free Mass -8 -10 -5 0 5 10 15 20 25 30 35 Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012).

Fasting & Fuel Mobilization Glycogenolysis 450 Lipolysis 400 Lipolysis Metabolic Flux (g/d) Proteolysis 350 300 250 Proteolysis 200 150 Glycogenolysis 100 50 0 -5 0 5 10 15 20 25 30 35 Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012).

Fasting & Fuel Utilization Carbohydrate Carbohydrate Oxidation 1500 Fat + Ketones Oxidation Rate (kcal/d) 1250 Protein Fat + Ketone Oxidation 1000 750 500 Protein Oxidation 250 0 -5 0 5 10 15 20 25 30 35 Days of Fasting KD Hall. In Comparative Physiology of Fasting, Starvation, and Food Limitation (2012).

Fasting & Respiratory Quotient Burning Carbs 1 Respiratory Quotient 0.95 0.9 0.85 0.8 0.75 0.7 Burning -5 0 5 10 15 20 25 30 35 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)

Fasting & Energy Expenditure TEE model 2400 TEE data 2200 Energy Rate (kcal/d) Total Energy Expenditure RMR model 2000 RMR data 1800 1600 Resting Metabolic Rate 1400 1200 1000 -5 0 5 10 15 20 25 30 35 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)

Fasting & Ketone Excretion 8 Ketone Excretion (g/d) 6 4 2 0 -5 0 5 10 15 20 25 30 35 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)

Fasting & Nitrogen Excretion 16 14 N excretion (g/d) 12 10 8 6 4 2 0 -5 0 5 10 15 20 25 30 35 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)

Leibel et al. NEJM 1995 3500 3000 10% Weight Loss 20% Weight Loss 2500 Energy Rate (kcal/d) 2000 1500 Energy Intake 1000 500 0 0 4 8 12 16 20 24 28 32 36 40 Time (weeks)

Leibel et al. NEJM 1995 140 120 Body Weight 100 Mass (kg) 80 Fat-Free Mass 60 40 Fat Mass 20 0 4 8 12 16 20 24 28 32 36 40 Time (weeks)

Leibel et al. NEJM 1995 3500 3000 Total Energy 2500 Energy Rate (kcal/d) Expenditure 2000 1500 Resting Metabolic Rate 1000 Physical Activity 500 0 0 4 8 12 16 20 24 28 32 36 40 Time (weeks)

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

Biggest Loser Model Simulations Isolated on Ranch At Home 20 0 Mass Change (kg) -20 Fat Mass -40 Body Weight -60 -80 -4 0 4 8 12 16 20 24 28 32 Time (weeks) K.D. Hall. Obesity (2013)

Biggest Loser Model Simulations 6000 Total Energy Expenditure 5000 Energy Rate (kcal/d) 4000 3000 Resting Metabolic Rate 2000 1000 Energy Intake Exercise 0 -4 0 4 8 12 16 20 24 28 32 Time (weeks) K.D. Hall. Obesity (2013)

Inverse Problem: Estimating Intake Baseline Demographics & Anthropometrics Mathematical Model Body Weight Energy Intake of Human Metabolism KD Hall. Am J Physiol. 298(3): E449-66 (2010) KD Hall, CC Chow. AJCN 94:66-74 (2011)

Weight Plateau and Regain 10 5 Weight Change (kg) 0 -5 -10 -15 -20 -6 0 6 12 18 24 30 36 Time (months) Data from LP Svetky et al. JAMA. 299:1139-1148 (2008)

Energy Balance Interpretation 2500 Energy Intake 2250 Energy Rate (kcal/d) Total Energy Expenditure 2000 Progressive Loss of Diet Adherence! 1750 1500 -6 0 6 12 18 24 30 36 Time (months) KD Hall. Am J Physiol. 298(3): E449-66 (2010).

Weight Loss Maintenance 0 -2 Mass Change (kg) -4 Fat Mass Change -6 -8 -10 Body Weight Change -12 -14 -6 0 6 12 18 24 30 36 Time (months) KD Hall. Am J Physiol. 298(3): E449-66 (2010).

Energy Intake for Maintenance 2500 ~200 kcal/d Energy Intake 2250 Energy Rate (kcal/d) Total Energy Expenditure 2000 1750 1500 -6 0 6 12 18 24 30 36 Time (months) KD Hall. Am J Physiol. 298(3): E449-66 (2010).

5% Weight Loss vs. Maintenance Maintenance of 5% Weight Loss in 6 months 5% Weight Loss BMI = 35 kg/m 2 -300 kcal/d -90 kcal/d BMI = 50 kg/m 2 -100 kcal/d -450 kcal/d

http://bwsimulator.niddk.nih.gov