The Calculus of Calories:
Quantitative Obesity Research
Kevin D. Hall, Ph.D.
National Institute of Diabetes & Digestive & Kidney
Diseases
July 29, 2016
Wrong,
Wrong,
Wrong!
2
Erroneous Weight Loss Projections
Body Weight (kg)
120
100
80
60
3500 kcal per pound
40
20
0
0
1
2
3
Time (years)
3
Balancing Calories In with Calories Out
Calories Out
Calories In
4
Regulation of Body Weight
Calories Out
Calories In
Leptin, etc.
5
Regulation of Body Weight
Calories Out
Calories In
Leptin, etc.
6
Δ Expenditure (kcal/d)
Calorie Expenditure Changes
0
-200
~20 kcal/d
per kg
-400
-600
-800
-1000
-35
-30
-25 -20 -15 -10
Δ Body Weight (kg)
-5
0
BA Swinburn et al. AJCN. 89:1723–8 (2009)
7
Δ Expenditure (kcal/d)
Calorie Expenditure Changes
0
-200
~20 kcal/d
per kg
-400
~30 kcal/d
per kg
-600
-800
-1000
-35
-30
-25 -20 -15 -10
Δ Body Weight (kg)
-5
0
BA Swinburn et al. AJCN. 89:1723–8 (2009)
RL Leibel et al. NEJM. 332: 621-628 (1995)
8
Mathematical Modeling of Metabolism
Baseline
Demographics &
Anthropometrics
Physical Activity
Food Intake
Mathematical Model
of Human Metabolism
Body Weight
Body Fat
KD Hall. The Lancet 378:826-37 (2011)
KD Hall. Am J Physiol. 298(3): E449-66 (2010)
9
BWplanner.niddk.nih.gov
10
Is a Calorie a Calorie?
11
The Carbohydrate-Insulin Model
“[Insulin] has triggered fat cells to suck
up and store too many calories from the
blood. Consequently, fewer calories are
available to fuel the energy needs of the
body. Perceiving a problem, the brain
unleashes a starvation response,
including measures to increase calorie
intake (hunger) and save energy (slow
metabolism).”
David Ludwig, MD, PhD
Always Hungry (2016).
12
Fat Balance at the Adipocyte
Insulin
LPL
Muscle
Carbohydrate
ATGL
HSL
TG
LPL
FFA
TG
FFA
Liver
Adipocyte
13
A Corollary of the Carb-Insulin Model
“Any diet that succeeds does so because the dieter
restricts fattening carbohydrates…Those who lose
fat on a diet do so because of what they are not
eating – the fattening carbohydrates”
Gary Taubes, Why we get fat
and what to do about it (2011).
14
Isocaloric 30% Calorie Restricted Diets
CI
Carbs
FI
Fat
PI
Protein
Δ Intake (g/d)
0
-50
-100
RC
-150
RF
-200
Mean ± 95% CI
-250
KD Hall et al. Cell Metabolism 22:427-436 (2015).
15
Only RC Decreased Insulin Secretion
24 hr C-peptide (% change)
20
N=19 obese men & women
10
0
RC
-10
RF
NS
-20
Mean ± 95% CI
* p<0.01
-30
-40
vs baseline
*
p = 0.001
KD Hall et al. Cell Metabolism 22:427-436 (2015).
16
Only RC Decreased Daily RQ
24hr Respiratory Qotient
Burning
Carbs
Burning
Fat
0.95
0.9
N=19 obese men & women
**
**
**
RC data
0.85
RC model
RF data
0.8
RF model
0.75
-3 -2 -1 0 1 2 3 4 5 6
Time (days)
Mean ± 95% CI
** p<0.001
KD Hall et al. Cell Metabolism 22:427-436 (2015).
17
Mathematical Modeling of Metabolism
dG
C
 CI  DNL  GNGP  GNGF  G3P  CarbOx
dt
dF
F
 3M FFA FI M TG   d DNL  KU excr  1   k  KTG  FatOx
dt
dP
P
 PI  GNGP  ProtOx
dt
DNL 
CI   G Ginit 
 G Ginit 
FFM  BM  ECF  ECP  LCM
 BM  ECF  ECP  ICW  P  G  ICS
ˆ  P(1  h )  G (1  h )  ICS
 BM  ECF  ECP  ICW
P
G
dECF
1

 Nadiet   Na  ECF  ECFinit   CI 1  CI CIb    ECF
dt
 Na 
 BW


(1   d ) DNL  (1   g )(GNGF  GNGP )  1   K  KTG
 N N excr  ( P   P ) DP   P
T
dP
dF
dG
  F DF   F
 G DG  G
dt
dt
dt
dT 
   EI EI b   T , if EI  EI b 

 1



EI
EI

T
,
else
dt 

b
 2

ˆFFM
dM i
  i
dFFM
i
 FFM  ˆFFM 1  1    T 
PAE   1   T  BW   BW
TEF   F FI   P PI   C CI
 F
DF  Dˆ F 
 FKeys

3
  Ldiet  LPA 

  M 
M 
GNGF  FI  C G   DF C  G 
  F M TG 
 M TG 

ˆ  P
GNGP  GNG
P 
 PKeys
2

  

LPA   
 1
  init  init


 CI 
 PI  






  C 



P
 CI b 
 PI b  

  DF Dˆ F 


PI 
G 
KTG   K DF  AK 
exp  k P
exp  kG



PI b 
Ginit  
  K K  DF Dˆ F 


0,
if KTG  K  KTGthresh 



KU excr    K KU max  KTG  K  KTGthresh 

,
else


 KTGmax  KTGthresh 


fC 
CarbOx  GNG f  GNG p  G3P  f C  TEE
ProtOx  f P  TEE
d
 K DNL

fF 
FatOx  KetOx  f F  TEE
 G 
DG  Dˆ G 

 Ginit 

 PI  
   

 PI b  

S
dLdiet K L L 1   AL  BL   exp  k L CI CI b   BL 
L

 Ldiet
SL
dt
K LSL  MAX 0,  F FKeys  1
d ECF
  BW  BW  BWinit   ECF
dt
TEE  TEF  PAE  RMR
RMR  Ec   B M B   FFM  FFM  M B  G 1  hg   ECF  ECFinit     F F
d
d
 P
DP  Dˆ P 
 PKeys
fP 
 PI
wG ( DG Dˆ G )  wC MAX 0, 1  SC CI CI b  G  Gmin  G 

wF DF Dˆ F
Z

Z

 

wP MAX 0, 1  Psig   DP Dˆ P S A exp   k A      b  b  
Z
dPsig
dt
 S P PI PI b  Psig
18
19
Δ Fat Oxidation (kcal/d)
Only RC Increased Daily Fat Oxidation
800
N=19 obese men & women
**
600
400
**
**
RC data
200
RC model
0
RF data
-200
RF model
-400
-3 -2 -1 0 1 2 3 4 5 6
Time (days)
Mean ± 95% CI
** p<0.001
KD Hall et al. Cell Metabolism 22:427-436 (2015).
20
Greater Fat Imbalance with RF
Δ Fat Balance (kcal/d)
200
N=19 obese men & women
0
-200
-400
**
*
**
-600
RC data
RC model
RF data
RF model
-800
-1000
-3 -2 -1 0 1 2 3 4 5 6
Time (days)
Mean ± 95% CI
** p<0.001
KD Hall et al. Cell Metabolism 22:427-436 (2015).
21
Cumulative Fat Change (g)
More Cumulative Body Fat Loss with RF
** N=19 obese men & women
0
**
-100
**
-200
RC data
-300
RC model
-400
RF data
-500
RF model
-600
0
1
2
3
4
Time (days)
5
6
KD Hall et al. Cell Metabolism 22:427-436 (2015).
Mean ± 95% CI
** p<0.001
22
Body Fat Changes via DXA
Δ Fat Mass via DXA (kg)
0
-0.1
-0.2
-0.3
RC data
-0.4
RF data
-0.5
Mean ± SE
-0.6
-0.7
-0.8
* p<0.002
vs baseline
*
*
p = 0.78
By any measure, the RF diet led to body fat loss
despite no significant change in daily insulin secretion.
KD Hall et al. Cell Metabolism 22:427-436 (2015).
23
Δ Energy Expenditure
(kcal/d)
Energy Expenditure Changes
40
20
0
-20
-40
-60
-80
-100
-120
-140
Sleep
24 hour
NS
RC data
RF data
NS
Mean ± SE
* p<0.005
vs baseline
*
p = 0.0024
*
p = 0.099
KD Hall et al. Cell Metabolism 22:427-436 (2015).
Mean ± SE
24
The Low Carb Community Responds
Recently, a study in Cell Metabolism by Kevin
Hall from the National Institutes of Health
attracted a lot of buzz in the news and
online…[but] there were some real problems
with the study, and things that were
overlooked by the media reports.
Here are the important considerations:
• The low-carb diet wasn’t low at all,
actually, with 29 percent of calories coming
from carbs, including refined carbs. A true
low-carb diet would have less than 10
percent of calories from carbs.
• It was a very short-duration study (only
six days) conducted on only nineteen people
who were contained in a metabolic ward
where all the food was provided…It showed
what happened in a vacuum but not in real
life.
Mark Hyman, MD
25
Eat Fat, Get Thin (2016)
24hr Respiratory Qotient
Hypothetical Extended Duration Study
0.95
0.9
RC data
0.85
RC model
RF data
0.8
RF model
Fat Adaptation!
0.75
-3 -2 -1 0 1 2 3 4 5 6
Time (days)
26
2 Month Isocaloric Ketogenic Diet Study
Day -28
Day -15
Day 0
4 weeks inpatient
Baseline Diet
Energy Intake
Adjustment
Day 15
Day 28
4 weeks inpatient
Low Carb Ketogenic Diet
Energy Intake
Clamped
2 days residing
in metabolic
chamber
DLW dose
DXA
KD Hall et al. AJCN In press (2016).
27
24 hr C-peptide (% change)
Rapid & Persistent Decrease in Insulin Secretion
N=17 overweight and class I obese men
40
20
0
-20
-40
-60
**
**
** *****
-80
-10
0
10
Time (days)
20
KD Hall et al. AJCN In press (2016).
30
Mean ± 95% CI
*p<0.0033
28
Rapid & Persistent Shift to Fat Oxidation
0.05
Δ 24hr RQ
0
0
Fat Adaptation?
-0.05
**
-0.1
**
**
-0.05
**
-0.1
-0.15
-0.15
-0.2
-0.2
-10
0
10
Time (days)
20
30
Mean ± 95% CI
KD Hall et al. AJCN In press (2016).
*p<0.0045
29
Δ Food Quotient
0.05
Δ EEchamber (kcal/d)
Small Effect on 24hr Energy Expenditure
300
250
200
150
100
50
0
-50
-100
*
-10
0
*
10
Time (days)
KD Hall et al. AJCN In press (2016).
20
30
Mean ± 95% CI
*p<0.0045
30
Δ SEE (kcal/d)
Small Effect on Sleeping Expenditure
300
250
200
150
100
50
0
-50
-100
**
*
-10
0
10
Time (days)
KD Hall et al. AJCN In press (2016).
20
30
Mean ± 95% CI
*p<0.0045
31
Predicted Effect on Energy Expenditure
Thermodynamics of Weight Loss Diets
Eugene J Fine & Richard D Feinman
Nutrition & Metabolism 2004
DOI: 10.1186/1743-7075-1-15
Very low carbohydrate diets, in their early
phases, also must supply substantial glucose
to the brain from gluconeogenesis…the
energy cost, at 4–5 kcal/gram could amount to
as much as 400–600 kcal/day. This is a
sizable metabolic advantage.
32
Predicted Effect on Energy Expenditure
Hall has developed a mathematical model
that can predict how different diets impact metabolism and
body composition. According to Hall's model, the low-carb,
low-insulin diet that the participants will eat … should have
at most a tiny effect on the total calories they burn.
33
Δ Body Weight (kg)
Weight Loss Increases post Ketogenic Diet
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-15
0
15
Time (days)
KD Hall et al. AJCN In press (2016).
30
Mean ± 95% CI
Mean ± 95% CI
- p<0.0012
34
Body Fat Loss Slows post Ketogenic Diet
Δ Body Fat (kg)
1.0
*
0.5
0.0
-0.5
-1.0
-15
0
15
Time (days)
KD Hall et al. AJCN In press (2016).
30
Mean ± 95% CI
*p<0.0167
35
Δ Urinary N Excretion (g/d)
Increased Protein Utilization
6
5
4
3
2
1
0
-1
-2
*
*
-10
0
*
10
Time (days)
KD Hall et al. AJCN In press (2016).
20
30
Mean ± 95% CI
*p<0.0045
36
The Body Adapts to a Wide Range of Diets
0
-2
-100
-4
-200
-6
-300
-8
-10
-400
-12
-500
0
20
40
60
Percent Carbohydrate
KD Hall et al. Cell Metabolism 22:427-436 (2015).
Δ Calorie Expenditure
(kcal/d)
Δ Fat Mass (kg)
0
80
37
Regulation of Body Weight
??
Calories Out
Calories In
Leptin, etc.
38
39
Math Models to Calculate Calorie Intake?
Baseline
Demographics &
Anthropometrics
Calorie Intake
Mathematical Model
of Human Metabolism
Calorie Expenditure
Body Weight
Body Fat
A. Sangvhi et al. Am J Clin Nutr.102:353-358 (2015)
40
Caloric Restriction for 2 Years
74
Expensive biomarker
measurements
Body Weight (kg)
72
70
N=140
68
66
64
62
0
13
26
39
52
65
Time (weeks)
78
91
104
Mean ± 95% CI
A. Sangvhi et al. Am J Clin Nutr.102:353-358 (2015)
41
Calorie Intake Changes over 2 Years
0-26 weeks
26-52 weeks 52-78 weeks 78-104 weeks
Energy Intake Change (kcal/d)
0
-100
-200
-300
N=117
N=115
N=125
-400
DLW/DXA
Biomarker
-500
N=135
Model
-600
Mean ± 95% CI
A. Sangvhi et al. Am J Clin Nutr.102:353-358 (2015)
42
Regulation of Body Weight
??
Calories Out
Calories In
Leptin, etc.
43
Regulation of Body Weight
??
Calories Out
Calories In
~90 g/d
glucose
Leptin, etc.
44
Weight Changes during SGLT2 Inhibition
Δ Body Weight (kg)
0
-1
N=153 adults with
Type 2 diabetes treated
with 300 mg/d canagliflozin
-2
-3
-4
-5
0
6
12
18
24 30 36
Time (weeks)
42
48
54
D. Polidori, A. Sanghvi, R. Seeley, K.D. Hall. Obesity, In press (2016)
45
Intake Changes during SGLT2 Inhibition
Δ Energy Intake (kcal/d)
500
400
300
200
~100 kcal/d
per kg BW loss
100
0
-100
0
6
12
18
24 30 36
Time (weeks)
42
48
54
D. Polidori, A. Sanghvi, R. Seeley, K.D. Hall. Obesity, In press (2016)
46
Regulation of Body Weight
~20-30 kcal/d
per kg
Calories Out
~100 kcal/d
per kg
Calories In
Leptin, etc.
47
Typical Weight Loss with Lifestyle Change
Body Weight (kg)
97
N=211 clients of Weight Watchers
95
93
91
89
87
85
0
3
6
9
12
15
Months
18
21
24
Mean ± SE
Data from S. Heshka et al. JAMA 289:1792-1798 (2003)
48
Intake and Expenditure
(kcal/d)
Corresponding Calorie Balance Dynamics
2700
2500
Calorie Expenditure
2300
Exponential decay
of diet adherence!
2100
Calorie Intake
1900
0
3
6
9
12 15
Months
18
21
D. Polidori, A. Sanghvi, R. Seeley, K.D. Hall. Obesity, In press (2016)
24
49
Intake and Expenditure
(kcal/d)
Interpreting Lifestyle Weight Loss
3500
Increased Appetite
3100
Perceived Effort
2700
2300
Calorie Intake
1900
0
3
6
9
12 15
Months
18
21
D. Polidori, A. Sanghvi, R. Seeley, K.D. Hall. Obesity, In press (2016)
24
50
kcal/d
Interpreting Lifestyle Weight Loss
800
600
400
200
0
-200
-400
-600
-800
Perceived Effort
Calorie Intake Change
0
3
6
9
12 15
Months
18
21
24
D. Polidori, A. Sanghvi, R. Seeley, K.D. Hall. Obesity, In press (2016)
51
Intramural NIH
Intramural NIDDK Extramural Collaborators
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)
Alison Baskin
Robert Brychta
Thomas Bemis
Dhruva Chandramohan
Kong Chen
I-Ling Chen
Helen Cheung
Kavya Devaraconda
Courtney Duckworth
Erin Fothergill
Stephanie Goodwin
Juen Guo
Gail Hall
Lilian Howard
Peter Jordan
Nick Knuth
Brooks Leitner
Bernard Miller
Laura Musse
Carla Prado
Emma Preuschl
Marc Reitman
Arjun Sanghvi
Mario Siervo
Monica Skarulis
Wayne Staton
Terri Wakefield
Mary Walter
Peter Walter
Laura Yannai
Naji Abumrad (Vanderbilt)
CALERIE Study Group
Britta Göbel (Sanofi)
Brian Gilmore (PBRC)
Robert Huizenga (UCLA)
Darcy Johannsen (PBRC)
Jennifer Kerns (DC VA Med Center)
Rudy Leibel (Columbia)
Pamela Marks-Shulman (Vanderbilt)
Corby Martin (PBRC)
Laurel Mayer (Columbia)
Eric Ravussin (PBRC)
David Polidori (J&J)
Leanne Redman (PBRC)
Jennifer Rood (PBRC)
Michael Rosenbaum (Columbia)
Robyn Tamboli (Vanderbilt)
Randy Seeley (U Michigan)
Steven R. Smith (TRI)
Jon Moon (MEI)
B. Tim Walsh (Columbia)
Special Thanks
Nursing Staff at the NIH MCRU
Volunteer Study Subjects
Nutrition Science Initiative