cellular and whole body models of glucose control on insulin secretion gianna maria toffolo morten...
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Cellular and Whole Body Models of Glucose Control on Insulin Secretion
Gianna Maria ToffoloMorten Gram Pedersen
Department of Information EngineeringUniversity of Padova
Padova, Italy
REx Workshop, February 17-18, 2009
Whole Body Models
• Simple models, with a few parameters to be identified on data of an individual
• Measure glucose control on insulin secretion
• Usable in clinical practice
• Based on plasma measurements (C-peptide and glucose) during a minimally invasive protocol
From i.v. and oral tests
Models to measure
Cellular Models Models to understand
IVGTT: Young vs Elderly SubjectsN = 59 vs 145 (Dr. Rizza & Basu, Mayo Clinic)
Young0
50
150
250
350
0 60 120 180 240t [min]
GLUCOSE
Elderly[mg
/dl]
0
400
800
1200
1600
2000
0 60 120 180 240t [min]
C-PEPTIDE
[pm
ol/
l]
t [min]0100
300
500
700
900
0 60 120 180 240
INSULIN
[pm
ol/
l]
CP1(t)= - (k01 + k21) CP1(t) + k12CP2(t) + SR(t)
CP2(t)= k21 CP1(t) - k12 CP2(t)
SR(t) = SRb + m X(t)
Basal Responsivity Φb=SRb
Gb
Y(t) = [Y(t) – Φ2 (G-h)]1
T
Delay2nd Phase Responsivity
IVGTT:C-peptide Minimal Model (Toffolo et al, 1995)
CP2
Rate of Increase of
Glucose ΔG
k01
k21
k12
CP1
Delay
1st Phase
2nd Phase
Glucose
ReleasableInsulin
SECRETION
m
X
Y
G1st Phase Responsivity Φ1=
X0
ΔG
X(t) = - m X(t) + Y(t) X(0)=X0
0
100
200
300
400
-30 0 60 120 180 240t [min]
[mg
/dl]
Glucose
IVGTT: Insulin Secretion Phases
-30 0 60 120 180 2400
1000
2000
3000
4000
t [min]
[pm
ol/
min
]
ISR
0
50
100
150
200
-30 0 60 120 180 240t [min]
BASAL
[pm
ol/
min
]
Φb: Basal ISR / Basal G
0
250
500
750
1000
-30 0 60 120 180 240t [min]
2nd PHASE
Φ2: Over Basal 2nd Phase ISR/ Over
Basal G
T: Delay between 2nd Phase ISR and G
t [min]
0
1000
2000
3000
4000
-30 0 60 120 180 240
1st PHASE
Φ1: 1st Phase ISR / G
IVGTT: β-Cell Responsivity Indices N=59Y vs 145E
EY
*
Φ1
[10
-9]
[10-9
min
-1]
EY
Φb
0
2
4
6
8
50
150
250
EY
[10-9
min
-1]
Φ2[m
in]
0
5
10
15 *T
EY0
5
10
15
20
0
* p<0.05
(OGTT or meal)
From IVGTT to more physiological protocols
GLUCOSE
INSULIN
100
300
500
0 120 240 360 420t [min]
C-PEPTIDE
1000
2000
3000
0 120 240 360 420t [min]
Meal: Young vs Elderly SubjectsN = 59 vs 145 (Dr. Rizza & Basu, Mayo Clinic)
80
120
160
200
0 120 240 360 420t [min]
Young
Elderly
[mg
/dl]
[pm
ol/
l][p
mo
l/l]
Rate of Increase of Glucose
(first 50-60 minutes)
k01
k21
k12
CP1 CP2
Delay
Dynamic Phase
Static Phase
GlucoseSECRETION
Meal: C-peptide Minimal Model (Toffolo et al, 2001; Breda et al, 2001, 2002)
CP1(t)= - (k01 + k21) CP1(t) + k12CP2(t) + SR(t)
CP2(t)= k21 CP1(t) - k12 CP2(t)
SR(t) = SRb + SRd(t) + SRs(t)
Basal Responsivity Φb=SRb
GbY(t) = [Y(t) – Φ2 (G-h)]1
T
Delay Static Responsivity
Static phase SRs = Y
Dynamic Responsivity
Dynamic Phase SRd(t) = Φd
dG
dt
Meal: Insulin Secretion PhasesISR
0
1000
2000
3000
4000
-30 0 60 120 180 240
t [min]
[pm
ol/
min
]
0
100
200
300
400
-30 0 60 120 180 240t [min]
GLUCOSE [mg
/dl]
0
50
100
150
200
-30 0 60 120 180 240t [min]
BASAL
[pm
ol/
min
]
Φb: Basal ISR / Basal G
t [min]
0
1000
2000
3000
4000
-30 0 60 120 180 240
DYNAMIC
Φd: Dynamic ISR / Glucose Rate of
Increase
0
250
500
750
1000
-30 0 60 120 180 240t [min]
STATIC
Φs: over basal static ISR /
over basal G
T: Delay between Static ISR and G
EY
Φb
[10-9
min
-1]
Meal: β-Cell Responsivity IndicesN=59Y vs 145E
*
Φd
[10
-9]
EY* p<0.05
0
2
4
6
8
0
200
400
600
800
Φs
[10-9
min
-1]
EY0
10
20
30
40 *
EY
T
[min
]
0
5
10
15
20
• Measurement of insulin secretion alone provides limited insight
• It is important to determine whether -cell secretion
is appropriate for the degree of insulin resistance
To quantify the efficiency of the glucose-insulin regulatory system…..
β-CELLS
LIVER GLUCOSE
INSULIN
BRAIN
MUSCLE
TISSUESDEGRADATION
SECRETION
LIVER
PRODUCTION UTILIZATION
+
B-cell Responsivity
-+
Insulin Sensitivity
Glucose Minimal Model
k3
k5
GLUCOSE TISSUES
k1
k4
k6
REMOTE INSULIN
k2
PLASMA INSULIN
LIVER
IVGTT
SI
IVGTT (Bergman & Cobelli, 1979)
OGTT/MEAL
k3
k5
GLUCOSE TISSUES
k1
k4
k6
REMOTE INSULIN k2
INSULIN
LIVER
Gastrointestinal Tract
SI
MEAL (Dalla Man & Cobelli, 2002)
Insulin Sensitivity 59 Y vs 145 E
*
[10-4
dl/k
g/m
in p
er
U/m
l]
EY0
4
8
12
EY
*
[10-4
dl/k
g/m
in p
er
U/m
l]
0
5
10
15
20
* p<0.05
Beta-Cell Responsivity
Beta-Cell Responsivity
Insulin Sensitivity Insulin Sensitivity
Normal ToleranceNormal
NormalReduced
I
II
2
Impaired Tolerance
Increased
Efficiency of the Control: Disposition Index(Bergman & Cobelli, 1981, Cobelli et at, 2007)
Insulin Sensitivity x Beta-Cell Function= Constant
Disposition Indices59 Y vs 145 E
* p<0.05
*
DI1
[10
-14 d
l/k
g/m
in p
er
pm
ol/
l]
EY0
1000
2000
3000
*
DI2
[10-1
4 d
l/k
g/m
in2
pe
r p
mo
l/l]
EY0
40
80
120
160
Meal IVGTT
[10
-14 d
l/k
g/m
in p
er
pm
ol/
l]
EY
*
DId
0
5000
10000
15000
20000
EY
*
DIs
[10
-14 d
l/k
g/m
in2 p
er
pm
ol/
l]
0
400
800
1200
Use in Pathophysiology
Role of age and gender (Basu et al, Diabetes 2006)
Pathogenesis of Prediabetes (Bock et al, Diabetes 2006)
Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006)
Diurnal Variation of Glucose Tolerance (Dr. E. Van Cauter, University of Chicago, Chicago, IL)
Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006)
Reduced OGTT & Meal Protocols (Dalla Man et al, Diabetes ,2006)
Type 2 Diabetes ( Basu et al, Diabetes Care, 2009)
Children and Adolescent (Sunehag et al, Obesity 2008)
Whole body models vs cellular events
Rate of Increase of Glucose
k01
k21
k12
CP1 CP2
Delay
Dynamic Phase
Static Phase
Glucose
Mechanistic intepretation of minimal model parameters Cellular Model
Dynamics of β-Cell Turnover in Rats(Manesso et al, EASD 2008)
β-Cell MassM
Replication Rate (RR)
Apoptosis Rate (RA)
Other Sources of β-Cells
(OSB)
?
dMdt = RR – RA + OSB
Pancreatic islet - himmunohystochemistry
(Dr P.Butler, UCLA)
OSB
0
8
16
0 5 10age [month]
[mg
/mo
nth
]
Thanks
CLAUDIO COBELLI
Elena Breda
Marco Campioni
Chiara Dalla Man
Erica Manesso
Paolo Denti
(Padua, Italy)
Andrea Caumo
(Milan, Italy)
ROBERT RIZZA
Rita Basu
Ananda Basu
F. John Service
(Rochester, MN)
PETER BUTLER
(UCLA, Los Angeles)
Whole body models vs cellular events
Rate of Increase of Glucose
k01
k21
k12
CP1 CP2
Delay
Dynamic Phase
Static Phase
Glucose
Mechanistic intepretation of minimal model parameters Cellular Model
Model Assessment
Insulin Secretion: Model vs Deconvolution
t [min]
[pm
ol/
min
]
C-Peptide Minimal Model
Deconvolution
0
400
800
1200
1600
0 100 200 300
Insulin Secretion
C-Peptide Minimal Model
t [min]
[pm
ol/
min
] Deconvolution
Model without Φd
0
400
800
1200
1600
0 100 200 300
Need of All the MM Ingredients
Insulin Secretion
e.g. Dynamic Glucose Control
(Steil et al, 2004)
Φ1IVGTT
(103 pmol/l/min)
Φ1H
GC
(1
03 p
mo
l/l/
min
)
IVGTT vs Hyperglycemic Clamp 1st Phase β-cell Responsivity
Meal vs Hyperglycemic Clamp Static β-cell Responsivity
Φsm
eal
(n
mo
l/m
in p
er
mm
ol/
l)
ΦsHGC
(pmol/min per mmol/l)
MM Indices vs HGC Counterparts
N=204
R=0.72, p<0.001
AIR (pmol/l∙ min)
Φ1
(10-9
)
Φ1: Correlation with Other Indexes
0
2000
4000
6000
8000
10000
0 100 200 300 400 500 600
VALIDATION PROBLEMS1. Simple net balance equations are not appropriate out of steady state
2. The transit time of the substance needs to be explicitly considered
MM Indices vs AV Measurements
GlucoseIncrease
DelayGlucose SRΦs
g(t)
F
CPA: C-peptide Femoral Artery
CPV: C-peptideHepatic Vein
Φd
C-peptide AV Model
0
SR(s)
FCPV(t) = CPA(s)+ g(t - s) ds
t
Distribution of transit times from femoral artery to
hepatic vein
C-peptide in Hepatic Vein
C-peptide in Femoral Artery Secretion
Blood Flow
Meal vs AV (N=12)
Φs
Meal AV
0
200
100
0
[l
109
min
-1]
Time [min]
0
250
500
750
1000
0 60 120 180 240 300 360
Meal
AV
[pm
ol
min
-1]
Insulin Secretion
Φd
Meal AV
0
3000
1500
0
[l
109
]
Protocols, Attributes and Information Content
Can Assess Beta-Cell Function?
Yes, but limited
Yes, but limited without a model
No
Yes, but limited without a model
Yes, but limited without a model
Yes, but limited without a model
BASAL STATE
Is it Physiological?
Yes
Is it Simple?
Yes
Can Assess Insulin Sensitivity?
Yes, but limited
INTRAVENOUS PERTURBATION
Hyperglycemic Clamp
Euglycemic Clamp
IVGTT
No
No
No
No
No
No
Yes, but requires a model
Yes
Yes, but limited without a model
ORAL PERTURBATION
OGTT
Meal
Yes, but no nutrients
Yes
Yes
Yes
Yes, but requires a model
Yes, but requires a model
Reproducibility: IVGTT
SI
Day A Day B
β - Cell Responsivity
Insulin Sensitivity
[10-4
dl/
kg
/min
p
er U
/ml]
[10-9
min
-1]
Φ2
0
50
250
500
Φ1
[10
-9]
Day A Day B Day A Day B
∆ = 4% ∆ = 17%
∆ = 12%
0
5
15
25
0
2
4
6
8
Reproducibility: Meal
SI
Day A Day B
β - Cell Responsivity
Insulin Sensitivity
Φd
[10
-9]
Day A Day B
Φs
[10
-9 m
in-1]
Day A Day B
[10-4
dl/
kg
/min
p
er U
/ml]
0
600
1200
1800
0
20
40
60∆ = 1% ∆ = 7%
∆ = 7%
0
4
8
12
16
-cell Function: IVGTT vs Meal
IVGTT vs Meal: β-Cell ResponsivityN=204
MealIVGTT
ΦdΦ1 ΦsΦ2
0
200
400
600
800
MealIVGTT0
10
20
30
40+ 251%*
• Incretin hormones?
• Differences in the pattern of glucose stimulus?
• Effect of fat/protein in the meal?
+ 253%*
IV vs Oral Glucose: Assessment of Incretin EffectN=10 (Dr. Rizza & Service, Mayo Clinic)
GLUCOSE
80
100
140
180
-30 0 60 120 180 240t [min]
IV-OGTT
OGTT[m
g/d
l]
C-PEPTIDE
2
4
6
-30 0 60 120 180 240t [min]
[ng
/ml]
INSULIN
10
30
50
-30 0 60 120 180 240t [min]
[uU
/ml]
Dynamic Secretion Static Secretion
t [min]
[pm
ol/
min
]
-200
0
200
400
0 60 120 180 240
t [min]
[pm
ol/
min
]
0
100
200
300
400
0 60 120 180 240
OGTTI-IVG
p<0.05
+ 55%*
+ 68%*
Φs
[10-9
min
-1]
10
20
30
OGTTIV-OGTT
200
400
600
OGTTIV-OGTT
[10
-9]
Φd
* p<0.05
Reduced Oral Protocols
OGTT (N=100)
0
60
120
0 60 1203000full
R=0.88, p<0.0001
red
(10-9
m
in-1)
0
30
60
full red
red
R=0.98, p<0.0001
0
1500
3000
0 1500
(10
-9 )
full red0
600
1200
full
Φd Φs
REDUCED
0 90 120 10 20 30 60
120 min – 7 Samples
Hepatic Insulin Extraction
Rationale
ISR
C-PEPTIDE
INSULIN
ISR
IDR
LIVER
-CELLS
LIVER I
n
k0,1
k2,1
k1,2
CP1 CP2
HEPATIC EXTRACTION =ISR - IDR
ISR
HEPATIC EXTRACTION =ISR - IDR
ISR
C-peptide Kinetics
Insulin Kinetics
IM-IVGTT
0
350
0
900
0
2000
0 60 120 180
0 60 120 180
0 60 120 180 240
240
240
time [min]
Glucose
Insulin
C-peptide
MEAL200
500
0 120 240 360 420
800 120 240 360 420
3000
0 120 240 360 420
0
0
time [min]
60 180 300
60 180 300
60 180 300
Glucose
Insulin
C-peptide
Estimation of Hepatic Insulin Extraction(Toffolo et al, 2006)
C-peptide Model
CP2
IncreaseGlucose
k01
k21
k12
CP1
Delay
GlucoseReleasableC-peptide
SECRETION KINETICS
ISR
Delay
SECRETION
IncreaseGlucose
Glucose
n
I
KINETICS
VI
IDR
Insulin Model
ReleasableInsulin
Insulin Bolus
From Insulin Bolus
Population Model(Van Cauter, 1991)
Population Model(Van Cauter, 1992)
Population Model
IVGTT: Hepatic Extraction
Profile
t [min]
0
0.2
0.4
0.6
0.8
1
0 60 120 180 240
ELDERLY
YOUNG
(%)
ISR(t) - IDR(t)
ISR(t)HE(t) =
N=59Y vs 145E
Index
0.00
0.20
0.40
0.60
0.80
1.00
EY
*
(%)
T
0
T
0
ISR(t)dt
ISR(t)dt – IDR(t)dt
HE =T
0
* p<0.05
Meal: Hepatic Extraction
0.00
0.20
0.40
0.60
0.80
1.00
0 60 120 180 240 300 360 420
ELDERLY
YOUNG
t [min]
(%)
Profile
0.00
0.20
0.40
0.60
0.80
1.00
EY
*(%)
Index
* p<0.05
N=59Y vs 145E
Disposition index
• Does the hyperbolic relation DI=Φ x SI hold in a population or is it DI=Φ x SIα?
• Average individual DI or value estimated in the population?
• Linear regression on log-trasformed variables or nonlinear regression on original variables?
• Ordinary regression with errors in one variable or regression with errors in two variables?
Open Questions
Average individual DI or value estimated in the population?
Averaging Φ x SI=732
XY fit
Φ x SI=732
Φ x SI0.68=330
Averaging
logXY fit Φ x SI0.77=578
XY fit Φ x SI0.68=330
Y fit Φ x SI0.19=135
XY fit Φ x SI0.68=330
SIivgtt [10-5 min-1 per pmol/l]
Φ1 [
10
-9]
Linear regression on log-trasnformed variables or nonlinear regression on original variables?
Does the hyperbolic relation DI= Φ x SI in a population or is it DI= Φ x Siα?
Regression with error in one variable or in two variables?
Disposition Index
The classical DI ignores the effect of hepatic insulin extraction
Φ1 [10-9]
SIivgtt [10-5 min-1 per pmol/l]
1-H
E [d
imen
sion
less
]
From 2D to 3D?
From IVGTT to slower profiles
CP2
Rate of Increase of
Glucose ΔG
k01
k21
k12
CP1
Delay
1st Phase
2nd Phase
Glucose
ReleasableInsulin
SECRETION
m
X
Y
• Since m is rapid (1/m=1-2 minutes) with respect to the slower (than IVGTT) time course of insulin and glucose concentration, m cannot be resolved from the data.
• 1st phase dynamic phase (related to dG/dt, active during the glucose rising phase)
• 2nd phase static phase (related to G)
GLUCOSE
Meal: Non Diabetics vs Type 2 Diabetics N=14 vs 11 (Dr. A. Basu)
t [min]
INSULIN
40
80
120
0 120 240 360
t [min]
200
400
0 120 240 360
Diabetics
Non Diabetics[m
g/d
l]
t [min]
C-PEPTIDE
1000
3000
5000
0 120 240 360
[pm
ol/
l][u
U/m
l]
Φb
β-Cell Responsivity Indices N=14 vs 11
* p<0.05
ND D0
4
8Φd
ND D
*
0
400
800
Φs
ND D
*
0
20
40
60
20
60
100
140
*
ND D
T
[10
-9 m
in-1]
[10
-9]
[10-9
min
-1]
[min
]
Type 2 Diabetes: Effect of Pioglitazone (Basu A. et al submitted)
Insulin
0
20
40
60
80
100
120
140
-60 0 60 120 180 240 300 360
time (min)
uU/m
l
Glucose
0
5
10
15
20
25
-60 0 60 120 180 240 300 360
Time (min)
mM
Pre-pioPost-pioNondiabetic
C-peptide
0.000
1.000
2.000
3.000
4.000
5.000
-60 0 60 120 180 240 300 360
time (min)
nmol
/L
Pre-pioPost-pioNondiabetic
Pre-pioPost-pioNondiabetic
* p<0.05 pre vs post treatment
^ p<0.05 post treatment vs nondiabetic
0
5
10
15
20
25
30
10^-
5 dl
/kg/
min
per
pm
ol/L
pre pio
post pio
Nondiabetic
*
0
100
200
300
400
500
600
700
800
10^-
9
pre pio
post pio
Nondiabetic
0
10
20
30
40
50
60
10^-
9 m
in^-
1
pre pio
post pio
Nondiabetic
SI ds
Children and Adolescents (Dr. Caprio)
GLUCOSE
0
20
40
60
80
100
120
140
160
180
0 30 60 90 120 150 180
min
mg/
dl
NGT_NFG
NGT_IFG
IGT_NFG
IGT_IFG
INSULIN
0
50
100
150
200
250
300
350
400
450
0 30 60 90 120 150 180
min
uU/m
l
C-PEPTIDE
0
1000
2000
3000
4000
5000
6000
7000
0 30 60 90 120 150 180
min
pmol
/l
SI
0
1
2
3
4
5
6
7
8
10-4 d
l/kg/
min
per
uU
/ml
NGT_NFG
NGT_IFG
IGT_NFG
IGT_IFG
* *^
*
* p<0.05 vs NGT-NFG; ^ p<0.05 vs NGT-IFG; # p<0.05 vs IGT-NFG
Φd
0
500
1000
1500
2000
2500
3000
10-9
*^
*
Φs
0
15
30
45
60
75
90
10-9 m
in-1
*#
*
Whole Body Models
• Provide estimates of beta cell function in an individual
• Based on plasma measurements (C-peptide and glucose) during a minimally invasive protocol
• Usable in clinical practice
From i.v. to oral tests
INSULIN SYSTEMSecretion+Kinetics
PLASMA GLUCOSE
PLASMA INSULIN
GLUCOSE SYSTEM
PLASMA C-peptide
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