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Minimal and Maximal Models of
Glucose Metabolism
Francesca Piccinini
PhD Student
Department of Information Engineering
Uni...
The Glucose-Insulin System
BRAIN
PRODUCTION

LIVER

GLUCOSE

-

UTILIZATION

Insulin Sensitivity

β-CELLS

+
SECRETION

β-...
Minimal Models
 Models to measure parameters

Maximal Models
 Models to perform In Silico Trials
The Glucose-Insulin System
BRAIN
PRODUCTION

LIVER

-

GLUCOSE
UTILIZATION

Insulin Sensitivity

β-CELLS

SECRETION

INSUL...
IVGTT Glucose Minimal Model
(Bergman & Cobelli, 1979)

IVGTT

k5
k1
GLUCOSE

LIVER

TISSUES

k4

SI
k6
REMOTE INSULIN

PLA...
Young vs Elderly Subjects
N = 59 vs 145 (Basu et al, 2006)

IVGTT
[mg/dl]

350

GLUCOSE

250

Elderly
150

Young

50
0
0

...
IVGTT Glucose Minimal Model
(Bergman & Cobelli, 1979)

Number of Papers Published / Year
60

50
40
30
20
10
0
1980

1985

...
Young vs Elderly Subjects
N = 59 vs 145 (Basu et al, 2006)

IVGTT
200

GLUCOSE
[mg/dl]

[mg/dl]

350

MEAL

250

Young

50...
Oral Glucose Minimal Model
(Dalla Man & Cobelli, 2002)
OGTT/MEAL

Gastrointestinal Tract
k5
k1
GLUCOSE

LIVER

SI

TISSUES...
Oral Glucose Minimal Model
(Dalla Man & Cobelli, 2002)
OGTT/MEAL

?

Gastrointestinal Tract
k5
k1
GLUCOSE

LIVER

SI

TISS...
Oral Glucose Minimal Model
(Dalla Man & Cobelli, 2002)

Glucose Ra

k5
k1
GLUCOSE

LIVER

SI

TISSUES
k4

k6
INSULIN
k2

R...
Fluxes Validation: Triple Tracer Meal
[1-13C] glucose oral

i.v. [6,6D 2] glucose
i.v. [6-3H]glucose

mimicking meal rate ...
SI Validation
Triple Tracer Method
(Dalla Man et al., 2004)
35

Euglycemic Clamp
(Dalla Man et al., 2005)

R=0.86, p<0.001...
Insulin Sensitivity
[10-4 dl/kg/min per mU/ml]

59 Y vs 145 E (Basu et al, 2006)

* p<0.05

SI
20

*

15
10
5
0

Y

E
E

Y...
The Glucose-Insulin System
BRAIN
PRODUCTION

GLUCOSE

LIVER

UTILIZATION

MUSCLE

β-CELLS

+
SECRETION

β-cell Responsivit...
C-peptide and Insulin System
(Toffolo et al, 2006)

C-PEPTIDE
k2,1

ISR
CP1

LIVER

k1,2

k0,1
ISR
-CELLS

INSULIN
IDR
I
...
β-Cell Responsivity Minimal Model
(Toffolo et al, 2001; Breda et al, 2001, 2002)

Glucose

SECRETION

Φs
Delay

k21

Stati...
β-Cell Responsivity Validation
(Steil et al, 2004)

(nmol/min per mmol/l)

Φsmeal

Static β-cell Responsivity vs
Hyperglyc...
β-Cell Responsivity Indices
59 Y vs 145 E

Φs

Φd
40

400

30
20

200

10

0

0

Y

E

14

30
25

12
10
8
6

Y
E

Y
16

[m...
FULL
Meal: 420 min – 21 samples
0 5 10 1520 30 40 50 60

75 90

120

150

180

210

240

260

280

300

OGTT: 300 min – 11...
OGTT

Meal

(N=100)

40
30

8
20
4

10

0

0
0

full

30

40

50

60

8

4

10

0

0

800

0

400

200

200

0

red

0

50...
The Glucose-Insulin System
BRAIN
PRODUCTION

LIVER

GLUCOSE

-

UTILIZATION

Insulin Sensitivity

β-CELLS

+
SECRETION

β-...
Efficiency of the Control: Disposition Index
(Bergman & Cobelli, 1981, Cobelli et at, 2007)
Insulin Sensitivity x βeta-Cel...
Disposition Index
120

βeta-Cell
Responsivity

60

Y: DI= 459
E: DI=313
0
0

20

40

60

80

Insulin Sensitivity
Hepatic Insulin Extraction
(Toffolo et al, 2006)

C-PEPTIDE
k2,1

ISR
CP1

LIVER

k1,2

k0,1
ISR
-CELLS

INSULIN
IDR
I

L...
Hepatic Extraction
(N=59Y vs 145E)

Index

Profile
T

0

0

 ISR(t)dt – IDR(t)dt

ISR(t) - IDR(t)

HE(t) =

T

HE =

T

...
What Happens If You Add A Tracer?

Tracers Allow Segregation of Glucose Disposal
from Production
Oral Glucose Minimal Model
(Dalla Man & Cobelli, 2002)

OGTT/MEAL

Gastrointestinal Tract
k5
k1
GLUCOSE

LIVER

SI

TISSUE...
Labelled Meal/OGTT
80

Glucose

8

Insulin

[mU ml-1]

60

6
4

40
20

3
0
0

60

120

180

240

300

360

0

420

0

60

...
Disposal Insulin Sensitivity
“COLD” MINIMAL MODEL

Production

Liver

“HOT” MINIMAL MODEL

Utilization

Utilization

Gluco...
SID

10-4 dl/kg/min per mU/ml

Meal: 59 Y vs 145 E

* p<0.01

20

*

15

10

5

0

Y

E
Hepatic Insulin Sensitivity
“COLD” MINIMAL MODEL

Liver

Production

“HOT” MINIMAL MODEL

Utilization

Utilization

Glucos...
20

Y

10-4 dl/kg/min per mU/ml

10-4 dl/kg/min per mU/ml

SI

15

*

10

5
10-4 dl/kg/min per mU/ml

Meal: 59 Y vs 145 E
...
Use in Pathophysiology
1) Role of age and gender (Basu et al, Diabetes 2006)
2) Pathogenesis of Prediabetes (Bock et al, D...
Role of age and gender
(Basu et al, 2006)
Subjects and Protocols
38 Elderly Men (EM), 29 Elderly Women (EW), 10 Young Men ...
Use in Pathophysiology
1) Role of age and gender (Basu et al, Diabetes 2006)
2) Pathogenesis of Prediabetes (Bock et al, D...
OGTT in IFG vs NFG
N=32 vs 28
(Bock et al, 2006)

Plasma Glucose

Plasma Insulin
750

15
IFG
NFG
pmol//l

9
6

IFG
NFG

50...
10-14 dl/kg/min -2 per pmol/L

10-14 dl/kg/min per pmol/L

10-14 dl/kg/min -2 per pmol/L

Disposition Indices
1200

DI

80...
Use in Pathophysiology
1) Role of age and gender (Basu et al, Diabetes 2006)
2) Pathogenesis of Prediabetes (Bock et al, D...
Type 2 Diabetes
(Basu A. et al 2009)
Φd

10-9

600
400

Φs

60
10-9 min-1

800

*

50
40

*

30
20

200
10
0

0

Diabetic ...
Use in Pathophysiology
1) Role of age and gender (Basu et al, Diabetes 2006)
2) Pathogenesis of Prediabetes (Bock et al, D...
Efficiency of Anti aging Drug
- 87 elderly men e 57 elderly women underwent a mixed meal test
- After a 2 yr DHEA or Testo...
Use in Pathophysiology
1) Role of age and gender (Basu et al, Diabetes 2006)
2) Pathogenesis of Prediabetes (Bock et al, D...
Children and Adolescents

NGT_NFG
NGT_IFG
IGT_NFG

(Calì et al, Diabetes Care 2009)
INSULIN

GLUCOSE
450

160

400

140

3...
Minimal Models
 Parameters measurement

Maximal Models
 In Silico Trials
Background


Models to Simulate:
often not possible, appropriate, convenient or desirable to
perform experiments in human...
47
New Generation of Simulation Models
Fluxes, in addition to concentrations, available
(N=204 Normals)
Glucose

Production

...
Healthy State Meal Simulator
(Dalla Man et al, 2007)
Meal

GASTRO-INTESTINAL
TRACT
12

Rate of
Appearance

Plasma Glucose
...
Identification: System Decomposition
& Forcing Function Strategy

Plasma
Glucose
GASTRO-INTESTINAL Glucose Rate of
Meal
Ap...
Muscle and Adipose Tissue Model
Plasma Insulin (I)
Glucose Production
(EGP)

MUSCLE AND
ADIPOSE TISSUE

Glucose Rate of
Ap...
Results

Utilization

Glucose
180
data
fit

8
7

data
fit

160

G (mg/dl)

U (mg/kg/min)

9

6
5
4
3
2

140
120
100
80

1
...
24 h Simulation: average model
Glucose

Insulin
(mg/kg/min)

(mg/dl)

(pmol/l)

160

1.2

200

140

120

100

100

Product...
Inter-Subject Variability
Rate Constant of Liver
Insulin Action

Liver
Insulin Sensitivity

Liver
Glucose Effectiveness
10...
Generation of virtual subjects
Generation of In Silico Normal Subjects
#1

#2

Glucose

Glucose

#3
Glucose

180

180

150

150

150

120
90

120
90
60

...
Healthy State Simulator
12 Differential Equations, 26 Parameters

Pre-diabetes Simulator
12 Differential Equations, 26 Par...
What is an Artificial Pancreas?
Traditional vs. Accelerated Development
Concept

Concept

Animal Trials

In Silico Trials

Clinical Trials

Clinical Trial...
Model of Type 1 Diabetes
Meal

Insulin
Pump

GASTRO-INTESTINAL
TRACT

SC
Insulin
Kinetics

Rate of
Appearance
Renal Excret...
Artificial Pancreas In Silico Trial
Meal

GASTRO-INTESTINAL
TRACT
Plasma Glucose

Subcutaneous
Subcutaneous
Insulin
Subcut...
Blood Glucose (mg/dl)

In Silico Selection of Control Strategy:
Proportionl-Integral-Derivative vs Model Predictive Contro...
Traditional vs. Accelerated Development

Concept

Animal Trials

Concept
In Silico Trials

Clinical Trials

Clinical Trial...
Conclusions
• Importance of System Models in Diabetes
• Minimal Models:
• Powerful Tools to Measure
Pathophysiology of Dia...
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Minimal and maximal models of glucose metabolism

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Minimal and maximal models of glucose metabolism

  1. 1. Minimal and Maximal Models of Glucose Metabolism Francesca Piccinini PhD Student Department of Information Engineering University of Padova, Italy Eindhoven, NL, December 12th, 2013
  2. 2. The Glucose-Insulin System BRAIN PRODUCTION LIVER GLUCOSE - UTILIZATION Insulin Sensitivity β-CELLS + SECRETION β-cell Responsivity INSULIN + DEGRADATION MUSCLE TISSUES
  3. 3. Minimal Models  Models to measure parameters Maximal Models  Models to perform In Silico Trials
  4. 4. The Glucose-Insulin System BRAIN PRODUCTION LIVER - GLUCOSE UTILIZATION Insulin Sensitivity β-CELLS SECRETION INSULIN + DEGRADATION MUSCLE TISSUES
  5. 5. IVGTT Glucose Minimal Model (Bergman & Cobelli, 1979) IVGTT k5 k1 GLUCOSE LIVER TISSUES k4 SI k6 REMOTE INSULIN PLASMA INSULIN k2 k3 SI: Insulin Sensitivity (liver & periphery)
  6. 6. Young vs Elderly Subjects N = 59 vs 145 (Basu et al, 2006) IVGTT [mg/dl] 350 GLUCOSE 250 Elderly 150 Young 50 0 0 60 [pmol/l] 900 120 180 t [min] 240 INSULIN 700 500 300 100 0 t [min] 0 [pmol/l] 2000 60 120 180 240 C-PEPTIDE 1600 1200 800 400 0 t [min]
  7. 7. IVGTT Glucose Minimal Model (Bergman & Cobelli, 1979) Number of Papers Published / Year 60 50 40 30 20 10 0 1980 1985 1990 Year 1995 2000 2005 2009
  8. 8. Young vs Elderly Subjects N = 59 vs 145 (Basu et al, 2006) IVGTT 200 GLUCOSE [mg/dl] [mg/dl] 350 MEAL 250 Young 50 0 0 60 180 Elderly Young 80 t [min] 240 0 120 500 900 700 500 300 240 360 420 t [min] 240 360 420 t [min] INSULIN INSULIN [pmol/l] [pmol/l] 120 160 120 Elderly 150 300 100 100 0 t [min] 2000 60 120 180 3000 C-PEPTIDE 1600 1200 800 2000 1000 400 0 0 240 [pmol/l] 0 [pmol/l] GLUCOSE t [min] 120 C-PEPTIDE
  9. 9. Oral Glucose Minimal Model (Dalla Man & Cobelli, 2002) OGTT/MEAL Gastrointestinal Tract k5 k1 GLUCOSE LIVER SI TISSUES k4 k6 INSULIN k2 REMOTE INSULIN k3 SI: Insulin Sensitivity (liver & periphery)
  10. 10. Oral Glucose Minimal Model (Dalla Man & Cobelli, 2002) OGTT/MEAL ? Gastrointestinal Tract k5 k1 GLUCOSE LIVER SI TISSUES k4 k6 INSULIN k2 REMOTE INSULIN k3 SI: Insulin Sensitivity (liver & periphery)
  11. 11. Oral Glucose Minimal Model (Dalla Man & Cobelli, 2002) Glucose Ra k5 k1 GLUCOSE LIVER SI TISSUES k4 k6 INSULIN k2 REMOTE INSULIN k3 SI: Insulin Sensitivity (liver & periphery)
  12. 12. Fluxes Validation: Triple Tracer Meal [1-13C] glucose oral i.v. [6,6D 2] glucose i.v. [6-3H]glucose mimicking meal rate of appearance mimicking endogenous glucose production Oral tracer ingested with the meal Tracer-to-tracee clamp technique virtually model-independent glucose fluxes Endogenous Glucose Production Model Model 10 Triple Tracer 1.5 1 mg/kg/min mg/kg/min 2 Rate of Appearance 12 2.5 Triple Tracer 8 6 4 0.5 0 2 0 60 120 180 240 min 300 360 420 0 0 60 120 180 240 min 300 360 420
  13. 13. SI Validation Triple Tracer Method (Dalla Man et al., 2004) 35 Euglycemic Clamp (Dalla Man et al., 2005) R=0.86, p<0.001 20 R=0.81, p<0.001 30 15 OGTT SI 25 20 15 10 10 5 5 0 0 0 5 10 15 20 SIref 25 30 35 0 10 20 Clamp 30
  14. 14. Insulin Sensitivity [10-4 dl/kg/min per mU/ml] 59 Y vs 145 E (Basu et al, 2006) * p<0.05 SI 20 * 15 10 5 0 Y E E Y 16 60 14 50 12 10 8 40 30 6 20 4 2 0 10 0
  15. 15. The Glucose-Insulin System BRAIN PRODUCTION GLUCOSE LIVER UTILIZATION MUSCLE β-CELLS + SECRETION β-cell Responsivity INSULIN DEGRADATION TISSUES
  16. 16. C-peptide and Insulin System (Toffolo et al, 2006) C-PEPTIDE k2,1 ISR CP1 LIVER k1,2 k0,1 ISR -CELLS INSULIN IDR I LIVER n CP2
  17. 17. β-Cell Responsivity Minimal Model (Toffolo et al, 2001; Breda et al, 2001, 2002) Glucose SECRETION Φs Delay k21 Static Phase Releasable Insulin CP1 k12 Dynamic Phase k01 Φd Rate of Increase of Glucose (first 50-60 minutes) Φd: Dynamic βeta-Cell Responsivity Φs: Static βeta-Cell Responsivity Φtot: Total βeta-Cell Responsivity CP2
  18. 18. β-Cell Responsivity Validation (Steil et al, 2004) (nmol/min per mmol/l) Φsmeal Static β-cell Responsivity vs Hyperglycemic Clamp ΦsHGC (pmol/min per mmol/l)
  19. 19. β-Cell Responsivity Indices 59 Y vs 145 E Φs Φd 40 400 30 20 200 10 0 0 Y E 14 30 25 12 10 8 6 Y E Y 16 [min] * 600 [10-9 min-1] [10-9] 800 E E Y 25 20 60 50 40 20 15 30 15 10 20 10 4 2 0 5 5 0 0 10 0 * p<0.05
  20. 20. FULL Meal: 420 min – 21 samples 0 5 10 1520 30 40 50 60 75 90 120 150 180 210 240 260 280 300 OGTT: 300 min – 11 samples 0 10 20 30 60 90 120 REDUCED 120 min – 7 Samples 0 10 20 30 60 90 120 150 180 240 300 360 420
  21. 21. OGTT Meal (N=100) 40 30 8 20 4 10 0 0 0 full 30 40 50 60 8 4 10 0 0 800 0 400 200 200 0 red 0 500 1000 1500 2000 2500 3000 full full Φs 40 120 R=0.88, p<0.0001 50 80 red 60 40 20 500 1000 1500 full Φs 90 R=0.90, p<0 .0001 70 30 40 30 0 80 100 (10-9 min-1) 60 0 red 60 20 red full (10-9 min-1) 800 100 0 50 600 200 500 40 1000 300 1000 30 R=0.91 p<0.0001 1200 red (10-9 ) red 400 20 1400 400 1500 10 full 500 2000 600 0 red Φd 600 3000 2500 30 20 full R=0.98, p<0.0 001 R=0.85, p<0. 0001 40 12 full 1000 (10-9 ) 20 red Φd 1200 10 50 red 12 (10-4 dl/kg/min per mU/ml) R=0.89, p <0.0001 50 16 SI 16 60 20 red (10-4 dl/kg/min per mU/ml) SI (N=100) 50 40 30 10 20 20 10 10 0 0 0 full red 20 40 60 full 80 100 120 0 0 0 20 40 60 80 100
  22. 22. The Glucose-Insulin System BRAIN PRODUCTION LIVER GLUCOSE - UTILIZATION Insulin Sensitivity β-CELLS + SECRETION β-cell Responsivity INSULIN + DEGRADATION MUSCLE TISSUES
  23. 23. Efficiency of the Control: Disposition Index (Bergman & Cobelli, 1981, Cobelli et at, 2007) Insulin Sensitivity x βeta-Cell Function= Constant βeta-Cell Responsivity Increased II Normal 2 I Normal Tolerance Impaired Tolerance Reduced Normal Insulin Sensitivity
  24. 24. Disposition Index 120 βeta-Cell Responsivity 60 Y: DI= 459 E: DI=313 0 0 20 40 60 80 Insulin Sensitivity
  25. 25. Hepatic Insulin Extraction (Toffolo et al, 2006) C-PEPTIDE k2,1 ISR CP1 LIVER k1,2 k0,1 ISR -CELLS INSULIN IDR I LIVER n CP2
  26. 26. Hepatic Extraction (N=59Y vs 145E) Index Profile T 0 0  ISR(t)dt – IDR(t)dt ISR(t) - IDR(t) HE(t) = T HE = T  ISR(t)dt ISR(t) 0 1.00 1.00 ELDERLY 0.80 * p<0.05 0.80 (%) (%) 0.60 0.40 0.60 * 0.40 0.20 YOUNG 0.20 0.00 0 60 120 180 240 t [min] 300 360 420 0.00 E Y
  27. 27. What Happens If You Add A Tracer? Tracers Allow Segregation of Glucose Disposal from Production
  28. 28. Oral Glucose Minimal Model (Dalla Man & Cobelli, 2002) OGTT/MEAL Gastrointestinal Tract k5 k1 GLUCOSE LIVER SI TISSUES k4 k6 INSULIN k2 REMOTE INSULIN k3 SI: Insulin Sensitivity (liver & periphery)
  29. 29. Labelled Meal/OGTT 80 Glucose 8 Insulin [mU ml-1] 60 6 4 40 20 3 0 0 60 120 180 240 300 360 0 420 0 60 120 Time [min] 0.6 0.4 0.2 0 0 180 240 Time [min] Stable Tracer Glucose 0.8 [mmol L-1] [mmol L-1] 10 60 120 180 240 300 Time [min] 360 420 300 360 420
  30. 30. Disposal Insulin Sensitivity “COLD” MINIMAL MODEL Production Liver “HOT” MINIMAL MODEL Utilization Utilization Glucose SI Insulin Remote Insulin SI: Insulin Sensitivity (Utilization + Production) Glucose SID Tissues Insulin Remote Insulin SID: Disposal Insulin Sensitivity (Utilization Only) Tissues
  31. 31. SID 10-4 dl/kg/min per mU/ml Meal: 59 Y vs 145 E * p<0.01 20 * 15 10 5 0 Y E
  32. 32. Hepatic Insulin Sensitivity “COLD” MINIMAL MODEL Liver Production “HOT” MINIMAL MODEL Utilization Utilization Glucose SI Insulin Remote Insulin From SI and SID Glucose SID Tissues Insulin Remote Insulin SIL = SI – SID Tissues
  33. 33. 20 Y 10-4 dl/kg/min per mU/ml 10-4 dl/kg/min per mU/ml SI 15 * 10 5 10-4 dl/kg/min per mU/ml Meal: 59 Y vs 145 E 8 Y 20 0 E SIL 6 4 2 0 E SI D Y * p<0.01 15 * 10 5 0 E
  34. 34. Use in Pathophysiology 1) Role of age and gender (Basu et al, Diabetes 2006) 2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006) 3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN) 4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006) 5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006) 6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009) 7) Children and Adolescent (Calì et al, Diabetes Care 2009) 8) Diurnal Variation of Glucose Tolerance Chicago, Chicago, IL) (Dr. E. Van Cauter, University of
  35. 35. Role of age and gender (Basu et al, 2006) Subjects and Protocols 38 Elderly Men (EM), 29 Elderly Women (EW), 10 Young Men (YM), 11 Young Women (YW) underwent a labelled mixed meal. Elderly vs Young SI 16 10-4 dl/kg/min per μU/ml 10-4 dl/kg/min per μU/ml * p<0.05 SI 20 Men vs Women 16 * 12 8 12 8 4 4 0 0 Elderly Young Men Women
  36. 36. Use in Pathophysiology 1) Role of age and gender (Basu et al, Diabetes 2006) 2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006) 3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN) 4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006) 5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006) 6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009) 7) Children and Adolescent (Calì et al, Diabetes Care 2009) 8) Diurnal Variation of Glucose Tolerance Chicago, Chicago, IL) (Dr. E. Van Cauter, University of
  37. 37. OGTT in IFG vs NFG N=32 vs 28 (Bock et al, 2006) Plasma Glucose Plasma Insulin 750 15 IFG NFG pmol//l 9 6 IFG NFG 500 250 3 0 0 -60 0 60 120 180 240 300 360 -60 0 60 120 minutes 5 IFG NFG 4 3 2 1 0 -60 180 minutes Plasma C-peptide nmol/l mmol/l 12 0 60 120 180 minutes 240 300 360 240 300 360
  38. 38. 10-14 dl/kg/min -2 per pmol/L 10-14 dl/kg/min per pmol/L 10-14 dl/kg/min -2 per pmol/L Disposition Indices 1200 DI 800 * * 400 0 16000 NFG NGT IFG IFG NGT NFG IGT * IFG IGT * IFG DM DId 12000 * * 8000 4000 0 1200 NFG NGT IFG IFG NGT NFG IGT * IFG IGT * IFG DM DIs 800 * * * NFG IGT IFG IGT 400 0 NFG NGT IFG IFG NGT * IFG DM
  39. 39. Use in Pathophysiology 1) Role of age and gender (Basu et al, Diabetes 2006) 2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006) 3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN) 4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006) 5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006) 6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009) 7) Children and Adolescent (Calì et al, Diabetes Care 2009) 8) Diurnal Variation of Glucose Tolerance Chicago, Chicago, IL) (Dr. E. Van Cauter, University of
  40. 40. Type 2 Diabetes (Basu A. et al 2009) Φd 10-9 600 400 Φs 60 10-9 min-1 800 * 50 40 * 30 20 200 10 0 0 Diabetic Normal Diabetic Normal SI DI 25 20 15 * 10 5 10-14 dl/kg/min2 per pmol/l 10-5 dl/kg/min per pmol/l 30 1600 1200 * 800 400 * 0 0 Diabetic Normal Diabetic Normal
  41. 41. Use in Pathophysiology 1) Role of age and gender (Basu et al, Diabetes 2006) 2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006) 3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN) 4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006) 5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006) 6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009) 7) Children and Adolescent (Calì et al, Diabetes Care 2009) 8) Diurnal Variation of Glucose Tolerance Chicago, Chicago, IL) (Dr. E. Van Cauter, University of
  42. 42. Efficiency of Anti aging Drug - 87 elderly men e 57 elderly women underwent a mixed meal test - After a 2 yr DHEA or Testosterone same test SI Men Women 20 Placebo DHEA Placebo DHEA Testosterone 10^-4 dl/kg/min per uU/ml 15 10 5 0 Pre Post Pre Post Pre Post Pre Post Pre Post
  43. 43. Use in Pathophysiology 1) Role of age and gender (Basu et al, Diabetes 2006) 2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006) 3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN) 4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006) 5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006) 6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009) 7) Children and Adolescent (Calì et al, Diabetes Care 2009) 8) Diurnal Variation of Glucose Tolerance Chicago, IL) (Dr. E. Van Cauter, University of Chicago,
  44. 44. Children and Adolescents NGT_NFG NGT_IFG IGT_NFG (Calì et al, Diabetes Care 2009) INSULIN GLUCOSE 450 160 400 140 350 120 300 100 C-PEPTIDE 250 7000 6000 5000 pmol/l uU/ml 180 200 80 60 150 40 100 20 50 0 60 90 120 150 180 1000 0 0 30 min 5 4 3 3000 NGT_IFG * * * ^ IGT_NFG IGT_IFG 120 150 * * ^ 2500 2000 10-9 6 90 180 0 30 60 1500 0 Φs 90 * 75 45 30 500 15 * p<0.05 vs NGT-NFG; ^ p<0.05 vs NGT-IFG; # p<0.05 vs IGT-NFG * # 60 1000 0 120 min 2 1 90 Φd NGT_NFG 7 60 min SI 8 3000 10-9 min-1 30 4000 2000 0 0 10-4 dl/kg/min per uU/ml mg/dl IGT_IFG 0 150 180
  45. 45. Minimal Models  Parameters measurement Maximal Models  In Silico Trials
  46. 46. Background  Models to Simulate: often not possible, appropriate, convenient or desirable to perform experiments in humans, e.g. testing of glucose sensors and insulin infusion algorithms for closed loop control during normal life condition  Can Models to Measure be used as Models to Simulate for in Silico Trial? No Models to Measure need to be minimal (parsimonious) Models to Simulate need to be maximal (large scale)
  47. 47. 47
  48. 48. New Generation of Simulation Models Fluxes, in addition to concentrations, available (N=204 Normals) Glucose Production Insulin 2.5 600 250 (pmol/l) (mg/dl) (mg/kg/min) 500 Data Range 200 400 300 150 200 100 100 50 0 60 180 240 300 360 420 Rate of Appearance 14 12 10 8 6 4 60 120 180 240 300 360 0 60 120 180 240 t (min) 300 360 420 Utilization 1 0.5 0 60 120 8 6 4 180 240 300 360 420 300 360 420 Secretion 16 10 0 1.5 0 420 2 2 0 0 12 (mg/kg/min) (mg/kg/min) 120 (pmol/kg/min) 0 2 14 12 10 8 6 4 2 0 0 60 120 180 240 t (min) 300 360 420 0 60 120 180 240 t (min)
  49. 49. Healthy State Meal Simulator (Dalla Man et al, 2007) Meal GASTRO-INTESTINAL TRACT 12 Rate of Appearance Plasma Glucose 180 10 8 6 4 2 0 0 60 120 180 240 300 360 420 160 140 120 100 80 60 0 60 120 180 240 300 360 420 Renal Excretion MUSCLE AND ADIPOSE TISSUE GLUCOSE SYSTEM LIVER Production Utilization 2 10 8 1.5 6 1 4 2 0.5 0 0 0 0 60 120 180 240 300 360 60 120 180 240 300 360 420 420 INSULIN SYSTEM BETA-CELL Secretion Plasma Insulin 700 600 500 400 300 200 500 400 100 300 0 200 0 100 0 0 60 120 180 240 300 360 420 60 120 180 240 300 360 420
  50. 50. Identification: System Decomposition & Forcing Function Strategy Plasma Glucose GASTRO-INTESTINAL Glucose Rate of Meal Appearance TRACT Plasma Insulin Plasma Insulin Glucose Production Glucose Rate of Appearance MUSCLE AND ADIPOSE TISSUE LIVER Plasma Glucose Rate of Glucose Change Glucose Utilization Plasma Glucose Glucose Production Plasma Insulin BETA CELL Insulin Secretion
  51. 51. Muscle and Adipose Tissue Model Plasma Insulin (I) Glucose Production (EGP) MUSCLE AND ADIPOSE TISSUE Glucose Rate of Appearance (Ra) Plasma Glucose (G) Glucose Utilization (U) Model I p2U Insulin Action X p2U Vm(X2) G EGP Ra Vm(X3) U(t) Vm(X1) k21 Plasma Gp k12 Tissues Gt Km(X3) Km(X2) Kg Ki U Km(X1) Gt(t) X1<X2<X3
  52. 52. Results Utilization Glucose 180 data fit 8 7 data fit 160 G (mg/dl) U (mg/kg/min) 9 6 5 4 3 2 140 120 100 80 1 60 0 0 60 120 180 t (min) 240 300 360 420 0 60 120 180 240 300 360 420 t (min) 52
  53. 53. 24 h Simulation: average model Glucose Insulin (mg/kg/min) (mg/dl) (pmol/l) 160 1.2 200 140 120 100 100 Production 1.8 300 180 0.6 80 0 60 3 6 9 12 15 18 21 0 6 24 9 12 15 18 21 24 6 9 12 15 18 21 24 0 Rate of Appearance Utilization 10 8 6 4 6 4 2 9 12 15 18 21 6 9 12 15 18 t (hours) t (hours) 45 g 70 g 24 70 g 6 4 0 0 6 8 2 2 0 Secretion 10 (pmol/kg/min) 8 (mg/kg/min) (mg/kg/min) 12 21 24 6 0 9 12 15 t (hours) 18 21 24
  54. 54. Inter-Subject Variability Rate Constant of Liver Insulin Action Liver Insulin Sensitivity Liver Glucose Effectiveness 100 100 100 80 80 80 60 60 60 40 40 40 20 20 20 0 0 0 min^-1 mg/kg/min/(pmol/l) min^-1 Rate Constant of Peripheral Insulin Action Peripheral Insulin Sensitivity Peripheral Glucose Effectiveness 100 100 100 80 80 80 60 60 60 40 40 40 20 20 20 0 0 0 mg/kg mg/kg/min per pmol/L min^-1
  55. 55. Generation of virtual subjects
  56. 56. Generation of In Silico Normal Subjects #1 #2 Glucose Glucose #3 Glucose 180 180 150 150 150 120 90 120 90 60 60 20 25 30 35 30 40 120 90 60 20 25 30 35 30 40 20 25 t (hours) t (hours) 30 35 40 35 40 t (hours) # 100 Glucose 200 180 ..... 150 (mg/dl) 30 (mg/dl) 200 (mg/dl) 200 180 (mg/dl) 200 120 90 60 30 20 25 30 t (hours)
  57. 57. Healthy State Simulator 12 Differential Equations, 26 Parameters Pre-diabetes Simulator 12 Differential Equations, 26 Parameters Type 2 Simulator 12 Differential Equations, 26 Parameters Type 1 Simulator 13 Differential Equations, 26 Parameters
  58. 58. What is an Artificial Pancreas?
  59. 59. Traditional vs. Accelerated Development Concept Concept Animal Trials In Silico Trials Clinical Trials Clinical Trials Product Product Saves Years
  60. 60. Model of Type 1 Diabetes Meal Insulin Pump GASTRO-INTESTINAL TRACT SC Insulin Kinetics Rate of Appearance Renal Excretion LIVER Production • Tested against, and showing excellent agreement with: Common clinical knowledge Lab traces of induced hypoglycemia Field data of children with T1DM BETA-CELL Secretio n PLASMA GLUCOSE PLASMA INSULIN Utilization Degradation MUSCLE & ADIPOSE TISSUE
  61. 61. Artificial Pancreas In Silico Trial Meal GASTRO-INTESTINAL TRACT Plasma Glucose Subcutaneous Subcutaneous Insulin Subcutaneous Insulin Subcutaneous Infusion Insulin Subcutaneous Infusion Insulin Pump Insulin Infusion Pump A Infusion Pump B Infusion Pump C Pump D Rate of Appearance 180 160 140 120 100 80 60 0 60 120 180 240 300 360 420 LIVER 2 1.5 1 0.5 0 0 Production PLASMA GLUCOSE 60 120180 240 300360420 BETA-CELL Secretion 700 600 500 400 300 200 100 0 0 12 10 8 6 4 2 0 0 PLASMA INSULIN 60 120 180 240 300 360 420 Renal Excretion Utilization 10 8 6 4 2 00 MUSCLE AND ADIPOSE TISSUE 60 120180 240 300360 420 Degradation Plasma Insulin 500 60 120 180 240 300 360 420 400 300 200 100 0 Controller A Controller Controller B Controller C Controller D 0 60 120180 240 300 360 420 Sensor Sensor I II Sensor III Sensor IV Sensor 61
  62. 62. Blood Glucose (mg/dl) In Silico Selection of Control Strategy: Proportionl-Integral-Derivative vs Model Predictive Control 0 12 24 36 48 60 Time (hours) Health T1DM + PID controller T1DM + Model Predictive Control 72
  63. 63. Traditional vs. Accelerated Development Concept Animal Trials Concept In Silico Trials Clinical Trials Clinical Trials Product Product January 18, 2008: Simulation accepted by FDA as substitute to animal trials (Master file #1521) Regulatory Approval for clinical trials based entirely on in silico testing: April 17, 2008 (UVA IDE); May 20, 2008 (Padova EC)
  64. 64. Conclusions • Importance of System Models in Diabetes • Minimal Models: • Powerful Tools to Measure Pathophysiology of Diabetes & Understand the • Maximal Models: • Importance of prediabetes, type 2 and type 1 diabetes simulators for in silico trials

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