minimal and maximal models of glucose metabolism

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Francesca Piccinini PhD Student Department of Information Engineering University of Padova, Italy Eindhoven, NL, December 12 th , 2013 Minimal and Maximal Models of Glucose Metabolism

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Page 1: Minimal and maximal models of glucose metabolism

Francesca Piccinini

PhD StudentDepartment of Information Engineering

University of Padova, Italy

Eindhoven, NL, December 12th, 2013

Minimal and Maximal Models of Glucose Metabolism

Page 2: Minimal and maximal models of glucose metabolism

β-CELLS

LIVER GLUCOSE

INSULIN

BRAIN

MUSCLE

TISSUES

PRODUCTION

DEGRADATIONSECRETION

UTILIZATION-

+Insulin Sensitivity

+

β-cell Responsivity

The Glucose-Insulin System

Page 3: Minimal and maximal models of glucose metabolism

Minimal Models Models to measure parameters

Maximal Models Models to perform In Silico Trials

Page 4: Minimal and maximal models of glucose metabolism

β-CELLS

LIVER GLUCOSE

INSULIN

BRAIN

MUSCLE

TISSUES

PRODUCTION

DEGRADATIONSECRETION

UTILIZATION-

+Insulin Sensitivity

The Glucose-Insulin System

Page 5: Minimal and maximal models of glucose metabolism

IVGTT Glucose Minimal Model (Bergman & Cobelli, 1979)

k3

k5

GLUCOSE TISSUES

k1

k4

k6

REMOTE INSULIN

k2

PLASMA INSULIN

LIVER

IVGTT

SI: Insulin Sensitivity (liver & periphery)

SI

Page 6: Minimal and maximal models of glucose metabolism

Young vs Elderly SubjectsN = 59 vs 145 (Basu et al, 2006)

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

]

IVGTT

Page 7: Minimal and maximal models of glucose metabolism

IVGTT Glucose Minimal Model (Bergman & Cobelli, 1979)

Year

0

10

20

30

40

50

60

Number of Papers Published / Year

1980 1985 1990 1995 20052000 2009

Page 8: Minimal and maximal models of glucose metabolism

Young vs Elderly SubjectsN = 59 vs 145 (Basu et al, 2006)

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

]

IVGTTGLUCOSE

INSULIN

100

300

500

0 120 240 360 420t [min]

C-PEPTIDE

1000

2000

3000

0 120 240 360 420

80

120

160

200

0 120 240 360 420t [min]

Young

Elderly

[mg/

dl]

[pm

ol/l

][p

mo

l/l]

MEAL

Page 9: Minimal and maximal models of glucose metabolism

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

SI: Insulin Sensitivity (liver & periphery)

OGTT/MEAL

k3

k5

GLUCOSE TISSUES

k1

k4

k6

REMOTE INSULIN k2

INSULIN

LIVER

Gastrointestinal Tract

SI

Page 10: Minimal and maximal models of glucose metabolism

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

SI: Insulin Sensitivity (liver & periphery)

OGTT/MEAL

k3

k5

GLUCOSE TISSUES

k1

k4

k6

REMOTE INSULIN k2

INSULIN

LIVER

Gastrointestinal Tract

SI

?

Page 11: Minimal and maximal models of glucose metabolism

SI: Insulin Sensitivity (liver & periphery)

k3

k5

GLUCOSE TISSUES

k1

k4

k6

REMOTE INSULIN k2

INSULIN

LIVER

SI

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

Glucose Ra

Page 12: Minimal and maximal models of glucose metabolism

mimicking endogenous glucose production

mimicking meal rate of appearance

i.v. [6,6D 2] glucose

i.v. [6-3H]glucose

[1-13C] glucose oral

Oral tracer ingested with the meal

Fluxes Validation: Triple Tracer Meal

Tracer-to-tracee clamp technique

virtually model-independent glucose fluxes

Rate of Appearance

Model

Triple Tracer

min

mg/

kg/m

in

0

2

4

6

8

10

12

0 60 120 180 240 300 360 4200

0.5

1

1.5

2

2.5

0 60 120 180 240 300 360 420

min

mg/

kg/m

in

Endogenous Glucose Production

Model

Triple Tracer

Page 13: Minimal and maximal models of glucose metabolism

SI Validation

SIref

SI

R=0.86, p<0.001

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

(Dalla Man et al., 2004)

Triple Tracer Method Euglycemic Clamp

(Dalla Man et al., 2005)

Clamp

OG

TT

R=0.81, p<0.001

0

5

10

15

20

0 10 20 30

Page 14: Minimal and maximal models of glucose metabolism

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

* p<0.05

EY

*

SI

[10

-4 d

l/k

g/m

in

pe

r m

U/m

l]

0

5

10

15

20

0

10

20

30

40

50

60

0 10 20 30 40 50

6

0

E

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50

6

0

Y

Page 15: Minimal and maximal models of glucose metabolism

β-CELLS

LIVER GLUCOSE

INSULIN

BRAIN

MUSCLE

TISSUES

PRODUCTION

DEGRADATIONSECRETION

UTILIZATION

+

β-cell Responsivity

The Glucose-Insulin System

Page 16: Minimal and maximal models of glucose metabolism

C-peptide and Insulin System(Toffolo et al, 2006)

ISR

C-PEPTIDE

INSULIN

ISR

IDR

LIVER

-CELLS

LIVER I

n

k0,1

k2,1

k1,2

CP1 CP2

Page 17: Minimal and maximal models of glucose metabolism

β-Cell Responsivity Minimal Model

(Toffolo et al, 2001; Breda et al, 2001, 2002)

Rate of Increase of Glucose (first 50-60 minutes)

k01

k21

k12

CP1 CP2

Delay

Dynamic Phase

Static Phase

Glucose

ReleasableInsulin

SECRETION

Φd

Φs

Φd: Dynamic βeta-Cell ResponsivityΦs: Static βeta-Cell ResponsivityΦtot: Total βeta-Cell Responsivity

Page 18: Minimal and maximal models of glucose metabolism

(Steil et al, 2004)

β-Cell Responsivity Validation

Φsm

eal

(nm

ol/m

in p

er m

mol

/l)

ΦsHGC

(pmol/min per mmol/l)

Static β-cell Responsivity vs Hyperglycemic Clamp

Page 19: Minimal and maximal models of glucose metabolism

β-Cell Responsivity Indices 59 Y vs 145 E

Φs

[10-9

min

-1]

EY

*

Φd

[10-9

]

EY

* p<0.05

[min

]

0

200

400

600

800

0

10

20

30

40

0

2

4

6

8

10

12

14

16

0200

400600

8001000

1200

0

5

10

15

20

25

30

0200

400600

8001000

1200

EY

0

10

20

30

40

50

60

0 20 40 60 80100

120

0

5

10

15

20

25

0 20 40 60 80100

120

EY

Page 20: Minimal and maximal models of glucose metabolism

FULL

0 15 40 90 120 150 180 240 420 10 5 20 30 50 60 75 210 260 280 300 360

0 90 120 150 180 240 10 20 30 60 300

OGTT: 300 min – 11 samples

Meal: 420 min – 21 samples

REDUCED

0 90 120 10 20 30 60

120 min – 7 Samples

Page 21: Minimal and maximal models of glucose metabolism

OGTT (N=100)

SI

red

R=0.89, p<0.0001

(10-4

dl/

kg/m

in p

er m

U/m

l)

full red

0

4

8

12

16

20

0

10

20

30

40

50

60

0 10 20 30 40 50 60

full

Φs

R=0.88, p<0.0001

full

red

0

20

40

60

80

100

120

0 20 40 60 80 100 120

(10-9

m

in-1

)

0

10

20

30

40

50

60

full red

Φd

red

R=0.98, p<0.0001

0

500

1000

1500

2000

2500

3000

0 500 1000 1500 2000 2500 3000

(10-9

)

full red

0

200

400

600

800

1000

1200

full

Meal (N=100)

SI

full

(10-4

dl/

kg/m

in p

er m

U/m

l)

full red

R=0.85, p<0.0001

red

0

10

20

30

40

50

0 10 20 30 40 500

4

8

12

16

Φs

full

(10-9

m

in-1

)

full redre

d

(10-9

)full red

full

R=0.91 p<0.0001

0

200

400

600

800

1000

1200

1400

0 500 1000 1500

0

100

200

300

400

500

600

red

R=0.90, p<0.0001

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 1000

10

20

30

40

Φd

Page 22: Minimal and maximal models of glucose metabolism

β-CELLS

LIVER GLUCOSE

INSULIN

BRAIN

MUSCLE

TISSUES

PRODUCTION

DEGRADATIONSECRETION

UTILIZATION-

+Insulin Sensitivity

+

β-cell Responsivity

The Glucose-Insulin System

Page 23: Minimal and maximal models of glucose metabolism

βeta-Cell Responsivity

βeta-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 βeta-Cell Function= Constant

Page 24: Minimal and maximal models of glucose metabolism

Disposition Index

0

60

120

0 20 40 60 80

βeta-Cell Responsivity

βeta-Cell Responsivity

Insulin Sensitivity Insulin Sensitivity

Y: DI= 459

E: DI=313

Page 25: Minimal and maximal models of glucose metabolism

Hepatic Insulin Extraction(Toffolo et al, 2006)

ISR

C-PEPTIDE

INSULIN

ISR

IDR

LIVER

-CELLS

LIVER I

n

k0,1

k2,1

k1,2

CP1 CP2

Page 26: Minimal and maximal models of glucose metabolism

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]

0.00

0.20

0.40

0.60

0.80

1.00

EY

*(%)(%

)* p<0.05

Profile

ISR(t) - IDR(t)

ISR(t)HE(t) =

Index

(N=59Y vs 145E)

T

ò

ò0

T

0

ISR(t)dt

ISR(t)dt – IDR(t)dt

HE =òT

0

Page 27: Minimal and maximal models of glucose metabolism

What Happens If You Add A Tracer?

Tracers Allow Segregation of Glucose Disposal from Production

Page 28: Minimal and maximal models of glucose metabolism

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

SI: Insulin Sensitivity (liver & periphery)

OGTT/MEAL

k3

k5

GLUCOSE TISSUES

k1

k4

k6

REMOTE INSULIN k2

INSULIN

LIVER

Gastrointestinal Tract

SI

Page 29: Minimal and maximal models of glucose metabolism

Glucose

Time [min] Time [min]

Stable Tracer Glucose

Time [min]

[mm

ol L

-1]

[mU

ml-1

]

Insulin

Labelled Meal/OGTT

0 60 120 180 240 300 360 420

[mm

ol L

-1]

0

3

4

6

8

10

0

20

40

60

80

0 60 120 180 240 300 360 420

0

0.2

0.4

0.6

0.8

0 60 120 180 240 300 360 420

Page 30: Minimal and maximal models of glucose metabolism

Disposal Insulin Sensitivity

Liver

Insulin

Glucose

Production Utilization

Tissues

Remote Insulin

SI

“COLD” MINIMAL MODEL

SI: Insulin Sensitivity

(Utilization + Production)

SID: Disposal Insulin Sensitivity

(Utilization Only)

Glucose

Utilization

Remote Insulin

SID

“HOT” MINIMAL MODEL

Tissues

Insulin

Page 31: Minimal and maximal models of glucose metabolism

SID

* p<0.01

0

5

10

Y E

*

10-4

dl/

kg/m

in p

er m

U/m

l

Meal: 59 Y vs 145 E

20

15

Page 32: Minimal and maximal models of glucose metabolism

Hepatic Insulin Sensitivity

SIL = SI – SI

DFrom SI and SID

Liver

Insulin

Glucose

Production Utilization

Tissues

Remote Insulin

SI

“COLD” MINIMAL MODEL

Insulin

Glucose

Utilization

Remote Insulin

SID

“HOT” MINIMAL MODEL

Tissues

Page 33: Minimal and maximal models of glucose metabolism

Meal: 59 Y vs 145 E

SID * p<0.01

0

5

10

Y E

*

10-4

dl/

kg/m

in p

er m

U/m

l

20

15

SI

0

5

10

Y E

*

10-4

dl/

kg/m

in p

er m

U/m

l

20

15

SIL

0

2

4

Y E

10-4

dl/

kg/m

in p

er m

U/m

l 8

6

Page 34: Minimal and maximal models of glucose metabolism

Use in Pathophysiology

1) Role of age and gender (Basu et al, Diabetes 2006)

2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006)

4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006)

8) Diurnal Variation of Glucose Tolerance (Dr. E. Van Cauter, University of Chicago, Chicago, IL)

5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006)

7) Children and Adolescent (Calì et al, Diabetes Care 2009)

3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN)

6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009)

Page 35: Minimal and maximal models of glucose metabolism

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

YoungElderly

0

4

8

12

16

20

10-4

dl/

kg/m

in p

er μ

U/m

l

SI

*

* p<0.05

10-4

dl/

kg/m

in p

er μ

U/m

l

SI

0

4

8

12

16

WomenMen

Men vs Women

Page 36: Minimal and maximal models of glucose metabolism

Use in Pathophysiology

1) Role of age and gender (Basu et al, Diabetes 2006)

2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006)

4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006)

8) Diurnal Variation of Glucose Tolerance (Dr. E. Van Cauter, University of Chicago, Chicago, IL)

5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006)

7) Children and Adolescent (Calì et al, Diabetes Care 2009)

3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN)

6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009)

Page 37: Minimal and maximal models of glucose metabolism

OGTT in IFG vs NFGN=32 vs 28

(Bock et al, 2006)Plasma Glucose

0

3

6

9

12

15

-60 0 60 120 180 240 300 360

mm

ol/l

IFG NFG

minutes

0

250

500

750

-60 0 60 120 180 240 300 360

IFGNFG

0

1

2

3

4

5

-60 0 60 120 180 240 300 360

IFGNFG

Plasma Insulin

Plasma C-peptide

nmol

/l

pmol

//l

minutesminutes

Page 38: Minimal and maximal models of glucose metabolism

0

400

800

1200

10-1

4 dl/

kg

/min

-2 p

er p

mo

l/L

0

400

800

1200

10

-14 d

l/kg

/min

-2 p

er p

mo

l/L

0

4000

8000

12000

16000

10-1

4 dl/

kg

/min

pe

r p

mo

l/L

DI

DId

DIs

Disposition Indices

IFG NGT NFG IGT IFG IGT IFG DM

*

*

*

*

*

*

*

*

*

*

*

*

NFGNGT

IFG

IFG NGT

IFG NGT

NFG IGT

NFG IGT

IFG IGT

IFG IGT

IFG DM

IFG DM

NFGNGT

IFG

NFGNGT

IFG

Page 39: Minimal and maximal models of glucose metabolism

Use in Pathophysiology

1) Role of age and gender (Basu et al, Diabetes 2006)

2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006)

4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006)

8) Diurnal Variation of Glucose Tolerance (Dr. E. Van Cauter, University of Chicago, Chicago, IL)

5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006)

7) Children and Adolescent (Calì et al, Diabetes Care 2009)

3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN)

6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009)

Page 40: Minimal and maximal models of glucose metabolism

SI

Φd Φs

DI

10-5

dl/

kg/m

in p

er p

mol

/l10

-9

10-9

min

-110

-14 d

l/kg

/min

2 per

pm

ol/l

NormalDiabetic

0

5

10

15

20

25

30

*

0

200

400

600

800

*

0

10

20

30

40

50

60

0

400

800

1200

1600

*

*

*

NormalDiabetic

NormalDiabetic NormalDiabetic

Type 2 Diabetes(Basu A. et al 2009)

Page 41: Minimal and maximal models of glucose metabolism

Use in Pathophysiology

1) Role of age and gender (Basu et al, Diabetes 2006)

2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006)

4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006)

8) Diurnal Variation of Glucose Tolerance (Dr. E. Van Cauter, University of Chicago, Chicago, IL)

5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006)

7) Children and Adolescent (Calì et al, Diabetes Care 2009)

3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN)

6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009)

Page 42: Minimal and maximal models of glucose metabolism

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

0

5

10

15

20

10^-

4 dl

/kg/

min

per

uU

/ml

Pre Post

Women

Placebo DHEA

Pre Post Pre Post

Men

Placebo DHEA

Pre Post

Testosterone

Pre Post

Page 43: Minimal and maximal models of glucose metabolism

Use in Pathophysiology

1) Role of age and gender (Basu et al, Diabetes 2006)

2) Pathogenesis of Prediabetes (Bock et al, Diabetes 2006)

4) Role of Race (Petersen et al, Proceedings of the National Academy of Science 2006)

8) Diurnal Variation of Glucose Tolerance (Dr. E. Van Cauter, University of Chicago, Chicago, IL)

5) Efficiency of Anti-aging Drugs (Nair et al, New England Journal of Medicine 2006)

7) Children and Adolescent (Calì et al, Diabetes Care 2009)

3) Type 2 Diabetes (Dr. A. Basu, Mayo Clinic Rochester, MN)

6) Effect of DPP-4 Inhibitors (Dalla Man et al, Diabetes Care 2009)

Page 44: Minimal and maximal models of glucose metabolism

Children and Adolescents (Calì et al, Diabetes Care 2009)

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

dl/

kg/m

in p

er u

U/m

l

NGT_NFG

NGT_IFG

IGT_NFGIGT_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

min

-1

*#

*

Page 45: Minimal and maximal models of glucose metabolism

Minimal Models Parameters measurement

Maximal Models In Silico Trials

Page 46: Minimal and maximal models of glucose metabolism

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)

Page 47: Minimal and maximal models of glucose metabolism

47

Page 48: Minimal and maximal models of glucose metabolism

(mg/

dl)

Glucose

50

100

150

200

250

0 60 120 180 240 300 360 420

(pm

ol/l

)

Insulin

0

100

200

300

400

500

600

0 60 120 180 240 300 360 420

Production

(mg/

kg/m

in)

0

0.5

1

1.5

2

2.5

0 60 120 180 240 300 360 420

t (min)

(mg/

kg/m

in)

Utilization

0

2

4

6

8

10

12

0 60 120 180 240 300 360 420

(pm

ol/k

g/m

in)

t (min)

Secretion

0

2

4

6

8

10

12

14

16

0 60 120 180 240 300 360 420

(mg/

kg/m

in)

Rate of Appearance

0

2

4

6

8

10

12

14

0 60 120 180 240 300 360 420

t (min)

(N=204 Normals)

Fluxes, in addition to concentrations, available

DataRange

New Generation of Simulation Models

Page 49: Minimal and maximal models of glucose metabolism

Healthy State Meal Simulator

Meal

GLUCOSESYSTEM

GASTRO-INTESTINAL TRACT

LIVER

BETA-CELL

MUSCLE AND ADIPOSE

TISSUE

INSULINSYSTEM

(Dalla Man et al, 2007)

Plasma Glucose

Plasma Insulin

60

80

100

120

140

160

180

0 60 120 180 240 300 360 420

0

100

200

300

400

500

0 60 120 180 240 300 360 420

Secretion

Production

0

2

4

6

8

10

12

0 60 120 180 240 300 360 420

0

2

4

6

8

10

0 60 120 180 240 300 360 420

0

100

200

300

400

500

600

700

0 60 120 180 240 300 360 420

0

0.5

1

1.5

2

0 60 120 180 240 300 360 420

Utilization

Rate of Appearance

Renal Excretion

Page 50: Minimal and maximal models of glucose metabolism

Identification: System Decomposition & Forcing Function Strategy

Plasma Insulin

LIVER

Plasma Glucose Glucose

Production

BETA CELL

Plasma Insulin

Insulin Secretion

Plasma Glucose

Glucose Rate of Change

Plasma Insulin

Glucose Rate of Appearance

MUSCLE AND ADIPOSE TISSUE

Glucose Production

Plasma Glucose

Glucose Utilization

GASTRO-INTESTINAL TRACTMeal

Glucose Rate of Appearance

Page 51: Minimal and maximal models of glucose metabolism

Muscle and Adipose Tissue ModelPlasma Insulin (I)

Glucose Rate of Appearance (Ra)

MUSCLE AND ADIPOSE TISSUE

Glucose Production (EGP)

Plasma Glucose (G)

Glucose Utilization (U)

Model

TissuesGt

k21

k12

Kg Ki

G

PlasmaGp

Insulin Action

X

I

EGP

Ra

p2Up2U

U

Gt(t)

U(t)

Vm(X1)

Vm(X2)

Vm(X3)

Km(X3) Km(X2) Km(X1)

X1<X2<X3

Page 52: Minimal and maximal models of glucose metabolism

52

Utilization

t (min)

U (

mg/

kg/m

in)

Glucose

t (min)

G (

mg/

dl)

0

1

2

3

4

5

6

7

8

9

0 60 120 180 240 300 360 420

data

fit

60

80

100

120

140

160

180

0 60 120 180 240 300 360 420

data

fit

Results

Page 53: Minimal and maximal models of glucose metabolism

24 h Simulation: average model

0

0t (hours) t (hours)

(mg

/dl)

(mg

/kg

/min

)

(mg

/kg

/min

)

(mg

/kg

/min

)

(pm

ol/k

g/m

in)

(pm

ol/l

)

Glucose Insulin Production

UtilizationRate of Appearance Secretion

0

2

4

6

8

10

12

6 9 12 15 18 21 24

60

80

100

120

140

160

180

3 6 9 12 15 18 21 24

0

100

200

300

6 9 12 15 18 21 24

0

0.6

1.2

1.8

6 9 12 15 18 21 24

0

2

4

6

8

6 9 12 15 18 21 24

0

2

4

6

8

10

6 9 12 15 18 21 24

t (hours)

45 g 70 g 70 g

Page 54: Minimal and maximal models of glucose metabolism

Rate Constant of Liver Insulin Action

0

20

40

60

80

100

0.0010.011

0.0220.032

0.0430.053

0.064

min^-1

0

20

40

60

80

100

0.0110.022

0.0320.043

0.0530.064

mg/kg/min/(pmol/l)

LiverGlucose Effectiveness

0

20

40

60

80

100

0.0000.003

0.0060.009

0.0120.015

0.018

min^-1

0

20

40

60

80

100

0.000.03

0.050.07

0.090.11

0.13

min^-1

0

20

40

60

80

100

0.000.03

0.060.09

0.120.15

0.18

mg/kg/min per pmol/L

0

20

40

60

80

100

1.251.45

1.651.86

2.062.26

mg/kg

LiverInsulin Sensitivity

Rate Constant of Peripheral Insulin Action

PeripheralGlucose Effectiveness

PeripheralInsulin Sensitivity

Inter-Subject Variability

Page 55: Minimal and maximal models of glucose metabolism

Generation of virtual subjects

Page 56: Minimal and maximal models of glucose metabolism

Generation of In Silico Normal Subjects

# 1

Glucose

t (hours)

20 25 30 403530

60

90

120

150

180

(mg/

dl)

200

# 2

Glucose

20 25 30 4035

(mg/

dl)

t (hours)

30

60

90

120

150

180

200

# 3

Glucose

20 25 30 4035

(mg/

dl)

t (hours)

30

60

90

120

150

180

200

# 100

.....

Glucose

20 25 30 4035

(mg/

dl)

t (hours)

30

60

90

120

150

180

200

Page 57: Minimal and maximal models of glucose metabolism

Healthy State Simulator12 Differential Equations, 26 Parameters

Pre-diabetes Simulator

12 Differential Equations, 26 Parameters

Type 2 Simulator12 Differential Equations, 26 Parameters

Type 1 Simulator

13 Differential Equations, 26 Parameters

Page 58: Minimal and maximal models of glucose metabolism

What is an Artificial Pancreas?

Page 59: Minimal and maximal models of glucose metabolism

SavesYears

Traditional vs. Accelerated Development

Concept

Animal Trials

Clinical Trials

Product

Concept

In Silico Trials

Clinical Trials

Product

Page 60: Minimal and maximal models of glucose metabolism

Model of Type 1 Diabetes

Insulin Pump

SCInsulinKinetics

Secretion

BETA-CELL

Renal Excretion

Meal

Rate of Appearance

Production UtilizationPLASMA GLUCOSE

GASTRO-INTESTINAL TRACT

LIVERMUSCLE

& ADIPOSE TISSUE

PLASMA INSULIN

Degradation• Tested against, and showing excellent agreement with:

Common clinical knowledgeLab traces of induced

hypoglycemiaField data of children with

T1DM

Page 61: Minimal and maximal models of glucose metabolism

61

02468

10

0 60 120180 240 300360 420

Artificial Pancreas In Silico Trial

Renal Excretion

Meal

Rate of Appearance

Production Utilization

Plasma Glucose

6080

100120140160180

0 60 120 180 240 300 360 420

PLASMA GLUCOSE

GASTRO-INTESTINAL TRACT

LIVER

Plasma Insulin

0

100

200

300

400

500

0 60 120180 240 300 360 420

MUSCLE AND ADIPOSE TISSUE

PLASMA INSULIN

Degradation

00.51

1.52

0 60 120180 240 300360420

02468

1012

0 60 120 180 240 300 360 420

SecretionBETA-CELL

0100200300400500600700

0 60 120 180 240 300 360 420

SubcutaneousInsulin Infusion Pump

SensorControllerController A Sensor IController B Sensor IIController C Sensor IIIController D Sensor IV

SubcutaneousInsulin Infusion Pump A

SubcutaneousInsulin Infusion Pump B

SubcutaneousInsulin Infusion Pump C

SubcutaneousInsulin Infusion Pump D

Page 62: Minimal and maximal models of glucose metabolism

In Silico Selection of Control Strategy:Proportionl-Integral-Derivative vs Model Predictive Control

Health T1DM + PID controller

T1DM + Model Predictive Control

Bloo

d G

luco

se (m

g/dl

)

Time (hours)0 12 24 36 48 60 72

Page 63: Minimal and maximal models of glucose metabolism

January 18, 2008:Simulation accepted by FDAas substitute to animal trials

(Master file #1521)

Concept

Animal Trials

Clinical Trials

Product

Concept

In Silico Trials

Clinical Trials

Product

Traditional vs. Accelerated Development

Regulatory Approval for clinical trialsbased entirely on in silico testing:

April 17, 2008 (UVA IDE);May 20, 2008 (Padova EC)

Page 64: Minimal and maximal models of glucose metabolism

Conclusions

• Importance of System Models in Diabetes

• Minimal Models:

• Powerful Tools to Measure & Understand the Pathophysiology of Diabetes

• Maximal Models:

• Importance of prediabetes, type 2 and type 1 diabetes simulators for in silico trials