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Introduction: I N D I A. Bangalore 2008 – Insulin/Glucose modelling. India, diabetes capital of the world (before China and US as No. of cases; data: WHO). India: 2000:32 mill 2020: 81 mill. Zimmet, Nature 2001. Type 2 DM: global epidemic. Prevalence depends on: Age

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Introduction i n d i a

Introduction:I N D I A

Bangalore 2008 – Insulin/Glucose modelling


India diabetes capital of the world before china and us as no of cases data who
India, diabetes capital of the world(before China and US as No. of cases; data: WHO)

India:

2000:32 mill

2020: 81 mill

Zimmet, Nature 2001


Type 2 dm global epidemic
Type 2 DM: global epidemic

Prevalence depends on:

  • Age

  • Residence(urban/rural)

  • Obesity

  • Physical activity

  • Ethnicity


Rising prevalence of obesity in urban india
Rising Prevalence of Obesity in Urban India

BMI >27 kg/m2

Gupta et al, IHJ 2002


Obese people develop diabetes
Obese people develop Diabetes

  • RR risk of DM in females (ref. BMI < 22)

    • 22-23: 3.0

    • 24-25: 5.0

    • > 31:40

      (Colditz & al, Ann Int Med, 1995, 122; 481-6)


Rising prevalence of diabetes in southern india
Rising prevalence of diabetes in Southern India

Ramchandran et al: Diab Care 92,

Diabetol 97, Diabetol 2001



Diabetes and cad risk 7 year incidence of cv events
Diabetes and CAD risk7 year incidence of CV events (%)

Haffner SM et al. N Engl J Med 1998;339:229-234.


Pathophysiology of the glucose insulin system

Pathophysiology of the glucose/insulin system

Andrea De Gaetano

CNR IASI BioMatLab – Rome Italy

Bangalore 2008


CNR

  • Consiglio Nazionale delle Ricerche (Italian National Research Council): the research organization of the Italian Government, 6000+ researchers distributed over 100+ Institutes in the Country.

  • Research ranging from humanities to genomics, linguistics, aerospace engineering, pure mathematics, …


Cnr iasi
CNR IASI

  • IASI, Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” (Institute for Systems Analysis and Informatics) in Rome: 30+ researchers, 20 administrative/technical personnel.

  • seven research areas

    • Systems and Control Theory

    • Mathematical Programming in Operations Research

    • Mathematical Modeling in Biology and Medicine

    • Algorithms, data structures and networks

    • Language and Programming theory

    • Information Systems and Knowledge Bases

    • Pathophysiology of Metabolism and Immunology


Cnr iasi biomatlab
CNR IASI BioMatLab

  • BioMathematics Lab, within the Catholic University School of Medicine (2000 bed hospital), Rome

  • 5 full-time lab researchers (1 biomathematician, 1 statistician, 3 engineers), clerical personnel, part-time associates.

  • ODE, DDE, SDE models: analytical study of behavior of solutions, numerical integration, statistical parameter estimation

www.biomatematica.it


Hypoglicemia
Hypoglicemia

  • Brain works on sugar

  • Little sugar: hunger, irritability, confusion, hyperactivity, cold sweat, tremor (adrenergic response)

  • No sugar: brain death.

  • COUNTERREGULATION: Adrenalin (fight-or-flight), glucagon, cortisol, Growth Hormone all INCREASE blood glucose levels.

  • Food......


But hyperglycemia
…but, Hyperglycemia

  • Acute above renal threshold: sweet, abundant urine (Diabetes Mellitus), dehydration.

  • Chronic: microvascular damage in retina (blindness), kidneys (renal insufficiency), extremities; peripheral neuropathy.


Diabetes type 1 and 2

Insulin resistance

lack of secretion

Diabetes type 1 and 2

Insulin dependent Glucose utilization (muscle)

Insulin independent Glucose utilization (brain)

Endogenous

Glucose production (liver, kidney)

insulinemia

glycemia

Exhogenous glucose administration

pancreatic

b-cell

Insulin secretion

Modified from A.Mari 2001


Insulin
Insulin

  • Proinsulin (86 AA) = C-Peptide (35 AA) + Insulin(51=A+B chain)

  • Secreted from pancreatic beta-cells (Langerhans islets) in response to: GLUCOSE, AA, neurotransmitters (AC, like after a meal), hormones (glucagon);FFA?

  • Increases Glycogen synthesis, inhibits Gluconeogenesis, inhibits lipases and increases FFA deposition in Adipose tissue


Portal circulation
Portal circulation


Insulin resistance operational definition
Insulin resistance: operational definition

Insulin resistance may be defined as

inappropriately high glycemia for the insulinemia,

or again as

inappropriately high insulinemia for the glycemia


Disposition index

Increasing

Glycemia

Disposition Index

Insulin secretion

Insulin sensitivity


An overview of energy metabolism

An overview of energy metabolism

following diagrams ...



Krebs cycle

glycolysis

protein

breakdown

lipid b-oxidation

DA oxidation

Krebs’ Cycle


Randle s cycle
Randle’s Cycle

  • 1963, Sir Philip Randle: cardiac and skeletal muscle shifts back and forth between CHOand fat oxidation depending onthe availability of FFA.

  • In vivo infusion of lipid increases fat oxidation and decreases glucose oxidation


How mcdonald kfc make you diabetic

Inhibition

of Lipases

Fat storage

Hyperinsulinemia

Insulin

resistance

Insulin secretion

Glucose Uptake

Hyperglycemia

(Randle)

FFA

TG

How McDonald & KFC make you diabetic!



Bpd and insulin resistance
BPD and insulin resistance

  • Insulin resistance after BPD drops dramatically, well before body weight does:Using EHC, whole body glucose uptake increased from 18.18.6 to 35.5 9.9 moles/min/kgbw after an average weight loss of only 11 kg reached 3 months after BPD. A marked reduction of both plasma FFA and TG was observed together with the therapeutic lipid malabsorption (Mingrone, Castagneto et al. Diabetologia 1997).

  • Also in normal weight subjects with a genetic defect of LPL activity, insulin resistance and frank diabetes mellitus were reversed by lowering plasma TG through lipid malabsorption induced by BPD (Mingrone, Castagneto et al. Diabetes 1999).


Models of the glucose insulin system

Models of the glucose-insulin system


Why modelling the g i system
Why modelling the G/I system?

To identify the components of insulin resistance and measure its level:

  • Diabetologist approach (lots of data, make a diagnosis)

  • Standard modeling approach (less data, try to figure out the whole system )


Models
Models

  • Tracer “hot” vs. “cold” models

  • Why cold? Our perspective is the clinical application.

  • TRACERS: Steele 1956 traced glucose constant infusion with approx computation of SteadyState cold inflow.



Bolie 1961
Bolie 1961

  • First attempt to understand actual time-concentration points in plasma.

  • Introduces plasma insulin and LGE

  • Problems?


- p1 G- p2 I+ p3

I2

I1

Insulinemia

G1

G2

Glycemia


Qualitative analysis reveals
qualitative analysis reveals ...

  • the actual model functional form, which allows negative solutions to appear, must have something in it which goes against the physiology as we think we know it

  • Bolie: no matter how little glucose there is in blood, by increasing insulin we would be able to make the tissues extract as much more as we wanted, linearly with insulin levels.

  • Mechanism seems wrong. Better to change model.


Ivgtt
IVGTT

  • three days of standard composition diet (55% carbohydrate, 30% fat, 15% protein) ad libitum with at least 250g carbohydrates per day

  • Overnight fast, at 8:00 AM 0.33 g/kgBW IV Glucose

  • Contralateral IV samples at -30, -15, 0, 2, 4, 6, 8, 10, 12, 15, 20, 25, 30, 35, 40, 50, 60, 80, 100, 120, 140, 160, 180 minutes (23 pts.)

  • On each blood sample determine Glucose, Insulin (C-peptide).


Ivgtt1

Plasma Glucose

Plasma Insulin

0 10 20 30 40 50

minutes

0 10 20 30 40 50

minutes

IVGTT

The K+ channel opens causing

depolarization

Glucose

increases the

ATP/ADP ratio

-

Glycogenolysis

Gluconeogenesis

Ca2+

b cell

Depolarization cause Ca2+ influx




S i derivation
SI : derivation


S i derivation1
SI : derivation

Solving Eq.2 MM for X


SI

  • For infinite time, SI = b3/b2

  • in one third to one half of studies on obese subjects SI cannot be estimated, due to insufficient variation of glucose decrement with insulin.

  • An IVGTT obvious for insulin resistance (high constant insulin levels) yields no estimable SI.


Applications of mm
Applications of MM

  • Physicians want a single test returning a single measure of insulin resistance, like M/I or SI

  • MM applied to diabetes, aging, hyperthyroidism, hyperparathyroidism, myotonic dystrophy, pregnancy and gynecological conditions, obesity, hypertension, cirrhosis, ethnical subpopulations, in siblings of diabetic patients, during pharmacological tests


Minimal model
Minimal model

  • Whole body, cold

  • Can compute SI …

  • …de-facto standard


Minimal problems
Minimal problems

  • Models only IVGTT (nonautonomous)

  • Fitting: piecewise?

  • SI strictly valid at infinite time, MM “valid” for 3 hrs.

  • SI not estimable in many interesting cases.


Structural problems
Structural problems

Suppose Gb > b5,

Then

In other words, for any value b5 < Gb the system does not admit an equilibrium.


Estimation problems
Estimation problems

  • Two-step procedure advocated by Authors

  • Each step fits one arm of feedback cycle

  • Interpolated observed concentrations used as forcing function

G

I


We would like
We would like:

  • single model, single fit of both feedback arms

  • positiveness, boundedness of solutions

  • stability WRT parameters & initial conditions

  • good fit, identifiability

  • direct physiological meaning




Sdm characteristics
SDM characteristics

  • Single locally attractive equilibrium at baseline

  • Positive, limited solutions

  • Global stability guaranteed under conditions on parameters*

  • Physiologically limited pancreatic secretion ability

  • Single pass GLS estimation

    *Giang, Lenbury, Palumbo, Panunzi, De Gaetano, 2006-2007


SDM: Subject with BMI >24 and <=30

12

300

10

200

8

100

6

4

0

0

100

200

0

100

200

SDM: Subject with BMI > 30 and <= 40

SDM: Subject with BMI >= 40

20

400

15

500

400

300

15

10

300

200

10

200

100

5

100

5

0

0

0

100

200

0

100

200

0

100

200

0

100

200

SDM: Subject with BMI >=24

16

600

14

12

400

Plasma Insulin (pM)

10

Plasma Glucose (mM)

8

200

6

4

0

0

100

200

0

100

200


Sdm vs mm over 74 subjects with widely varying bmi 20 60
SDM vs. MMOver 74 subjects with widely varying BMI (20 – 60)

  • KxgI from the SDM

    • identifiable (CV < 52%) in 73 out of 74 subjects (one 68%)

    • All estimates within physiological limits (1.25 × 10-5 to 4.36 × 10-4 )

  • SI from the MM

    • not identifiable in 36 subjects out of 74, with coefficients of variation ranging from 52.76 % to 2.3610+9 %

    • in 11 subjects estimates doubtfully large (from 3.99 to 890)

    • in 8 subjects estimates very small (≤ 1.5 × 10-6, “zero-SI”)


Ehc the euglycemic hyperinsulinemic clamp
EHC, the Euglycemic Hyperinsulinemic Clamp

  • Administer a large I.V. infusion of insulin

  • Prevent hypoglycemia by external glucose I.V. infusion, with rate adjusted q5’ on the basis of glycemia determination and algorithm (Defronzo, 1979).


Ehc interpretation
EHC: interpretation

  • Large insulin infusion: suppression of Liver Glucose Excretion, then…

  • …at SteadyState exogenous administration (measured) and Tissue Uptake must be equal. Hence:

  • Smaller than normal M (average G administration rate) implies insulin resistance.


Ehc problems

M

M/I

I

EHC: problems

  • Clearly, M = M(mass, age, sex,…) and normalizations necessary.

  • Still, M = M(I), hopefully monotonic increasing (in fact, nonlinear saturating)

  • First correction: M/I. But this implies linearity, which is false:


The industrious diabetologist

M

DM/DI

I

The industrious diabetologist

  • Second correction: two-step clamp, and compute ΔM/ΔI.

  • This also assumes linearity (and a 3-5hr session):


Ehc more problems
EHC: more problems

  • Doubtful physiological meaning of index derived from several hours maximum insulinization.

  • Obese: typically depressed M at 2 hrs, normal at 5 hrs…


Ehc huge success
EHC: huge success!

  • MOST research diabetologists use EHC over modelling methods:

  • “No need to perform complicated CALCULATIONS, this is something we understand”

  • Doubtful attitude towards validity of models “You can show anything and its opposite…” (e.g. compartmental assumptions)


Ehc a gold data mine
EHC: a gold data mine?

Decades of experimentation have produced a huge amount of EHC data.


A deterministic clamp model
A deterministic Clamp model

2005 Picchini et al. TBMM


A good subject
a good subject


What s wrong
What’s wrong?

  • NO model we could think of fits the peaks/troughs

  • ACCIDENTAL factors generate/shift oscillations, hence …

  • … a deterministic model will do its best to AVERAGE disturbances OR …

  • … be overparametrized and fit perfectly only one individual realization.

  • Need something else!












Please do not forget
Please do not forget …

  • Denmark 2008 (more about this from Susanne…)

  • and …


Sicily italy 13 26 sept 2009
Sicily (Italy) 13-26 Sept. 2009

  • Parameter Estimation in Dynamical Models

  • Glucose/Insulin Modelling


Thank you
Thank you

www.biomatematica.it


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