Mathematical methods and models2

Mathematical Methods and Models for

Clinical Research on Metabolism, Diabetes

and Its Complications

Metodi e Modelli Matematici per la Ricerca Clinica

sul Metabolismo, il Diabete e sue Complicanze

ISIB-CNR

Institute of Biomedical Engineering

Chairperson: Ferdinando GRANDORI

Giovanni Bortolan, Andrea Mari, Giovanni Pacini, Karl Thomaseth, Andrea Tura

Collaboratori

Type 1

Type 2

TOTAL

3.5 million

114.8 million

118.4 million

4.4 million

146.8 million

151.2 million

5.5 million

215.3 million

220.7 million

1995 2000 2010

D ia be t e s

defect in t he regulat ion of blood glucose

blood glucose

insulin

pancreatic

β

cell

insulin

secretion

glucose production

(liver)

glucose utilization

(muscle, fat)

exogenous

glucose

8

8

insulin

resistance

8

impaired

secretion

• Insulin Sensitivity

• Beta-cell Function

quantification of insulin action to promote glucose disappearance from blood (lowering glycemia)

SECREZIONE

β

-cell model

Design, development and use of clinical tests

•

simple, accurate and of widespread clinical use

•

high information content for specific analyses

on particular aspects

Oral glucose tolerance test (OGTT) with model analysis

-OGIS model for insulin sensitivity : ~100+ citations from other groups

-Insulin, C-peptide and proinsulin kinetic models : widely used for

physiological studies

-Insulin secretion model : ~30 articles on major journals on pharma agents

- Pharmacokinetic studies

-

Urea kinetics in hemodialysis (artificial kidney)

COOPERATIONS (Europe)

Int’l

Italian

INTERNATIONAL COOPERATIONS (The World)

Japan

New Zealand

Australia

European Project RISC (5th FP)

IP Eur. Project NeuroFAST (7th FP) The Integrated Neurobiology of Food Intake,

Addiction and Stress (2009-14)

Amylin-Eli Lilly (USA) Novartis, Basel (CH) Novartis, E.Hanover (USA)

Bellco (Italia) Bayer (Italia) Novo-Nordisk (DK)

Glaxo-Smith & Kline (USA) Takeda (UK) Mannkind (USA)

Fresenius (Germania) Merck (USA) La Roche (CH)

Consulting and Service Agreements

years 2004-2009 mostly with drug companies

EFSD ● B-cell Function (2001-04)

Projects ● Insulin Secr. and Insulin Sens. Following Bariatric Surgery (2007-09)

● Prophylactic use of DPP-4 inhibition in glucocorticoid-induced beta-cell dysfunction (2008-11)

Int’l Projects

Innovative Medicines Initiative (IMI) Project:

Surrogate markers for Micro- and Macro-vascular hard endpoints for Innovative diabetes Tools” (SUMMIT) (2009-14)

Austrian Science Fund (FWF) Project:

• Biologia e fisiologia clinica del tessuto adiposo. (PRIN – 2007-09)

• Sviluppo di un metodo accessibile via web per l'analisi con modelli matematici della cinetica del glucosio. (Ricerca a tema libero CNR – 2007)

• Tessuto adiposo e farmaci: biologia e clinica. (PRIN – 2005-07)

• Biologia cellulare e fenotipo clinico nella sindrome metabolica. (PRIN – 2001-03; rinnovato per 2003-05)

• Metodi e modelli matematici nello studio dei fenomeni biologici. (Progetto strategico CNR – 1998-99)

• Development and validation of a mathematical model for the study of glucose metabolism. (Progetto bilaterale CNR Italia-Australia – 1998-2000)

Italian Projects

Other Activities

• Members of Editorial Board of journals in the field of Diabetes, Modeling and Simulation.

• Invited Reviewers for prestigious int’l journals in the field of Diabetes, Modeling and Simulation.

0 5 10 15 20 25 30 35

2004 2005 2006 2007 2008 2009

PAPERS ON PEER-REVIEWED INTERNATIONAL JOURNALS

(source ISI Thompson)

*

Expertise

• Design, implementation

and

use

of

mathematical models

for studies on

metabolism, pharmacokinetics and pharmacodynamics

• Analysis

of experimental data for the estimation of

physiological

and

clinical parameters

and their dependence on specific covariates (BW,

age, gender, BP,…)

• Design

of

experimental tests

(based mostly on mathematical modelling)

for estimating insulin sensitivity, beta cell function, renal function,

assessament of ECG parameters and of those of the autonomic nervous

system

case studies:

insulin sensitivity

Glucose Tolerance

Insulin

Resistance

Insulin

Secretion

Why focussing on

CVD risk

Hyperglycaemia Hyperinsulinaemia Hypertension

Dyslipidaemia

Decreased fibrinolytic activity (↑PAI-1)

Endothelial dysfunction Inflammatory markers of atherosclerosis

Microalbuminuria

Insulin

resistance

Insulin sensitivity measures insulin

resistance, which is strictly linked to several

vital diseases

Insulin Resistance

Insulin resistance is measured by

Insulin sensitivity

The glucose clamp

0 20 40 60 80 100 120 0 2 4 6 8 10

glucose infusion

mg/min/kg

0 20 40 60 80 100 120 0 20 40 60 80 100

glucose concentration

mg/dl

0 20 40 60 80 100 120 0 50 100 150 200 250 mU/min

insulin infusion

0 20 40 60 80 100 120 0 20 40 60 80 100

insulin concentration

µ U/ml

mean

infusion rate: M

mean insulin

concentration: I

Insulin sensitivity

(clamp model)

=

M

I

IVGTT and the Minimal Model

mathematical model

parameter estimation

glucose

insulin

0 1.0 2.0

0 60 120 180 0

10 20

0 60 120 180

Insulin sensitivity index (SI)

0 5 10 15 20 mM 0 0.5 1.0 1.5 2.0 2.5 nM

-30 0 30 60 90 120 150 180

insulinemia

time min

TEST

direct

measurement

MODEL

estimated parameter

validation

clamp

minmod

Simple(r) method for the assessment of

insulin sensitivity from the IVGTT

Metabolic Unit

Padova, Italy

National

Research

Council

Andrea Tura, Giovanni Pacini

with cooperation of

Is there a way of simplifying the estimation

of insulin sensitivity from an IVGTT ?

Until the first

hour, glucose

keeps

decreasing

from the initial

peak

60 90 60 90

Glucose Conc

.

t

₄

t

₃

t

₄

– t

₃

1

(I(t) – Ib) dt

slope (log G(t))

t

₁

t

₂

CS

I

=

INSULIN SENSITIVITY FROM IVGTT

simplified formula

Units:

min

-1

/(µU/ml)

N=144, r=0.934, p<0.0001 CS

I

= 0.3 × S

I

MM

S

_I MM

CS

_I

0

14

0

4.5

Relationship between computed (

CS

_I

) and minimal

model estimated (

S

_I

MM

) insulin sensitivity in

control

subjects

of various age and weight

Slope = 0.97, p > 0.2

vs.

slope=1; r = 0.907, p < 0.0001

Relationship between

CS

I

[normalized with the

factor 0.3 of CNT]

and

S

I

MM

in 127 IGT

subjects

10

4

min

-1

(µU/ml)

-1

S

_I MM

CS

_I

0

10

0

12

Comparison between

CS

_I

and

Clamp M

in normo

glucose tolerant (circles), impaired tolerant (squares)

and diabetic (triangles) subjects

regression lines are virtually equivalent to the identity line

TEST

FORMULA

direct

measurement

calculated parameter

MODEL

estimated parameter

validation

further simplification

CS

I

• Catanzaro

cooperation for the realization

• Copenhagen

use in minipigs

• Malmö

cooperation for the realization

• Lund

use in mice

• Melbourne (?)

use in rats

Methods for Measuring Insulin Sensitivity

difficult

difficult

experiment

IVGTT (MINMOD)

eu- and hyper-glycemic glucose clamp

OGTT

(OGIS, ISI_comp)

easy

calculation

--model

basal (HOMA) IVGTT (K_G) lower

info

Insulin sensitivity

IVGTT

(with simple formula and short protocol)

provides an index similar to the minimal model

and to the euglycemic glucose clamp

•

does not require a com put er program and expert ise t o solve

m at hem at ical m odels, j ust a spread sheet

•

requires a few sam ples

•

does not require addit ional inj ect ions of insulin

•

can be used also in larger populat ion size

•

t he exact BEST t im ing m ay be funct ion of t he t ype of

populat ion under st udy

•

t he possibilit y of including

“ glucose effect iveness”

int o t he

Mathematical models for

β

-cell

function assessment in vivo

Andrea Mari

Andrea Tura, Valentina Nofrate

Padova-Pisa:

more than 20 years friendship

1986-2000: tracer kinetics, insulin sensitivity

2001-2009:

β

-cell function

In vivo

β

-cell modeling project:

aims

●

To understand how the

β

cell responds to

glucose stimulation in normal living

conditions quantitatively, using modeling

●

To develop a widely applicable

model-based test for

β

-cell function based on an

oral glucose load or meal

β

-cell model for oral glucose tests:

reconsidering potentiation

glucose

concentration

insulin

secretion

dose-response

function

glucose secretio n

early secretion

(function of glucose derivative)

potentiation

Mari … Ferrannini 2002

f(G)

+

k

_d

dG

dt

P(t)

Roadmap

2001 2002 2003 2004 2005 2006 2007 2008 2009 model ready

IGIS meeting I

effects of GLP-1

1st _{large population study nateglinide 1}st _vildagliptin

1st _{prospective study}

1st _review

1st _{bariatric surgery}

exenatide

thiazolidinediones liraglutide

1st _{genetic study (RISC)}

incretin effects IGIS meeting II EASD meeting

Dissemination

Perspectives

●

Still a long way to go with the current

approach

♦

The RISC study – Genetics

♦

Bariatric surgery

♦

Pharmas