Mathematical modelling of disease progression

A mechanism-based disease progression model to analyse long-term treatment

effects on disease processes underlying type 2 diabetes

Workshop“The interplay of fat and carbohydrate metabolism with application in Metabolic Syndrome and Type 2

Diabetes”

December 12th 2013

Yvonne Rozendaaly.j.w.rozendaal@tue.nl

Introduction

• Disease progression– multi-scale problem

– how to assess/measure?

• Treatment interventions– effect of treatment on disease progression?

short-term vs long-term

• How to simulate adaptations & interventions?

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Type 2 Diabetes Mellitus (T2DM)

• Impaired beta-cell function

• Reduced insulin sensitivity

• Monitoring glycemic control: biomarkers

– FPG: fasting plasma glucose

– FSI: fasting serum insulin

– HbA1c: glycosylated hemoglobin

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chronic loss of glycemic control

secondaryglycemic markers

primary glycemic marker

how to derivedisease status?

T2DM treatment

• hypoglycemic effect: short-term

– immediate symptomatic effects on glycemiccontrol

• inhibitory effect on disease progression: long-term

– protect against T2DM progression

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Objective

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metabolic biomarkersFPGFSI

HbA1c

treatment interventionspharmacological therapy

disease progressionprogressive loss of beta-cell

function and insulin sensitivityadaptations in

biological network

disease progression model introduction to ADAPT application of ADAPT

computational model:description and quantification of inputs

test functionality of method on minimal model: human vs. mouse glucose vs. lipid metabolism

minimal model

• Disentangle treatment effects– long-term

loss of beta-cell functionand insulin sensitivity

– short-termanti-hyperglycemic effects

• Computational model:study & quantifytime-course effects

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de Winter et al. (2006) J Pharmacokinet Pharmacodyn,33(3):313-343

Modelling disease progression (1)

disease progression model introduction to ADAPT application of ADAPT

PK/PD modelling

• PharmacoKinetic-PharmacoDynamic modelling

• Simple kinetics are modelled using minimal/macroscopic models

• e.g. absorption profiles

7disease progression model introduction to ADAPT application of ADAPT

T2DM disease progression model (1)glucose – insulin – HbA1c

• Model components– FPG: fasting plasma glucose

– FSI: fasting serum insulin

– HbA1c: glycosylated hemoglobin

• Physiological FPG-FSI homeostasis:– feedback between FSI and FPG

FPG stimulates FSI production: FSI production rate ∝ FPG concentration

– feed-forward between FPG and HbA1cHbA1c production rate ∝ to FSI concentration

8disease progression model introduction to ADAPT application of ADAPT

9

ink

ink

ink

outk

outk

outk

B: beta-cell function(disease status)

S: insulin sensitivity(disease status)

FPG

HbA1c

FSI

EFS: insulin sensitizingeffect of treatment

EFB: treatment effecton insulin secretion

feed-forward

homeostaticfeed-backs

T2DM disease progression model (2)model structure

disease progression model introduction to ADAPT application of ADAPT

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1cHbA1cHbA

FPG

FPG

FSIFSI

1c

1c HbAFPGt

HbA

FPGFSIt

FPG

FSI)5.3FPG(t

FSI

outin

out

S

in

outinB

kkd

d

kSEF

k

d

d

kkBEFd

d

disease status:fraction of remaining beta-cell function

disease status:fraction of remaining insulin sensitivity

treatment specific factor of insulin-

sensitizers

treatment specific factor of insulin-

secretogogues

T2DM disease progression model (3)model equations

disease progression model introduction to ADAPT application of ADAPT

• Beta-cell functionfraction of remainingbeta-cell function

• Insulin sensitivityfraction of remaininghepatic insulin-sensitivity

• Assumption: asympotically decrease over time

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)exp(1

1

0trb

B

B

)exp(1

1

0trs

S

S

shift of disease progression curve

slope of disease

progression curve

T2DM disease progression model (1)disease status

disease progression model introduction to ADAPT application of ADAPT

Model comparison with data (1)

• Long-term (1y) follow-up of treatment-naïve T2DM patients

• 3 treatment arms: monotherapy with different hypoglycemic agents– pioglitazone: insulin sensitizer

• enhances peripheral glucose uptake• reduces hepatic glucose production

– metformin: insulin sensitizer• decreases hepatic glucose production

– gliclazide: insulin secretogogue• stimulates insulin secretion by the pancreatic beta-cells

12disease progression model introduction to ADAPT application of ADAPT

Model comparison with data (2)

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FPG

[m

mo

l/L]

disease progression model introduction to ADAPT application of ADAPT

Reproduction of results (1)

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Metabolic biomarkers over time

although initial decrease, glycemiccontrol still gradually decreases over time

disease progression model introduction to ADAPT application of ADAPT

Reproduction of results (2)

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Disease status

however, morphology of disease progression curves unknown...

gliclazide:insulin secretogogue

pioglitazone & metformin:insulin sensitizers

disease progression model introduction to ADAPT application of ADAPT

Introduction to ADAPT (1)

• Phenotype transition over time

• Analysis of Dynamic Adaptations in Parameter Trajectories

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treatment interventionsmedication, surgery, ... disease progression

which adaptations occur?

Tiemann et al. (2011). BMC Syst Biol,26(5):174Tiemann et al. (2013). PLoS Comput Biol,9(8):e1003166

phenotype A phenotype B

disease progression model introduction to ADAPT application of ADAPT

Introduction to ADAPT (2)

• Phenotype transition:– gradual, long-term processes– measurements at metabolome level

• Adaptation at proteome and transcriptome level

• Model at metabolome level

• Time-dependency implemented using time-varying parameters

17disease progression model introduction to ADAPT application of ADAPT

Modelling phenotype transition (1)

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treatment

disease progression

long-term discrete data: different phenotypes

disease progression model introduction to ADAPT application of ADAPT

Modelling phenotype transition (2)

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long-term discrete data: different phenotypes estimate continuous data: cubic smooth spline

introduce artificialintermediate phenotypes

disease progression model introduction to ADAPT application of ADAPT

Modelling phenotype transition (3)

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long-term discrete data: different phenotypes estimate continuous data: cubic smooth spline incorporate uncertainty in data: multiple describing functions

disease progression model introduction to ADAPT application of ADAPT

Parameter estimation (1)

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steady state model

disease progression model introduction to ADAPT application of ADAPT

Parameter estimation (2)

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steady state model iteratively calibrate model to data: estimate parameters over time

minimize difference between data and model simulation

disease progression model introduction to ADAPT application of ADAPT

Parameter estimation (2)

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steady state model iteratively calibrate model to data: estimate parameters over time

disease progression model introduction to ADAPT application of ADAPT

Parameter estimation (2)

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steady state model iteratively calibrate model to data: estimate parameters over time

disease progression model introduction to ADAPT application of ADAPT

Parameter estimation (2)

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steady state model iteratively calibrate model to data: estimate parameters over time

disease progression model introduction to ADAPT application of ADAPT

Estimated parameter trajectories

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up-regulation

down-regulation

unaffectedstochastic

behaviour...

effect of parameter adaptations on underlying processes?

physiologically unrealistic

disease progression model introduction to ADAPT application of ADAPT

Possible applications for ADAPT

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• Unravel which processes in network might be responsible for phenotype transition

• Guide new experiment design

• Define possible pharmacological targets

disease progression model introduction to ADAPT application of ADAPT

Application of ADAPT indisease progression model

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1cHbA1cHbA

FPG

FPG

FSIFSI

HbA1cFPGt

HbA

FPGFSIt

FPG

FSI)5.3FPG(t

FSI

1c

outin

out

in

outin

kkd

d

kS

k

d

d

kkBd

d

fraction of beta-cell function:time-dependent parameter

fraction of insulin sensitivity:time-dependent parameter

time-constantparameters

disease progression model introduction to ADAPT application of ADAPT

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Metabolic biomarkers over timetreatment with pioglitazone

Disease progression modelvs. application of ADAPT (1)

disease progression model introduction to ADAPT application of ADAPT

HbA1c:performance ADAPT

FPG & FSI:ADAPT reproduces model predictions

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Parameter trajectories: disease statustreatment with pioglitazone

Disease progression modelvs. application of ADAPT (2)

disease progression model introduction to ADAPT application of ADAPT

ADAPT suggests dynamic disease progression curves rather than pre-defined mathematical functions by de Winter et al.

Disease progression modelvs. application of ADAPT (2)

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Parameter trajectories: disease statustreatment with pioglitazone

disease progression model introduction to ADAPT application of ADAPT

ADAPT suggests dynamic disease progression curves rather than pre-defined mathematical functions by de Winter et al.

Conclusions & Future work

• Disease progression model & ADAPT approach both useful for monitoring disease status

• ADAPT– applicable to both mice/human, glucose/lipoprotein

metabolism and multiscale models– more dynamically correct representation of beta-cell

function and insulin sensitivity using ADAPT

• However;– How to disentangle disease progression effects from hypoglycemic effects?– How to estimate time-varying parameters in conjunction with time-constant

parameters?

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Acknowledgements