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Mathematical modelling of disease progression
1. A mechanism-based disease progression
model to analyse long-term treatment
effects on disease processes underlying
type 2 diabetes
Workshop
Yvonne Rozendaal
y.j.w.rozendaal@tue.nl
âThe interplay of fat and carbohydrate metabolism
with application in Metabolic Syndrome and Type 2
Diabetesâ
December 12th 2013
2. Introduction
âą Disease progression
â multi-scale problem
â how to assess/measure?
âą Treatment interventions
â effect of treatment on disease progression?
short-term vs long-term
âą How to simulate adaptations & interventions?
2
3. Type 2 Diabetes Mellitus (T2DM)
âą Impaired beta-cell function
âą Reduced insulin sensitivity
chronic loss of
glycemic control
âą Monitoring glycemic control: biomarkers
â FPG: fasting plasma glucose
secondary
â FSI: fasting serum insulin glycemic markers
â HbA1c: glycosylated hemoglobin
primary glycemic marker
how to derive
disease status?
3
4. T2DM treatment
âą hypoglycemic effect: short-term
â immediate symptomatic effects on glycemic
control
âą inhibitory effect on disease progression:
long-term
â protect against T2DM progression
4
5. Objective
disease progression
progressive loss of beta-cell
function and insulin sensitivity
metabolic biomarkers
adaptations in
biological network
FPG
FSI
HbA1c
treatment interventions
pharmacological therapy
computational model:
description and quantification of inputs
minimal model
disease progression model
test functionality of method on minimal model:
ï± human vs. mouse
ï± glucose vs. lipid metabolism
introduction to ADAPT
application of ADAPT
5
6. Modelling disease progression (1)
âą Disentangle treatment effects
â long-term
loss of beta-cell function
and insulin sensitivity
â short-term
anti-hyperglycemic effects
âą Computational model:
study & quantify
time-course effects
de Winter et al. (2006) J Pharmacokinet Pharmacodyn,33(3):313-343
disease progression model
introduction to ADAPT
application of ADAPT
6
7. PK/PD modelling
âą PharmacoKinetic-PharmacoDynamic modelling
âą Simple kinetics are modelled using
minimal/macroscopic models
âą e.g. absorption profiles
disease progression model
introduction to ADAPT
application of ADAPT
7
8. T2DM disease progression model (1)
glucose â insulin â HbA1c
âą Model components
â FPG: fasting plasma glucose
â FSI: fasting serum insulin
â HbA1c: glycosylated hemoglobin
âą Physiological FPG-FSI homeostasis:
â feedback between FSI and FPG
FPG stimulates FSI production: FSI production rate â FPG concentration
â feed-forward between FPG and HbA1c
HbA1c production rate â to FSI concentration
disease progression model
introduction to ADAPT
application of ADAPT
8
9. T2DM disease progression model (2)
model structure
B: beta-cell function
(disease status) k
in
EFB: treatment effect
on insulin secretion
S: insulin sensitivity
(disease status)
k in
EFS: insulin sensitizing
effect of treatment
k in
disease progression model
FSI
k out
homeostatic
feed-backs
FPG
k out
feed-forward
HbA1c
introduction to ADAPT
k out
application of ADAPT
9
10. T2DM disease progression model (3)
model equations
treatment specific
factor of insulinsecretogogues
d FSI
disease status:
fraction of remaining beta-cell function
EF B B ( FPG
dt
d FPG
k in FPG
dt
EF S S FSI
d HbA
1c
dt
FPG k in HbA
treatment specific
factor of insulinsensitizers
disease progression model
3 . 5 ) k in FSI
FSI k out FSI
FPG k out FPG
HbA
1c
1c
k out HbA
1c
disease status:
fraction of remaining insulin sensitivity
introduction to ADAPT
application of ADAPT
10
11. T2DM disease progression model (1)
disease status
âą Beta-cell function
1
B
fraction of remaining
beta-cell function
1
exp( b 0
shift of disease
progression curve
âą Insulin sensitivity
fraction of remaining
hepatic insulin-sensitivity
S
1
1
exp( s 0
rB t )
slope of
disease
progression
curve
rS t )
âą Assumption: asympotically decrease over time
disease progression model
introduction to ADAPT
application of ADAPT
11
12. Model comparison with data (1)
âą Long-term (1y) follow-up of treatment-naĂŻve T2DM
patients
âą 3 treatment arms: monotherapy with different
hypoglycemic agents
â pioglitazone: insulin sensitizer
âą enhances peripheral glucose uptake
âą reduces hepatic glucose production
â metformin: insulin sensitizer
âą decreases hepatic glucose production
â gliclazide: insulin secretogogue
âą stimulates insulin secretion by the pancreatic beta-cells
disease progression model
introduction to ADAPT
application of ADAPT
12
14. Reproduction of results (1)
ï± Metabolic biomarkers over time
although initial
decrease, glycemic
control still gradually
decreases over time
disease progression model
introduction to ADAPT
application of ADAPT
14
15. Reproduction of results (2)
ï± Disease status
gliclazide:
insulin secretogogue
pioglitazone & metformin:
insulin sensitizers
however, morphology
of disease progression
curves unknown...
disease progression model
introduction to ADAPT
application of ADAPT
15
16. Introduction to ADAPT (1)
âą Phenotype transition over time
treatment interventions
medication, surgery, ...
disease progression
phenotype A
phenotype B
which adaptations
occur?
âą Analysis of Dynamic Adaptations in Parameter
Trajectories
Tiemann et al. (2011). BMC Syst Biol,26(5):174
Tiemann et al. (2013). PLoS Comput Biol,9(8):e1003166
disease progression model
introduction to ADAPT
application of ADAPT
16
17. Introduction to ADAPT (2)
âą Phenotype transition:
â gradual, long-term processes
â measurements at metabolome level
âą Adaptation at proteome and transcriptome level
âą Model at metabolome level
âą Time-dependency implemented using timevarying parameters
disease progression model
introduction to ADAPT
application of ADAPT
17
18. Modelling phenotype transition (1)
ï± long-term discrete data: different phenotypes
treatment
disease progression
disease progression model
introduction to ADAPT
application of ADAPT
18
19. Modelling phenotype transition (2)
ï± long-term discrete data: different phenotypes
ï± estimate continuous data: cubic smooth spline
introduce artificial
intermediate phenotypes
disease progression model
introduction to ADAPT
application of ADAPT
19
20. Modelling phenotype transition (3)
ï± long-term discrete data: different phenotypes
ï± estimate continuous data: cubic smooth spline
ï± incorporate uncertainty in data: multiple describing functions
disease progression model
introduction to ADAPT
application of ADAPT
20
21. Parameter estimation (1)
ï± steady state model
disease progression model
introduction to ADAPT
application of ADAPT
21
22. Parameter estimation (2)
ï± steady state model
ï± 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
22
23. Parameter estimation (2)
ï± steady state model
ï± iteratively calibrate model to data: estimate parameters over time
disease progression model
introduction to ADAPT
application of ADAPT
23
24. Parameter estimation (2)
ï± steady state model
ï± iteratively calibrate model to data: estimate parameters over time
disease progression model
introduction to ADAPT
application of ADAPT
24
25. Parameter estimation (2)
ï± steady state model
ï± iteratively calibrate model to data: estimate parameters over time
disease progression model
introduction to ADAPT
application of ADAPT
25
26. Estimated parameter trajectories
ï± effect of parameter adaptations on underlying processes?
down-regulation
up-regulation
stochastic
behaviour...
unaffected
physiologically
unrealistic
disease progression model
introduction to ADAPT
application of ADAPT
26
27. Possible applications for ADAPT
âą Unravel which processes in network might be
responsible for phenotype transition
âą Guide new experiment design
âą Define possible pharmacological targets
disease progression model
introduction to ADAPT
application of ADAPT
27
28. Application of ADAPT in
disease progression model
fraction of beta-cell function:
time-dependent parameter
d FSI
B ( FPG
dt
d FPG
k in FPG
dt
S FSI
d HbA
dt
1c
3 . 5 ) k in FSI
FSI k out FSI
time-constant
parameters
FPG k out FPG
FPG k in HbA
HbA1c
1c
k out HbA
1c
fraction of insulin sensitivity:
time-dependent parameter
disease progression model
introduction to ADAPT
application of ADAPT
28
29. Disease progression model
vs. application of ADAPT (1)
ï± Metabolic biomarkers over time
treatment with pioglitazone
FPG & FSI:
ADAPT reproduces
model predictions
HbA1c:
performance ADAPT
disease progression model
introduction to ADAPT
application of ADAPT
29
30. Disease progression model
vs. application of ADAPT (2)
ï± Parameter trajectories: disease status
treatment with pioglitazone
ADAPT suggests dynamic
disease progression curves
rather than pre-defined
mathematical functions by
de Winter et al.
disease progression model
introduction to ADAPT
application of ADAPT
30
31. Disease progression model
vs. application of ADAPT (2)
ï± Parameter trajectories: disease status
treatment with pioglitazone
ADAPT suggests dynamic
disease progression curves
rather than pre-defined
mathematical functions by
de Winter et al.
disease progression model
introduction to ADAPT
application of ADAPT
31
32. Conclusions & Future work
âą Disease progression model & ADAPT approach both
useful for monitoring disease status
âą ADAPT
â applicable to both mice/human, glucose/lipoprotein
metabolism and multiscale models
â more dynamically correct representation of beta-cell
function and insulin sensitivity using ADAPT
âą However;
â How to disentangle disease progression effects from hypoglycemic effects?
â How to estimate time-varying parameters in conjunction with time-constant
parameters?
32
âThe goal is to transform data into information, and information into insightâ (CarlyFiorina, Executive and president of Hewlett-Packard Co. in 1999)
PK: what the body does with a dose of a drug kinetics ï motion (absorption, distribution, metabolism, excretion)PD: what the drug does to the body dynamics ï change [mechanism is known]âPopulation modelâ ï model involves random effects
healthy,untreatedindividual: B=1, S=1,EFb=1 EFs=1EFb, EFs: step-functions of time (incl. delay)
Group 1: pioglitazonevsmetforminn=1176Group 2: pioglitazonevsgliclaziden=1232