mathematical modelling of disease progression
TRANSCRIPT
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 [email protected]
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?
2
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
3
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
4
Objective
5
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
6
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
10
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
11
)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)
13
FPG
[m
mo
l/L]
disease progression model introduction to ADAPT application of ADAPT
Reproduction of results (1)
14
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)
15
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
16
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)
18
treatment
disease progression
long-term discrete data: different phenotypes
disease progression model introduction to ADAPT application of ADAPT
Modelling phenotype transition (2)
19
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)
20
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)
21
steady state model
disease progression model introduction to ADAPT application of ADAPT
Parameter estimation (2)
22
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)
23
steady state model iteratively calibrate model to data: estimate parameters over time
disease progression model introduction to ADAPT application of ADAPT
Parameter estimation (2)
24
steady state model iteratively calibrate model to data: estimate parameters over time
disease progression model introduction to ADAPT application of ADAPT
Parameter estimation (2)
25
steady state model iteratively calibrate model to data: estimate parameters over time
disease progression model introduction to ADAPT application of ADAPT
Estimated parameter trajectories
26
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
27
• 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
28
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
29
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
30
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)
31
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?
32
Acknowledgements