mathematical modelling of disease progression
TRANSCRIPT
![Page 1: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/1.jpg)
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]
![Page 2: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/2.jpg)
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
![Page 3: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/3.jpg)
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?
![Page 4: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/4.jpg)
T2DM treatment
• hypoglycemic effect: short-term
– immediate symptomatic effects on glycemiccontrol
• inhibitory effect on disease progression: long-term
– protect against T2DM progression
4
![Page 5: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/5.jpg)
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
![Page 6: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/6.jpg)
• 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
![Page 7: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/7.jpg)
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
![Page 8: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/8.jpg)
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
![Page 9: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/9.jpg)
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
![Page 10: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/10.jpg)
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
![Page 11: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/11.jpg)
• 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
![Page 12: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/12.jpg)
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
![Page 13: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/13.jpg)
Model comparison with data (2)
13
FPG
[m
mo
l/L]
disease progression model introduction to ADAPT application of ADAPT
![Page 14: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/14.jpg)
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
![Page 15: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/15.jpg)
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
![Page 16: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/16.jpg)
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
![Page 17: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/17.jpg)
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
![Page 18: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/18.jpg)
Modelling phenotype transition (1)
18
treatment
disease progression
long-term discrete data: different phenotypes
disease progression model introduction to ADAPT application of ADAPT
![Page 19: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/19.jpg)
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
![Page 20: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/20.jpg)
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
![Page 21: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/21.jpg)
Parameter estimation (1)
21
steady state model
disease progression model introduction to ADAPT application of ADAPT
![Page 22: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/22.jpg)
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
![Page 23: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/23.jpg)
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
![Page 24: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/24.jpg)
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
![Page 25: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/25.jpg)
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
![Page 26: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/26.jpg)
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
![Page 27: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/27.jpg)
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
![Page 28: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/28.jpg)
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
![Page 29: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/29.jpg)
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
![Page 30: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/30.jpg)
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.
![Page 31: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/31.jpg)
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.
![Page 32: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/32.jpg)
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
![Page 33: Mathematical modelling of disease progression](https://reader031.vdocument.in/reader031/viewer/2022030402/58ac8dcf1a28abad118b5f0d/html5/thumbnails/33.jpg)
Acknowledgements