Royal Society International Seminar 'Incorporating Uncertainty into Cardiac Physiome Simulations', 15-16th Feb. 2017, Chicheley, UK

1. Royal Society International Seminar
February 15, 2017
Natal van Riel
Eindhoven University of Technology | University of Amsterdam
Dept of Biomedical Engineering | Academic Medical Center
Systems Biology and Metabolic Diseases
n.a.w.v.riel@tue.nl
@nvanriel

2. Systems Biology and Metabolic Diseases
Metabolic Syndrome and
comorbidities
• A multifaceted, multi-scale
problem
– macro-models
– micro-models
• Models of metabolism and its
regulatory systems
• Models for science
(understanding)
• Computational diagnostics
2
Rask-Madsen et al. (2012) Arterioscler
Thromb Vasc Biol, 32(9):2052-2059

3. Modelling in Systems Biology and Physiome
• Quantitative and Predictive Modelling
3
TOP-DOWN
BOTTOM-UP
…to whole
organisms
and physiology
From molecules
and pathways…
Data-driven
(statistics)
Hypothesis –
based
(mechanistic
modelling)

4. Physiology-based models of dynamic biological
systems
• Data-driven mechanistic models
• Physiological endpoints
4
Time-series data

5. Developing models of dynamic systems
Explaining the data & understanding the system
• Estimating models
• Identifying and implementing a set of constraints (at different levels
and scales – components, system behavior)
• Comparing alternative hypotheses (differences in model structure)
• Given a fixed model structure, find sets of parameter values that
yield a model that accurately describes empirical observations
5
 
^
arg min Deviation from Observations Penalty on Flexibility
ModelClass
Model  
Model complexity / granularity

6. Model parameterization
• Direct measurement of (kinetic) parameters of model components
• Taking numbers from the literature, including stitching together
(sub)components of existing models
• Testing model plausibility
• The ‘Frankenstein model’ as prior knowledge for parameter
identification
• Calibrating the model to in vivo / physiological data
6

7. Uncertainty
7
• Structural uncertainty resides in simplifications that are inherent
to the process of model building and assumptions that are made in
case the nature and / or kinetic details of certain interactions (e.g.
metabolic pathways, regulatory signals) are unknown or disputed
• Since model parameters are estimated by calibrating the model to
experimental data, uncertainty in the data (noise, errors) will
propagate into the parameter estimates, which subsequently will
limit the accuracy of the model predictions.
• E.g. in case of dietary intervention studies a source of uncertainty
originates from the fact that not all participants will be fully compliant.

8. Reducing bias while
controlling variance
8

9. Bias - variance
• Networks impose strong constraints on system dynamics
9

10. Rethinking Maximum Likelihood Estimation
10
• The bias - variance trade-off is often reached for rather large bias
• Typically, we are far away from the asymptotic situation in which
Maximum Likelihood Estimation (MLE) provides the best possible
estimates

11. Room for more flexibility
• Instead of increasing structural complexity (increasing model size)
• Introduce more freedom in model parameters to compensate for bias
(‘undermodelling’) in the original model structure
• Increasing model flexibility using time-varying parameters
•ADAPT
Analysis of Dynamic Adaptations in Parameter Trajectories
11
Tiemann et al. (2011) BMC Syst Biol, 5:174
Van Riel et al. (2013) Interface Focus 3(2): 20120084,
Tiemann et al. (2013) PloS Comput Biol, 9(8):e1003166
Dynamical Systems Theory:
(Extended) Kalman Filter

12. 12
Parameter space
State space
 .

initial condition
state
 trajectories
Data space
time-series
Output space
ensemble
parameter
trajectories




13. 13 Nyman 2016, Interface Focus 6: 20150075

14. Disease progression and treatment of T2DM
• 1 year follow-up of treatment-naïve T2DM patients (n=2408)
• 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
14
FPG[mmol/L]
Schernthaner et al, Clin. Endocrinol. Metab. 89:6068–6076 (2004)
Charbonnel et al, Diabetic Med. 22:399–405 (2004)
FPG: fasting plasma glucose

15. Glucose-insulin homeostasis model
• Pharmaco-Dynamic model
• 3 ODE’s, 15 parameters
15
hepatic glucose
production
glucose
utilization
insulin secretion
glucose (FPG)
insulin
sensitivity (S)
insulin (FSI)HbA1c
beta-cell
function (B)
OHA
(insulin sensitizer)
OHA
(insulin secretagogue)
1 2
1 2
1 2
1
2
compensation phase: hyperinsulinemia
exhaustion phase: disease onset
treatment effects
De Winter et al. (2006) J Pharmacokinet
Pharmcodyn, 33(3):313-343
FPG: fasting plasma glucose
FSI: fasting serum insulin
HbA1c: glycosylated hemoglobin A1c

16. T2DM disease progression model
• Fixed parameters
• Adaptive changes in -cell function B(t) and insulin sensitivity S(t)
• Parameter trajectories
16
Nyman et al, Interface Focus.
2016 Apr 6;6(2): 20150075

17. Reducing bias while controlling variance
• The common way to handle the flexibility constraint is to restrict /
broaden the model class
• If an explicit penalty is added, this is known as regularization
• In case of parameter estimation:
17
 
^
arg min Deviation from Observations Penalty on Flexibility
ModelClass
Model  
 2ˆ
arg min ( ) ( )

      r
r r r

18. Regularization of parameter trajectories
18
 
[ ]
ˆ
[ ] arg min Deviation from Data Penalty on Parameters Changes
n
n

  r
r
• Shrinkage of changes in parameters values
• Selection of parameters that change

19. Assessing credibility of computational modeling
and simulation results
19
Verification, validation and uncertainty quantification (VVUQ)
Verification Does the computational implementation solve the mathematical model
correctly?
» robust solvers for stiff nonlinear differential equations
Validation Does the mathematical model correctly represent the reality of
interest?
» plausibility, physiological realism (population level) - metabolic
physiology (e.g., post-prandial response dynamics)
» database of individual responses (quantitative resource)
Uncertainty Quantification What is the uncertainty in the inputs (e.g. parameter values, initial
conditions), and what is the resultant uncertainty in the model outputs?
» Maximum Likelihood Estimation, Bayesian inference, Profile
Likelihood Analysis (PLA), Prediction Uncertainty Analysis (PUA),
Global Sensitivity Analysis
Applicability How applicable is the validation evidence to support using the model
in the context of use?
» follow-up data after the intervention serve as validation of predictions
for each individual with his/her personalized model
Credibility Can the computational model make predictions that are reliable in the
context of use?
» platform to generate and test novel hypotheses
» Independent cohorts
» assess the effectiveness of interventions.

20. Uncertainty Quantification
20
NCSB Workshop: Parameter Estimation and Uncertainty Analysis in Systems Biology,
EURANDOM workshop “Parameter Estimation for Dynamical Systems“ (PEDS-II), 2012

21. Conclusions
• The network structure of the biological systems imposes strong
constraints on possible solutions of a model
• The bias - variance trade-off is often reached for rather large bias,
not favoring MLE
• Dynamic models, despite their size and complexity, are not always
flexible enough to correctly describe the data of biological systems
• Computational techniques to introduce more degrees of freedom in
models, but simultaneously enforcing sparsity if extra flexibility is not
required (ADAPT)
• Model estimation tools are complemented with ‘regularization’
methods to reduce the error (bias) in models without escalating
uncertainties (variance)
21

22. 22
Systems Biology of Disease Progression - ADAPT
modeling
http://www.youtube.com/watch?v=x54ysJDS7i8