modelling physiological uncertainty
TRANSCRIPT
Royal Society International Seminar
February 15, 2017
Natal van RielEindhoven University of Technology | University of Amsterdam
Dept of Biomedical Engineering | Academic Medical Center
Systems Biology and Metabolic Diseases
@nvanriel
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
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Rask-Madsen et al. (2012) ArteriosclerThromb Vasc Biol, 32(9):2052-2059
Modelling in Systems Biology and Physiome
• Quantitative and Predictive Modelling
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TOP-DOWN
BOTTOM-UP
…to whole organisms
and physiology
From molecules and pathways…
Data-driven (statistics)
Hypothesis –based (mechanistic modelling)
Physiology-based models of dynamic biological
systems
• Data-driven mechanistic models
• Physiological endpoints
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Time-series data
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 FlexibilityModelClass
Model
Model complexity / granularity
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
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Uncertainty
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• 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.
Rethinking Maximum Likelihood Estimation
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• 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
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
•ADAPTAnalysis of Dynamic Adaptations in Parameter Trajectories
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Tiemann et al. (2011) BMC Syst Biol, 5:174Van 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
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Parameter space
State space
.
initial condition
state trajectories
Data space
time-series
Output space
ensemble
parameter trajectories
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
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FPG
[m
mo
l/L]
Schernthaner et al, Clin. Endocrinol. Metab. 89:6068–6076 (2004)Charbonnel et al, Diabetic Med. 22:399–405 (2004)
FPG: fasting plasma glucose
Glucose-insulin homeostasis model
• Pharmaco-Dynamic model
• 3 ODE’s, 15 parameters
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hepatic glucose production
glucose utilization
insulin secretion
glucose (FPG)
insulinsensitivity (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 PharmacokinetPharmcodyn, 33(3):313-343
FPG: fasting plasma glucoseFSI: fasting serum insulinHbA1c: glycosylated hemoglobin A1c
T2DM disease progression model
• Fixed parameters
• Adaptive changes in -cell function B(t) and insulin sensitivity S(t)
• Parameter trajectories
16Nyman et al, Interface Focus. 2016 Apr 6;6(2): 20150075
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:
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^
arg min Deviation from Observations Penalty on FlexibilityModelClass
Model
2ˆarg min ( ) ( )
r
r r r
Regularization of parameter trajectories
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[ ]
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
Assessing credibility of computational modeling
and simulation results
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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.
Uncertainty Quantification
20NCSB Workshop: Parameter Estimation and Uncertainty Analysis in Systems Biology,EURANDOM workshop “Parameter Estimation for Dynamical Systems“ (PEDS-II), 2012
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)
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• Fianne Sips
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Systems Biology of Disease Progression - ADAPT modelinghttp://www.youtube.com/watch?v=x54ysJDS7i8