Structural Identifiability and Indistinguishability in
Systems Pharmacology
1,2,3,4
Janzén
,
1
Yates , Johan
2
Gabrielsson
David
James
3
4
4
Mats Jirstrand , Neil Evans , Michael Chappell
University of Agricultural Sciences, 3Fraunhofer-Chalmers Research Centre Industrial Mathematics, 4University of Warwick School of Engineering
Aim and Motivation
Application
A prerequisite of making reliable
predictions is to determine whether a
model is structurally identifiable,
i.e. whether there is a unique solution
to the problem of determine the
parameters given noise-free and
continuous data in time and space.
The following four parallel systems
pharmacology modelling projects will be
included in the workflow depicted in
Figure 1b.
Dose – Response Time Outcome
Relationship
Figure 1
a)
b)
Model Structure
Model Structure
Project summary:
• Development of mechanism-based
models for local/systemic administration
• Characterization of signature profiles of
dose-response
• Application of identifiability and
deconvolution techniques
IdentifiabilityIndistinguishability
analysis
Figure 2
Unreliable
predictions
In a) the conventional workflow no concern of the
parameter identifiability is taken, potentially
leading to unreliable predictions. In b), structurally
identifiability analysis is applied generating three
possible outcomes; (i) refinement of the model, (ii)
design of new experiments to achieve
identifiability (iii) having shown identifiability the
process is moved on to data fitting and reliable
predictions in the sense of identifiability.
Methods
There are several methods of
determining identifiability for both
linear and nonlinear systems. The most
appropriate approach depends on the
structure and the size of the model. A
few examples of approaches that will be
used in this project are
• Laplace transform
• Taylor series, generating series
• Similarity transformation
• Input-output relationship
• Differential algebra
• Probabilistic semi-numerical method
• Numerical approaches
Figure 4
Cardiovascular Safety – Target
Engagement - Exposure
Data fitting
Reliable
predictions
Project summary:
• Model prediction of target exposure
to unbound drug in the lung after
administration
• Modelling of the mechanism and
kinetics of target occupancy
• Structural identifiability analysis will
be performed on these models
By using an identifiable model of the receptor
binding mechanism and kinetics in the lung,
reliable predictions can be made of both the
systemic and lung exposure of the drug under
different conditions.
Experiment design
Data fitting
Evaluation of lung tissue target
exposure to inhaled drug using
modelling of pharmacologic data
Typically, the parameters in a pharmacokinetic (PK)
model are estimated first. The PK-model is then
used as an input function in the pharmacodynamic
model (PD)( (upper panel). However, when only PD
data is available much information is still available
such as turnover response characteristics, the drugs
biophase kinetics and PD dynamics (lower panel).
This is especially true when combining different
dose selection and different administration routes.
Deconvolution in nonlinear
differential equations for
Quantitative and Systems
Pharmacology
Project summary:
• Development and improvement of
new deconvolution techniques
• A set of benchmark problems will be
used for evaluation of the developed
techniques
• Structural identifiability will be
addressed throughout the project
Figure 3
u(t)
Unknown
Nonlinear model
y(t)
Known
Known
Here, the focus is on determining the unknown input
function u(t) when both the structure of the
nonlinear model and the output function y(t) is
known.
Project summary:
• Modelling of exposure-effect
relationship for cardiovascular
parameters in different species
• Use translational systems
pharmacology to separate drug-and
system specific parameters
• Application of identifiability analysis
on the PK-model prior to
development of PD-and
translational model
Figure 5
translation
of effect
man
1AstraZeneca, 2Swedish
preclinical
species
time
time
log(conc)
Predictions from PKPD-models across different
preclinical species will be used in a translational
sense to estimate cardiovascular safety in
humans.
Summary
A structural identifiability project will be
run alongside four parallel modelling
projects. These four projects will all be
subject to identifiability analysis to
ensure reliable predictions.
Email: D.L.I.Janzen@warwick.ac.uk
This work is funded through the Marie Curie FP7 People ITN European Industrial Doctorate (EID) project, IMPACT (Innovative Modelling for Pharmacological Advances
through Collaborative Training).