Input-Dependent Structural Identifiability of Nonlinear Systems

A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation.

[1]  Eric Walter,et al.  Qualitative and quantitative experiment design for phenomenological models - A survey , 1990, Autom..

[2]  Yoram Rudy,et al.  Computational biology in the study of cardiac ion channels and cell electrophysiology , 2006, Quarterly Reviews of Biophysics.

[3]  Julio R. Banga,et al.  Dynamical compensation and structural identifiability of biological models: Analysis, implications, and reconciliation , 2017, PLoS Comput. Biol..

[4]  Ghislaine Joly-Blanchard,et al.  Some effective approaches to check the identifiability of uncontrolled nonlinear systems , 2001 .

[5]  Nicolette Meshkat,et al.  On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation , 2014, PloS one.

[6]  W. Marsden.  I and J , 2012 .

[7]  J. Banga,et al.  Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions , 2017 .

[8]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[9]  Johan Karlsson,et al.  Minimal output sets for identifiability. , 2012, Mathematical biosciences.

[10]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[11]  J. D. Stigter,et al.  A fast algorithm to assess local structural identifiability , 2015, Autom..

[12]  Neil D. Evans,et al.  Structural identifiability analysis via symmetries of differential equations , 2009, Autom..

[13]  Ghislaine Joly-Blanchard,et al.  An easy to check criterion for (un)indentifiability of uncontrolled systems and its applications , 2000, IEEE Trans. Autom. Control..

[14]  Denis Noble,et al.  Markov models for ion channels: versatility versus identifiability and speed , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  C. Cobelli,et al.  Qualitative experiment design in physiological system identification , 1992, IEEE Control Systems.

[16]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[17]  C. Cobelli,et al.  Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. , 1980, The American journal of physiology.

[18]  Xiaohua Xia,et al.  Identifiability of nonlinear systems with application to HIV/AIDS models , 2003, IEEE Trans. Autom. Control..

[19]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[20]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[21]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[22]  Maria Pia Saccomani,et al.  DAISY: A new software tool to test global identifiability of biological and physiological systems , 2007, Comput. Methods Programs Biomed..

[23]  Elias August.  Parameter Identifiability and Optimal Experimental Design , 2009, 2009 International Conference on Computational Science and Engineering.

[24]  Antonis Papachristodoulou,et al.  Structural Identifiability of Dynamic Systems Biology Models , 2016, PLoS Comput. Biol..

[25]  Fabian J. Theis,et al.  Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems , 2015, Bioinform..

[26]  Johan Karlsson,et al.  An Efficient Method for Structural Identifiability Analysis of Large Dynamic Systems , 2012 .

[27]  Eva Balsa-Canto,et al.  Bioinformatics Applications Note Systems Biology Genssi: a Software Toolbox for Structural Identifiability Analysis of Biological Models , 2022 .

[28]  Eva Balsa-Canto,et al.  GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models , 2017, Bioinform..

[29]  Keith R. Godfrey,et al.  Identifiability of uncontrolled nonlinear rational systems , 2002, Autom..

[30]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[31]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[32]  Maria Pia Saccomani,et al.  Parameter identifiability of nonlinear systems: the role of initial conditions , 2003, Autom..

[33]  Julio R. Banga,et al.  Sufficiently Exciting Inputs for Structurally Identifiable Systems Biology Models , 2018 .

[34]  R. Bellman,et al.  On structural identifiability , 1970 .