Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions

summary:In this paper a novel method is proposed for the structural identifiability analysis of nonlinear time delayed systems. It is assumed that all the nonlinearities are analytic functions and the time delays are constant. We consider the joint structural identifiability of models with respect to the ordinary system parameters and time delays by including delays into a unified parameter set. We employ the Volterra series representation of nonlinear dynamical systems and make use of the frequency domain representations of the Volterra kernels, i. e. the Generalized Frequency Response Functions (GFRFs), in order to test the unique computability of the parameters. The advantage of representing nonlinear systems with their GFRFs is that in the frequency domain representation the time delay parameters appear explicitly in the exponents of complex exponential functions from which they can be easily extracted. Since the GFRFs can be symmetrized to be unique, they provide us with an exhaustive summary of the underlying model structure. We use the GFRFs to derive equations for testing structural identifiability. Unique solution of the composed equations with respect to the parameters provides sufficient conditions for structural identifiability. Our method is illustrated on non-linear dynamical system models of different degrees of non-linearities and multiple time delayed terms. Since Volterra series representation can be applied for input-output models, it is also shown that after differential algebraic elimination of unobserved state variables, the proposed method can be suitable for identifiability analysis of a more general class of non-linear time delayed state space models

Physiological modeling of isoprene dynamics in exhaled breath

Human breath contains a myriad of endogenous volatile organic compounds (VOCs) which are reflective of ongoing metabolic or physiological processes. While research into the diagnostic potential and general medical relevance of these trace gases is conducted on a considerable scale, little focus has been given so far to a sound analysis of the quantitative relationships between breath levels and the underlying systemic concentrations. This paper is devoted to a thorough modeling study of the end-tidal breath dynamics associated with isoprene, which serves as a paradigmatic example for the class of low-soluble, blood-borne VOCs. Real-time measurements of exhaled breath under an ergometer challenge reveal characteristic changes of isoprene output in response to variations in ventilation and perfusion. Here, a valid compartmental description of these profiles is developed. By comparison with experimental data it is inferred that the major part of breath isoprene variability during exercise conditions can be attributed to an increased fractional perfusion of potential storage and production sites, leading to higher levels of mixed venous blood concentrations at the onset of physical activity. In this context, various lines of supportive evidence for an extrahepatic tissue source of isoprene are presented. Our model is a first step towards new guidelines for the breath gas analysis of isoprene and is expected to aid further investigations regarding the exhalation, storage, transport and biotransformation processes associated with this important compound.Comment: 14 page

Identifiability and algebraic identification of time delay systems

International audienceIdentifiability and algebraic identification of time delay systems are investigated in this paper. Identifiability results are first presented for linear delay systems described by convolution equations. On-line algorithms are next proposed for both parameters and delay estimation. Based on a distributional technique, these algorithms enable an algebraic and simultaneous estimation by solving a generalized eigenvalue problem. Simulation studies with noisy data and experimental results show the performance of the proposed approach

Physiological modeling of isoprene dynamics in exhaled breath

Human breath contains a myriad of endogenous volatile organic compounds (VOCs) which are reflective of ongoing metabolic or physiological processes. While research into the diagnostic potential and general medical relevance of these trace gases is conducted on a considerable scale, little focus has been given so far to a sound analysis of the quantitative relationships between breath levels and the underlying systemic concentrations. This paper is devoted to a thorough modeling study of the end-tidal breath dynamics associated with isoprene, which serves as a paradigmatic example for the class of low-soluble, blood-borne VOCs. Real-time measurements of exhaled breath under an ergometer challenge reveal characteristic changes of isoprene output in response to variations in ventilation and perfusion. Here, a valid compartmental description of these profiles is developed. By comparison with experimental data it is inferred that the major part of breath isoprene variability during exercise conditions can be attributed to an increased fractional perfusion of potential storage and production sites, leading to higher levels of mixed venous blood concentrations at the onset of physical activity. In this context, various lines of supportive evidence for an extrahepatic tissue source of isoprene are presented. Our model is a first step towards new guidelines for the breath gas analysis of isoprene and is expected to aid further investigations regarding the exhalation, storage, transport and biotransformation processes associated with this important compound.Comment: 14 page

Parameters estimation of systems with delayed and structured entries

International audienceThis paper deals with on-line identification of continuous-time systems with structured entries. Such entries, which may consist in inputs, perturbations or piecewise polynomial (time varying) parameters, can be defined as signals that can be easily annihilated. The proposed cancellation method allows to obtain non asymptotic estimators for the unknown coefficients. Application to delayed and switching hybrid systems are proposed. Numerical simulations with noisy data but also experimental results on a delay process are provided

Dynamic modeling and parameter estimation for an ethlyene-propylene-diene polymerization process

New Page 1 A general dynamic model for continuous EPDM polymerization in which crosslinking and gel formation are attributable to reactions between pendant double bonds has been developed. A pseudo-kinetic rate constant method is introduced to construct a moment model for a pseudo-homopolymer that approximates the behavior of the actual terpolymer under long chain and quasi-steady state assumptions. The pseudo-homopolymer model is then used as the basis for application of the numerical fractionation method. The proposed dynamic model is capable of predicting polydispersities and molecular weight distributions near the gel point with as few as eleven generations, and in the post-gel region with as few as five. The overall molecular weight distribution (MWD) of the sol was constructed by assuming a Schulz two parameter distribution for each generation. A parameter selection procedure is proposed to determine the kinetic parameters that can be estimated from the limited plant data. The procedure is based on the steady-state parameter output sensitivity matrix. The overall effect of each parameter on the measured outputs is determined using Principal Component Analysis (PCA). The angles between the sensitivity vectors are used as a measure of collinearity between parameters. A simple algorithm which provides a tradeoff between overall parameter effect on key outputs and collinearity yields a ranking of parameters by ease of estimation, independent of the available data. Its nonlinear and dynamic extensions are also developed and tested to address the nonlinearity and dynamics of the parameters\u27 effects on the outputs. The key kinetic parameters determined by the parameter selection procedure were estimated from steady-state data extracted from dynamic plant data, using a newly developed steady state detection tool. A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters of the EPDM kinetic model. The estimator design is based on decomposing the dynamic model into two subsystems, by exploiting the triangular model structure and the different sampling frequencies of the on-line and laboratory measurements directly related to the state variables of each subsystem. Simulation tests show that the hierarchical EKF generates satisfactory predictions even in the presence of measurement noise and plant/model mismatch

Biological Networks

Networks of coordinated interactions among biological entities govern a myriad of biological functions that span a wide range of both length and time scales—from ecosystems to individual cells and from years to milliseconds. For these networks, the concept “the whole is greater than the sum of its parts” applies as a norm rather than an exception. Meanwhile, continued advances in molecular biology and high-throughput technology have enabled a broad and systematic interrogation of whole-cell networks, allowing the investigation of biological processes and functions at unprecedented breadth and resolution—even down to the single-cell level. The explosion of biological data, especially molecular-level intracellular data, necessitates new paradigms for unraveling the complexity of biological networks and for understanding how biological functions emerge from such networks. These paradigms introduce new challenges related to the analysis of networks in which quantitative approaches such as machine learning and mathematical modeling play an indispensable role. The Special Issue on “Biological Networks” showcases advances in the development and application of in silico network modeling and analysis of biological systems