Parameter Identification in a Respiratory Control System Model with Delay
In this paper we study parameter identification issues by computational means for a set of nonlinear delay equations which have been proposed to model the dynamics of a simplified version of the respiratory control system. We design specific inputs for ou
- PDF / 582,726 Bytes
- 14 Pages / 439.36 x 666.15 pts Page_size
- 3 Downloads / 214 Views
Parameter Identification in a Respiratory Control System Model with Delay Ferenc Hartung and Janos Turi
Abstract In this paper we study parameter identification issues by computational means for a set of nonlinear delay equations which have been proposed to model the dynamics of a simplified version of the respiratory control system. We design specific inputs for our system to produce “information rich” output data needed to determine values of unknown parameters. We also consider the effects of noisy measurements in the identification process. Several case studies are included.
6.1 Introduction Mathematical models describing the chemical balance mechanism of the respiratory control system are given in the form of nonlinear, parameter dependent, delay differential equations [3–5]. The physiological features of the respiratory system including a transport delay in the feedback control mechanism is reviewed in Chap. 8. The analysis of the direct problem (i.e., it is assumed that the values of the parameters are known) corresponding to the model equations shows that the system has a unique equilibrium, and that the stability of this equilibrium depends on the parameter values (see [5] for details). This observation leads naturally to the question of parameter identification in the model equations based on available, but possibly noisy, measurements. In this paper we present a computational procedure, applicable for large classes of functional differential equations [11, 15, 17] which
F. Hartung Department of Mathematics, University of Pannonia, Veszpr´em, H-8201, Hungary e-mail: [email protected] J. Turi () Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083, USA e-mail: [email protected] J.J. Batzel et al. (eds.), Mathematical Modeling and Validation in Physiology, Lecture Notes in Mathematics 2064, DOI 10.1007/978-3-642-32882-4 6, © Springer-Verlag Berlin Heidelberg 2013
105
106
F. Hartung and J. Turi
can be used to perform parameter estimation in respiratory control models. We also illustrate how information rich data can enhance the effectiveness of the estimation process. Another issue we study is what are the most promising measurements available for identification purposes (i.e., should one measure gas concentrations or ventilation volumes)? In Sect. 6.2 we introduce our model equations, in Sect. 6.3 we describe the numerical method we use to run simulations on the model equations. Section 6.4 outlines the parameter estimation process and contains several case studies. In Sect. 6.5 we provide a discussion of our findings.
6.2 Model Equations We consider following [5] and [3] the system of nonlinear delay equations describing a simple model of the human respiratory control system x.t/ P D a11 a12 x.t/ a13 V .t; x.t /; y.t //.x.t/ xI /;
(6.1)
y.t/ P D a21 a22 y.t/ C a23 V .t; x.t /; y.t //.yI y.t//;
(6.2)
where x.t/ and y.t/ denote the arterial CO2 and O2 concentrations, respectively, V .; ; / is the ventilation function, is t
Data Loading...
