Parameter Estimation in Mathematical Models of Biological Systems

Publisher Summary This chapter provides an overview of the parameter identification field and highlights its applications to a variety of respiratory system problems. It focuses on an area of system science that can be expected to have increasing importance in the study of biological systems. Estimation of state variables from noisy data, determination of optimum inputs for parameter identification, and criteria for identifiability of given model structures are among the topics that are likely to influence the development of mathematical models of biological systems in the near future. The chapter reviews the basic structure of a parametric identification problem. Both parametric and nonparametric methods have been applied extensively to the identification of a variety of complex engineering systems. The identification techniques designed for systems where input and output signals can be clearly isolated may not work at all in the biological situation. The very nature of the living organism, particularly in higher animals, leads to such a complex of interconnections of subsystems that isolation of a portion of the system may destroy its natural function and, thus, lead to identification of a purely hypothetical process. On the other hand, in the cases when input and output can be isolated, often by exceedingly clever surgical procedures, and the system in question is approximately linear, frequency response methods have been applied with considerable success.

[1]  R. C. White.  A survey of random methods for parameter optimization , 1971 .

[2]  J. Hill,et al.  An application of digital computers to linear system identification , 1964 .

[3]  A. C. Young,et al.  Compartmental analysis of the distribution of gas in the lungs. , 1967, Journal of applied physiology.

[4]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[5]  J S ROBERTSON,et al.  Lung ventilation patterns determined by analysis of nitrogen elimination rates; use of mass spectrometer as a continuous gas analyzer. , 1950, The Journal of clinical investigation.

[6]  Hugh D. Van Liew,et al.  Semilogarithmic Plots of Data Which Reflect a Continuum of Exponential Processes. , 1962 .

[7]  J. Crank,et al.  Persistent discretization errors in partial differential equations of parabolic type , 1964, Comput. J..

[8]  D. Audley,et al.  III-posed and well-posed problems in systems identification , 1974 .

[9]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[10]  J. Willems,et al.  Parametrizations of linear dynamical systems: Canonical forms and identifiability , 1974 .

[11]  R. Mehra,et al.  Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations , 1974 .

[12]  Raman K. Mehra,et al.  Optimal input signals for parameter estimation in dynamic systems--Survey and new results , 1974 .

[13]  Jerry M. Mendel.  Gradient, error-correction identification algorithms , 1968, Inf. Sci..

[14]  D. Gómez,et al.  A mathematical treatment of the distribution of tidal volume throughout the lung. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[15]  F. Grodins,et al.  MATHEMATICAL MODELS OF RESPIRATORY REGULATION * , 1963, Annals of the New York Academy of Sciences.

[16]  J. S. Meditch,et al.  Least squares estimation of respiratory system parameters , 1970 .

[17]  W. S. Fowler,et al.  Lung function studies. VIII. Analysis of alveolar ventilation by pulmonary N2 clearance curves. , 1952, The Journal of clinical investigation.