Abstract
We propose a novel algorithm to select a model that is consistent with the time series of observed data. In the first step, the kinetics for describing a biological phenomenon is expressed by a system of differential equations, assuming that the relationships between the variables are linear. Simultaneously, the time series of the data are numerically fitted as a series of exponentials. In the next step, both the system of differential equations with the kinetic parameters and the series of exponentials fitted to the observed data are transformed into the corresponding system of algebraic equations, by the Laplace transformation. Finally, the two systems of algebraic equations are compared by an algebraic approach. The present method estimates the model’s consistency with the observed data and the determined kinetic parameters. One of the merits of the present method is that it allows a kinetic model with cyclic relationships between variables that cannot be handled by the usual approaches. The plausibility of the present method is illustrated by the actual relationships between specific leaf area, leaf nitrogen and leaf gas exchange with the corresponding simulated data.
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References
Audoly, S., D’Angiò, L., Saccomani, M.P., Cobelli, C.: Global identifiability of linear compartmental models — A computer algebra algorithm. IEEE Trans. Biomed. Eng. 45, 36–47 (1998)
Bisits, A.M., Smith, R., Mesiano, S., Yeo, G., Kwek, K., MacIntyre, D., Chan, E.C.: Inflammatory aetiology of human myometrial activation tested using directed graphs. PLoS Comput. Biol. 1, 132–136 (2005)
Buchberger, B.: An Algorithmic Criterion for the Solvability of a System of Algebraic Equations. In: Buchberger, B., Winkler, F. (eds.) Gröbner Bases and Applications. London Mathematical Society Lecture Notes Series, vol. 251, pp. 535–545. Cambridge University Press, Cambridge (1998)
Calvano, S.E., Xiao, W., Richards, D.R., Felciano, R.M., Baker, H.V., Cho, R.J., Chen, R.O., Brownstein, B.H., Cobb, J.P., Tschoeke, S.K., Miller-Graziano, C., Moldawer, L.L., Mindrinos, M.N., Davis, R.W., Tompkins, R.G., Lowry, S.F.: Inflammation and Host Response to Injury Large Scale Collab. Res. Program: A network-based analysis of systemic inflammation in humans. Nature 437, 1032–1037 (2005)
Cobelli, C., Foster, D., Toffolo, G.: Tracer Kinetics in Biomedical Research: From Data to Model. Kluwer Academic/Plenum Publishers (2000)
Cobelli, C., Toffolo, G.: Theoretical aspects and practical strategies for the identification of unidentifiable compartmental systems. ch. 8, pp. 85–91. Pergamon Press, Oxford (1987)
Hanzon, B., Jibetean, D.: Global minimization of a multivariate polynomial using matrix methods. Journal of Global Optimization 27, 1–23 (2003)
Joreskog, K.G.: A general method for analysis of covariance structures. Biometrika 57, 239–251 (1970)
Meziane, D., Shipley, B.: Direct and Indirect Relationships Between Specific Leaf Area, Leaf Nitrogen and Leaf Gas Exchange. Effects of Irradiance and Nutrient Supply. Annals of Botany 88, 915–927 (2001)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, San Francisco (1988)
Shipley, B.: A new inferential test for path models based on directed acyclic graphs. Structural Equation Modeling 7, 206–218 (2000)
Wright, S.: The method of path coefficients. Ann. Math. Statist. 5, 161–215 (1934)
Yoshida, H., Nakagawa, K., Anai, H., Horimoto, K.: Exact parameter determination for Parkinson’s disease diagnosis with PET using an algebraic approach. In: Anai, H., Horimoto, K., Kutsia, T. (eds.) Algebraic Biology 2007. LNCS, vol. 4545, pp. 110–124. Springer, Heidelberg (2007)
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Yoshida, H., Nakagawa, K., Anai, H., Horimoto, K. (2007). An Algebraic-Numeric Algorithm for the Model Selection in Kinetic Networks. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_35
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DOI: https://doi.org/10.1007/978-3-540-75187-8_35
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