Abstract
Compartmental models are a very popular tool for the analysis of experiments in living systems. There are three main aspects that have to be taken into account: the degree of detail of the model, its a priori identifiability and thea posteriori (numerical) identifiability. In some cases, where standard approaches are adopted, the models can be eithera priori ora posteriori unidentifiable. The paper proposes model identification within a Bayesian framework, to solvea posteriori unidentifiability problems. In particular, a stochastic simulation algorithm is proposed to perform a Bayesian identification of compartmental models, and an empirical Bayesian technique is proposed to propagate information among multiple experiments. The power of this methodology was demonstrated by evaluating the kinetics of thiamine under several experimental conditions. The complexity of the existing model (nine parameters) and limited experimental data (8/12 for each model) causeda posteriori identifiability problems when standard approaches were adopted. The application of the methodology identifies all 28 models (four tissues under seven different conditions).
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References
Audoly, S., D'Angio, L., Saccomani, M. P., andCobelli, C. (1998): ‘Global identifiability of linear compartmental models — a computer algebra algorithm’,IEEE Trans. Biomed. Eng.,45, pp. 36–47
Bellazzi, R., Magni, P., andDe Nicolao, G. (1997): ‘Dynamic probabilistic networks for modelling and identifying dynamic systems: a MCMC approach’,Intell. Data Anal. Int. J.,1, (4), pp. 245–262
Bettendorff, L. (1994): ‘Thiamine in excitable tissue: reflections on a non-cofactor role’,Metab. Brain Dis.,9, pp. 183–209
Carlin, B. P., andLouis, T. A. (1996): ‘Bayes and empirical Bayes methods for data analysis’ (Chapman & Hall, London, 1996)
Carson, E. R., Cobelli, C., andFinkelstein, L. (1983): ‘The mathematical modeling of metabolic and endocrine systems’ (John Wiley, New York, 1983)
Cobelli, C., andDiStefano, J. J. III. (1980): ‘Parameter and structural identifiability concepts and ambiguities: a critical review and analysis’,Am. J. Physiol.,239, pp. R7-R24
Cooper, J. R., andPincus, J. H. (1979): ‘The role of thiamine in nervous tissue’,Neurochem. Res.,4, pp. 223–239
Gilks, W. R., Richardson, S., andSpiegelhalter, D. J. (1996): ‘Markov chain Monte Carlo in practice’ (Chapman & Hall, London, UK, 1996)
Godfrey, K. R., andDiStefano, J. J. III. (1987): ‘Identifiability of model parameters’ inWalter, E. (Ed.): ‘Identifiability of parametric models’ (Pergamon, Oxford, UK, 1987), chap. 1, pp. 1–20
Jacquez, J. A. (1996): ‘Compartmental analysis in biology and medicine’ (BioMedware, Ann Arbor, 1996)
Magni, P., Bellazzi, R., andDe Nicolao, G. (1998): ‘Bayesian function learning using MCMC methods’,IEEE Trans. Pattern Anal. Mach. Intell.,20, (12), pp. 1319–1331
Nauti, A., Patrini, C., Reggiani, C., Merighi, A., Bellazzi, R., andRindi, G. (1997): ‘In vivo study of kinetics of thiamine and its phosphoesters in the deafferented rat cerebellum’,Metabolic Brain Dis.,12, pp. 145–159
Patrini, C., Perucca, E., Reggiani, C., andRindi, G. (1993): ‘Effects of phenytoin on the in vivo kinetics of thiamine and its phosphoesters in rat nervous tissues’,Brain Res.,628, pp. 179–186
Raftery, A. E., andLewis, S. M. (1996): ‘Implementing MCMC’ inGilks, W. R., Richardson, S., andSpiegelhalter, D. J. (Eds): ‘Markov chain Monte Carlo in practice’ (Chapman & Hall, London, UK, 1996), chap. 7, pp. 115–130
Reggiani, C., Patrini, C., andRindi, G. (1984): ‘Nervous tissue thiamine metabolism in vivo. I. Transport of thiamine and thiamine monophosphate from plasma to different brain regions of the rat’,Brain Res.,293, pp. 319–327
Rindi, G. (1996): ‘Thiamin’ inZiegler, E. E., andZiles, J. (Eds): ‘Recent knowledge in nutrition’ (ILSI, Washington, DC, 1996), pp. 160–166
Rindi, G., Patrini, C., Comincioli, V., andReggiani, C. (1980): ‘Thamine content and turnover rates of some rat nervous regions, using labeled thiamine as a tracer’,Brain Res.,181, pp. 369–380
Rindi, G., De Giuseppe, L., andSciorelli, G. (1968): ‘Thiamine monophosphate a normal constituent of rat plasma’,J. Nutrit.,94, pp. 447–454
Rindi, G., Comincioli, V., Reggiani, C., andPatrini, C. (1984): ‘Nervous tissue thiamine metabolism in vivo. II. Thiamine and its phosphoesters dynamics in different brain regions and sciatic nerve of the rat’,Brain Res.,293, pp. 329–342
Rindi, G., Comincioli, V., Reggiani, C., andPatrini, C. (1987): ‘Nervous tissue thiamine metabolismin vivo. III. Influence of ethanol intake on the dynamics of thiamine and its phosphoesters in different brain regions and sciatic nerve of rat’,Brain Res.,413, pp. 23–35
SAAM Institute Inc. (1997): ‘SAAM II: user guide’ (University of Washington)
Wakefield, J., Smith, A. F. M., Racine-Poon, A., andGelfand, A. (1994): ‘Bayesian analysis of linear and nonlinear population models using the Gibbs sampler’,Appl. Statist.,41, pp. 201–221
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Magni, P., Bellazzi, R., Nauti, A. et al. Compartmental model identification based on an empirical Bayesian approach: The case of thiamine kinetics in rats. Med. Biol. Eng. Comput. 39, 700–706 (2001). https://doi.org/10.1007/BF02345445
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DOI: https://doi.org/10.1007/BF02345445