Bio-medical Ontologies Maintenance and Change Management

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The Minimal Model of Glucose Disappearance in Type I Diabetes 313 Anderson-Darling test shows evidence that 7 out of 13 windows (54%) have random residuals (p-value < 0.05) in contrast with 6 (46%) of them (p-value > 0.05). When using the new modelling approach, with the glucose absorption model of Lehmann and Deutsch [16] and the insulin absorption model from Willinska et al. [19], regarded as the new input models (NIM) hereafter, all windows (n = 13) again show residuals that are correlated for both the LMM and MM (p-value < 0.01). The Anderson-Darling test shows evidence for the LMM that 7 out of 13 windows have random residuals, whilst 6 have not, and this is 8 out of 13 for the MM (p-value < 0.05) with 5 showing a non ramdom pattern (p-value > 0.05). If we compare the R 2 value for the LMM reported in columns 1 and 2 in Table 1 obtained for the old and new modelling approaches we can see that differences between the OIM and NIM are not statistically significant according to the Wilcoxon signed rank test (p-value > 0.05). Also, the test did not find evidence that the R 2 values for the MM reported in columns 3 and 4 are different for the old and new modelling approaches (p-value > 0.05). This results suggests that in terms of fitting the new input models have no significant effect when compared to the old approach, and this is true for both the LMM and MM. If we also compare the R 2 values of the LMM and MM together for the old modelling approach reported in columns 1 and 3 in Table 1, the test also confirms these values are statistically equivalent (p-value > 0.05). The same applies to the new modelling strategy between columns 2 and 4 in Table 1. According to this analysis both the LMM and MM provide a goodness of fit that is equivalent in terms of the R 2 measure, for both the old and new input modelling approaches. The results obtained highlight the minimal model limitations in following the experimental data despite the fact that new models of superior quality in terms of data fitting have been included. According to this, the lack of insulin measurements together with the minimal model physiological constraints on the system dynamics can be said to be the possible sources of error. However, the fact that residuals still show a systematic pattern could also be explained by the presence of structured noise. A preliminary study has been carried out in this respect but conclusions can not be drawn at the present stage. Further studies should be carried out for better models to be proposed and/or structured noise to be removed. 6 Conclusions First of all, this study confirms that the minimal model of glucose disappearance, either the classic or linear version (MM and LMM respectively), is unable to describe the observed experimental data possibly as a result of the physiological constraints imposed by the minimal model approach on the system dynamics, together with possible errors derived from the unmeasured insulin dynamics. If including insulin measurements or a complex model of the glucose dynamics would result in a better approximation remains to be tested.
314 M. Fernandez, M. Villasana, and D. Streja The presence of structured noise could also explain the fact that residuals still show a systematic pattern. Further work should be carried out to test this hypothesis. In the second place, this study also confirms that the LMM is equivalent to the MM in terms of data fitting for the experimental data under study. This result, together with the experiments already reported in the literature, [10, 14, 9, 15, 12] they have all contributed to this linear approximation to be further validated. References 1. Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley Series in Probability and Statistics. Wiley-Interscience, Hoboken (2003) 2. Anderson, T.W., Darling, D.A.: A test of goodness of fit. J. Am. Stat. Assoc. 49, 765–769 (1954) 3. Bergman, R.N., Ider, Y.Z., Bowden, C.R., Cobelli, C.: Quantitative estimation of insulin sensitivity. Am. J. Physiol. 236(6), E667–E677 (1979) 4. Carson, E.R., Cobelli, C., Finkelstein, L.: The Mathematical Modeling of Metabolic and Endocrine Systems. John Wiley & Sons, New York (1983) 5. Caumo, A., Bergman, R.N., Cobelli, C.: Insulin sensitivity studies from meal tolerance tests in normal subjects: a minimal model index. J. Clin. Endocrinol. Metab. 85(11), 4396–4402 (2000) 6. Cobelli, C., Mari, A.: Validation of mathematical models of complex endocrinemetabolic systems. A case study on a model of glucose regulation. Med. Biol. Eng. Comput. 21, 390–399 (1983) 7. Cobelli, C., Ruggeri, A.: Evaluation of portal/peripheral route and of algorithms for insulin delivery in the closed-loop control of glucose in diabetes. A modeling study. IEEE. Trans. Biomed. Eng. BME-30(2), 93–103 (1983) 8. Cobelli, C., Vicini, P., Toffolo, G., Caumo, A.: The hot IVGTT minimal models: simultaneous assessment of disposal indices and hepatic glucose release. In: Lovejoy, J., Bergman, R.N. (eds.) The minimal model approach and determinants of glucose tolerance, vol. 262, pp. E968–E975. Louisiana State University Press, Baton Rouge (1997) 9. Fernandez, M., Acosta, D., Quiroz, A.: Improving the precision of model parameters using model based signal enhancement and the linear minimal model following an IVGTT in the healthy man. Appl. Math. Comput. 196(1), 185–192 (2008) 10. Fernandez, M., Acosta, D., Villasana, M., Streja, D.: Enhancing parameter precision and the minimal modeling approach in type I diabetes. In: Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 797–800. IEEE Press, Los Alamitos (2004) 11. Fernandez, M., Atherton, D.P.: Linearisation and simplification of a nonlinear model of the glucose regulatory system. Diabetes Nutr. Metab. 11(1), 86 (1998); Abstracts, Symposium on Computers in Diabetes 1998 12. Fernandez, M., Atherton, D.P.: Analysis of insulin sensitivity estimates from linear models of glucose disappearance. Appl. Math. Comput. 167(1), 528–538 (2005) 13. Fernandez, M., Villasana, M.: Letter to the editor: on a model of glucose absorption. Med. Eng. Phys. 30(4), 538–540 (2008) 14. Fernandez, M., Villasana, M., Streja, D.: Glucose dynamics in type I diabetes: insights from the classic and linear minimal models. Comput. Biol. Med. 37(5), 611–627 (2007) 15. Fernandez-Chas, M.: Insulin sensitivity estimates from a linear model of glucose disappearance. Ph.D. thesis, University of Sussex, Brighton, UK (2001)
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Amandeep S. Sidhu and Tharam S. Dil
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Amandeep S. Sidhu and Tharam S. Dil
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Preface The molecular biology commu
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Preface VII biomedical systems, and
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X Contents Mining Clinical, Immunol
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2 A.S. Sidhu, M. Bellgard, and T.S.
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Towards Bioinformatics Resourceomes
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2 The New Waves Towards Bioinformat
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2.4 Semantic Web Towards Bioinforma
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A Summary of Genomic Databases: Ove
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Appendix A Summary of Genomic Datab
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Protein Data Integration Problem Am
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Protein Data Integration Problem 57
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Fig. 3. Class Hierarchy of Protein
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