Bio-medical Ontologies Maintenance and Change Management

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.