Bio-medical Ontologies Maintenance and Change Management

The Minimal Model of Glucose Disappearance in Type I Diabetes 305
1. At least one of the coefficients of variation (CVs) was greater than 100%. The
CV was estimated as the ratio between the standard deviation and mean value
of each estimated parameter [4].
2. The R 2 measured was less than 0.80. This measure is interpreted as the fraction
of the total variance of the data that is explained by the model, and the sum of
squared residuals (SSR).
4.1 Goodness of Fit
The models were built in MATLAB/Simulink in a PC based environment and parameter
estimation was performed using nonlinear least squares methods from Matlab/Optimization
Toolbox.
The goodness of fit was qualitatively assessed by plotting against time the predicted
model response and the experimental data. A quantitative measure was also
given by means of the R 2 value.
The Wilcoxon signed rank test was used to evaluate optimal parameter differences
between the R 2 values obtained by the old and new input models approaches,
for both the MM and LMM models. This test returns the significance for a test of
the null hypothesis that the median difference between two samples is zero. The null
hypothesis H0 that the medians are not significantly different is accepted when the
p-value is greater than the α significance level and is rejected otherwise.
4.2 Analysis of Residuals
The residuals were tested for randomness by means of the Anderson-Darling test
[2] and plotted against time to detect possible outliers or systematic deviations.
The correlation of errors was also studied by computing the Pearson’s correlation
coefficient between e(1)...e(N − 1) and e(2)...e(N) for each data set, where e(i) is
the i-th residual and N is the total number of points, and performing a t-test on the
transformed coefficients [1].
5 Results
The output of the simulations are displayed in Fig. 7 to Fig. 19. In each figure the
first subplot shows the amount of carbohydrate ingested (right panel) and the rate of
glucose absorption RA (left panel), the second subplot includes the bolus injection
and continuous insulin infusion IR (right) together with the simulated plasma insulin
dynamics y2 (left) and finally the third subplot shows the dynamics of plasma
glucose concentration y1.
Overall the precision of the model parameters is good (CV