Homeostasis as a proportional–integral control system

Figures

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  Fig. 1. Construction of the representative peak for one subject. a Three days of raw data. The shaded time segments were averaged to find a representative peak. The dashed line corresponds to the set point glucose level esp. b The three selected peaks (gray) and the representative peak (black). The set point is taken to be the minimum over the representative peak. Two data points at the set point are added to the representative peak at the end. The fit for this representative peak is shown in the rightmost inlay in Fig. 2.

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  Fig. 2. Scatter plot of the optimal model parameters for all subjects. Shown are A1 and A2, nondimensionalized by the standard deviation of each subject's time series of the glucose level, σe, and the corresponding maximum of the control variable, um. Three illustrative results of the fitting procedure are shown in inlays. In these, the black lines correspond to the representative peaks and the red lines to the output e(t) of the control model (1–3). The normalized input function, F(t)/λ, and the normalized control variable, σeu(t)/λ, are shown in green and blue, respectively.

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  Fig. 3. Distribution of the indicator R = σe(A2 − A1)/um over test subjects. The number of subjects per bin is on the vertical axis, while individual data are indicated with dots on the horixontal axis. The dashed lines labeled a, b, and c correspond to the inlays in Fig. 2.