Unidentifiability of s_i from measurements of glucose off steady state.

The upper plot shows the time-course of plasma glucose concentration in the βIG model in a regime of periodic inputs (pulses) of external glucose from meals, similarly as in Figs 2 and 3. At time 100000 there is a sudden change in the insulin sensitivity parameter, s_i, which is halved as a result of external perturbations. This produces an abrupt change in the glucose level, which then undergoes a long period of adaptation until its baseline returns to the original level. The lower plots show in more detail the behaviour of glucose and the other two state variables, insulin and β-cell mass, in the hours immediately before and after the change in s_i. These plots illustrate that it is not possible to infer the value of the s_i parameter in the βIG model by measuring only glucose, even if measurements off steady state are available and p is known. This is indicated by the fact that the dynamic time-course of glucose concentration (G) is identical for and (left plot in lower row), as long as the initial conditions of the two unmeasured states, insulin (middle plot) and β-cell mass (right plot), are multiplied by the same factor k. The figure shows results for k = 3 and .