Nonlinear modeling of the insulin-glucose dynamic relationship in dogs

Using experimental time-series measurements of spontaneous variations of plasma glucose and insulin in dogs, we have derived a nonlinear model of the dynamic relationship between spontaneous insulin variations (input) and glucose variations (output) employing our modeling methodology based on Laguerre-Volterra networks. The obtained model is put in a block-structured form that is readily interpretable in a physiological context, since it is comprised of two parallel branches corresponding to the two primary effects of insulin on plasma glucose levels: the reduction of glucose levels (glucolepsis) and the generation of new glucose (glucogenesis). Each branch of the model (glucolepsis and glucogenesis) is composed of a linear filter receiving the insulin input, followed by a static nonlinearity that transforms the output of the filter into the glucoleptic or glucogenic component of the observed plasma glucose level. It must be emphasized that the obtained model form is derived from the data (empirical or inductive modeling) and is not postulated a priori as in previous parametric modeling studies of this system. Although the presented results are preliminary, they seem to support the efficacy of this approach.