  We present a method to estimate parameters in pharmacokinetic (PK) and
pharmacodynamic (PD) models for glucose insulin dynamics in humans. The method
combines 1) experimental glucose infusion rate (GIR) data from glucose clamp
studies and 2) a PK-PD model to estimate parameters such that the model fits
the data. Assuming that the glucose clamp is perfect, we do not need to know
the details of the controller in the clamp, and the GIR can be computed
directly from the PK-PD model. To illustrate the procedure, we use the
glucoregulatory model developed by Hovorka and modify it to have a smooth
non-negative endogeneous glucose production (EGP) term. We estimate PK-PD
parameters for rapid-acting insulin analogs (Fiasp and NovoRapid). We use these
PK-PD parameters to illustrate GIR for insulin analogs with 30% and 50% faster
absorption time than currently available rapid-acting insulin analogs. We
discuss the role of system identification using GIR data from glucose clamp
studies and how such identified models can be used in automated insulin dosing
(AID) systems with ultra rapid-acting insulin.
