Pharmacokinetical models of subcutaneous injection of insulin analogues for type 1 diabetes

Subcutaneous injection of exogenous insulin or insulin analogues needs to be performed one or more times daily for type 1 diabetics. The timing and dosage of insulin administration have been a critical research area since the invention of insulin analogues. Several mathematical models have been proposed and some are applied clinically in modeling various insulin therapies. However, these models are not systematic since the plasma insulin concentration has to be computed separately. Furthermore, no analytical study has been done in all existing models. In this paper, we propose two systematic and simplified models to model the subcutaneous injection of rapid-acting insulin analogues and long-acting insulin analogues, respectively. The profiles of plasma insulin concentrations obtained from these two models are in agreement with the experimental data. We also systematically analyze the dynamics of insulin analogue, and plasma insulin concentrations.