Systemically modeling the dynamics of plasma insulin insubcutaneous injection of insulin analogues for type 1 diabetes - Jiaxu Li; Yang Kuang (Mathematical Biosciences and Engineering)
Type 1 diabetics must inject exogenous insulin or insulinanalogues one or more times daily. The timing and dosage ofinsulin administration have been a critical research area sincethe invention of insulin analogues. Several pharmacokineticalmodels have been proposed, and some are applied clinically inmodeling various insulin therapies. However, their plasma insulinconcentration must be computed separately from the models' output.Furthermore, minimal analytical study was performed in theseexisting models. We propose two systemic and simplified ordinarydifferential equation models to model the subcutaneous injectionof rapid-acting insulin analogues and long-acting insulinanalogues, respectively. Our models explicitly model the plasmainsulin and hence have the advantage of computing the plasmainsulin directly. The profiles of plasma insulin concentrationsobtained from these two models are in good agreement with theexperimental data. We also study the dynamics of insulinanalogues, plasma insulin concentrations, and, in particular, theshape of the dynamics of plasma insulin concentrations.