In Vivo Simulations of the Intravenous Dynamics of Submicrometer Particles of pH-Responsive Cationic Hydrogels in Diabetic Patients

A mathematical model describing glucose-dependent pH swelling and insulin release is developed for pH-sensitive cationic hydrogels in which glucose oxidase and catalase have been immobilized and insulin imbibed. Glucose-based swelling and insulin release are simulated for intravenously injected particles at various design conditions. The effects of particle size, the number of injected particles, insulin loading, enzyme loading, monomer functional group loading and pK(a), and hydrogel cross-linking ratio on insulin release and glucose sensitivity are investigated to optimally design the device for use. Increased insulin infusion is shown to result from increasing the number of circulating gels, increasing the collapsed particle size, or decreasing the cross-linking ratio of the system. Release duration is shown to be dependent only upon the particle size and the achievable diffusion coefficient of the system. Glucose sensitivity, as measured by gluconic acid production and by the system pH, is a function of glucose oxidase loading and the concentration and pK(a) of the monomer used in the hydrogel. The necessary submicrometer particle size results in very rapid device insulin depletion. When the device is designed without considering constraints, the resulting release profile resembles that of an on/off switching mechanism. Future work will focus on simulations of swelling and release when the device is implanted in an alternative administration site.