, Volume 17, Issue 1, pp 67-87

Modeling absorption kinetics of subcutaneous injected soluble insulin

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Abstract

Absorption of subcutaneously injected soluble insulin deviates markedly from simple first-order kinetics and depends both on the volume and concentration of the injected solution. This paper presents a model of the absorption process in which insulin is presumed to be present in subcutis in a low molecular weight form, a high molecular weight form, and an immobile form where the molecules are bound to the tissue. The model describes how diffusion and absorption gradually reduce the insulin concentrations in the subcutaneous depot and thereby shift the balance between the three forms in accordance with usual laws of chemical kinetics. By presuming that primarily low molecular weight insulin penetrates the capillary walls, the model can account for experimentally observed variations in the absorption rate over a wide range of volumes and of concentrations. The model is used to determine the effective diffusion constant D for insulin in subcutis, the absorption rate constant B for low molecular weight insulin, the equilibrium constant Q between high and low molecular weight insulin, the binding capacity C for insulin in the tissue, and the average life time T for insulin in its bound state. Typical values for a bolus injection in the thigh of fasting type I diabetic patients are D=0.9 × 10−4 cm2/min, B=1.3 × 10−2/min, and Q=0.13 (ml/IU)2. Binding of insulin in the tissue is significant only at small concentrations. The binding capacity is of the order of C=0.05 IU/cm3 with a typical average life time in the bound state of T=800 min. Combined with a simplified model for distribution and degradation of insulin in the body, the absorption model is used to simulate variations in plasma free insulin concentrations with different delivery schedules, i.e., bolus injection and dosage by means of an infusion pump. The simulations show that a pump repetition frequency of 1–2 per hr is sufficient to secure an almost constant plasma insulin concentration.