Modeling Subcutaneous Absorption of Fast-Acting Insulin in Type 1 Diabetes

Objective: Subcutaneous (sc) administration of fast-acting insulin analogues is the key in conventional therapy of type 1 diabetes (T1D). A model of sc insulin absorption would be helpful for optimizing insulin therapy and test new open- and closed-loop treatment strategies in in silico platforms. Some models have been published in the literature, but none was assessed on a frequently-sampled large dataset of T1D subjects. The aim here is to propose a model of sc absorption of fast-acting insulin, which is able to describe the data and precisely estimate model parameters with a clear physiological interpretation. Methods: Three candidate models were identified on 116 T1D subjects, who underwent a single sc injection of fast-acting insulin and were compared on the basis of their ability to describe the data and their numerical identifiability. Results: A linear two-compartment model including a subject-specific delay in sc insulin absorption is proposed. On average, a delay of 7.6 min in insulin appearance in the first compartment is detected, then the insulin is slowly absorbed into plasma (in 23% of the subjects) with a rate of 0.0034 min
^-1
, while the remaining diffuses into the second compartment, with a rate constant of 0.028 min
^-1
, and then finally absorbed into plasma with a rate constant of 0.014 min
^-1
. Conclusion: Among the three tested models, the one proposed here is the only one able to both accurately describe plasma insulin data after a single sc injection and precisely estimate physiologically plausible parameters. The model needs to be further tested in case of variable sc insulin delivery and/or multiple insulin doses. Significance: Results are expected to help the development of new open- and closed-loop insulin treatment strategies.