Use of a dynamic systems framework to quantify the insulin transition gap to reduce treatment complications in diabetic ketoacidosis

Diabetic ketoacidosis (DKA) affects over 200,000 adult hospitalizations annually in the United States. Despite established treatment protocols, iatrogenic complications remain common, with hypoglycemia occurring in 5–25% of cases. The transition from intravenous to subcutaneous insulin is particularly vulnerable to rebound ketoacidosis due to the pharmacokinetic mismatch between rapid intravenous (IV) insulin clearance and delayed subcutaneous (SC) absorption. We developed a three-compartment ordinary differential equation model incorporating plasma glucose, intravenous insulin, and subcutaneous insulin depot dynamics. Through dynamical system and dimensional analysis, we derived timescales governing DKA treatment to allow better prediction of effect when transitioning from IV to SC insulin. Mathematical analysis identified three distinct timescales governing DKA treatment: rapid insulin clearance (τI ≈ 5–10 min), intermediate glucose decline (τG ≈ 60 min), and slow subcutaneous absorption (τS = 2–24 hr). A disparity between these timescales quantifies the ‘insulin gap’ phenomenon. Sensitivity analysis of the composite dimensionless parameter s (renamed here ‘glucose disposal efficiency per unit insulin’) revealed the largest influence on time to glucose target, explaining inter-patient variability in insulin requirements during acute illness. A supplementary analysis directly varying the physiological insulin sensitivity SI (0.5×–2× baseline) confirmed this heterogeneity, producing a 3.5-fold range in time to target (2.85–9.93 h). This dynamical systems framework reconfirms the current recommendations about the need for an overlap between IV insulin and the SC insulin and furthermore provides quantitative recommendation for the IV-SC insulin overlap timing and dextrose initiation thresholds. The model-derived dimensionless parameters offer trajectory-aware metrics for protocol optimization and could guide personalized insulin titration in patients with altered insulin sensitivity. Future applications include integration with continuous glucose and ketone monitoring for real-time risk stratification.