A 28-year-old woman with type 1 diabetes mellitus presents to the emergency department with a 2-day history of polyuria, polydipsia, and progressive dyspnea. She admits to missing her insulin injections for the past 3 days. On examination: BP 100/65 mmHg, HR 110/min, RR 28/min, temperature 37.2°C. Arterial blood gas shows pH 7.18, HCO₃⁻ 12 mEq/L, PaCO₂ 28 mmHg. Serum glucose is 580 mg/dL, and serum osmolality is elevated. Urine shows 3+ ketones. Which of the following best explains the mechanism of excessive ketone body production in this patient?