A 52-year-old man with a 15-year history of type 2 diabetes mellitus presents with a 1-week history of severe vomiting and abdominal pain. He has been fasting due to illness. On examination: BP 92/58 mmHg, HR 118/min, RR 32/min, and breath has a fruity odor. Laboratory findings: pH 7.22, HCO₃⁻ 10 mEq/L, PaCO₂ 24 mmHg, glucose 320 mg/dL, β-hydroxybutyrate 6.8 mmol/L (normal <0.6). Serum osmolality is 310 mOsm/kg. Urine ketones are strongly positive. Which tissue is responsible for the primary synthesis of the ketone bodies that are accumulating in this patient's blood?