A client with type 1 diabetes mellitus presents to the emergency department with nausea, vomiting, and abdominal pain. Assessment findings include: Blood glucose: 420 mg/dL. Arterial pH: 7.25. Serum bicarbonate: 15 mEq/L. Respirations: deep and rapid. Breath odor: fruity. Which pathophysiologic process is primarily responsible for this client's condition?