A 54-year-old man is hospitalized for necrotizing pancreatitis. His course has been complicated by acute respiratory distress syndrome requiring ventilator support. He is hemodynamically unstable and requires an intravenous norepinephrine infusion to maintain a mean arterial blood pressure of 65 mm Hg. On the third hospital day, he develops increasing norepinephrine and oxygen requirements and increasing ventilator airway pressures, and he becomes oliguric. Medications are propofol and fentanyl.

On physical examination, blood pressure is 80/60 mm Hg, pulse rate is 92/min, and respiration rate is 12/min. Estimated central venous pressure is 12 cm H2O. Heart sounds are normal. There are diffuse pulmonary crackles. The abdomen is modestly distended and tense. Bilateral lower extremity and flank edema are present.

Laboratory studies:

Hemoglobin

9.0 g/dL (90 g/L)

INR

2.0

Creatinine

2.1 mg/dL (185.6 µmol/L) (on admission, 0.9 mg/dL [79.6 µmol/L])

Urine sodium

<10 mEq/L (10 mmol/L)

Urinalysis

Specific gravity 1.022; pH 6.0; 0-1 erythrocytes/hpf; 0-2 leukocytes/hpf; occasional hyaline casts

Kidney ultrasound reveals normal-sized kidneys and no hydronephrosis.

Which of the following is the most appropriate next step in management?