Question

A 22-year-old woman with a history of type 1 diabetes mellitus is admitted to the intensive care unit with a two-day history of high fever, productive cough, and progressive lethargy. She has been unable to tolerate oral intake and missed her last four doses of insulin. On arrival, her temperature is $38.9^\circ\text{C}$ ($102^\circ\text{F}$), pulse is $132\text{/min}$, respiratory rate is $36\text{/min}$, and blood pressure is $88/54\text{ mm Hg}$. Oxygen saturation is $89\%$ on ambient air. Physical examination reveals deep, rapid breathing and bronchial breath sounds with crackles in the right lower lung field. Laboratory studies show a serum glucose of $510\text{ mg/dL}$, sodium of $134\text{ mEq/L}$, potassium of $4.9\text{ mEq/L}$, chloride of $98\text{ mEq/L}$, and bicarbonate of $10\text{ mEq/L}$. A chest radiograph confirms a right lower lobe consolidation. The patient is resuscitated with intravenous normal saline, started on a continuous insulin infusion, and administered intravenous ceftriaxone and azithromycin. Two hours later, her respiratory effort wanes and she becomes severely hypoxemic, necessitating endotracheal intubation. She is placed on volume assist-control mechanical ventilation with a tidal volume of $400\text{ mL}$, a respiratory rate of $14\text{/min}$, $FiO_2$ of $0.70$, and positive end-expiratory pressure (PEEP) of $5\text{ cm }H_2O$. Thirty minutes later, arterial blood gas analysis reveals:

$pH$: $7.15$
$PaCO_2$: $38\text{ mm Hg}$
$PaO_2$: $72\text{ mm Hg}$
$HCO_3^-$: $10\text{ mEq/L}$

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