The most likely diagnosis is intrapulmonary shunt. This patient's profound hypoxia is most likely due to intrapulmonary shunting of blood through his collapsed right lower lobe. Evidence of a collapsed right lower lobe is indicated by the triangular opacity above the diaphragm on the right side on his chest radiograph. Right-to-left intrapulmonary shunts may be anatomical or physiological, but all result in hypoxemia that does not readily correct with supplemental oxygen, as seen in this patient. This patient's physiological shunt results in perfusion of nonventilated alveoli of the collapsed right lower lobe. In most situations, a lobar collapse will not cause such severe shunting because of hypoxic vasoconstriction of arterioles in parts of the lung that are not ventilated; however, in some cases, such as this patient, this compensatory mechanism directing blood flow to other aerated areas of the lung is ineffective.

Hepatopulmonary syndrome, intracardiac shunt, and pulmonary arteriovenous malformation are all examples of anatomic shunts. Although these conditions can be responsible for hypoxemia that is difficult to correct with supplemental oxygen, this patient's trauma, splinting, and abnormal radiographic findings suggest a lower lobe collapse as the most likely diagnosis. In conditions of diagnostic uncertainty, a bubble contrast echocardiogram could be performed. These anatomic shunts are associated with the appearance of left atrial or ventricular bubbles after several cardiac cycles.

Hepatopulmonary syndrome should be suspected in patients with cirrhosis who develop hypoxemia in the absence of other causes. Their shunt worsens with upright posture (orthodeoxia). However, this is not a likely diagnosis in a patient without evidence of cirrhosis.