This patient should be further evaluated with echocardiography; she likely has hemolysis due to her mechanical aortic valve. She has evidence of hemolytic anemia based on her low serum haptoglobin and high lactate dehydrogenase levels. The peripheral blood smear shows schistocytes, which are often found in clinical conditions in which erythrocytes are damaged in small blood vessels (microangiopathic hemolytic anemia), but schistocytes may also occur from trauma in larger blood vessels (macroangiopathic hemolytic anemia). The patient has a mechanical heart valve with a significant murmur, suggesting possible valve dysfunction, and, in the absence of other likely causes of a microangiopathic hemolytic anemia, this is likely the cause of her hemolysis. Therefore, echocardiography to identify a regurgitant jet or paravalvular leak, suggested by the murmur present in this patient, would be the most appropriate next diagnostic study. In patients with suspected valve-associated hemolysis, transesophageal echocardiography is the preferred study because of its ability to effectively visualize the aortic valve structures for this potential complication. Patients with chronic intravascular hemolysis may ultimately develop iron deficiency anemia as the heme iron released from the hemolysis passes through the kidneys and is lost in the urine.

Thrombotic thrombocytopenic purpura (TTP) is a cause of microangiopathic hemolytic anemia and should be considered in this patient. However, her normal platelet count and the slowly progressive onset of her symptoms make this diagnosis unlikely. In patients with TTP, an ADAMTS-13 assay may be helpful in estimating prognosis, but would not be an appropriate study in this patient.

Disseminated intravascular coagulation (DIC) is an acquired form of microangiopathic hemolytic anemia. Acute DIC is associated with evidence of accelerated fibrinolysis, including increased fibrin degradation products and D-dimer. However, this patient has no other clinical findings consistent with DIC (such as bleeding or thrombocytopenia), making this an unlikely diagnosis and a D-dimer measurement unnecessary.

The direct antiglobulin (Coombs) test is used to determine an autoimmune cause of hemolytic anemia. However, neither warm nor cold autoimmune hemolytic anemia causes schistocytes as seen in this patient's blood smear, making this diagnosis unlikely. Therefore, this test would be of low diagnostic yield.