You are requested to evaluate a 15-year-old Caucasian girl who has been feeling unwell for a few days. She has been experiencing intermittent fevers and chills and complains of extreme fatigue. Suddenly, half an hour before her admission to the hospital, she lost all vision in her left eye.

During the examination, the patient appears pale and unwell. Her vital signs are as follows: temperature 38.5°C, pulse 120/minute, regular, blood pressure 100/55 mmHg, and respiratory rate 22/minute. A pansystolic murmur is audible at the apex and lower left sternal border. Both lungs are clear.

The right pupil reacts normally to light, but there is no reaction from the left pupil, which remains fixed and dilated. The patient has complete loss of vision in the left eye, and the left fundus appears paler than the right, with no papilloedema. The only additional finding on examination was a paronychia on her right thumb, and light pressure on the nail bed was very uncomfortable.

Investigations reveal the following results: Hb 109 g/L (115-165), WBC 14.1 ×109/L (4-11), Neutrophils 9.0 ×109/L (1.5-7), Lymphocytes 4.8 ×109/L (1.5-4), Monocytes 0.29 ×109/L (0-0.8), Eosinophils 0.01 ×109/L (0.04-0.4), and Platelets 550 ×109/L (150-400).

What is the most crucial investigation to determine the cause of her illness?