The fact that the kidneys of a 32-year-old female patient were failing required that she be placed on dialysis. However, the search in her upper limb for a suitable vein was unexpectedly difficult. The major vein on the lateral side of the arm was too small; others were too delicate. Finally, a vein was found on the medial side of the arm that passed through the superficial and deep fascia to join veins beside the brachial artery. Which of the following veins was this?