Final answer:
The posterior interventricular artery, a branch of the right coronary artery, runs along the posterior interventricular sulcus and supplies oxygenated blood to the walls of the ventricles.
Step-by-step explanation:
The structure in question is the posterior interventricular artery, also known as the posterior descending artery. It is a branch of the right coronary artery that traverses the posterior interventricular sulcus towards the apex of the heart. The artery provides oxygenated blood to the walls of the ventricles, more specifically to the interventricular septum and sections of both the left and right ventricles. Adjacent to the artery is the middle cardiac vein, which drains the regions supplied by the posterior interventricular artery.