Round ligament of the uterus-the round ligament of the uterus passes through the deep inguinal ring and runs through the inguinal canal. it is a derivative of the gubernaculum, a structure which pulled the gonads into place during embryonic development. in males, the scrotal ligament is what remains from the gubernaculum. also keep in mind that, in males, the spermatic cord passes through the deep inguinal ring. of the other answer choices, the ilioinguinal nerve is the only other one that courses through the inguinal canal. remember-it leaves through the superficial ring and gives off the anterior labial or scrotal branch as a cutaneous continuation. however, the ilioinguinal nerve does not pass through the deep ring - it enters the inguinal canal on the side. the iliohypogastric nerves run between the internal oblique and transversus abdominis in the abdominal wall, piercing the internal oblique at the anterior superior iliac spine to travel deep to just the external oblique. the inferior epigastric artery runs between the transversus abdominis and the peritoneum, forming the lateral umbilical fold. the medial umbilical ligament is the obliterated umbilical artery-it lies within the medial umbilical fold of peritoneum.