Final answer:
The superior epigastric artery and inferior epigastric artery supply the upper and lower anterior abdominal walls respectively, and both run through the rectus sheath.
Step-by-step explanation:
The superior epigastric artery arises from the internal thoracic artery and runs through the posterior rectus sheath before entering the rectus abdominis muscle. It supplies the upper anterior abdominal wall. The inferior epigastric artery originates from the external iliac artery and ascends within the rectus sheath, also supplying the lower anterior abdominal wall. Both arteries are important for the collateral circulation of the abdominal wall.