The abdominal wall is supplied by the follow arteries:

  1. superior epigastric artery
  2. inferior epigastric artery
  3. lumbar arteries
  4. deep circumflex iliac

Note: the inferior epigastric artery runs superiorly on the transversalis fascia and enters the arcuate line to gain the rectus sheath. 

Note: the superior epigastric artery enters the rectus sheath superiorly just inferior to the 7th costal cartilage.