lateral thoracic vein lateral thoracic vein the lateral thoracic vein (sometimes debatably referred to as the long thoracic vein) is a tributary of the axillary vein. it runs with the lateral thoracic artery and drains the serratus anterior muscle and the pectoralis major muscle. lateral thoracic veinthe veins of the right axilla, viewed from in front. (lateral thoracic vein not labeled but region is visible.)detailsdrains toaxillary veinarterylateral thoracic arteryidentifierslatinvena thoracica lateralista98a12.3.08.011ta24971fma71210anatomical terminology normally, the thoracoepigastric vein exists between this vein and superficial epigastric vein (a tributary of femoral vein), to act as a shunt for blood if the portal system (through the liver) develops hypertension or a blockage.