Live Operating room footage. Vascular surgeon uses laser to treat saphenous vein and phlebectomy for varicosities. Here are some explanation of before mentioned terms. The vascular surgeon is trained in the diagnosis and management of diseases affecting all parts of the vascular system except that of the heart and brain. The saphenous veins serve as the principal veins running superficially (near the surface) up the leg. Phlebectomy is surgical removal or all or part of a vein; sometimes done in cases of severe varicose veins. Varicosity – varix or varicose condition in which a vein is swollen and tortuous.