Angelica Sabuco, 2, right, and her twin sister Angelina play together at the Lucile Packard Children's Hospital, Monday, Oct. 31, 2011 in Stanford, Calif. The Stanford hospital is preparing for surgical procedure to separate the two-year old girls, who were born joined at the chest and abdomen. (AP Photo/Marcio Jose Sanchez)

(AP) -- Surgery is under way in Northern California to separate twin girls joined at the chest and abdomen.

The complex procedure to separate Angelina and Angelica Sabuco, of San Jose, began at Stanford University's Lucile Packard Children's Hospital around 6:30 a.m. Tuesday.

Hospital spokeswoman Reena Mukamal says that if all goes according to plan, the 2-year-olds will be out of surgery by mid-afternoon.

The operation will involve cutting along the girls' skin and muscle and separating their diaphragms and livers.

Lead surgeon Gary Hartman says severing the will be the riskiest part of the procedure because of potential .

Hartman has done five separation procedures at medical centers around the country and says he expects the operation to go well.