UPDATE: After a "Preventable Error" at Cedars-Sinai, Dennis Quaid's Twins Given Accidental Overdose, Fighting for Their Lives

Dennis Quaid's newborn twins are in stable condition after being given an accidental drug overdose at Cedars-Sinai Medical Center in Los Angeles.

"This was a preventable error, involving a failure to follow our standard policies and procedures," Dr. Michael L. Langberg, the Chief Medical Officer of Cedars-Sinai said in a statement to Usmagazine.com "I want to extend my deepest apologies to the families who were affected by this situation," Langberg said.

In a statement to Us, Quaid's rep said: "Dennis and [his wife] Kimberly appreciate everyone's thoughts and prayers and hope they can maintain their privacy at this difficult time."

Thomas Boone and Zoe Grace -- whom Quaid and his wife welcomed via a surrogate on November 8 -- were given a 10,000 units of Heparin, an anti-coagulant used to flush out IV lines and prevent blood clots this past Sunday and began to "bleed out," TMZ.com first reported Tuesday. (Babies typically get 10 units.)

"They are doing well, much better," the twins' grandmother, Delia Buffington, 62, told the New York Daily News. "I certainly am thankful for that."

The newborns, who are in the hospital's neo-natal intensive care unit, are being given protamine sulfate, which reverses the effects of Heparin. Doctors are continuing to closely monitor the three patients who were affected by the drug mix up, according to Langberg.

"We are conducting a comprehensive investigation, cooperating fully with the California Department of Public Health and will take all necessary steps to ensure that this never happens again," the Chief Medical Officer said.