Dennis Quaid's Newborn Twins in Medical Nightmare

TMZ has learned that Dennis Quaid's newborn twins are fighting for their lives after being inadvertently overdosed at Cedars-Sinai Medical Center in Los Angeles.

Sources tell us the twins -- Thomas Boone and Zoe Grace -- were accidentally given a massive dose of Heparin, an anti-coagulant. Babies typically get 10 units. Our sources say they were each mistakenly given 10,000 units. The drug is used to flush out IV lines and prevent blood clots. We're told one dose was given on Sunday morning, another on Sunday evening.

We're told late Sunday night, both babies started to "bleed out." Both babies are now at Cedars in the neo-natal intensive care unit where we're told they are stable.

The twins were born to Quaid and wife Kimberly Buffington November 8 via surrogate.

A rep for Quaid did not immediately return our call for comment and there was no immediate comment from Cedars.

We're told a technician stored the Heparin in the wrong place, and when a nurse grabbed the medicine for the babies without looking -- it was the wrong dosage.

A source says the babies are now being given Protamine, which reverses the effects of Heparin.

UPDATE: We're told as many as thirteen patients at Cedars were mistakenly given the overdose of Heparin, but the effects are more critical because of the age and weight of the twins.