The woman who was riding in a bike lane when she was hit by a car Saturday morning on the North Shore has been identified as Claire Matthews, 31, of Hale'iwa.

Matthews is the wife of Petty Officer Russ Matthews, a rescue swimmer with the Coast Guard, said Coast Guard Lt. John Titchen.

The couple have been in Hawai'i since the summer of 2007, when Russ Matthews was assigned to Air Station Barbers Point, Titchen said. Earlier, they were at Air Station Borinquen, Puerto Rico.

On Saturday, Claire Matthews was taken to The Queen's Medical Center in critical condition and her two sons, ages 5 and 3, were taken to Queen's in serious condition. Matthews is still in critical condition, but both of her children are OK, police said.

Members of the Coast Guard are standing vigil at the hospital with the Matthews family, Titchen said.

Capt. Steve Mehling, acting Coast Guard district commander, said the Coast Guard is praying for the best.

"Since the time of the accident, our thoughts and prayers have been with our fellow Coast Guardsman, Petty Officer Mat-thews, and his family," Mehling said.

Matthews was riding her bicycle near Ke Waena Road, in Pupukea, with her two children behind her in a two-wheel trailer when a Nissan sedan driven by a 44-year-old Hale'iwa woman veered into the bike lane and hit her head-on, police said.

Matthews was thrown from the bicycle, hit the car's windshield and rolled onto the shoulder of the highway, suffering critical head injuries, police said. Her two children in the trailer were pushed by the car for 80 feet until the car came to a stop.