HOUSTON (CBS/AP) – The Houston hospital treating Rep. Gabrielle Giffords said Sunday that her condition is improving daily, but gave no update on the buildup of brain fluid that has kept the Arizona congresswoman in intensive care.

A hospital statement said Giffords would continue to receive therapy in the intensive care unit “until her physicians determine she is ready for transfer” to a nearby center where she would begin a full rehabilitation program.

They said the next medical updates would be provided when that happens.

Giffords was flown to Memorial Hermann Texas Medical Center Hospital on Friday from Tucson, where she was shot in the forehead on January 8 while meeting with constituents.

CBS News correspondent Don Teague reports that doctors had hoped to move Giffords into the rehabilitation unit by this stage. The congresswoman is still unable to speak and is experiencing weakness or paralysis on her right side.

“It’s improving,” said Dr. Gerard Francisco, the chief medical officer at Hermann hospital. “We’re continuing to assess that.”

Meanwhile, investigators have been poring over surveillance video, interviewing witnesses and analyzing items seized from the suspected shooter’s home as they build a case in the assassination attempt against Giffords.

The case against Jared Lee Loughner likely will take years to play out as it goes through the many phases of the criminal justice system: prosecutions by both federal and state authorities, proceedings over whether to move the case to a different venue, a possible insanity defense by Loughner and prosecutors’ likely push for the death penalty.

At a news conference shortly after Giffords’ arrival in Houston, doctors said she had been given a tube to drain excess cerebrospinal fluid. Everyone makes such fluid, but an injury can cause the fluid to not be cleared away as rapidly as normal. A backup can cause pressure and swelling within the brain.

“It’s a common problem,” occurring in 15 to 20 percent of people with a brain injury or brain surgery, said Dr. Reid C. Thompson, chairman of neurological surgery at Vanderbilt University Medical Center in Nashville, who is not involved in Giffords’ care.

Another possible reason for a drainage tube: “After a gunshot wound to the head and brain where there is a lot of soft tissue injury, it is common to develop a leak of spinal fluid. This raises the risk of a meningitis and slows down wound healing,” he said.

The tube is a short-term solution that doctors usually don’t use for longer than a week or two because of the risk of infection, said Dr. Steve Williams, rehab chief at Boston Medical Center and Boston University School of Medicine.

If the problem persists, this temporary catheter can be converted to a permanent one called a shunt. That involves an hour-long surgery to tunnel a thin tube from inside the brain down the neck and under the skin to the abdomen, where the fluid can drain and be dispersed in the belly, Williams said.

That is less than ideal – those can clog over time, requiring medical attention.

(©2011 CBS Local Media, a division of CBS Radio Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)