TUCSON — Recovering from a gunshot wound to the head depends on the bullet's path, and while doctors Sunday are optimistic about Rep. Gabrielle Giffords' odds, it can take weeks to months to tell the damage.

Doctors say the bullet traveled the length of the left side of the Arizona congresswoman's brain, entering the back of the skull and exiting the front.

Fortunately, it stayed on one side of her brain, not hitting the so-called "eloquent areas" in the brain's center where such wounds almost always prove fatal.

Importantly, Giffords was responding nonverbally to simple commands in the emergency room — things like "squeeze my hand."

That implies "a very high level of functioning in the brain," said Dr. Michael Lemole of Tucson's University Medical Center, Giffords' neurosurgeon.

Now, her biggest threat is brain swelling. Surgeons removed half of her skull to give the tissues room to expand without additional bruising, Lemole said.

That bone is being preserved and can be reimplanted once the swelling abates, a technique the military uses with war injuries, added his colleague and trauma surgeon Dr. Peter Rhee.

Adding to Giffords' good prospects is that paramedics got her to the operating room in 38 minutes, her doctors said. Now she is being kept in a medically induced coma, deep sedation that rests her brain. It requires a ventilator, meaning she cannot speak. Doctors periodically lift her sedation to do tests and said she continues to respond well to commands.

The brain's left side does control speech abilities and the movement and sensation of the body's right side, Lemole noted. But he wouldn't speculate on lasting damage, saying, "we've seen the full gamut" in such trauma.

That's the mystery of brain injury: There's no way to predict just how much disability a wound that traverses multiple regions will leave, because our neural connections are so individual.

"The same injury in me and you could have different effects," said Dr. Bizhan Aarabi, chief of neurotrauma at the University of Maryland's Shock Trauma Center, who has long studied penetrating brain injuries.

"The belief is if you get shot in the head, you're dead, but it isn't like that," agreed the University of Miami's Dr. Ross Bullock, chief of neurotrauma at Jackson Memorial Hospital. He cared for a man shot in the head with an AK-47 who two years later is back to work full-time and "a normal person."

"Every patient is an individual and more so with a gunshot than anything else," he said.

There are few statistics, but doctors agree that well over 90 percent of gunshot wounds to the head are fatal. Aarabi cited his own study of 600 Maryland cases that found 95 percent were dead before arriving at the hospital.

Survivors have something in common with Giffords, Aarabi said: A good "Glasgow coma score," a way to measure responsiveness, upon arriving at the hospital. That pre-surgery outlook is important because doctors can't reverse the bullet's damage, just remove fragments to fight infection and swelling. Giffords' surgeons said they didn't have to remove a lot of dead brain tissue.

The amount of disability depends on how much damage is done to what brain region. A bullet that crosses into both sides, or hemispheres, can leave extensive lasting damage. That's what happened with James Brady, President Ronald Reagan's press secretary, who was left with slurred speech and uses a wheelchair after being shot during the 1981 assassination attempt on Reagan.

In contrast, one of neurology's most famous cases was Phineas Gage who in 1848 survived a 3-foot iron rod blasting into his skull but suffered personality changes from damage to the prefrontal cortex.

It can take weeks to tell the extent of damage, and months of intense rehabilitation to try to spur the brain's capacity to recover. In addition, more than half of survivors go on to suffer seizures and need anti-epilepsy medication, Miami's Bullock said.

"We talk about recovery in months to years," said Griffords' surgeon Lemole.

WASHINGTON - Searching for unity out of tragedy, President Barack Obama will honor the victims of the Arizona mass shooting in personal terms and remind those in grief that an entire nation is with them. The president is again stepping into his role as national consoler, a test of leadership that comes with the job.

His mission at Wednesday's memorial is to uplift and rally, not to examine political incivility.

Set to speak during an evening gathering in Tucson, Obama will remember the six people killed in a point-blank assassination attempt against a congresswoman who had been meeting with constituents outside a grocery store. Remarkably, Rep. Gabrielle Giffords is showing greater signs of recovery — including breathing on her own — just three days after a bullet shot through her brain.

The White House said Obama would meet privately with the victims' families before the service.

The shootings have consumed national attention since the weekend. In total, 19 people were shot, six fatally. Others were injured trying to flee the shooting.

Obama was crafting his speech and aides were reluctant to discuss it even broadly in its unfinished form, other than to say it would emphasize the memories of those lost. Still, Obama's comments since the shooting Saturday and his experience dealing with other tragedies offer guidance.

His main mission will be to honor those who were killed by describing them in personal terms, so the country remembers how they lived, not how they died.

He will seek to assure families in grief that the whole country is behind them.

And to those grasping for answers, Obama will probably explore how "we can come together as a stronger nation" in the aftermath of the tragedy, as he put it earlier this week.

What the speech is not likely to be: an examination of divisive partisan rhetoric or whether it is connected in any way to the rampage. Those matters have soared to the forefront of media debate. But while addressing a grieving community, Obama is expected to focus on a memorial, not a commentary on politics.

This moment as chief consoler comes to all presidents — often many times. And this will not be Obama's first.

Among the events that people remember the most, recent history alone recalls George W. Bush with a bullhorn amid the rubble of Sept. 11, 2001; Bill Clinton's leadership after the Oklahoma City bombing in 1995; and Ronald Reagan's response to the explosion of the Space Shuttle Challenger in 1986, when he spoke about being "pained to the core."

For Obama, the most instructive lesson may be one from his own presidency.

He led the memorial at the Fort Hood, Texas, Army post in November 2009, trying to help a shaken nation cope with a mass shooting there that left 13 people dead and 29 wounded. He spent the first part of that speech naming the people who had been killed and describing how they spent their lives; he used the second half to remind everyone of American endurance and justice.

In April 2010, Obama eulogized 29 coal workers killed in the worst mine accident in a generation. He said they lived as they died, pursuing the American dream.

Even before accepting the invitation to speak at the University of Arizona memorial service, Obama previewed his own approach.

"It's going to be important, I think, for the country as a whole, as well as the people of Arizona, to feel as if we are speaking directly to our sense of loss, but also speaking to our hopes for the future and how out of this tragedy we can come together as a stronger nation," the president said Monday. He will be attending with his wife, first lady Michelle Obama.

The six people killed were attending a community outreach gathering sponsored by Giffords outside a grocery store. The six were Arizona's chief federal judge, a 30-year-old aide to Giffords, a 9-year-old girl and three retirees in their mid-to-late 70s.

The president is expected to offer words of comfort to the injured survivors of the shooting. And he is sure to commend, as he has once in public already, the courage of people who intervened to help Giffords, tackle the gunman and grab his ammunition.

"When the people can hear the president of the United States talk about their neighbor, their husband, their daughter, it is incredibly comforting and uplifting at the same time," said Kevin Sullivan, who served as communications director for President George W. Bush in his second term, which included a mass shooting at Virginia Tech.

In the current case, the suspect, 22-year-old Jared Lee Loughner, is being held without bail in a Phoenix jail.

So far, Obama has said nothing about whether the violence can fairly be connected to the vitriol of today's partisan politics — or, more broadly, whether this is a time for Obama to renew his call for more civil American debate.

Obama's approach has been to let the criminal investigation unfold and keep the country looking forward; the timing and the setting will help drive any broader message he has.

"This is about the grief of the victims and the families who have been affected," Sullivan said. "There should be no element of political commentary because that would undermine the president's natural ability and skill and uplifting the families."

Thousands of people are expected to attend the memorial service at the university's basketball arena. The event is open to the public. Students, state and federal officials and the school president are all expected to speak, along with Obama.

The president will be joined by Supreme Court Justice Anthony Kennedy, Attorney General Eric Holder and Homeland Security Secretary Janet Napolitano, another sign of the message he wants to send: U.S. solidarity. House Democratic Leader Nancy Pelosi and Republican members of Arizona's congressional delegation also are traveling with Obama.

In Washington on Wednesday, in the chamber where Giffords serves, the House honored her, the victims of the shooting and those who sought to help them.

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Associated Press writers Julie Pace and Mark Sherman contributed to this report.