PHILADELPHIA -- The family of late Pro Bowl safety Dave Duerson will appeal this week's NFL concussion settlement amid concerns it doesn't include future awards for the brain decay diagnosed after his 2011 suicide.

An appeal could hold up the settlement approved Wednesday by a federal judge in Philadelphia. The potential $1 billion deal is designed to monitor more than 20,000 NFL retirees over 65 years and compensate those with dementia, Alzheimer's disease and other serious neurological conditions.

But the plan doesn't include future awards for chronic traumatic encephalopathy, often called the signature disease of football.

The judge concluded CTE research is in its "infancy" and suspected early symptoms, including violence, mood swings and depression, shouldn't by themselves trigger awards.

The 50-year-old Duerson, who spent most of his 10-year career with the Chicago Bears, left behind four children and a note asking that his brain be studied.

Lawyer Thomas Demetrio said the children "are pretty adamant that their father would want them to forge ahead for the benefit of these unsuspecting former players."

"They saw firsthand how mood and behavioral problems impact a man and a family," he said. "It would have been awfully nice if the NFL -- who could well afford it -- had allowed CTE to be compensated."

Senior U.S. District Judge Anita B. Brody, during more than two years of negotiations, persuaded the NFL to lift a $765 million cap on the settlement fund. The NFL, with $10 billion in annual revenue, could now spend more than $1 billion over time, including inflation and $112 million in lawyer fees sought by the other side.

The judge found many athletes diagnosed posthumously with CTE also had Lou Gehrig's disease, Alzheimer's disease, Parkinson's disease or dementia, which are compensated.

She rejected pleas from other NFL families that behavioral disorders such as depression be compensated.

Some experts, including Boston University's Dr. Robert Stern, who has studied CTE-damaged brains, believe they are early signs of CTE-related illness.

The judge, citing other experts, said retired players have higher rates of sleep apnea, drug and alcohol abuse, chronic pain, high body mass and major lifestyle changes that could also be risk factors for mood disorders and suicide.

"An individual retired player would have a difficult time showing that head impacts, as opposed to any one of these other factors, explain his symptoms," the judge wrote.

Demetrio estimated the Duersons under the settlement would receive $2.2 million, which he calls inadequate for their loss.

Dave Duerson was an honors graduate and trustee of Notre Dame, a four-time Pro Bowler, a 1987 recipient of the NFL's Man of the Year award for his on-field and community work, and a onetime member of a committee that reviewed NFL disability applications.

Junior Seau, the league's 1994 Man of the Year recipient, killed himself in 2012. Like Duerson, his last years were marked by sometimes erratic behavior. He also was found to have CTE.

The Seau family has opted out of the class-action settlement and will pursue an individual lawsuit against the NFL.

The plan pays up to $4 million for CTE-linked suicides through Wednesday's settlement, a cutoff designed to avoid incentivizing future suicides. The maximum $5 million award compensates men with amyotrophic lateral sclerosis.

Lawyers for players such as Kevin Turner, who requires oxygen and a feeding tube because of ALS, fear appeals will hold up much-needed awards for at least a year.

"That is just very unfortunate for players that now need treatment," lawyer Craig Mitnick said.