PHILADELPHIA » Former players appealing the NFL’s $1 billion plan to address concussion-linked injuries asked a court today to reject the settlement because it excludes what they call the signature brain disease of football.

Critics insist that any deal include future payments for chronic traumatic encephalopathy, the brain decay found in dozens of former players after their deaths.

"CTE was the soundpiece of the original (lawsuit)," lawyer Steven F. Molo argued before the 3rd U.S. Circuit Court of Appeals. "It is a fundamental issue in the case. It is mentioned 14 times."

The settlement would resolve thousands of lawsuits and cover more than 20,000 NFL retirees for the next 65 years. The league estimates that 6,000 former players, or nearly three in 10, could develop Alzheimer’s disease or moderate dementia.

They would receive an average of $190,000, although the awards could reach several million dollars in the most serious cases, which include young men with Parkinson’s disease or Lou Gehrig’s disease.

The lead negotiators, in response to the criticism, said former players might otherwise have gotten nothing because the NFL had pushed for the complaints to be thrown out of court and sent to arbitration. And the science behind CTE is in its early stages; the damage cannot currently be diagnosed in the living.

"The science could determine that all that matters for CTE is the concussive hits you took before your 18th birthday," lawyer Paul Clement, a former U.S. solicitor general, argued today for the NFL.

The settlement grants up to $4 million for prior deaths involving CTE, but it set an April 2015 cutoff date to avoid incentivizing suicides.

The list of former players who have killed themselves and been diagnosed with CTE includes Hall of Fame center Mike Webster of Pittsburgh; Pro Bowler Junior Seau of San Diego; and Ray Easterling of Atlanta, a named plaintiff in a 2011 concussion lawsuit before his death the following year.

Senior U.S. District Court Judge Anita B. Brody steered the parties to mediation and approved the settlement in April, after persuading the NFL to remove a $765 million cap so the fund doesn’t run out. The settlement also sets aside money for baseline testing, education and research.

Some of the approximately 90 objectors complain that it compensates only a few neurological conditions, and not the depression and mood disorders they link to concussions and CTE.

That led Circuit Judge Thomas M. Hardiman to ask if the settlement should be "watered down by every field goal kicker who’s depressed?"

The lead plaintiff lawyers who negotiated with the NFL argue that time is of the essence for people like former Philadelphia Eagle Kevin Turner, who is battling Lou Gehrig’s disease, a fatal neuromuscular disease. However, their critics note that they stand to collect up to $112 million in fees if the deal goes through.

"They didn’t even go after the memos in NFL headquarters about what they knew about CTE and when," lawyer Deepak Gupta argued today for the appellants, complaining that the case was settled before much evidence was exchanged.

The three-judge panel is expected to rule early next year.