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The NFL and its players' union have said changes to concussion protocol are needed to "enhance" player safety.

Miami Dolphins' Tua Tagovailoa suffered a concussion against the Cincinnati Bengals, four days after being injured in their previous game.

In a joint statement, the NFL and the NFLPA said an investigation was ongoing but changes to protocol were likely.

It that the doctor who cleared quarterback Tagovailoa for Thursday's game has been fired.

"The NFL and the NFLPA agree that modifications are needed to the concussion protocol to enhance player safety," they said.

"We anticipate changes to the protocol being made in the coming days based on what has been learned thus far in the review process."

In a game against the Buffalo Bills last Sunday, Tagovailoa looked unsteady on his feet after a big tackle, but he was evaluated after the incident and cleared to return to the field for the second half.

However, his hands appeared to spasm and he was taken off on a stretcher against the Bengals on Thursday.

The NFL said that every indication was that proper protocol had been followed on Sunday.

NFL chief medical officer Dr Allen Sills said Tagovailoa was checked for concussion symptoms before being cleared to play on Thursday by an independent neurologist.

"The NFL and NFLPA share a strong appreciation for the unaffiliated neurotrauma consultants who contribute their time and expertise to our game solely to advance player safety," the statement said.

"This program has made our game safer for the athletes who play it for the past 12 seasons."