BOSTON, MA - DECEMBER 8: Chris Wilcox #44 of the Boston Celtics drives to the basket for a layup against the Philadelphia 76ers during the game on December 8, 2012 at TD Garden in Boston, Massachusetts. NOTE TO USER: User expressly acknowledges and agrees that, by downloading and or using this photograph, User is consenting to the terms and conditions of the Getty Images License Agreement. (Photo by Jared Wickerham/Getty Images)
Chris Wilcox, seen here shooting against the 76ers on Dec. 8, is the latest Celtics big-man casualty. (Getty Images)
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WALTHAM — The Celtics will enter their critical four-game road trip beginning Tuesday with just 11 active players, as once again keeping their centers healthy remains difficult.

At practice Sunday, coach Doc Rivers revealed that Chris Wilcox will miss perhaps a month with a sprained ulnar collateral ligament in his right thumb, sustained in Tuesday’s loss to the Chicago Bulls.

Wilcox attended the team’s Christmas party for local children with a brace on his right hand. With his absence, the Celtics have one true center on the roster — Jason Collins — despite having addressed the position in the offseason.

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President of basketball operations Danny Ainge re-signed Wilcox and added Darko Milicic and Collins, and drafted Syracuse’s Fab Melo for support. Milicic left the team after less than a month to be with his ill mother in Serbia and Melo is playing for Maine of the NBA Development League.

Melo set a league record with 14 blocked shots in Maine’s loss to Erie Saturday, but Rivers said that would have no impact on a potential promotion to the Celtics.

When asked about Melo, Rivers said, “I talked to Fab, as in, ‘How you doing?’ I haven’t talked to anyone that thinks he’s ready to come up yet.”

With Kevin Garnett having been moved back to his natural power forward position, Rivers admitted that the club needs another center, and there is an open roster spot.

“You would think [the team would sign someone],” he said. “But obviously that’s the one position where they don’t grow on trees. We just have to be patient. Obviously we need another big with Chris being out. I don’t know if we’re going to get another big on this trip.”

An NBA source told the Globe this month that the Celtics had veteran free agent Erick Dampier on their radar. Dampier, 37, played 15 regular-season games last season with the Atlanta Hawks and four against the Celtics during their first-round playoff series, averaging 4 points. He scored 6 points and had six rebounds in Game 1.

Veteran Kenyon Martin, who turns 35 on Dec. 30, is also a free agent.

Meanwhile, guard Avery Bradley participated in his second practice in his recovery from double shoulder surgery. While Bradley said Friday his projected return date was Jan. 2, Rivers would not count him out playing as early as Tuesday.

“I think there’s a chance, but I don’t know what the chances are,” Rivers said. “I haven’t talked to anybody. I mean the fact that he went through today’s practice games [and will practice Monday] . . . but I don’t know. I just try to stay out of that. It’s close. I don’t want anyone to feel like I am pressuring them. Avery wants to play. I guarantee you he wants to play the next game.”

Bradley has shown no ill effects from his surgeries during the workouts and teammates have raved about his energy and impact.

“He could play, there’s no doubt he’s ready to play,” Rivers said. “But I don’t know about the healing part of it. Does it take those extra two weeks? He had two [surgeries], the first one was on one date and the second was a lot later. That’s the shoulder that still needs to heal.

“Now if you can get through a practice, the way we’ve gone, especially today, can he play in a game? He may be able to, but maybe it’s still too early. I don’t know the answer.”

Bradley’s teammates are eagerly anticipating his arrival.

“He’s looked great,” forward Paul Pierce said. “He just brings that energy that you want. It could be contagious. He’s everywhere on the court. He’s defending. He’s guarding three positions. You could tell that he’s anxious to get back out there and play.”

The Celtics will have Jeff Green for Tuesday’s game against the Brooklyn Nets. He took an elbow to the face from Milwaukee’s Ersan Ilyasova in overtime of Friday night’s loss, bruising his left cheekbone and chipping three teeth. He was back at practice Sunday with a shiner under his left eye.

“It just added to my character,” Green said of the eye injury. “Just another bruise that I’ve got to fight through.”

Green said he passed concussion tests late Friday night.

“I thought I broke [the bone] right under my eye,” he said. “I thought it was cracked, my nose broke or something happened, because I was in a lot of pain. I couldn’t really open my left eye.”

Swingman Kris Joseph was recalled from Maine for Tuesday’s game. Rivers said guard Leandro Barbosa (personal matter) won’t join the team until Thursday’s road game against the Los Angeles Clippers.