Burkhead hurt his knee in the team's Dec. 17 win over the Pittsburgh Steelers, while Branch's knee injury came Dec. 11 against the Miami Dolphins. Burkhead missed the final two regular season games, while Branch has been out for the past three.
Burkhead's return to action would be a boost for the Patriots' offense, which sputtered at times in December and could benefit from someone other than running back Dion Lewis and tight end Rob Gronkowski stepping up to consistently make plays. His dual threat as a rusher and pass-catcher also provides offensive coordinator Josh McDaniels with flexibility, sometimes opening the door for there to be two running backs on the field at the same time.
As for Branch, he is a third option behind Lawrence Guy and Malcom Brown at the big-bodied defensive tackle spot and his powerful presence has shown up against the run and at times pushing the pocket (e.g. at Buffalo when his rush contributed to Eric Lee's end-zone interception). Veteran Ricky Jean Francois has filled that role in his absence.
While Burkhead and Branch both returned to practice, running back Mike Gillislee (knee) and defensive end Eric Lee (ankle) were not spotted at the start of the session. Gillislee injured his ankle Dec. 24 against the Bills and missed the regular-season finale, while Lee had missed last Friday's practice but still played in the final regular-season game.
The Patriots also had linebacker Trevor Reilly back on the practice field, as he appears to have been re-signed to the practice squad.