Ledley returned to action for the Hoops in their 4-1 victory over Hearts on Saturday for the first time since 8 December.
The 25-year-old has a pelvis problem like Brown suffered from during the first half of the season.
And Ledley hopes he will respond to the treatment which has worked so well for the Celtic skipper.
"It is my pelvis, similar to Brownie," said Ledley. "It depends how I feel. Sometimes when I wake up it is okay, the next day it can be hurting. So I just take it day by day.
"We had exactly the same injection and Brownie is flying now so hopefully it can continue with me.
"I have been out for while so it was nice to be back playing and being involved in the squad, and back on a winning side as well."