The FDA is cautious in this area because historically a number of stem cell injection therapies have led to tumor formations in the CNS.

That said they were not autologous mesenchymal stem cells. This study gives hope.

Refs: http://www.nature.com/stemcells/2009/0902/090226/full/stemce...

http://journals.plos.org/plosmedicine/article?id=10.1371/jou...

Old review from early 2000s http://onlinelibrary.wiley.com/doi/10.1002/ana.60000/full