The invention provides for methods of obtaining cells from mammalian, preferably human, postpartum umbilical cord arterial tissue and use of these cells to treat ocular degenerative conditions. In particular, methods of the invention result in the isolation of a homogenous population of human postpartum umbilical cord arterial tissue-derived cells. In certain embodiments, the cells: express CD13, CD90, NG2, and HLA-ABC do not express one or more of CD31, CD34, CD45, CD117, FSP1, and E-cadherin. In other embodiments, the cells secrete one or more of thrombospondin-1, BDNF and sVEGFR1.