The outer surface of a bone is lined by a thin layer of connective tissue that is very similar in morphology and function to endosteum. It is called the periosteum, or the periosteal surface.During bone growth, the width of the bone increases as osteoblasts lay new bone tissue at the periosteum.n anatomy the endosteum (plural endostea) is a thin vascular membrane of connective tissue that lines the surface of the bony tissue that forms the medullary cavity of long bones.