alveolar periosteum. Etymology: L, alveolus, little hollow; Gk, peri, near, osteon, bone. a dense layer of connective tissue that lines the alveolar cavities of the upper and lower jaws, joining the bones to the horizontal fibers on the cementum of the teeth.See also periosteum.The fibrous membrane that forms the covering of bones except at their articular surfaces; consists of a dense external layer containing numerous blood vessels and an inner layer of connective tissue cells that function as osteoblasts when the bone is injured and then participate in new bone formation.lveolar periosteum. Etymology: L, alveolus, little hollow; Gk, peri, near, osteon, bone. a dense layer of connective tissue that lines the alveolar cavities of the upper and lower jaws, joining the bones to the horizontal fibers on the cementum of the teeth. See also periosteum.