1. Department of Orthodontics and Dentofacial Orthopedics, The University of Tokushima Graduate School of Oral Sciences, 3-18-15 Kuramoto-cho, Tokushima 770-8504, Japan;
2. Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, KS, USA; and
3. Department of Surgery, Division of Oral and Maxillofacial Surgery, Stritch School of Medicine, Loyola University Medical Center, Maywood, IL, USA