1. Department of Orthodontics, The School of Dentistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, and Assistant Professor, Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Dentistry, Osaka University, Osaka, Japan.
2. Department of Orthodontics and Dentofacial Orthopedics, Graduate School of Dentistry, and Adjunct Professor, Center for Advanced Medical Engineering and Informatics, Osaka University, Osaka, Japan.
3. Department of Surgery, The School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina.
4. Department of Orthodontics, University of Maryland Dental School, Baltimore, Maryland, and Adjunct Professor, Department of Orthodontics, The School of Dentistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina.