1. Department of Orthodontics, Nihon University School of Dentistry at Matsudo, Matsudo, Chiba 271-8587, Japan
2. Department of Orthodontics, Nihon University Graduate School of Dentistry at Matsudo, Matsudo, Chiba 271-8587, Japan
3. Department of Mathematical Sciences, Nihon University School of Dentistry at Matsudo, Matsudo, Chiba 271-8587, Japan