1. PhD candidate, Section of Orthodontics and Dentofacial Orthopedics, Faculty of Dental Science, Kyushu University, Fukuoka, Japan.
2. Associate Professor, Section of Orthodontics and Dentofacial Orthopedics, Faculty of Dental Science, Kyushu University, Fukuoka, Japan.
3. Associate Professor, Research Institute of Applied Mechanics, Kyushu University, Kasuga, Japan.
4. Professor and Chairman, Department of Mathematics, National Defense Academy of Japan, Yokosuka, Japan.
5. Professor and Chairman, Section of Orthodontics and Dentofacial Orthopedics, Faculty of Dental Science, Kyushu University, Fukuoka, Japan.