Identity of the density of states of simple excitations in close-packed lattices

Abstract

Anthropometric evaluation of cleft lip nasal growth has generally been done based on Mulliken's method. However, this method does not allow sufficient evaluation of nasal tip position. Nasal tip position is the most important parameter for evaluation of nasal growth. Therefore, an anthropometric study was performed including vertical nasal tip position.Fifteen normal subjects in early childhood (Normal Group), 15 age-matched subjects with complete unilateral cleft lip and alveolus or complete unilateral cleft lip, alveolus, and palate without rhinoplasty (No Rhinoplasty Group), and 16 age-matched subjects with complete unilateral cleft lip and alveolus or complete unilateral cleft lip, alveolus, and palate with synchronous rhinoplasty during primary repair of cleft lip (Primary Rhinoplasty Group) were compared. Nasolabial angle (β), nasal tip angle (α), nasal width (al-al), columellar length (sn-c'), nasal tip protrusion (sn-prn), and vertical nasal tip position (sn'-prn'/sn'-n') were measured.With the exception of vertical nasal tip position, the measurement data of the Primary Rhinoplasty Group were excellent. In the cleft lip groups, vertical nasal tip position was significantly higher than that in the Normal Group.Our results showed that the nasal tips of cleft lip patients showed significant congenital upward deviation in comparison with normal children. In Mulliken's method, this upward deviation cannot be evaluated properly. After synchronous rhinoplasty, measurement results showed improvement in our patients without significant deterioration of tip position. These findings represent evidence in support of synchronous rhinoplasty.