Three-dimensional analysis of upper airway morphology in skeletal Class III patients with and without mandibular asymmetry

ABSTRACT Objective: To compare the three-dimensional (3D) morphology of the upper airway in skeletal Class III patients with and without mandibular asymmetry and to investigate the possible underlying correlations between the morphology of the upper airway and mandibular deviation. Materials and Methods: Cone-beam computed tomography images of 54 subjects with skeletal Class III malocclusion (ANB angle ≤ 0.4°, Wits ≤ −5.5°) were taken and 3D upper airway models were reconstructed using Dolphin 3D software. According to the distance (d) from symphysis menti to the sagittal plane, all subjects were divided into a symmetry group (d ≤ 2 mm) and an asymmetry group (d ≥ 4 mm). Based on the severity of mandibular deviation, the asymmetry group was divided into subgroup I (4 mm ≤d <10 mm) and subgroup II (d ≥ 10 mm). Cross-sectional linear distances, areas, and volumetric variables of the upper airway were measured in the 3D airway model. Results: Width of the inferior limit of the glossopharynx (P3W), cross-sectional area of the anterior limit of the nasal airway (P5S), and height of the glossopharynx (GPH) in the asymmetry group were significantly larger than in the symmetry group. As for subjects with severe mandibular deviation in subgroup II (d ≥ 10 mm), volume of the glossopharynx (GPV), total volume of the pharynx (TPV), length of the inferior limit of the velopharynx (P2L), and ratio of length to width of the inferior limit of the velopharynx (P2L/P2W) showed significantly negative correlations with mandibular deviation (r > 0.7, P < .05). Conclusions: In Class III subjects with severe mandibular asymmetry, the pharyngeal airway showed a tendency toward constriction and presented a more elliptical shape as mandibular deviation became more severe (P < .01).

Risk Level Assessment in Construction Projects Using the Schedule Performance Index

Construction projects are risky in both physical implementation and management. The characteristics of the risk reinforce the necessity of efficient management to increase the chances of success without commitment to its goals. This study explores the correlation of delay and the schedule performance index (SPI) to evaluate the risk of a construction project completed with time overruns. The hypothesis that the SPI of projects with a delay is distinct from those projects without a delay is assumed. A database with 19 elements was used to test this hypothesis and to calculate limit values to the SPI. Therefore, the risk of delay will be small when the observed SPI is greater than the superior limit and large when the SPI is below the inferior limit. The simplicity involved in the calculation of these values showed an advantage in comparison with other methods of risk evaluation. Another strong point observed is that any company can determine the value of risk by considering its own history and support decisions like doing corrective actions.

The rhinopalatine line as a reliable predictor of the inferior extent of endonasal odontoidectomies

OBJECT The endoscopic endonasal approach (EEA) provides a minimally invasive corridor through which the cervicomedullary junction can be decompressed with reduced morbidity rates compared to those with the classic transoral approaches. The limit of the EEA is its inferior extent, and preoperative estimation of its reach is vital for determining its suitability. The aim of this study was to evaluate the actual inferior limit of the EEA in a surgical series of patients and develop an accurate and reliable predictor that can be used in planning endonasal odontoidectomies. METHODS The actual inferior extent of surgery was determined in a series of 6 patients with adequate preoperative and postoperative imaging who underwent endoscopie endonasal odontoidectomy. The medians of the differences between several previously described predictive lines, namely the nasopalatine line (NPL) and nasoaxial line (NAxL), were compared with the actual surgical limit and the hard-palate line by using nonparametric statistics. A novel line, called the rhinopalatine line (RPL), was established and corresponded best with the actual limit of the surgery. RESULTS There were 4 adult and 2 pediatric patients included in this study. The NPL overestimated the inferior extent of the surgery by an average (± SD) of 21.9 ± 8.1 mm (range 14.7-32.5 mm). The NAxL and RPL overestimated the inferior limit of surgery by averages of 6.9 ± 3.8 mm (range 3.7-13.3 mm) and 1.7 ± 3.7 mm (range −2.8 to 8.3 mm), respectively. The medians of the differences between the NPL and NAxL and the actual surgery were statistically different (both p = 0.0313). In contrast, there was no statistically significant difference between the RPL and the inferior limit of surgery (p = 0.4375). CONCLUSIONS The RPL predicted the inferior limit of the EEA to the craniovertebral junction more accurately than previously described lines. The use of the RPL may help surgeons in choosing suitable candidates for the EEA and in selecting those for whom surgery through the oropharynx or the facial bones is the better approach.

Three-body problem, the measure of oscillating types. A short review

The theoretical three body problem, with three given non infinitesimal point masses, has two types of oscillating motions. In the first type at least two mutual distances are unbounded, but their inferior limit is bounded: there are an infinite number of larger and larger ejections, but without escape. In the second type, it is the velocities that are unbounded: there are an infinite number of nearer and nearer quasi-collisions, without exact collisions.The first type has only a theoretical interest: its measure in phase space is zero. But the second type has a positive measure in phase space and a physical interest: it governs most of the collisions of stars.