Base Angle Research Articles

Interobserver and intraobserver reliability of skull base angles measured on magnetic resonance images.

Determination of platybasia and basilar kyphosis are significant parts of routine cranial magnetic resonance (MR) interpretations. These situations may explain a patient's symptoms or may be associated with other anomalies. To indicate the interobserver and intraobserver reliability of the skull base angles (SBA) (Koenigsberg standard) and modified SBA (mSBA) measurement techniques. In total, 391 patients who had undergone cranial MR imaging were re-assessed regarding the SBA measurements. The SBA and mSBA techniques were used on MR images. Two reviewers independently measured the same angles twice within a 15-day interval, using different monitors. Intraclass correlation coefficient (ICC) was calculated to reveal the intraobserver and interobserver agreements. There was an excellent agreement between reviewers regarding both angle measurements (ICC was 0.998 for SBA and mSBA). Excellent agreement levels were also observed for intraobserver measurements. ICC was 0.998 for SBA and 0.999 for mSBA for reviewer 1. ICC was 0.997 for SBA and 0.999 for mSBA according to the measurement results of reviewer 2. Higher SBA and mSBA values were observed for females compared to males. There was no correlation between SBA and age for SBA. However, a negative and low-level correlation was observed between mSBA values and age for both reviewers. SBA and mSBA measurements indicated excellent agreement regarding interobserver and intraobserver differences. The study results showed that SBA angles were reliable measurement techniques to be used on MR images.

Clinical features and outcomes of basilar invagination.

Basilar invagination has been classified into two types by Goel: Type A is defined mechanical instability of the atlantoaxial joint with upward displacement of the odontoid process while Type B is characterized by stable atlantoaxial joints. This study reviews the association between radiological features and symptomatology and prognosis of two types of basilar invagination for better clinical management. A retrospective analysis was conducted including 141 patients diagnosed with basilar invagination who underwent surgical treatment from January 2016 to December 2020. The neurological function was assessed by the JOA scores, and Short-Form 12 scores. Logistic univariate and multivariate analyses were performed to predict prognostic risk factors. Type A patients (21/101, 20.8%) with more cases of dizziness, lower preoperative JOA scores and SF-12 PCS scores (JOA, 13.0 vs. 13.9, P = 0.042; SF-12 PCS, 37.48 vs. 38.42, P = 0.034) compared to type B (2/40, 5%) (P = 0.022). Type B (22/40, 55%) with more cases of ataxia than type A (35/101, 34.7%) (P = 0.026). Patients with type B demonstrated a significantly higher improvement rate in SF-12 PCS than type A (P = 0.018). Further logistic regression revealed that onset age ≥ 45 years (OR 4.654, 95% CI 1.645-13.165; p = 0.004) and basal angle ≥ 125° (OR 28.139, 95% CI 1.090-726.239; p = 0.044) were independent risk factors for type A and type B, respectively. Type A patients with more cases of dizziness, and type B patients with more cases of ataxia, can achieve better long-term prognosis following clinical intervention.

Cranial Base Changes After Trans-sutural Distraction Osteogenesis in Growing Patients With Cleft Lip/Palate and Midface Hypoplasia

Background: Transesutural distraction osteogenesis (TSDO) is a method of correcting midfacial hypoplasia (MH) secondary to cleft lip and palate (CLP) without osteotomy. However, there has been little research on how the morphology of the cranial base changes postoperatively or whether any correction of the cranial base occurs. Materials and Methods: This retrospective study included 35 pediatric patients with MH secondary to CLP, who underwent TSDO treatment. Pre-treatment and post-treatment cranial computed tomography (CT) images were collected for cranial base measurements using 3-dimensional (3D) modeling reconstruction. For the comparative analysis, 102 children with normal craniofacial CT images were selected after matching for age and sex. Results: Comparison with normal children of the same age showed that the lengths and angles of several cranial base segments approached normal levels after treatment. In total, the authors found extreme extension in the anterior segment of the sphenoid bone, and in the middle cranial fossa. Simultaneously, TSDO therapy led to the anteroposterior diameter of the lateral pterygoid processes and vomer bone greatly exceeding the normal range, thus causing forward development of the midface skeleton. Conclusion: After the TSDO procedure, the cranial base length and angles approached normal dimensions, accompanied by the forward advancement of the midfacial skeleton. Among the cranial base structures, TSDO resulted in the most noticeable increase in the sphenoid bone in terms of linear measurements and angles, thus promoting midfacial development in children.

Graded metastructure design for linearly auxetic deformation under tension: From 2D honeycombs to 3D truncated cones

Mechanical metamaterials exhibit special properties that cannot be realized in traditional materials. To enable a metamaterial with a sequential Poisson’s ratio and controllable expansion, a 2D-graded hybrid re-entrant honeycomb is designed in this work by coupling graded re-entrant unit cells with negative and positive Poisson’s ratios. The correlation between Poisson’s ratio and structural location under tension is studied by finite element analysis and experiments. The influence of microstructural parameters, including base angle, height ratio, and internal angle, on the relationship between the Poisson’s ratio and structural location is systematically analyzed. The theoretical analysis shows that the 2D-graded hybrid metastructures exhibit auxetic behavior with a linearly declined Poisson’s ratio along the tensile direction due to the introduction of a height ratio, resulting in gradual expansion and elongation. Furthermore, adjusting the variation of internal angles at a small height ratio can enhance the negative Poisson’s ratio of the 2D-graded hybrid re-entrant honeycomb. Finally, a 3D-graded conical metastructure exhibiting linear auxeticity is constructed based on the 2D-graded lattice. Considering their designed linearity of deformation under tension, the 2D- and 3D-graded metastructures can facilitate the design of conical profiles for an extendable rocket nozzle and other deployable devices.

Evaluation of clinical effects of Advansync 2 fixed functional appliance in skeletal Class II malocclusion: A retrospective cephalometric study

To evaluate the treatment effects of AdvancSync 2 in patients of skeletal Class II malocclusion in selected skeletal, dental, soft tissue and airway parameters. Pretreatment and post-functional lateral cephalograms of 12 patients (06 males and 06 females with mean age of 14.25+0.75) with skeletal Class II malocclusion treated using AdvanSync 2 were evaluated. Paired t-test and Wilcoxon rank-sum intraclass correlation (ICC) test results were calculated.Statistically significant changes were found in skeletal parameters ofSNB, Wits, maxillo-mandibular differential, Björk’s sum, basal plane angle, Sn-GoGn, lower anterior facial height (LAFH), Na-perp-Pog. Changes in dental parameters U1-NA (angular and linear), L1 to NB (angular and linear), U1-SN angle, IMPA, Inter-incisal angle, L1 to A-Pog and U1 to A-Pog were also observed to be statistically significant at T1. Soft tissue skeletal convexity and nasolabial angle improved significantly post treatment, while, statistically significant change was observed only in posterior pharyngeal airway space among the chosen cephalometric airway parameters.Treatment with AdvanSync 2 corrected the Class II malocclusion by producing skeletal and dentoalveolar changes. Soft tissue facial convexity and nasolabial angle improved with treatment. Further, linear dimension of the posterior pharyngeal airway space showed significant improvement with AdvanSync 2 therapy.

Long-Term Outcomes of Nonsyndromic Isolated Unilateral Lambdoid Craniosynostosis

This study combined qualitative and quantitative approaches to evaluate outcomes of isolated nonsyndromic unilateral lambdoid synostosis at the Children's Hospital of Philadelphia. Volumetric, linear, and angular analyses were performed on long-term postoperative and normal control scans. Preoperative and postoperative clinical photographs were evaluated for the presence of dysmorphic frontofacial features. Among 26 included patients, median age of surgery was 10 months and mean postoperative follow-up was 5.9±5.7 years. Two (7.7%) patients underwent secondary cranial vault procedures. At most recent follow-up, 2 (7.7%) subjects reported intermittent headaches. Twenty (90.9%) of 22 patients were assigned Whitaker grade I. Among 9 subjects with long-term imaging at age 11.5±5.3, posterior vault asymmetry, posterior fossa deflection angle, cranial base angle, and ear position asymmetry all remained greater than in the control group. Of subjects included in the frontofacial feature analysis (n=10), 50% had resolution of all dysmorphic frontofacial features present preoperatively. Overall, most subjects who underwent PVR did not require revisional surgery and had good outcomes both aesthetically and functionally. Despite residual abnormalities in the cranial base and posterior vault, most had resolution of parietal bossing and facial scoliosis. Ear position asymmetry was the most common dysmorphic feature at long-term follow-up.

Influence of astigmatic aberration on partially coherent Gaussian-Schell vortex beam focused by lensacon

Based on the mathematical framework of the partially coherent Gaussian Schell model vortex (PCGSMV) beam and the Huygens-Fresnel integral, we conducted a study to analyze the intensity distribution and depth of focus (DOF) of the PCGSMV beam as it propagates through a classical axicon. Our numerical results indicate the influence of factors such as the beam width, spatial degree of coherence, topological charge, and axicon base angle on the intensity distribution and DOF. In addition, we investigated the relationship between the beam spot size and propagation distance, as well as the effects of the spatial degree of coherence and propagation distance on the intensity profile. Our findings highlight the importance of the intensity values along the DOF for various applications, including the optical trapping and manipulation of micro particles.

Multi-objective ergonomics design model optimization for micro electric cars via response surface methodology

Despite advancements in ergonomic comfort assessments in automotive design, optimizing seat dimensions within the constrained spaces of micro-electric cars presents a substantial challenge. In this study, response surface methodology (RSM) is utilized for the ergonomics design of a micro electric car in the conceptual design phase. Specifically, five critical seat dimensions are analyzed: Seatback Angle, Seat Base Angle, Steering Wheel Height from Car Base, Distance from Seat Base to Pedals, and Distance from Seat Base to Steering Wheel. The analysis took place using a 2-level full factorial design L32 orthogonal array. The optimal dimensions are determined using RSM, such as the mean comfort level and signal-to-noise ratio are maximized, and the standard deviation for multiple drivers is minimized. Three regression models are formulated for the three responses, and their adequacy is checked using different methods. The optimal dimensions are obtained and verified through digital human modeling simulation. This research offers practical guidelines for the ergonomic seating design in micro-electric vehicles, enhancing comfort without compromising space efficiency.

Morphometric analysis of the skull base and palatal regions for gender identification using CBCT: a retrospective study.

The objectives of this study were to evaluate the accuracy of morphometry of skull base and palate in gender discrimination using cone beam computed tomography (CBCT) scanning and to assess the accuracy of the results among a sample of the Arab population. Using CBCT scans, a cross-sectional analysis was conducted on 142 consented patients who underwent various dental procedures at the University Dental Hospital, Sharjah (UDHS). Of these patients, 70 were females and 72 were males, with respective means of 38.5 and 36.2 years. Eleven parameters related to skull base and palatal region were measured on the CBCT scans by two expert radiologists followed by statistical analysis. There was significant gender-based difference in the mean palatal width (PW) (p=0.001), mean palatal height (PH) (p=0.005). Among other skull base region parameters that were significant in term of gender-based difference like; the clivus length (CL) (p<0.001), occipital condyle height (OCH) (p<0.001), basal angle (BA) (p=0.006) and transverse diameter of foramen magnum (p=0.003). Only palate variables showed a significant age difference. Discriminant analysis related to gender showed that occipital condyle height was the most accurate and best discriminator among the skull base region parameters. The use of discriminant analysis in CBCT based on skull base and palatal region variables provides an efficient method for determining gender, which is particularly valuable in forensic science and anthropological research. Accurate gender identification is crucial in forensic investigations, and the skull base region, being a stable and sexually dimorphic anatomical feature, can serve as a reliable marker for this purpose.

Variation of chin morphology and mandibular incisor length in different facial divergence patterns: New insights from CBCT records.

Evaluate constitutional differences in chin morphology and volume, and mandibular tooth size, between different facial divergence patterns. The sample consisted of 284 pretreatment cone beam computed tomography (CBCT) images of growing and non-growing patients who were stratified into 4 groups based on mandibular plane inclination to cranial base (SN) angle. Linear and angular measurements were made on the lateral CBCT images: mandibular lateral incisor crown (I-C) total (I-A) lengths, the distances between point D (centre of symphysis) and both incisor apex (D-A) and menton (D-Me) and between cemento-enamel junction and menton (CEJ-Me); chin width at the level of the central incisor apex (CWA) and point D (CWD); and the angles of the anterior and posterior symphyseal slopes. The volume of the symphysis was measured using a specialized 3D imaging software. Group differences and associations between parameters were gauged through the three-way ANOVA analysis. I-C, I-A, D-A, D-Me and CEJ-Me were greater in the hyperdivergent group (p < .001). CWA and CWD were wider in the hypodivergent group (p = .003). Volume of the chin and inter-slope angles were similar in all groups (p > .05). The anterior slope angle decreased with hyperdivegence (p < .005) in opposite pattern to the posterior slope angle (p < .005). Shape differences in mandibular symphysis were observed between opposite divergence patterns. Mandibular incisors were longer with hyperdivergence and shorter with hypodivergence. However, chin volumes were similar across divergence groups. These findings underline the role of genetic and environmental factors that impact facial growth.

Research on Carbon Dioxide Computational Fluid Dynamics Simulation of Urban Green Spaces under Different Vegetation Spatial Layout Morphologies

Urban green spaces (UGSs) are considered an important natural approach for improving urban climatic conditions, promoting sustainable urban development, and advancing the global “Carbon Peak and Carbon Neutrality” targets. Previous studies have found that different vegetation spatial morphologies significantly impact the capacity to obstruct and absorb CO2, but it is not yet well understood which morphology can retain and absorb more CO2. This study takes Nantong Central Park as an example and conducts a CFD (Computational Fluid Dynamics) carbon flow simulation for CO2 under different vegetation spatial morphologies to identify their CO2 retention and absorption effects. First, the carbon sink benefits of elements such as “vegetation, soil, and wetlands” within the park were calculated, and the elements with the highest carbon sink benefits were identified. Then, the park was divided into carbon welcoming zones, carbon flow zones, and carbon shadow zones for carbon flow simulation with the highest carbon sink benefits. The results show that in the carbon welcome area, the one-block long fan-shaped plant community with a spatial density of 40 m thickness can best meet the requirements of absorption and induction of a small amount of carbon dioxide, with the smallest air vortex and uniform distribution of carbon dioxide in the surrounding area. In the carbon flow area, combined with the visual effect, the planting pattern of 6 m spacing herringbone combined with natural structure was adopted, which has a good carbon dioxide blocking and absorption capacity. In the carbon-shaded area, a herringbone planting pattern with a total width of 40 m and a base angle of 60° was chosen, which had the strongest hindrance and absorption capacity. Urban park environment optimization can use Fluent simulation to analyze the flow of carbon dioxide between different elements affected by wind dynamics at the same time. Based on the results, the form, layout, and spatial distance are adjusted and optimized. This study can better guide the spatial layout of vegetation and contribute to the realization of the goal of “carbon peak and carbon neutrality”.

Study of the dynamic impact spalling of ductile materials based on Gurson-type phase-field model

The formation of void damage and spalling failure in ductile metallic materials under strong impact is a well-established phenomenon. In aerospace and defense technology engineering design, understanding the spalling failure process and related mechanisms is of utmost importance. This paper develops an explicit Gurson-type phase-field model that can simulate the void evolution and spalling damage of three-dimensional ductile metallic materials under high-velocity impacts based on the study of Aldakheel et al.. The model incorporates the Gurson-type void evolution equation and the phase-field approach while taking into account the pressure-dependent bulk modulus and inertia effects. This model is used to study the main processes and mechanisms of impacted layer cracking of metals in different dimensions. Meanwhile based on the study of complex spallation cracking processes in metals in two and three dimensions, observing and proposing the formation mechanism of complex spallation cracking modes in materials due to lateral and edge (base angle) rarefied effects.

Comprehensive analysis of alar base inclination and lip line cant following orthognathic correction of maxillomandibular asymmetry: A retrospective study

This paper examines the relationship between roll rotation of the jaws and changes in alar base or lip line asymmetry in the coronal plane following orthognathic correction. The study involved patients with preoperative frontal alar base and lip line asymmetries greater than 0.5° (because it corresponds to the minimum asymmetry perception threshold) and underwent bimaxillary orthognathic surgery without (Group I) or with (Group II) genioplasty. The alar base angle (ABA), lip line cant angle (LLCA), maxillary cant angle (MxCA), and mandibular cant angle (MnCA) were measured using preoperative and 12 months postoperative cone beam computed tomography (CBCT) images. Thirty-four patients were included in the study. Significant correlations were found between changes in MxCA and ABA besides between changes in MnCA and LCA in Groups I (P = 0.016, P˂0.001, respectively) and II (P = 0.002, P˂0.001, respectively). The mean of the change in ABA/the change in MxCA and the change in LLCA/the change in MnCA ratios for Group I were 0.59 ± 1.57 and 0.73 ± 0.94, respectively, while those for Group II were 0.46 ± 3.70 and 0.39 ± 2.00, respectively. Angular measurements from jugular and mental foramina points, aligned with the bony midline, offer a convenient tool for predicting alar base and lip symmetry during bimaxillary orthognathic surgery planning.

The Relationship Between Craniocervical Morphology and the Presence and Level of Cervical Facet Joint Degeneration.

To investigate the relationship between craniocervical morphology and the presence and level of cervical facet joint degeneration (FJD). A total of 108 consecutive female patients aged 45-55 years who had undergone neck + brain CT angiography were included in this retrospective sectional study. Only patients of a certain age and of the same gender were included in order to eliminate the differences that create a disposition to the development of spinal degeneration. The presence of facet joint (FJ) arthritis (grade ≥2 degeneration in at least one affected facet joint) and the grade of the facet joint degeneration for each patient were recorded. A total of 20 lengths and 3 angles of craniocervical morphology were measured. The differences between the individuals with and without FJ arthritis were investigated with the independent-sample t test, and the relationship between the FJD grade and craniocervical morphology was investigated using the Spearman correlation test. Individuals with FJ arthritis were found to have longer Grabb-Oakes measurement, shorter FM AP length, lower ADI, lower EOP thickness, higher clivus length, higher crista gall-ATS distance, lower CCA angle, lower distance between the C1 vertebra lateral masses, and higher BAI than those without FJ arthritis (P ˂ 0.05). Besides, we found that the FJD grade increased as the Grabb-Oakes measurement increased, ADI distance decreased, FM AP length decreased, EOP thickness decreased, clivus length increased, basal angle increased, distance between the C1 vertebra lateral masses decreased, and BAI increased (P ˂ 0.05). Differences in craniocervical morphology are statistically associated with degenerative processes that result in degenerative changes in the facet joint. Therefore, some morphological changes in craniocervical anatomy cause changes in the momentum and distribution of the load on the facet joints, predisposing the patient to facet arthropathy and osteoarthritis.

Effect of the Basilar Invagination (Type B) on Cervical Spine: A Case-control Study with MRI

To evaluate the effect of the basilar invagination (BI) type B on cervical spine. The research protocol used head magnetic resonance imaging (MRI) exams from 41 participants with BI type B and 158 controls. The criterion for BI was the distance of the odontoid apex to Chamberlain's line (DOCL) equal to or greater than 7 mm. The clivus length (CLI), clivus canal angle (CCA), Welcker's basal angle (WBA), Boogaard's angle (BOA), upper cervical lordosis angle (UCL), and total cervical lordosis angle (CL) were evaluated. The descriptive analysis, group comparisons, and correlations between skull base and cervical spine parameters were performed at the 95% confidence interval. Participants with BI type B showed shorter clivus length (CLI: 25.7mm±7.3); greater angulation of the skull base (WBA: 126.5±10.4); greater inclination foramen magnum (BOA: 151.5±14.5); decrease in the value of the (CCA: 131.6±15); and greater angulations of UCL (17.9 ±13.8) and CL (29.7 ±19.9) in comparison to the control group (P < 0.05). Clivus length and CCA correlated inversely with UCL and CL, while BOA correlated directly with UCL and CL. The WBA did not correlate with CL (P < 0.05). The deformation of skull base in the BI of type B caused, on average, a hyperlordosis of almost 30 degrees in the C2-C6 segment. This change was approximately 17º in the C2-C4, with the clivus hypoplasia being a risk factor for cervical hyperlordosis.

Maxillary advancement surgery with vertical component: Impact on the nasolabial aesthetics

The aim of this study is to evaluate the changes in nasolabial soft tissues following Le Fort I osteotomies, focusing on the impact of maxillary vertical repositioning.This retrospective study included 39 patients with a history of Le Fort 1 osteotomy between 2013 and 2021. Patients were grouped based on their maxillary movement into three categories: pure advancement (group A), advancement with impaction (group B), and advancement with downward repositioning (group C). Preoperative and postoperative CBCT (Cone Beam Computed Tomography) data were analyzed to measure the changes in nasolabial soft tissues. The current study utilized Mimics Suite 20.0 for measuring linear and angular variables. The evaluated variables included intercanthal distance, nasal dorsal length, tip protrusion, mouth width, alar width, upper lip height, nostril dimensions, and angles of nasolabial, alar base, and upper lip. Among them intercanthal distance, nasal dorsal length, or tip protrusion showed no statistical difference (p > 0,05). Mouth width, alar width, alar base angle were increased and upper lip angle was decreased significantly (p < 0.001). Changes in upper lip height and nasolabial angle differed among the groups of the study. While upper lip height increased significantly in groups A and C (p < 0.05), there was a slight decrease in Group B with no significance (p > 0.05). Nasolabial angle decrased significantly on Groups A and B (p < 0.05).The results of this study revealed changes in several soft tissue parameters, some of which occurred regardless of vertical repositioning of the maxilla. Within the limitations of the study, maxillary advancement surgery can affect the aesthetics of the nasolabial region and cause specific changes in related soft tissues. Understanding these changes is essential to establish realistic patient expectations and achieve optimal functional and aesthetic outcomes.

Craniofacial Cephalometric Morphology in Polish Adolescents with Cleft Palate Only.

Background: Cephalometric studies indicate that craniofacial morphology in patients with cleft palate only (CPO) differs from other forms of orofacial clefts and healthy patients. Planning orthodontic treatment for patients with different craniofacial deformities requires knowledge on the craniofacial complex. The aim of the present study was to describe the cephalometric craniofacial morphology in adolescents with cleft palate only compared to generally healthy orthodontic patients. Methods: The study comprised 100 lateral cephalograms (taken in the years 2003-2020) of Polish patients with cleft palate only aged from 11.1 to 14.2 (mean age 12.43 y) and a matched control group of 100 children without orofacial clefts aged 12-14 (mean age 12.25). All digital images were analyzed in specialized cephalometric software. Results: Statistically significantly lower values of both SNA (p < 0.001) and ANB (p < 0.001) were found in the study group versus the control group. Mandibular line to cranial base angle (ML-NSL) as well as maxillary base to cranial base (NL-NSL) were significantly higher in the CPO group. Both the maxilla and mandible were rotated distally in CPO. Moreover, the intermaxillary vertical angle (ML-NL) was reduced in CPO. Mandibular angle in CPO was significantly higher (p = 0.005), reflecting posterior mandibular rotation. Conclusions: In adolescents with CPO, maxillary deficiency is found, without a severe sagittal jaw discrepancy, with a slight compensatory lingual inclination of the lower incisors. Mandibular deficiency in CPO is concurrent with posterior rotation and an increased mandibular angle.

Study of adhesive wear mechanisms in asperity junctions based on phase field fracture method

Adhesive wear that is mostly induced by adhesion between asperities of rough surfaces in contact is one of the most common forms of wear of materials. However, the adhesive wear mechanisms are still not fully understood. In this work, the phase field fracture method that does not require any assumption on the crack path is used to explore the debris formation mechanism during asperity separation in adhesive wear. It is found that for ideal materials without defects the size of wear particles depends on the contact length. A small contact length leads to fracture at the junction and the formation of small wear particles. On the contrary, a large contact length will cause fracture in the bulk, resulting in large wear particles. Moreover, the angle of crack propagation decreases with increasing base angle of asperity and the ratio of the asperity height to the base edge width. The variation of fracture angle is mainly related to the ratio of asperity height to the base edge width that will influence the angle of the interaction force between asperities in the wear process. For materials with initial hole defect, the formation mechanism of wear particles will be little affected when the hole is rather small or far away from the junction. However, as the hole diameter further increases, the wear particles will change from large particles to small ones. And for materials with initial crack defect, the crack propagation always starts from the initial crack during adhesive wear. Moreover, for adhesive wear of materials with an initial crack at the bottom of asperity, fracture angle in the bulk is significantly positively correlated with the contact length and large wear particles are easy to form. However, during adhesive wear of asperity with the initial crack inside the bulk of asperity, small particles are more likely to form. This work contributes to further understanding of adhesive wear process.

A scoping review of cephalometric normative data in children.

Understanding the orofacial characteristics and growth patterns in children is essential for both orthodontics and research on children with orofacial abnormalities. However, a concise resource of normative data on the size and relative position of these structures in different populations is not available. Our objective was to aggregate normative data to assess the growth of the orofacial skeletal structures in children with a well-balanced face and normal occlusion. The MEDLINE, Embase, and Scopus databases were searched. Inclusion criteria included longitudinal and cross-sectional studies on cephalometric measurement of skeletal tissues and a study population ≤ 18 years with a well-balanced face and normal occlusion. Key study parameters were extracted, and knowledge was synthesized. A quality appraisal was performed using a 10-point scale. The final selection comprised of 12 longitudinal and 33 cross-sectional studies, the quality of which ranged from good to excellent. Our results showed that from childhood to adulthood, the length of the cranial base increased significantly while the cranial base angle remained constant; both the maxilla and mandible moved forward and downward. The profile becomes straighter with age. Growth patterns in children with a well-balanced face and normal occlusion follow accepted theories of growth.

Parallel Covering an Obtuse Triangle with Squares

Suppose that 𝑇 (𝛼, 𝛽) is an obtuse triangle with base length 1 and with base angles 𝛼 and 𝛽 (where 𝛽 &gt; 90◦). In this note a tight lower bound of the sum of the areas of squares that can parallel cover 𝑇 (𝛼, 𝛽) is given. This result complements the previous lower bound obtained for the triangles with the interior angles at the base of the measure not greater than 90◦.