Plane Angle Research Articles

Hinge Position Dominance Over Osteotomy Inclination in Medial Open-Wedge High Tibial Osteotomy: A Key Factor in Posterior Tibial Slope Changes.

A medial open-wedge high tibial osteotomy (MOWHTO) may increase the posterior tibial slope (PTS). The purpose of this study was to determine the effect of the osteotomy inclination angle (in the sagittal plane) in combination with different hinge positions (in the transverse plane) on the change in PTS due to a MOWHTO. We developed a mathematical approach to determine the effect of the osteotomy inclination angle combined with different hinge positions. The change in PTS was determined for different osteotomy inclination angles, hinge positions, and intended wedge angles. Anterior-inclined, parallel, and posterior-inclined osteotomy inclination angles were simulated. Hinge positions varied between 5° anterolateral and -45° posterolateral. The wedge angles were 5°, 10°, and 15°. Moreover, 2 in silico osteotomies were performed to verify the results of the mathematical model. The PTS was maintained when the osteotomy cut was performed parallel to the tibial plateau with a lateral hinge position. The PTS changed when the osteotomy was not aligned in the sagittal plane, ranging between 0.0° and 0.6°. Different hinge positions, however, had a large effect on postoperative PTS change, ranging between 0.1° and 10.7°. Our mathematical approach showed that the hinge position has a strong effect on the PTS. The sagittal osteotomy inclination angle had little effect on the PTS. An inclination angle parallel to the medial tibial plateau combined with a lateral hinge position does not change the PTS.

Anatomical investigation of safety determining factors for keyhole drilling trajectories for robotic cochlear implant surgery.

Cochlear implants (CI) are the most successful bioprosthesis in medicine probably due to the tonotopic anatomy of the auditory pathway and of course the brain plasticity. Correct placement of the CI arrays, respecting the inner ear anatomy are therefore important. The ideal trajectory to insert a cochlear implant array is defined by an entrance through the round window membrane and continues as long as possible parallel to the basal turn of the cochlea. Image-guided surgery can directly drill with a robotic arm through the mastoid and execute an exact drilling of this precalculated most ideal trajectory. Here, we aim to identify critical anatomical structures determining the safest keyhole drilling trajectory by comparing easy and difficult CI surgeries performed with the HEARO Procedure: a robotic tool for image-guided surgery. Cone-beam computed tomography images of patients who underwent robot-assisted cochlear implantation surgery (RACIS) were included. Three of 25 cases had to be converted to conventional surgery because of the current safety mitigations based on anatomical distance. Radiological images in DICOM format were transferred to dedicated software (OTOPLAN® Cascination GMHB Bern Switzerland) for analyses. Surgical segmentation and previously planned trajectories were analyzed for these 25 cases by comparing cochlear sizes, facial recess sizes, round window sizes, and trajectory angles. In addition, facial recess angle, and cochlear orientation angles were measured with RadiAnt DICOM Viewer (Medixant, Pozan, Poland). Facial recess size, facial recess angle, and distance between the facial nerve and safe trajectory were smaller in patient who converted from robotic surgery to conventional. A significant positive correlation existed between basal turn angle and in-plane angle (p = 0.001, r = 0.859). In addition, there was a significant negative correlation between the basal turn length and the last electrode insertion depth degree (p = 0.007, r = 0.545). In our robotic surgery cases, we demonstrate that the limiting factors of anatomical relationships are constituted by the dimensions of the facial recess and the cochlear orientation. The findings of this study are considered to be a reference for future studies in achieving collision-free trajectory planning in robotic-assisted cochlear implant surgery.

All-angle unidirectional flat-band acoustic metasurfaces

Flat bands have empowered novel phenomena such as robust canalization with strong localization, high-collimation and low-loss propagation. However, the spatial symmetry protection in photonic or acoustic lattices naturally forces flat bands to manifest in pairs aligned at an inherently specific angle, resulting in a fixed bidirectional canalization. Here, we report an acoustic flat-band metasurface, allowing not only unidirectional canalization at all in-plane angles but also robust tunability in band alignment. The twist, tilt, and skew angles of the bilayer metasurface can be flexibly controlled to break both in-plane and out-of-plane spatial symmetries. These features can thereby turn arbitrary twist angles between bilayers into ‘magic angles’, while maintaining all unidirectional canalization and band alignment tunability. This work may significantly contribute to pushing twisted moiré physics into higher dimensions and facilitate the application of advanced acoustic or optical devices.

Angle-controlled strong and weak coupling in photon molecules

Strong light-matter coupling occurs when the rate of energy exchange between the electromagnetic mode and the molecular ensemble exceeds the competitive dissipation process. Coupled photon molecules with near-field light-matter interactions may produce new hybridized states when they reach the strong coupling region. Tunable Terahertz (THz) meta materials can be used to design sensors, optical modulators, etc., to improve imaging sensitivity and resolution. In this work, we use the scattering-type scanning near-field microscopy (s-SNOM) to demonstrate an angle-controlled coupling strength in a tunable photon molecules system. The system consists of a base waveguide layer and a single ribbon structure. By changing the in-plane angle between ribbon and incidence, the coupling strength between ribbon resonance and waveguide mode ranges from 0.03 to 0.08 THz, leading to the system’s transformation from weak to strong coupling. This work offers a new platform for actively controlling strong light-matter interaction and further applications in strong coupling.

Test-Retest Reliability and Validity of TecnoBody D-Wall to Assess the Range of Motion During Overhead Squat in Healthy Individuals.

This study evaluated the validity and reliability of the TecnoBody D-Wall system in assessing joint range of motion (ROM) during overhead squat movements in healthy individuals, using Kinovea as a reference tool for data comparison. A total of 29 participants (16 males, 13 females) with a mean age of 28.41 ± 6.66 years were included. Measurements were conducted for hip and knee joint angles in the sagittal plane, with three repetitions per participant analyzed using both systems. The D-Wall system employed a 3D Kinect V2 camera and force platform, while Kinovea used 2D video-based motion analysis. The results demonstrated excellent agreement between the two systems, with intra-class correlation coefficients (ICC) ranging from 0.79 to 0.99. For the knee joint, the test-retest ICC values were 0.99 (95% CI: 0.97-0.99) for Kinovea and 0.98 (95% CI: 0.95-0.99) for the D-Wall on the right side, and 0.98 (95% CI: 0.97-0.99) for Kinovea and 0.88 (95% CI: 0.79-0.94) for the D-Wall on the left side. For the hip joint, test-retest ICC values were 0.99 (95% CI: 0.97-0.99) for Kinovea and 0.94 (95% CI: 0.88-0.97) for the D-Wall on the right side, and 0.98 (95% CI: 0.97-0.99) for Kinovea and 0.93 (95% CI: 0.87-0.97) for the D-Wall on the left side. Bland-Altman plots confirmed good agreement, with no significant systematic bias observed. Both systems showed statistically insignificant differences (p > 0.05) between measurements, and correlation values ranged from 0.83 to 0.99, indicating strong associations. These findings highlight the high validity and reliability of both TecnoBody D-Wall and Kinovea systems in measuring joint angles during dynamic movements. The comparable accuracy between systems suggests that either system can be effectively utilized in clinical or research settings, depending on specific needs and resource availability.

Reliability and Validity of the Articulation Motion Assessment System Using a Rotary Encoder

This study aimed to validate the effectiveness of the Articulation Motion Assessment System (AMAS), a joint kinematic evaluation system, for clinical applications. AMAS enables synchronised measurement using neurophysiological indicators, overcoming laboratory setting limitations. We compared AMAS-based ankle joint kinematic evaluations, particularly the sagittal and frontal plane angles, with two-dimensional (2D) motion analysis to determine the validity and reliability of AMAS. Both AMAS and 2D motion analysis reliably detected significant differences in angles within the sagittal and frontal planes. Correlation analysis revealed a significant moderate-to-strong correlation between the AMAS and the conventional method of 2D motion analysis, proving the measurement validity of the AMAS (ρ = 0.53–0.77 for sagittal plane angles; ρ = 0.46–0.72 for frontal plane angles). The average root mean squared error (RMSE) was significantly lower in AMAS (10.90 ± 2.93° for sagittal plane angles; 13.44 ± 1.09° for frontal plane angles) than in the inertial sensor-based three-dimensional (3D) motion analysis. Reliability analysis revealed high reliability of measurements (intraclass correlation coefficients (ICC) ≥ 0.76). However, the Bland–Altman analysis identified a slightly lower fixed bias, which was observed as a characteristic of each measurement system. The AMAS accurately detects ankle joint angles without being constrained by measurement environment limitations. Synchronised measurements using neurophysiological indicators potentially contribute to understanding ankle joint control mechanisms and developing rehabilitation strategies.

Tuning anomalous Hall conductivity via antiferromagnetic configurations in GdPtBi.

The magnetic, electronic, and topological properties of GdPtBi were systematically investigated using first-principles density functional theory (DFT) calculations. Various magnetic configurations were examined, including ferromagnetic (FM) and antiferromagnetic (AFM) states, with particular focus on AFM states where the Gd magnetic moments align either parallel (AFM‖) or perpendicular (AFM⊥) to the [111] crystal direction. For AFM⊥, the in-plane angles ϕ were varied at ϕ = 0°, 15°, and 30° (denoted as AFM⊥,ϕ=0°, AFM⊥,ϕ=15°, and AFM⊥,ϕ=30°, respectively). The ground-state magnetic structure of GdPtBi was validated through dipolar magnetic field calculations at the muon sites, corroborating the internal magnetic fields observed in muon spin relaxation (μSR) experiments. The results indicate that the AFM⊥,ϕ=30° configuration aligns with the μSR-measured internal field. The DFT-calculated band structure and Berry curvature reveal that AFM⊥ belongs to the triple-point semimetals (TPSMs) where the triple-point nodes positioned along the Z-Γ-Z and F-Γ-F paths have energies that shift as the spin-orbit coupling strength varies with ϕ. Notably, this shift in triple-point energy corresponds to a significant change in the anomalous Hall conductivity (AHC, σxy), with a difference of 75.06 Ω-1 cm-1 at the Fermi energy between AFM⊥,ϕ=0° and AFM⊥,ϕ=30°. These findings highlight the potential for controlling the AHC through precise manipulation of the AFM structure.

Moiré metasurfaces with tunable near-infrared-I chiroptical responses for biomolecular chirality discrimination.

Manipulating circular dichroism in chiral metasurfaces has been increasingly important for a wide range of polarization-sensitive photonic applications. However, simple methods for presenting chiral nanostructures with tunable and considerable chiroptical responses in the near-infrared-I regime remains underexplored. Herein, two sheets of suspended symmetric bilayer metagratings fabricated via single-step electron beam lithography are stacked into a moiré metasurface with its circular dichroism value reaching up to 20.9°. The chirality of the moiré metasurface can be fully tuned in terms of both its sign and magnitude by adjusting the in-plane angle between the two twisted sheets of metagratings. The multilayered design is accessible to the coupling of hybridized plasmons for governing the chiroptical properties in the near-infrared-I regime. The ratio between the resonance wavelength and the grating period is about 1.65, which is much lower compared to that in most existing moiré metasurfaces with strong chiroptical responses. Furthermore, the superchiral fields in the inter-sheet region are further exploited for label-free enantiodiscrimination with ultrahigh sensitivity of 10.17 nm fmol-1 mm2. The proposed moiré metasurfaces with strong near-infrared-I chirality hold great potential for supporting polarization engineering and biomolecular detection, paving a way for advanced applications in medical diagnosis, biomedical imaging, and display technologies.

Trunk fatigue effect on lower limb kinematic and electromyographic patterns during the single-leg drop-landing test in female novice runners

Trunk muscle fatigue could influence the dynamic control of the lower limbs in runners, and the single-leg drop-landing (SLDL) test could simulate the landing and reveal those changes. This study compared the effect of trunk muscle fatigue on the kinematic and electromyographic patterns of the lower limb during SLDL in female novice runners. The kinematics of the main joints and electromyographic (EMG) of the main muscles of the lower limb during SLDL pre- and post-fatigue muscle trunk were registered in 18 female novice runners. The integrated EMG (iEMG) was calculated into 3 phases (F1, before movement starts; F2, eccentric; and F3, concentric). There was an increase in the tibialis anterior and soleus mean iEMG in F1, a reduction in tibialis anterior (TA) and gastrocnemius medialis (GM) maximum iEMG in F2, and an increase in the biceps femoris (BF) minimal iEMG in F2. Also, we found a reduced ankle angle, increased hip angle in the sagittal plane, and a reduced knee angle in the frontal plane post-intervention. The induction of trunk muscle fatigue in female novice runners influenced the TA, SO, GM, and BF EMG changes, the kinematic pattern of the ankle and hip in the sagittal plane, and the knee in the frontal plane during the SDLD.

Anisotropic in-plane field angle dependence of critical current in commercial REBCO tapes and its impact on toroidal field magnet for compact tokamak fusion device

Abstract The critical current (I c) of commercial rare-earth barium copper oxide (REBCO) tapes is generally assumed to exhibit isotropic behavior with respect to the magnetic field angle applied within the tape’s basal plane (in-plane). This paper investigates the field angle dependence of critical current, both in-plane and out-of-plane, for commercial REBCO tapes manufactured by SuperOX, under fields ranging from 0 T to 8 T at 20 K. Remarkably, the in-plane field angle dependence of I c shows significant anisotropy, with the minimum I c no longer occurring at the traditional 90° (parallel to the ab-plane), but instead shifting to approximately 130°, a phenomenon reported for the first time. This novel anisotropic in-plane field angle dependence of I c can substantially affect the performance of toroidal field magnets for compact tokamak fusion devices. Simulations indicate that considering versus neglecting the anisotropic in-plane field angle dependence of I c can lead to I c variations of up to 19.58% within the D-shaped coils of the toroidal field magnets. The locations of maximum deviation vary across different double-pancake coils within the D-shaped winding packs. This study highlights the complexity of I c distribution in toroidal field magnets for compact fusion applications, urging further consideration of anisotropic in-plane field angle dependence of I c of commercial REBCO tapes in fusion magnet design.

Quantifying Gait Asymmetry in Stroke Patients: A Statistical Parametric Mapping (SPM) Approach.

BACKGROUND The VICON Toolkit enables three-dimensional (3D) motion capture for gait analysis. Statistical parametric mapping (SPM) is a voxel-based neuroimaging approach used to identify region-specific effects. This study aimed to apply SPM to analyze the joint angles of the hip, knee, and ankle during gait in 20 post-stroke patients using the VICON motion capture system. MATERIAL AND METHODS A total of 20 post-stroke patients participated in the study. A 10-camera VICON motion capture system (250 Hz) was used to record 3D kinematic data. Joint angles were assessed in the sagittal, frontal, and transverse planes using SPM. The data were normalized to 100% of the gait cycle, and a paired t test was performed to assess asymmetry between affected (AS) and unaffected sides (UAS), with P<0.05 considered statistically significant. RESULTS Significant asymmetry was observed in the hip and knee joint angles in the sagittal plane. The hip joint showed differences during 0-39% of the stance phase and 40-100% of the swing phase. The knee joint exhibited differences during 98-100% of the stance phase and 0-79% of the swing phase (P<0.05). CONCLUSIONS The study highlights the importance of addressing asymmetry in the hip and knee joints in post-stroke rehabilitation programs. The findings indicate the need for improving hip and knee joint mobility to enhance functional gait outcomes. The use of SPM provides a more comprehensive analysis of gait asymmetry, offering insights that go beyond traditional spatiotemporal methods.

Outcomes and Craniometric Analyses of the Champy Technique in the Treatment of Mandibular Angle Fractures: A Retrospective Study.

The aim of this study is to examine the outcomes of superiorly placed monocortical single miniplate fixation in the treatment of mandibular angle fractures and evaluate treatment efficacy through craniometric measurements. Postoperative craniometrics were compared with both the preoperative measurements and the control group. Thirty-four patients were included with a mean follow-up of 3.1 years. Complications were observed in 6 patients, with 4 treated surgically and 2 managed nonoperatively. In the craniometric analyses, there was no significant difference between the preoperative and postoperative measurements of the gonial angle and condyle-midsagittal plane distance on both the fracture side and the contralateral side. The only significant difference was found in comparison of the degree of the mentum deviation (P=0.001). Postoperative mandibular morphometry was comparable to that of the control group. Single miniplate fixation corrects mentum deviation without resulting in any changes in condyle position and can achieve healthy mandibular morphometry.

The 'roller coaster effect' in premolar extraction cases: clear aligners vs. straight-wire appliance.

This study aimed to quantitatively investigate the intractable 'roller coaster effect' (RCE) that occurs in premolar extraction cases treated with clear aligner therapy (CAT) or straight-wire appliance (SWA). Protrusion cases treated with extraction of bilateral first premolars were included. Pre- and post-treatment cephalograms were obtained to measure the bending angle of occlusal plane (BAOP), namely the occlusal intersection angle between the anterior occlusal plane (AOP) and posterior occlusal plane (POP). BAOP is proposed as the indicator for quantifying RCE in this study. In the maxillary dentition, BAOP significantly decreased from 177.50 ± 5.57° to 171.10 ± 3.32° in the SWA group (n = 30), and from 178.00 ± 4.66° to 168.10 ± 5.63° in the CAT group (n = 36). In the mandibular dentition, BAOP had no significant change (from 164.90 ± 5.00° to 164.30 ± 6.40°) in the SWA group (n = 29), while significantly decreased from 163.40 ± 6.36° to 155.90 ± 7.48° in the CAT group (n = 37). In the both dentitions, the post-treatment BAOP was significantly smaller in the CAT compared to SWA group. Decrease of BAOP in the CAT group resulted from bending of the AOP rather than POP. Multiple linear regression analysis revealed that the mandibular canine crown length had a positive correlation with the mandibular post-treatment BAOP. Only two-dimensional cephalometric measurements were conducted. In premolar extraction cases, CAT undergoes more severe RCE at completion of its first-phase treatment compared to SWA at the end of treatment. Longer mandibular canine crown may mitigate mandibular RCE in CAT.

A FEM‐DEM Coupling Analysis on Bearing Capacity of Sandy Soil Foundation Considering Fabric Anisotropy

ABSTRACTWith the acceleration of urbanization, the stability of the foundation is being more crucial to the performance and service of the superstructure. As our understanding of the factors influencing soil's physical and mechanical behavior deepens, it becomes increasingly challenging for traditional limit equilibrium and limit analysis methods to accurately consider the complex factors affecting foundation stability, such as initial fabric anisotropy caused by the particle morphology and geological deposition in sand. Although some scholars had used advanced constitutive models in the finite element method (FEM) to investigate the influence of initial fabric anisotropy on mechanical responses of foundations, this approach failed to reveal the microscopic information underlying the shear failure of sandy soil foundations. In this study, the influence of the initial fabric anisotropy of sandy soil on the ultimate bearing capacity and shear failure mode of shallow foundation is studied using the hierarchical FEM and discrete element method (DEM) coupling analysis method. Four representative volume elements (RVEs) with varying initial bedding plane angles are constructed in DEM for characterizing different initial fabric anisotropies, and the specific stress–strain information of DEM RVEs is directly passed into the corresponding Gauss points in FEM to replace the conventional constitutive model. Numerical results show that the initial fabric anisotropy affects the ultimate bearing capacity and shear failure mode of shallow foundations significantly, and the corresponding micromechanical behaviors at different local Gauss points have been explored, which advances our understanding of the micromechanisms underlying the progressive shear failure of sandy soil foundations significantly.

Do Different Next-to-Skin Garments Change Thermal Sensation, Jump Height and Landing Knee Valgus After Cold Exposure?

Exposure to the cold can negatively affect muscle performance. This study compared the effects of two different full-length, lower body, next-to-skin garments on thermal sensation, countermovement jump (CMJ) height and knee frontal plane angle upon landing following cold exposure against a control. After familiarisation, 13 male and 11 female recreationally active adults attended three separate laboratory testing sessions where a randomly assigned next-to-skin garment was used (compression, thermal and control (shorts)). A pre- and post-testing protocol comprising CMJ and drop landings interspersed with a sedentary cooling period of 40 min at 0 °C was adopted. High-speed motion analysis and subjective ratings of thermal sensation were recorded. Exposure to the cold significantly reduced thermal sensation (p &lt; 0.001) scores and CMJ height (p &lt; 0.001). Only female participants felt significantly warmer (p ≤ 0.009) in the next-to-skin garments. Losses in CMJ height were significantly reduced by the next-to-skin garments compared to the control with the thermal garment producing better results. There was little change in knee frontal plane angle upon landing in all the garments tested. Ambient cooling at 0 °C for 40 min had a significant effect on CMJ height and thermal sensation but not knee valgus upon landing. Participants in winter sports should consider next-to-skin garments in conjunction with proper warm-ups and re-warming techniques to protect themselves from the negative effects of the cold.

Influence of inherent anisotropy on the mechanical properties of normally consolidated clays with a wide range of plasticity indices

Inherent (fabric) anisotropy is one of the most important properties of earthen materials which has a significant influence on their strength and stiffness characteristics. In this study, a comprehensive series of unconfined and constrained compression tests is performed on normally consolidated (NC) clay samples with different plasticity indices to examine the effect of inherent anisotropy on their mechanical characteristics. Accordingly, several cylindrical clay samples with different proportions of kaolinite and bentonite are reconstituted at a wide range of deposition angles and then subjected to both unconfined and constrained compressive loadings. According to the experimental results, for a clay sample with a particular plasticity index, the highest and lowest values of the unconfined compressive strength (UCS), the secant modulus (E50), and the constrained Young's modulus (Eoed) are observed to be associated with the deposition angles of 0o and 90o, respectively. The results also show that at a certain bedding plane angle, the sample containing 30% bentonite (PI = 110%) exhibits the highest UCS, E50, and Eoed values. Several practical empirical correlations are developed to estimate the strength and stiffness properties of NC clays using their plasticity indices and bedding plane directions. Scanning Electron Microscopy (SEM) analysis is also conducted to explore the microstructure of samples containing varying percentages of kaolinite and bentonite.

Specific postural alignment alterations due to long-face deformity in patients with maxillo-mandibular deformities.

A specific pathological postural adaptation is suspected in patients exhibiting maxillo-mandibular deformity (MMD); however, none study reported a correlation between facial dimensions and posture. In this study, we hypothesized that pathological postural adaptations are related to long-face deformity and subsequent oral breathing in patients with MMD METHODS: Thirty patients with MMD and 20 healthy subjects. Breathing mode, postural alignment and cephalometry were analyzed through a biplanar X-ray (EOS imaging®) of the skeleton in an upright position, followed by three-dimensional reconstruction. Patients with MMD exhibited hyperkyphosis of the lower region of the cervical spine (C3-C7 angle: 10.6° [3.9; 17.5] vs. 3.2° [-6.4; 7.6], p < 0.01), forward head posture (OD-C7 angle: 10.5° [8.5; 15.1] vs. 6.2° [3.0; 8.4], p < 0.01), and backward sagittal balance compared with controls (sagittal vertical axis:15.7 mm [-25.9; -5.2] vs. -1.4 mm [-17.8; 7.0], p = 0.014). Cervical hyperkyphosis, the forward head posture, and the backward sagittal balance were related to higher values of the Frankfort-mandibular plane angle (a cephalometric variable used to assess face length). In patient with MMD, oral breathing was correlated to the FMA angle. MMD is associated with a specific pathological postural adaptation which is correlated with Long-face deformity and oral breathing. Our results suggest that the altered posture originates from the upper airways.

Methodology for the correction of a CBCT volume from the skull to the natural head position

The orientation of the head during the acquisition of cone beam computed tomography (CBCT) is crucial for accurate cephalometric measurements. However, involuntary head movements during the scan can result in misaligned images. This study presents a method to correct the natural head position (NHP) in CBCT skull images after acquisition. Initially, slices were reorganized, and volumes were oriented in RAI coordinates. Next, the Yaw angle in the axial plane was estimated using the fronto-zygomatic sutures (FZS). The Roll angle in the coronal plane was estimated using the centroids of the ocular cavities. Finally, the Pitch angle in the sagittal plane was measured (by the Sella Turcica (S) and Nasion (N) as reference points) and adjusted to reference values of 3.8° for males and 4.1° for females. These calculated angles are used to adjust the CBCT volumes, aligning the images with the NHP.•The method corrects misalignment in CBCT skull images due to involuntary head movements, ensuring accurate cephalometric measurements.•Reference points like fronto-zygomatic sutures, ocular cavity centroids, and the Sella-Nasion line were used to adjust head position in all anatomical planes.•The approach aligns CBCT volumes to the NHP after capture, reducing errors in cephalometric analysis and enhancing diagnostic accuracy.

Phase field modelling of tunnel excavation damage in transversely isotropic rocks

Layered rocks, prevalent in geological formations, exhibit complex failure behaviours driven by pronounced anisotropy in their mechanical properties. However, the intricate failure mechanisms remain inadequately understood due to the spatial complexity of these mechanical responses. To address this challenge, this study proposes a novel phase field model tailored for layered rocks. A new strain energy decomposition method is introduced, uniquely formulated based on stress components and designed for transversely isotropic constitutive models. Numerical solutions to the coupled stress-phase field equations are obtained using user-defined element and material subroutines, implemented through a staggered solution scheme. The accuracy and robustness of the numerical approach are validated through simulations of a composite panel with a central hole under tensile loading. Additionally, the model is applied to the excavation of the layered soft rock tunnel, revealing the significant influence of bedding plane angles on displacement and stress field distributions, as well as post-excavation failure modes. Notably, the model captures the predominant shear-slip failure along bedding planes following excavation, effectively reflecting the complex mechanical interactions in layered rocks. This proposed model represents a significant advancement in understanding the failure mechanisms of layered rocks, providing a valuable tool for future geotechnical applications.

Functional Units Analysis of Mandibular Morphology in Patients With Parry-Romberg Syndrome.

To characterize mandibular morphology in patients with Parry-Romberg syndrome (PRS). Retrospective study. A craniofacial center. Thirty-three patients with PRS affecting mandible. Preoperative computed tomography data were analyzed using Mimics 26.0 (Materialise Inc.). Distances between landmarks-condyle process (Con), coronoid process (Cor), mandibular foramen (IAF), gonion (Go), and mental foramen-were measured to represent the sizes of skeletal units. Positional asymmetry was reflected by angles between lines connecting bilateral landmarks and the occlusal plane. Bilateral differences in unit sizes were compared. Absolute difference (Δ) > 5 mm and relative size (RS) < 80% were set to evaluate the severity of hypoplasia. Angular measurements were compared to 0° using one-sample t tests. Pearson correlation analysis was conducted to examine the relationship between onset ages and both RS and angular measurements. The affected side's skeletal units were smaller. Severe hypoplasia was more common in the angular unit. Angles between Con-Con', Cor-Cor', IAF-IAF', and the occlusal plane were less than 0°, whereas the angle with Go-Go' was greater than 0°. Age of onset was positively correlated with the condylar unit size and the Con-Con' to occlusal plane angle. Patients with PRS affecting mandible exhibit smaller skeletal units on the affected side, particularly in the angular unit. Most landmarks on affected side tend to cluster toward the occlusal plane. Earlier onset of PRS correlates with more pronounced condylar asymmetry. Evaluating the severity of functional units involvement and implementing appropriate treatment should be considered.