Plane Displacements Research Articles

Analysis of the anisotropic mechanical properties of structural adhesive joints with curing-induced pre-deformations

In modern lightweight construction, multi-material design has become increasingly important. An increasing number of structures are being adhered because adhesive joining technology can be used regardless of the material of the bonded partners. Owing to the dissimilar coefficients of thermal expansion, thermally induced relative displacements of the adherend occur during heat curing. Following these pre-deformations, changes in the mechanical properties of adhesive joints were observed. In this study, thick adherend shear specimens were used to induce defined relative displacements in the shear plane during the curing process. Quasi-static tests showed a directional dependence in the pre-deformation. This anisotropic behaviour was investigated in detail. Results showed that shear band formation occurred in the adhesive owing to the load during the cooling of joined structures. The restructuring of the polymer structure leads to changes in the mechanical properties.

Graviception Uncertainty, Spatial Anxiety, and Derealization in Patients with Persistent Postural-Perceptual Dizziness

Objectives: Persistent Postural-Perceptual Dizziness (PPPD) is a frequent diagnosis in patients with chronic dizziness, ineffective postural control, visual dependence, and emotional symptoms. Methods: 53 patients with PPPD (25–84 years old) and 53 adults (29–84 years old) with no vestibular disease agreed to participate in this study. Assessments included: vestibular function tests (sinusoidal yaw rotation and vestibular-evoked myogenic potentials); accuracy and precision of Subjective Visual Vertical (SVV) estimation while static and during on-axis yaw rotation; static posturography with open/closed eyes and 30° neck extension, while standing on hard/soft surface; questionnaires on symptoms of unsteadiness, spatial anxiety, dizziness-related handicap, anxiety/depression, depersonalization/derealization, and perceived stress. After preliminary bivariate analyses, analysis of covariance was performed on the measurements of postural sway, spatial anxiety, and dizziness-related handicap (p < 0.05). Results: Higher intraindividual variability (reduced precision) on SVV estimations was evident in patients with PPPD compared to adults with no vestibular disease, which was related to the length of postural sway, to velocity displacement in the sagittal plane, as well as to spatial anxiety and common mental symptoms (including depersonalization/derealization symptoms). Covariance analysis showed contribution of these factors to the dizziness-related handicap reported by the patients. Conclusions: Unprecise graviception could be a contributing factor to the postural instability and mental symptoms reported by patients with PPPD, which in turn contribute to their dizziness-related handicap.

The Effect of First Metatarsal Shortening and Sagittal Displacement on Forefoot Pressure in Minimally Invasive Hallux Valgus Correction.

Minimally invasive (MIS) treatment of hallux valgus (HV) deformity is increasing in popularity. A 2-mm diameter burr is used to create a distal first metatarsal osteotomy prior to capital fragment translation and fixation. The metatarsal will shorten by the burr's diameter (2 mm). Plantar or dorsal capital fragment displacement may also cause load transference and possibly transfer metatarsalgia. The purpose of this study is to examine the effect of MIS HV on forefoot loading mechanics with respect to metatarsal shortening and sagittal plane displacement. Four lower-limb cadaveric specimens were studied. A pedobarography pressure-sensing mat was used to record forefoot plantar pressure in a controlled weight-bearing stance position. Control and postosteotomy measurements were obtained with the capital fragment fixated in 3 possible positions: 0 mm, 5 mm dorsal, and 5 mm plantar displacement. Pedobarography data yielded pressure data within measurable graphical depictions. Raw mean contact pressure measurements were taken under the first and fourth metatarsal heads to establish medial and lateral forefoot loading pressure ratios. An a priori power analysis was performed based on previous peer-reviewed pedobarographic data, and our study was adequately powered. Around 40 measurements were recorded, and ratios of medial-to-lateral forefoot loading were constructed. Medial forefoot pressure control versus 0 mm displacement, and control versus dorsal displacement were not found to be statistically significant (p = 0.525, p = 0.55, respectively). Medial pressure significantly increased when comparing control versus plantar displacement (P = .006). Lateral pressure significantly increased with dorsal displacement of the osteotomy (P = .013). Our study found that MIS HV correction did not cause an increase in lateral forefoot pressure loading when sagittal plane displacements were controlled. Plantar displacement increased medial loading, and dorsal displacement increased lateral loading. It may be valuable for surgeons to consider metatarsal head position postosteotomy, as a decrease in medial loading and subsequent increase in lateral loading may lead to lateral forefoot pain and transfer metatarsalgia. IV.

Intriguing Low-Temperature Phase in the Antiferromagnetic Kagome Metal FeGe.

The properties of kagome metals are governed by the interdependence of band topology and electronic correlations resulting in remarkably rich phase diagrams. Here, we study the temperature evolution of the bulk electronic structure of the antiferromagnetic kagome metal FeGe using infrared spectroscopy. We uncover drastic changes in the low-energy interband absorption at the 100K structural phase transition that has been linked to a charge-density-wave (CDW) instability. We explain this effect by the minuscule Fe displacement in the kagome plane, which results in parallel bands in the vicinity of the Fermi level. In contrast to conventional CDW materials, however, the spectral weight shifts to low energies, ruling out the opening of a CDW gap in FeGe.

Giant Modulation of Refractive Index from Picoscale Atomic Displacements.

It is shown that structural disorder-in the form of anisotropic, picoscale atomic displacements-modulates the refractive index tensor and results in the giant optical anisotropy observed in BaTiS3, a quasi-1D hexagonal chalcogenide. Single-crystal X-ray diffraction studies reveal the presence of antipolar displacements of Ti atoms within adjacent TiS6 chains along the c-axis, and threefold degenerate Ti displacements in the a-b plane. 47/49Ti solid-state NMR provides additional evidence for those Ti displacements in the form of a three-horned NMR lineshape resulting from a low symmetry local environment around Ti atoms. Scanning transmission electron microscopy is used to directly observe the globally disordered Ti a-b plane displacements and find them to be ordered locally over a few unit cells. First-principles calculations show that the Ti a-b plane displacements selectively reduce the refractive index along the ab-plane, while having minimal impact on the refractive index along the chain direction, thus resulting in a giant enhancement in the optical anisotropy. By showing a strong connection between structural disorder with picoscale displacements and the optical response in BaTiS3, this study opens a pathway for designing optical materials with high refractive index and functionalities such as large optical anisotropy and nonlinearity.

Formation of multibeam dynamic gradient interference light fields with refractive optical elements

This paper presents methods for the formation and properties of light fields that controllably vary in time and space, obtained as a result of the interference of three or four coherent light beams using refractive optical elements. The formation of three-beam and four-beam interference fields is carried out using trihedral and tetrahedral glass pyramids respectively. The possibility of the interference field displacement in the transverse plane is ensured by devices for controlled phase changes of at least two of the interfering beams. The directions of propagation of these beams do not lie in the same plane with the optical axis of the original beam incident on the pyramid. In threeand four-beam dynamic interference fields the peak intensity values are higher than in the original laser beams and two-beam interference fields, so it is advisable to use them for processing flat objects with laser radiation, moving the interference maxima along the surface of the object. With a pairwise azimuthal displacement of the propagation directions of four interfering beams around the longitudinal axis, a dynamic interference field is formed, the periodically structured maxima of which cyclically smoothly change their shape from cells to band and back. At different speeds of pairs of directions the interference structure of the maxima rotates around the longitudinal axis. Therefore, this field can be used for therapeutic effects on biological tissues and for mixing microparticles in suspensions and emulsions. Since the local maxima of the intensity of all these interference fields have dimensions of the order of several micrometers while exceeding in value the maximum intensity of the initial light beam, these fields in the cross section are gradient and therefore can be used not only for laser exposure, but also for moving ensembles of microparticles including for sorting and changing concentration.

The Effect of First Metatarsal Shortening and Sagittal Displacement on Forefoot Pressure in MIS Hallux Valgus Correction

Introduction/Purpose: Minimally invasive surgical (MIS) treatment of hallux valgus (HV) deformity is increasing in popularity. A 2mm-diameter burr is used to create a distal first metatarsal osteotomy prior to capital fragment translation and fixation. The metatarsal will shorten by the burr’s diameter (2mm). Plantar or dorsal capital fragment displacement may also cause load transference and possibly transfer metatarsalgia. In this study, we examine the effect of MIS HV on forefoot loading mechanics with respect to metatarsal shortening and sagittal plane displacement. Methods: Four lower-limb cadaveric specimens were studied. A pedobarography pressure-sensing mat was used to record forefoot plantar pressure in a controlled weightbearing stance position.10 Control and post-osteotomy measurements were obtained with the capital fragment fixated in 3 possible positions: 0mm, 5mm dorsal, and 5mm plantar displacement. Pedobarography data yielded pressure data within measurable graphical depictions. Raw mean contact pressure measurements were taken under the first and fifth metatarsal heads to establish medial and lateral forefoot loading pressure ratios. A priori power analysis was performed based on previous peer-reviewed pedobarographic data and our study was adequately powered. Results: 40 measurements were recorded and ratios of medial-to-lateral forefoot loading were constructed. Medial forefoot pressure change control versus 0mm displacement, and control versus dorsal displacement was not found to be statistically significant (p=0.525, p=0.55 respectively). Significant medial pressure increase was identified comparing control versus plantar displacement (p=0.006). Lateral pressure increased significantly with dorsal displacement of the osteotomy (p=0.013). Conclusion: MIS hallux valgus correction does not appear to cause increase in lateral forefoot pressure loading when sagittal plane displacements are controlled. Plantar displacement increases medial loading, and dorsal displacement increases lateral loading. The clinician must consider metatarsal head position post-osteotomy, as decrease in medial loading and subsequent increase in lateral loading may lead to lateral forefoot pain and transfer metatarsalgia.

Measurement proprieties of the CROM instrument for assessing head posture, neck retraction and protraction

BackgroundThe CROM instrument is widely used clinically and in research to measure neck range of motion. However, its measurement proprieties during the assessment of protraction and retraction movements were not examined so far. ObjectiveTo analyse the intra- and inter-rater reliability, the concurrent validity of the CROM for measuring head posture, retraction and protraction in healthy subjects. MethodsThirty-three asymptomatic subjects were recruited and assigned in a random order to one of two raters. After a 10-min break, they were examined by a second rater (Assessment 1). After a 30-min break, both raters repeated the examination (Assessment 2). The examination consisted of measuring the head posture, maximum head protraction and maximum retraction. Each movement was repeated 3 times and measured simultaneously with the CROM and with a 3D capture system laboratory. ResultsThe intra-rater reliability of the CROM was excellent for both raters for head posture and all head movements (ICC>0.9, 95% CI: 0.82–0.99, p < 0.01). The inter-rater reliability was excellent for head posture (ICC>0.95, 95% CI: 0.92–0.98, p < 0.01) and good-to-excellent for all movements at both time-points (ICC = 0.73–0.98, 95%CI: 0.45–0.99, p < 0.01). The validity analysis showed moderate-to-strong correlation between instruments for the head posture and head movements [(r) = -0.47 to −0.78), 95% CI: 0.99 to −0.24, p < 0.01]. ConclusionThe CROM instrument has good-to-excellent reliability and adequate validity for measuring cervical position and displacement in the sagittal plane.

Analytical and numerical analysis on the mechanical response and damage characteristics of tunnels subjected to multiple normal faulting

Multiple fault planes often coexist within a fault zone during fault dislocation. However, all the previous analytical models assume that there is only one fault plane during a fault dislocation, which is inconsistent with the actual engineering conditions. In this paper, theoretical analysis and numerical simulations are used to investigate the mechanical response and damage characteristics of tunnels subjected to multiple normal faulting. A nonlinear theoretical model is established for analyzing the mechanical response of tunnels subjected to multiple normal faulting. The number of fault planes, the shear effect of the soil and the tunnel, the fault zone width, and the nonlinear soil−tunnel interaction are applied inside the theoretical model, significantly improving the analysis accuracy and applied range. The corresponding numerical simulation based on the Concrete Damaged Plasticity (CDP) Model is carried out to study the damage characteristics of the tunnel. The proposed theoretical model is verified by model tests and numerical simulations, which exhibit consistency in both qualitative and quantitative aspects. A parametric analysis is presented, wherein the impacts of varying numbers of fault planes, fault plane distances (d), fault displacement ratios (ξ), and buried depths (C) on the tunnel response are investigated. The results show that an increasing number of fault planes leads to a reduced peak bending moment (Mmax) and shear force (Vmax). As the number of fault planes increased from one to four, Mmax and Vmax decreased by 1.57 times and 3.31 times, respectively. Expanding d corresponds to a reduction in both Mmax and Vmax. The minimum Vmax within the tunnel materializes at ξ4 (Δfd1 = Δfd2 = Δfd3), and the tunnel's Vmax appears at the fault plane of maximum fault displacement. Moreover, with the augmentation of C, an increase in both Mmax and Vmax was observed. Additionally, upon attaining a normal fault displacement of 0.2 m, the tunnel lining undergoes both tensile and compressive failure at the fault plane. As the normal fault displacement surpasses 0.4 m, the failure range of the tunnel at the fault plane undergoes a precipitous escalation, marked by a maximum increase of 68.8 % in tensile failure and a 29.6 % increase in compressive failure.

Incompatible Deformations of Elastic Plates

This article considers the methods for mathematical modeling of incompatible finite deformations of elastic plates by using the principles of the differential geometry theory underlying continuously distributed defects. Equilibrium equations were derived by asymptotic expansions of the finite strain measures with respect to two small parameters. One parameter defines the order of smallness of displacements from the reference shape (self-stressed state), while the other specifies the thickness. Asymptotic orders were different for the deflections and displacements in the plate plane, as well as for their derivatives. They were selected in such a way that, with additional assumptions on the possibility of ignoring certain terms in the resulting expressions and the compatibility of deformations, the equations could be reduced to the system of F¨oppl–von Ka´rm´an equations.

On the Construction of Confidence Regions for Uncertain Planar Displacements.

This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.

High-precision two-dimensional displacement metrology based on matrix metasurface.

A long-range, high-precision, and compact transverse displacement metrology is of crucial importance in both industries and scientific researches. However, it is a great challenge to measure arbitrary two-dimensional (2D) displacement with angstrom-level precision and hundred-micrometer range. Here, we demonstrated a prototype of high-precision 2D-displacement metrology with matrix metasurface. Light passing through the metasurface is diffracted into three beams in horizontal (H), vertical (V), and diagonal (D) linear polarization. 2D transverse displacement of the metasurface relative to the incident light beam is retrieved from the interferential optical powers arisen from coherent superposition between H-polarized and D-polarized beams or V-polarized and D-polarized beams. We experimentally demonstrate that arbitrary displacement in 2D plane can be determined with high precision down to 0.3 nm in a large range of 200 micrometers. Our work broadens the application scope of metasurface and paves the way for development of ultrasensitive optical 2D displacement metrology.

Open reduction and internal fixation of crescent fracture-dislocation: anterior or posterior approach?

To date, the approach that prevails in the open reduction and internal fixation of crescent fracture-dislocations (CFD) remains unknown. This study aimed to compare the outcomes of CFD treated via the anterior or posterior approach. Data from 64 cases of CFDs openly reduced through an anterior (group A, n = 31) or a posterior (group B, n = 33) approach were retrospectively analyzed. Functional results, reduction quality, residual displacements in the axial and coronal planes, pelvic asymmetry deformity, and correlations between Day's classification were compared. Complications and fracture union were also recorded. All patients were followed up for at least 12months. The functional scores were similar between the two groups, and all fractures achieved good or excellent reduction postoperatively. In the coronal plane, the excellent/good ratio in group B was higher than in group A. The mean residual displacement in the coronal plane was significantly higher in group A than in group B, with group A showing greater displacement in both planes for Day I fractures and in the coronal plane for Day II fractures. The residual displacement in both planes for Day III fractures was comparable between the groups. The pelvic asymmetry deformity was equal between the two groups and among the different Day's fracture types. Open reduction and internal fixation of CFDs obtained satisfactory outcomes through an anterior or posterior approach. The posterior approach achieved a better sacroiliac joint reduction. The optimal indication for the posterior approach was a Day I fracture, followed by a Day II fracture. No correlation was found between the surgical approach and reduction quality in Day III fractures.

Radiographic Evidence of Sufficient Transverse Plane Alignment after Weil Osteotomy without Screw Fixation.

Weil osteotomy is a proven procedure to restore the harmonic distal parabola of the forefoot. In addition to the proximal displacement of the head in the sagittal plane, a displacement in the transverse plane may be necessary, with the refixation of the displaced metatarsal head historically performed by screw fixation. We aimed to determine the radiological differences among 136 feet of 127 patients with 256 Weil osteotomies retrospectively enrolled and divided into groups with (n = 182) and without (n = 74) screw fixation. Demographic data, radiographic union, pre- and postoperative metatarsal angles, and differences in the dorsoplantar view were evaluated. The mean follow-up period was 3.6 months. The mean preoperative metatarsophalangeal angle was 9.24°, and the mean postoperative angle was 12.99°. The restoration of the transversal alignment plane was equally successful in both groups, with a mean extent of angle correction of 10.58°. No nonunions of the osteotomized metatarsals were observed. The radiographic comparisons revealed no significant difference between the groups (p > 0.05). However, visibility of the joint space of the metatarsophalangeal joint was achieved significantly more often in the group without screw fixation (p < 0.05). In the absence of bony malunion and the satisfactory restoration of a harmonious parabola of the forefoot, apparently there does not appear to be a necessity for regular screw fixation after Weil osteotomy based on the available data from the present study.

The effect of surgical repair of the chest on postural stability among patients with pectus excavatum.

Pectus excavatum is the most encountered of chest wall deformities. It may produce respiratory and cardiovascular symptoms, hence surgical repair of this defect is performed. The procedure involving the insertion of metal bars under the sternum (the Nuss procedure) usually brings significant improvement to patients. However, the effect of the repair on the postural stability of patients has not been studied so far. To investigate the problem of patients' stability in the postoperative period male patients with pectus excavatum (n = 21) and healthy controls (n = 22) were included in the study. Using posturography methods, we showed a negative impact of the pectus excavatum repair surgery on patients' postural stability in the first postoperative phase. The centre of pressure displacement parameters used to measure postural stability were lower after the repair for both, the frontal and sagittal plane as well as for the velocity of displacements in the sagittal plane in the double stance with eyes open. Poorer postural stability was also found in patients with pectus excavatum when compared to healthy controls. Our findings may be useful for functional monitoring in the evaluation and surgical management of pectus excavatum patients and also when designing the rehabilitation of patients undergoing the Nuss procedure.

Biomechanical Effects of Dominant or Nondominant Limb on Asymmetry during Running Stance Phase

Purpose. This study explores lower limb joint displacement differences during the stance phase and to examine the effects of limb dominance on asymmetry. A total of 32 healthy male amateur marathon runners were recruited (age: 35.33 ± 6.90 years, height: 174.17 ± 3.34 cm, weight: 63.92 ± 4.53 kg). The experiment employed a Vicon eight‐camera motion capture system synchronized with an AMTI force plate to record the phase from heel strike to toe‐off. The continuous relative phase (CRP) between the dominant and nondominant limbs was assessed using of independent t‐test of SPM1d. Results. The hip–knee joint of the dominant limb had a larger maximum CRP (t = 1.104, p &gt; 0.05, effect size = 0.270), smaller minimum CRP (t = −2.672, p &lt; 0.05, effect size = 0.653), larger values of mean absolute relative phase (MARF) (t = 3.275, p &lt; 0.05, effect size = 0.122), and deviation phase (DP) (t = 7.582, p &lt; 0.001, effect size = 0.717) than that of the nondominant limb. Comparing the dominant limb of the knee–ankle joints with the nondominant, there are smaller maximum CRP (t = −0.422, p &gt; 0.05, effect size = 0.144), smaller DP (t = −7.237, p &lt; 0.001, effect size = 0.754), a larger minimum CRP (t = 7.909, p &lt; 0.001, effect size = 2.704), and larger MARF (t = 0.355, p &gt; 0.05, effect size = 0.801). Furthermore, during the stance phases, there are significant differences in coordination modes between the dominant limb and nondominant limb of intersegmental joints (p &lt; 0.05). Conclusion. Throughout different phases of the stance phase, asymmetry in the sagittal plane of lower limb joint displacement is evident. The dominant limb undergoes significant changes in joint leading phase coordination modes, with notably less in‐phase coordination compared to the nondominant limb. This predisposes muscles to overstretching, thereby increasing the risk of muscle strains, while the nondominant limb compensates for lower muscle strength. Recognizing and addressing such asymmetries is key to optimizing nondominant limb strength and minimizing muscle overstretching in the dominant limb, leading to improved stability and movement efficiency during marathon running. Consequently, when designing exercise programs or physical therapy, it is crucial to consider limb dominance‐related symmetry differences to mitigate the risk of injury resulting from interlimb disparities in motion.

Changes to balance dynamics following a high-intensity run are associated with future injury occurrence in recreational runners

Background: Fatigue is associated with increased injury risk along with changes in balance control and task performance. Musculoskeletal injury rates in runners are high and often result from an inability to adapt to the demands of exercise and a breakdown in the interaction among different biological systems. This study aimed to investigate whether changes in balance dynamics during a single-leg squat task following a high-intensity run could distinguish groups of recreational runners who did and did not sustain a running-related injury within 6 months.Methods: Thirty-one healthy recreational runners completed 60 s of single-leg squat before and after a high-intensity run. Six months after the assessment, this cohort was separated into two groups of 13 matched individuals with one group reporting injury within this period and the other not. Task performance was assessed by the number of repetitions, cycle time, amplitude, and speed. To evaluate balance dynamics, the regularity and temporal correlation structure of the center of mass (CoM) displacements in the transverse plane was analyzed. The interaction between groups (injury, non-injured) and time (pre, post) was assessed through a two-way ANOVA. Additionally, a one-way ANOVA investigated the percent change difference of each group across time.Results: The injured group presented more regular (reduced entropy; 15.6%) and diffusive (increased short-term persistence correlation; 5.6%) CoM displacements after a high-intensity run. No changes were observed in the non-injured group. The within-subject percent change was more sensitive in demonstrating the effects of fatigue and distinguishing the groups, compared to group absolute values. No differences were observed in task performance.Discussion: Runners who were injured in the future demonstrate changes in balance dynamics compared to runners who remain injury-free after fatigue. The single-leg squat test adopted appears to be a potential screening protocol that provides valuable information about balance dynamics for identifying a diminished ability to respond to training and exercise.

Helical Plating Compared with Straight Plating and Nailing for Treatment of Proximal Third Humeral Shaft Fractures-A Biomechanical Study.

Background and Objectives: The surgical treatment of proximal humeral shaft fractures usually considers application of either long straight plates or intramedullary nails. By being able to spare the rotator cuff and avoid the radial nerve distally, the implementation of helical plates might overcome the downsides of common fixation methods. The aims of the current study were (1) to explore the biomechanical competence of different plate designs and (2) to compare their performance versus the alternative treatment option of using intramedullary nails. Materials and Methods: Twenty-four artificial humeri were assigned to the following four groups for simulation of an unstable proximal humeral shaft fracture and instrumentation: Group 1 (Straight-PHILOS), Group 2 (MULTILOC-Nail), Group 3 (45°-Helical-PHILOS), and Group 4 (90°-Helical-PHILOS). All specimens underwent non-destructive, quasi-static biomechanical testing under loading in axial compression, torsion in internal/external rotation, and pure bending in four directions, accompanied by motion tracking. Results: Axial stiffness/displacement in Group 2 was significantly higher/smaller than in all other groups (p ≤ 0.010). Torsional displacement in Group 2 was significantly bigger than in all other groups (p ≤ 0.017). Significantly smaller coronal plane displacement was identified in Group 2 versus all other groups (p < 0.001) and in Group 4 versus Group 1 (p = 0.022). Significantly bigger sagittal plane displacement was detected in Group 4 versus all other groups (p ≤ 0.024) and in Group 1 versus Group 2 (p < 0.001). Conclusions: Intramedullary nails demonstrated higher axial stiffness and smaller axial interfragmentary movements compared with all investigated plate designs. However, they were associated with bigger torsional movements at the fracture site. Although 90°-helical plates revealed bigger interfragmentary movements in the sagittal plane, they demonstrated improved resistance against displacements in the coronal plane when compared with straight lateral plates. In addition, 45°-helical plates manifested similar biomechanical competence to straight plates and may be considered a valid alternative to the latter from a biomechanical standpoint.

Percutaneous sacral screw fixation alone sufficient for mildly displaced U-type sacral fractures with preserved osseous fixation pathways

PurposeTo describe U-type sacral fracture characteristics amenable to percutaneous sacral screw fixation.MethodsU-type sacral fractures were identified from a trauma registry at a level 1 trauma center from 2014 to 2020. Patient demographics, injury mechanism, fracture characteristics, and fixation construct were retrospectively retrieved. Associations between fracture pattern and surgical fixation were identified.Results82 U-type sacral fractures were reviewed. Six treated with lumbopelvic fixation (LPF) and 76 were treated with percutaneous sacral screws (PSS) alone. Patients receiving LBF had greater sacral fracture displacement in coronal, sagittal, and axial planes compared to patients receiving PSS alone (P < 0.05), negating osseous fixation pathways. All patients went onto sacral union and there were no implant failures or unplanned reoperations for either group.ConclusionIf osseous fixation pathways are present, U-type sacral fractures can be successfully treated with percutaneous sacral screws. LPF may be indicated in more displaced fractures with loss of spinopelvic alignment. Both techniques for U-type sacral fractures result in reliable fixation and healing without reoperations.

Spatial and temporal characteristics of spontaneous parametric down-conversion with varying focal planes of interacting beams

Spontaneous parametric down-conversion (SPDC) is a widely used process to prepare entangled photon pairs. In SPDC, a second-order nonlinear crystal is pumped by a coherent laser beam to generate photon pairs. The photon pairs are usually detected by single-mode fibers (SMF), where only photons in a Gaussian mode can be collected. The collection modes possess typical Gaussian parameters, namely a beam waist and a focal plane position. The collection efficiency of photons highly depends on the choice of both parameters. The exact focal plane position of the pump beam relative to those of the detection modes is difficult to determine in a real experiment. Usually, theoretical and experimental studies assume that the focal plane positions of the pump and the generated beams are positioned in the center of the crystal. The displacement of beam focal planes can lead to deviations from expected results and the coupling efficiency into SMF can decrease. In this study, we theoretically examine variable positions of focal planes in the Laguerre–Gaussian basis, a popular experimental modal decomposition of the spatial biphoton state. We explore how the choice of focal plane positions affects the spatial and temporal properties and the purity of the photon pairs. We present SPDC setups where precise knowledge of the focal plane position is essential and scenarios where focal plane displacements have negligible impact on experimental outcomes.Graphical