Tangential Research Articles

Laterally Protruded Cephalomedullary Nail Lag Screws are a Source of Consistent Thigh Pain After Pertrochanteric Fracture.

To assess the correlation between the amount of proximal screw lateralization and clinical symptoms in patients treated with a cephalomedullary nail (CMN) after a pertrochanteric fracture. Retrospective study. Level 1 trauma center. Patients operated for a pertrochanteric fracture (OTA/AO A1, A2, A3) between 2019 and 2022 and treated with a CMN were included. Three measurements were evaluated: D1 distance between the most laterally prominent point of the lag screw and the line tangent to the greater trochanter, D2 distance between the lateral femoral cortex and the most laterally prominent point of the lag screw, and D3 distance between the point where the lag screw emerges at the lateral edge of the femur shaft and the skin's surface. Clinical scores and information regarding lateral thigh pain were obtained, and a correlation analysis was performed. Mean age of the study cohort (n = 134) was 77.9 ± 12.3 years. Patients with categorical protrusion (considered present in cases where the distance between the lateral tip of the lag screw and the lateral border of the greater trochanter was ≥0.2 mm) had significantly higher rates of lateral thigh pain ( P = 0.007) and discomfort while lying on the side ( P = 0.032) compared with those without protrusion. Correlation analyses showed a positive correlation between measurements D1 and D2 and lateral thigh pain (r = 0.324 and r = 0.334, respectively, P < 0.001) and a negative correlation between D3 and lateral thigh pain (r = -0.286, P = 0.001). Regression analysis showed that higher D1 and D2 distances and shorter D3 distances are risk factors for lateral thigh pain ( P = 0.001, 0.001, and 0.002, respectively). Increasing lateral protrusion of the lag screw leads to significantly greater clinical complaints and lateral hip pain in patients treated with a CMN. Patients with lower distance between the lateral femoral wall and the skin are at higher risk of lateral pain. Prognostic Level III. See Instructions for Authors for a complete description of levels of evidence.

Thermal runaway and induced electrical failure of epoxy resin in high‐frequency transformers: Insulation design reference

AbstractSolid‐state transformers (SSTs) have applications in medium‐voltage (MV) DC grids and compact power systems. High‐frequency transformer (HFT) is the core component of SSTs. High levels of high frequency high dv/dt voltage stresses challenged the integrity of the galvanic insulation of HFTs. However, dielectric thermal runaway and resultant electrical failure mechanisms in epoxy resin (EP) cast insulation remain unclear. Dielectric heating of EP across varying voltages, frequencies, rising edges, duty cycles and DC biases were measured and corroborated by simulation. The thermal runaway threshold mainly depends on the tangency point of the loss generation and heat dissipation curves below the glass transition temperature. Observations reveal that thermal runaway does not directly cause breakdown; instead, thermal decomposition above 200°C triggers discharge and eventual failure. Simulations demonstrate that temperature rise mainly depends on the average field within the electrode region and inter‐segment and inter‐layer distances within the HFT winding definitively impact insulation thermal runaway. By applying different criteria for MV and high‐voltage (HV) transformers, the reference electric fields for insulation design with unfilled and filled EP were obtained. For instance, limiting dielectric heating below 5 K at 50 kHz necessitates an RMS average field less than 0.44 V/mm, which is much lower than dry‐type transformer conventions. The authors prove the necessity of re‐evaluating the permissible field strength in HFT insulation design.

Crosstalk reduction for Arrayed waveguide gratings on Silicon-on-Insulator platform

Ultracompact silicon-based arrayed waveguide gratings (AWGs) with low loss and low crosstalk are essential for on-chip optical interconnect and miniaturized spectroscopic analysis systems. In our previous research, we demonstrated the crosstalk reduction by utilizing constant projection period for phased array waveguide on the tangent line to the grating pole to reduce the imaging error induced by phased array waveguide end point positions [1] and using deep etching waveguides at the interface of free propagation region to further decrease the footprint of phase region of an AWG to reduce fabrication imperfections induced phase error [2]. Here we first study the effect of curved waveguides in the phased array of 16 × 400 GHz AWGs on the adjacent crosstalk of output channels. According to the AWGs made in our fabrication platform and the testing results of five dies from one wafer at different locations, the AWGs with equal length of single-mode curved waveguides have an average adjacent crosstalk level of ∼ 4 dB smaller than those with equal length of narrow single-mode waveguides composed of straight and curved waveguides in their phased array. Based on the design of equal curved waveguide length in phased array, in combination with our reported approaches on crosstalk reduction, 16 × 200 GHz, 8 × 800 GHz and 8 × 1250 GHz AWGs are fabricated. For characterization, five dies including all designs from different locations of the fabricated wafer are tested. Experimental results show that among these five dies, the best adjacent crosstalk levels are less than − 21.97 dB, −25.72 dB, −24.83 dB and the worst adjacent crosstalk levels are less than − 20.51 dB, −25.03 dB, −24.34 dB for 16 × 200 GHz, 8 × 800 GHz and 8 × 1250 GHz AWGs with FPR angle of 120°, respectively, within the passband width of 25 % channel spacing. The on-chip insertion losses for all output channels of these fabricated AWGs are less than 3 dB.

The accuracy and feasibility study of freehand pedicle screw insertion for subaxial cervical spine assisted with safe core-referred technique

Objectives: To construct the "safe core" of the pedicle screw trajectory using CT imaging data of the subaxial cervical spine in adults, and to assess the accuracy and feasibility of the pedicle screw insertion assisted with the "safe core-referred technique" for subaxial cervical spine with a cadaver specimen study. Methods: This is an experimental study. From January 2015 to March 2020,60 adults' CT images data of the cervical spine were collected from the database of the First Affiliated Hospital of Gannan Medical University,and were imported into Mimics 20.0 software. Virtual cervical pedicle trajectory and safe core were constructed according to the self-designed "virtual construction method of pedicle in the subaxial cervical spine". The success rate of the construction and the spatial position data of the virtual safe core of was recorded,including the distance between the safe core and the tangent line of the upper and lower outer edge of Luschka's joint on coronal plane,and the distance between the safe core and the posterior edge of the vertebral body on sagittal plane.The 3.5 mm column was used to simulate the pedicle screw placement,using the safe core as the only hub in pedicle screw trajectory.The length of the anterior pedicle screw trajectory,the interval of the abductive angle of the pedicle screw in axial plane, and the projection area of the entry area on periapical radiograph was calculated.In addition,8 adult cervical cadaver specimens were collected for the pedicle screw insertion experiment.The left side group used the "safe core-referred technique" for pedicle screw insertion,while the right side group used the Abumi method for pedicle screw insertion.The accuracy of pedicle screw placement was verified by CT scan.The difference between the accuracy of subjective judgment based on X-ray monitoring of operator and the actual accuracy of pedicle screw insertion verified by CT scan was compared between the two groups.The chi-square test was used to compare the intergroup data. Results: The total success rate of the virtual construction method for the safe core of the subaxial cervical spine was 97.0% (291/300); The distance between the safe core and the tangent line of the upper and lower outer edge of Luschka's joint on coronal plane was (M(IQR)) 0.91 (0.98) mm (range: 0 to 1.85 mm);The distance between the safe core and the posterior wall on the sagittal plane of the vertebral body was (2.01±0.86) mm (range: 0.67 to 3.53 mm). The distance (anterior pedicle screw trajectory) from the posterior cortex to the central point of the safe core was (11.58±1.00)mm (range: 8.27 to 14.93 mm).The projection area of the entry point on the coronal plane was (36.18±11.67) mm2 (range: 13.38 to 83.11 mm2). Pedicle screw insertion experiment in cervical cadaver specimen showed the rate of intraoperative correction of the pedicle screw trajectory was 7.5% (3/40) in the experimental group and 12.5% (5/40) in the control group (χ2=0.139,P=0.709). The operator 's correct rate of subjective judgment on CT in the stage of pedicle screw trajectory preparation was 100% (40/40) in the experimental group and 82.5% (33/40) in the control group, the difference was statistically significant (χ2=5.638,P=0.018). The actual correct rate of CT verification in the stage of pedicle screw insertion was 100% (40/40) in the experimental group and 90.0% (36/40) in the control group, the difference was statistically significant (χ2=2.368,P=0.124); The operator 's correct rate of subjective judgment in the stage of pedicle screw insertion completion was 100% (83/83) in the experimental group and 92.9% (79/85) in the control group (χ2=4.199,P=0.040). Conclusions: The virtual safe-core of subaxial cervical spine can be use as a reliable anatomical fluoroscopy landmark for freehand pedicle screw insertion."Safe core-referred technique" can improve the accuracy rate of the operator's subjective judgment on the intraoperative fluoroscopy monitoring,and hence improve the accuracy of freehand pedicle screw insertion technology for subaxial cervical spine. And it still needs to be further verified in clinical practice.

Research on Fatigue Self-healing of Asphalts Modified by Thermoplastic Polyurethane (TPU) with Different Soft Segments

Research on asphalt fatigue and self-healing performance can more accurately model the damage and self-healing evolution principles in practical applications. In order to analyze the rationality of evaluation indexes based on rheology to evaluate the self-healing properties of TPU modified asphalt, a dynamic shear rheometer (DSR) was used in this study to perform time, temperature, and frequency sweep tests of TPU modified asphalt for analyzing the fatigue self-healing properties of TPU modified asphalt over a broader range of temperatures and loading frequencies. This method can improve the accuracy of the fatigue failure determination criteria of TPU modified asphalt and clarify the material performance parameters of TPU asphalt modifiers. The results showed that the increase in hard segment content (Ch) and isocyanate radical index (r) can effectively alleviate the decrease in shear deformation resistance of modified asphalt caused by the increase in N (load repetition). Nf50 (the number of loads when the normalized modulus drops to 0.5) is more suitable to evaluate the fatigue life of TPU modified asphalt compared with Np20 (the number of loads when the DER-N curve is offset by 20% deviation from the linear undamaged line) and N2 (the number of load times corresponding to the intersection point of the tangent line of the DER–N fitted curve and the undamaged line). The degree of self-healing will also increase with the increase in Ch and r. Besides, the higher the healing temperature and the healing time, the longer the fatigue life. The effects of the self-healing evaluation index (HI) on the self-healing index of TPU modified asphalt were as follows: healing temperature > healing time > soft segment >Ch >r > degree of damage > degree of aging > degree of self-healing.

An Improved VO Method for Collision Avoidance of Ships in Open Sea

In order to effectively deal with collisions in various encounter situations in open water environments, a ship collision avoidance model was established, and multiple constraints were introduced into the velocity obstacle method, a method to determine the ship domain by calculating the safe distance of approach was proposed. At the same time, the ship collision avoidance model based on the ship domain is analyzed, and the relative velocity set of the collision cone is obtained by solving the common tangent line within the ellipse. The timing of starting collision avoidance is determined by calculating the ship collision risk, and a method for ending collision avoidance is proposed. Finally, by comparing the simulation experiments of the improved algorithm with those of the traditional algorithm and the actual ship experiment results of manual ship maneuvering, it is shown that the method can effectively avoid collisions based on safe encounter distances that comply with navigation experience in different encounter situations. At the same time, it has better performance in collision avoidance behavior. It has certain feasibility and practical applicability.

Winding pattern design of composite cylinders considering the effect of fiber stacking

Winding pattern design is a critical step in the production of composite cylinders. Traditional design methods often overlook the impact of stacking fibers layer by layer, leading to deviations between the actual and intended winding trajectories. To ensure consistence between the actual winding outcomes and design objectives, the effect of fiber stacking on the winding patterns was examined in this study. Two winding pattern design methods were proposed: the fixed tangent-point method (FTPM) and the minimum center angle deviation method (MCADM). A comparison was conducted on the variations in the number of tangent points, thread guide round trips, and the radius of the polar hole under the two different methods. Winding experiments were then employed to verify the feasibility of these approaches. The results showed that fiber stacking on the dome was the main reason for the change in winding patterns. Priority can be given to schemes within the design overlap domain for the design of multi-layer winding patterns. While FTPM ensures consistent fiber coverage and tape spacing, it may lead to hole expansion. Additionally, applying multiple layers can alter the dome's shape significantly from the original design. In contrast, MCADM offers slightly variable fiber coverage and spacing without causing hole expansion, achieving the desired dome shape more accurately.

A total distance ranking approach to fuzzy AHP-based MCDM method for selecting sustainable manufacturing facility location

Selecting a sustainable facility location is a crucial strategy for manufacturing companies to achieve long-term success in today’s competitive environment. Various quantitative and qualitative criteria with different importance in a multiple level structure must be considered and aggregated to assist the company in decision-making. How to determine these criteria weights and select the sustainable manufacturing facility locations have become research questions. To resolve this problem, this paper proposes a total distance ranking approach to fuzzy analytic hierarchical process (AHP)-based multiple criteria decision-making (MCDM) method. Currently, the membership functions of fuzzy weighted ratings in the MCDM with a multilevel structure cannot be developed. A ranking method is needed to defuzzify those fuzzy numbers used for fuzzy AHP and qualitative criteria in the MCDM for better executing decision-making procedure. The total distance ranking method related to the centroid on x-axis, centroid on y-axis and the distances of centroids point to the two tangent lines of a fuzzy number are considered in the proposed ranking approach. Formulas of the proposed approach will be presented, and some properties will be investigated to derive formulas for trapezoidal and triangular fuzzy numbers. A comparison with relevant ranking methods will be made to show the advantages of the proposed ranking approach. The proposed ranking approach is then applied to defuzzify the fuzzy numbers used in fuzzy AHP and linguistic values under qualitative criteria to obtain the criteria weights under multi-level structure and crisp values under qualitative criteria, respectively. The final scores of alternatives can be obtained by aggregating crisp criteria values and their corresponding weights by simple additive weighting method to obtain the ranking result. A numerical example will be conducted to show the effectiveness of the proposed model. Finally, a comparison with Best-Worst method (BWM) will be presented to show the persuasiveness of the proposed method.

Random Fourier Surrogate for simulation calibration

In this paper we propose Random Fourier Surrogate (RFS) as a method for simulation calibration. Computer simulations are actively used in various fields to model and analyze complex real-world phenomena, enabling practitioners to explore situations inaccessible by other means. To create a simulation that accurately reflects the desired real-world scenario requires calibrating the simulation parameters, a non-trivial process that requires domain expertise and iterative trial-and-error. The model-bridge paradigm has been proposed to automatize this process, where a more computationally efficient surrogate model is used in lieu of the real simulation, and a bridge model is used to map the noninterpretable surrogate parameters to calibrated simulation parameters, which are physically interpretable. Recently an efficient solution called tangent slope-intercept (TSI) descriptors has been proposed, where tangent lines of a principal curve are used to represent the simulation in low dimensionality. However, we find that it has two key problems: it is prone to overfitting and is sensitive to initialization. We address these issues using Random Fourier Features to construct a surrogate model, thereby reducing calibration time by avoiding complex computations, while retaining high accuracy. We evaluate the effectiveness of our method with different experiments on synthetic signal simulations and physical simulations of turbulent flow dynamics.

An argumentation experience regarding concepts of calculus with ChatGPT

ABSTRACT ChatGPT, an artificial intelligence-supported chatbot, has become a resource in the field of education for students across various disciplines. The conversation that unfolds based on the user-generated questions and ChatGPT’s responses implies the emergence of an argumentation between the student and ChatGPT. In this study, the argumentation between a university student and ChatGPT, conducted to examine situations where a tangent line cannot be drawn to a function’s graph, was analyzed using Toulmin’s model enriched with Habermas’ construct of rationality. The findings indicate that ChatGPT offers rational support to the warrant in student’s reasoning in the of context epistemic rationality regarding the definitions of continuity, derivative, and tangent concepts. However, ChatGPT provides problematic responses in the context of epistemic rationality regarding the relationship between continuity and derivative, as well as in the context of communicative rationality concerning the geometric interpretation of the derivative and the definition of the tangent line. ChatGPT has not provided reliable and stable support to the student in the reasoning process. It can be concluded that ChatGPT, which is considered to have the potential to assist learning processes, requires expertise in calculus concepts for its use in mathematical reasoning processes. Otherwise, it may be confusing and/or misleading.

FILIPPOV TYPE PREY–PREDATOR SYSTEM FOR SELECTIVE HARVESTING OF PREY

In this paper, the dynamics of a Filippov system with logistically growing prey and Holling Type II predation is explored. The selective nonlinear harvesting of prey is carried out when the ratio of prey to predator is above a specified threshold value. In order to prevent the extinction of both the species and sustainable economic gains, no harvesting is allowed when the ratio is below a threshold value. The equilibrium states and their stability for the individual smooth are analyzed. Filippov convex method is applied to determine the dynamics on the boundary. The sliding mode dynamics is scrutinized, and it is observed that there is no escaping region. The existence of boundary points, tangent points and pseudo-equilibrium points are established. The conditions are obtained for the visibility of the tangent points. The complex behavior within the sliding region is studied by experimenting with different initial conditions. The increase in harvesting effort may lead to extinction of both the species through the sliding region of the boundary. The change in the stability behavior of both the interior equilibrium states is investigated with respect to model parameters. Border cross bifurcates with threshold value as the bifurcation parameter is shown for both the interior equilibrium states.

Two-parametric unfoldings for planar invisible double-tangency singularities.

We consider the family of planar discontinuous piecewise linear systems in two regions with a straight line as boundary and one tangency point in each region. First, we recall a seven-parametric canonical form for such a family. Next, we select two parameters as bifurcation parameters. One of them represents the distance between the tangency points. It is known that this bifurcation parameter unfolds the called pseudo-Hopf bifurcation. The coefficient that determines the stability of the crossing limit cycle that emerges from this bifurcation mechanism, called the first Lyapunov coefficient, is considered our second bifurcation parameter. Finally, with these two bifurcation parameters, we give a two-parametric unfolding for the invisible fold-fold and focus-fold singularities. The bifurcation diagram for each unfolding consists of two curves of bifurcation points: a curve of pseudo-Hopf bifurcation points and a curve of saddle-node bifurcation points for crossing limit cycles. We call this phenomenon the pseudo-Bautin (pB) bifurcation because of the dynamical behavior that is same as the Bautin bifurcation for smooth dynamical systems.

Microphone array based on tangent line method.

The tangent line method (TLM) was originally proposed for loudspeaker arrays to generate curvilinear acoustic beams. In this study, the TLM was applied to a microphone array. Based on reciprocity, the TLM-based microphone array can be used to form curvilinear beams. A curvilinear beam is produced as an envelope for the tangent lines. Tangent lines, which are straight beams with different angles, are generated by applying a delay-and-sum (DAS) beamformer. Because the envelope length is specified, the distance discrimination in the sensitivity is better using the TLM than the DAS beamformer. Case studies have indicated that directivity is better in the former TLM than in the latter. The TLM is realizable with fixed delay times for each microphone unless the formation of curvilinear trajectory is altered according to reproduction frequencies. Hence, the same simplicity of implementing the DAS beamformer can be achieved by optimizing the curvilinear trajectory based average frequency. Optimization is conducted such that the acoustic contrast between the focal point and elsewhere is maximized. In summary, the frequency-averaged optimal TLM can be a fixed beamformer with better performance than and the same simplicity as the DAS beamformer.

Exact A(α)-Stability Angles for Fractional Linear Multi-step Methods

A new criterion for evaluating exact values for the maximum angles of A(α)-stability for linear multistep methods is proposed. This criterion gives an equation to be solved for a complex point corresponding to the tangent line from the origin to the root locus curve of the stability boundary. The maximum angle for A(α)-stability sector is then obtained from the tangent point. This criterion is applied to find the A(α)-stability angles for several fractional backward difference formula type (BDF-type) numerical methods for fractional initial value problems.

Slow divergence integral in regularized piecewise smooth systems

In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence integral is invariant under smooth equivalences. This is a natural generalization of the notion of slow divergence integral along normally hyperbolic portions of curve of singularities in smooth planar slow-fast systems. We give an interesting application of the integral in a model with visible-invisible two-fold of type V I 3 . It is related to a connection between so-called Minkowski dimension of bounded and monotone "entry-exit" sequences and the number of sliding limit cycles produced by so-called canard cycles.

Оснащенное гиперполосное распределение аффинного пространства

A rigged hyperstrip distribution is a special class of hyperstrips. The study of hyperstrips and their generalizations in spaces with various fun­damental groups is of great interest due to numerous applications in mathematics and physics. A special place is occupied by regular hyper­strips, for which the characteristic planes of families of principal tangent hyperplanes do not contain directions tangent to the base surface of the hyperstrip. In this work, we use E. Cartan’s method of external differen­tial forms and the group-theoretic method of G. F. Laptev. In affine space, a hyperstrip distribution is considered, which at each point of the base surface is equipped with a tangent plane and a conjugate tangent line. The specification of the studied hyperstrip distribution in an affine space with respect to a 1st order reference and an existence theorem are given. The fields of affine normals of the 1st kind for Blaschke and Transon are constructed and the conditions for their coincidence are found. The definition of normal affine connection and normal centroaffine connection on the studied framed hyperstrip distribution is given.

Golden Ratio Flap Designed Using the Golden Ratio Rectangle.

Rotation flaps are arcuate repairs that redistribute tension vectors and recruit adjacent and/or distant tissue laxity. The incision curve could be a logarithmic spiral curve to reduce the length of an incision. We propose a rotation flap-the golden ratio flap-designed using a golden rectangle. The flap incision is an arc though the major square which is beside the minor square of a golden rectangle. The defect is attached to the line of another minor square and diagonal to the major square. The bottom line runs from the incision end to the tangent point of the circle or the oval, and the perpendicular height line runs from the bottom line to the cross point of the flap incision. These parameters were analyzed retrospectively for four superficial sarcomas that were treated using a rotation flap with an incision approximating the logarithmic spiral curve. The ratio of height to bottom of the golden ratio flap design was highly similar to the preoperative flap design in the four cases assessed. With the new design, the ratio of bottom to the defect diameter (minor axis in the oval defect) was 1.3, and for the height, it was 1.4. The golden ratio flap, designed using the golden rectangle, is reproducible. The parameters of height and bottom approximate the flap shape, or the length and width, respectively. For clinical applications, step-by-step guidance for drawing the new flap are also proposed.

Defining Critical Humeral Bone Loss: Inferior Craniocaudal Hill-Sachs Extension as Predictor of Recurrent Instability After Primary Arthroscopic Bankart Repair

Background: The glenoid track concept for shoulder instability primarily describes the medial-lateral relationship between a Hill-Sachs lesion and the glenoid. However, the Hill-Sachs position in the craniocaudal dimension has not been thoroughly studied. Hypothesis: Hill-Sachs lesions with greater inferior extension are associated with increased risk of recurrent instability after primary arthroscopic Bankart repair. Study Design: Case-control study; Level of evidence, 3. Methods: The authors performed a retrospective analysis of patients with on-track Hill-Sachs lesions who underwent primary arthroscopic Bankart repair (without remplissage) between 2007 and 2019 and had a minimum 2-year follow-up. Recurrent instability was defined as recurrent dislocation or subluxation after the index procedure. The craniocaudal position of the Hill-Sachs lesion was measured against the midhumeral axis on sagittal magnetic resonance imaging (MRI) using either a Hill-Sachs bisecting line through the humeral head center (sagittal midpoint angle [SMA], a measure of Hill-Sachs craniocaudal position) or a line tangent to the inferior Hill-Sachs edge (lower-edge angle [LEA], a measure of Hill-Sachs caudal extension). Univariate and multivariate regression were used to determine the predictive value of both SMA and LEA for recurrent instability. Results: In total, 176 patients were included with a mean age of 20.6 years, mean follow-up of 5.9 years, and contact sport participation of 69.3%. Of these patients, 42 (23.9%) experienced recurrent instability (30 dislocations, 12 subluxations) at a mean time of 1.7 years after surgery. Recurrent instability was found to be significantly associated with LEA >90° (ie, Hill-Sachs lesions extending below the humeral head equator), with an OR of 3.29 (P = .022). SMA predicted recurrent instability to a lesser degree (OR, 2.22; P = .052). Post hoc evaluation demonstrated that LEA >90° predicted recurrent dislocations (subset of recurrent instability) with an OR of 4.80 (P = .003). LEA and SMA were found to be collinear with Hill-Sachs interval and distance to dislocation, suggesting that greater LEA and SMA proportionally reflect lesion severity in both the craniocaudal and medial-lateral dimensions. Conclusion: Inferior extension of an otherwise on-track Hill-Sachs lesion is a highly predictive risk factor for recurrent instability after primary arthroscopic Bankart repair. Evaluation of Hill-Sachs extension below the humeral equator (inferior equatorial extension) on sagittal MRI is a clinically facile screening tool for higher-risk lesions with subcritical glenoid bone loss. This threshold for critical humeral bone loss may inform surgical stratification for procedures such as remplissage or other approaches for at-risk on-track lesions.

Increased Intra-Articular Internal Tibial Rotation Is Associated With Unstable Medial Meniscus Ramp Lesions in Anterior Cruciate Ligament-Injured Athletes

To analyze internal tibial rotation through magnetic resonance imaging (MRI) of patients with anterior cruciate ligament (ACL) injuries with and without an unstable medial meniscal ramp lesion (MMRL). Retrospective analysis of prospectively data was performed to include all consecutive patients who underwent primary ACL reconstruction (ACLR) between January 2022 and June 2022. Two groups, ACLR+ unstable MMRL and ACLR without MMRL, were constituted. Propensity score matching analysis was used to limit selection bias. The angle between surgical epicondylar axes (SEAs) and the tangent line of the posterior tibial condyles (PTCs) was measured to analyze the rotational alignment between distal femur and proximal tibia. MMRLs were defined unstable if they were ≥1 cm, if the lesions extend beyond the lower pole of the femoral condyle, and/or if there was displacement into the medial compartment by anterior probing. Twenty-eight propensity-matched pairs were included. The ACLR+ unstable MMRL presented a significantly greater internal rotation of the tibia compared to ACLR without MMRL (P < .001). An internal tibial rotation was associated with unstable ramp lesions in ACL-injured patients (odds ratio [OR], 0.36; 95% CI, 0.25-0.41; P < .0001). If SEA-PTC was 0°, the sensitivity and specificity of the SEA-PTC angle to detect unstable MMRL were respectively 100% (95% CI, 85%-100%) and 18% (95% CI, 8%-36%). Otherwise, if SEA-PTC angle was -10°, the sensitivity and specificity of the SEA-PTC angle to detect unstable MMRL were respectively 43% (95% CI, 27%-61%) and 96% (95% CI, 81%-100%). Bone edema of the posterior medial tibial plateau was significantly associated with unstable ramp lesions (OR, 1.58; 95% CI, 1.21-2.06; P= .029). Unstable MMRL concomitant to an ACL rupture was associated with an increased tibial internal rotation. Level III, retrospective comparative trial.

Numerical investigation on influences of injection angle of bottom blowing bubbles on multiphase flow characteristics and wall erosion of converter

In this work, a novel bottom blowing approach based on inclined injection bubbles to enhance the multiphase flow mixing is proposed. An Eulerian-Eulerian model, validated via published experimental data, is established to numerically reproduce the stirring process of a bottom blowing converter. The effects of injection angle on the multiphase flow characteristics and wall erosion are then systematically investigated. Firstly, the influence of bottom blowing flow rate (10 m/s, 14 m/s, 20 m/s) on the mixing efficiency is discussed. Then, the effects of injection angle (0°, 5°, 10°, 15°, 20°) on the flow characteristics, mixing efficiency and wall erosion are studied in detail based on the bottom blowing flow rate of 14 m/s. The results show that increasing the bottom blowing flow rate is beneficial to shorten the mixing time. With the increase of the injection angle, the mixing time first decreases and then increases. As a result, the optimal angle for the most efficient mixing is determined as 5° when the flow rate is 14 m/s. When the injection angle is 5°, the air velocity on the axis and the negative tangent line is maximum. But the velocity is minimal on the positive tangent line. The injected air forms bubble plume that promotes the circulation of water. The most serious erosion area of the converter wall is located at the junction of molten steel surface and converter wall, followed by vicinity of the tuyere. However, with the increase of the injection angle, the average wall shear stress fluctuates only slightly. The obtained results are helpful to better understand the mechanism of bubble flow field in gas-liquid two-phase and also to improve the smelting efficiency in iron and steel metallurgy.