Wedge Space Research Articles

Application of Autologous Bone Graft versus Non Grafting in Medial Opening Wedge High Tibial Osteotomy Less than 14 mm: A Systematic Review and Meta-Analysis

Abstract Background Unicompartmental Knee osteoarthritis KOA due to varus malalignment is increased in young active patients which occurs predominantly in the medial compartment. Aim of the Work The objective of this study to compare MOWHTOs with autologous bone graft and without bone graft (wedge space mean less than 14 mm) in treatment of unicompartmental KOA and varus malalignment of the knee to determine which is better in decision-making according to outcomes. Patients and Methods Studies that matched the inclusion criteria were included in this meta-analysis. participants with medial compartmental knee osteoarthritis and varus malalignment were shown in the investigation. The age of the participants was unrestricted. Plate as a fixation method was the only option regardless of plate type. During 2000 and 2021, a research study of internet databases (Egyptian Universities Research, Medline, PubMed, Cochran library, medical journals) was conducted. Following that, the references from the user research were examined, and specialists were approached for assistance in locating other papers. Two independent reviewers extracted data separately and cross-checked it. Results The Knee Society Knee score (KSKS) and Knee Society Function score (KSFS) are most commonly used for the assessment of the knee joint reveled that there is no statically significant difference between bone graft vs non graft. Regarding this systematic review the radiological outcomes, the clinical bone union and the full weight bearing movement, are rendering any statistical analysis meaningless. Regarding complications presented, there was a similar tendency for complication rate when compared according to grafting or non- grafting. The use of autograft accelerates radiographic healing of the osteotomy gap after OWHTO while shorten the union time but confers no advantages in terms of functional or patient elated out comes at 3 or 12 months postoperatively. Conclusion MOWHTO can be performed without a graft with less operative time and avoiding graft harvest comorbidity with similar clinical and radiological results regarding bone union and posterior tibial slope alteration and knee scores.

Use of patient-specific guides and 3D model in scapula osteotomy for symptomatic malunion

BackgroundScapular osteotomy for malunion can lead to resolution of pain and functional improvement in scapula fracture sequelae. Understanding three-dimensional bone morphology and analysing post-traumatic deformity is the main step of planning and the key to success of the procedure. 3D models and patient-specific guides are a growing technology to enhance accuracy of planning and to assist during surgery.Case presentationWe report the case of a 50 years old male, complaining of pain and limited function after a malunited scapular body fracture. Clinical assessment showed a severe impairment of shoulder function with active and passive forward flexion limited to 80°, absent external rotation, and internal rotation limited to the buttock. X-rays and CT scan showed an excessive lateral border offset of 53 mm and complete displacement of the glenoid segment anteriorly and medially to the scapular body, with impingement between the lateral most prominent scapular bone spur and humeral shaft. Glenopolar angle was 19°, scapular body angulation on the sagittal plane was 12°. Corrective osteotomy was planned on a virtual interactive rendering and on 3D printed models. Patient-specific guides were developed to perform a body-spine osteotomy with removal of a bone wedge, and a glenoid-spine osteotomy; a patient-specific wedge spacer was used to hold the reduction during plate fixation. Follow-up up to 12 months after surgery demonstrated improvement in scapula anatomy, shoulder girdle function, and patient-reported outcomes.ConclusionsFor the first time in scapula malunion surgery, patient-specific osteotomy guides were succesfully used during surgery to perform osteotomies and to assist in reduction maneuvers.

Arc spaces and wedge spaces for toric varieties

Arc spaces and wedge spaces for toric varieties

A Novel Method for Lengthening Iliac Crest Grafts for Mandibular Reconstruction.

The objective of this article is to propose a technique for mandibular reconstructions of up to 17cm, in order to obtain anterior iliac crest grafts smaller than those required, and then lengthen them using corticotomies. This technique has been performed in 5 patients with an indication for reconstruction after partial mandibulectomy due to pathology. Reconstruction of the body of the mandible, including the angle in some cases, was performed using nonvascularized anterior iliac crest grafts. These were elongated using corticotomies and fixed to cover the defect using reconstruction plates and screws (2.4 system). The wedge spaces that were formed by lengthening the bone block were grafted with autologous medullary bone and platelet-rich plasma. There was no loss of any of the grafts and there was no need for second surgical times to place more grafts. All cases were able to be rehabilitated with removable prostheses or dental implants. This method optimizes the amount of graft obtained, favors revascularization of the graft, reduces hypoxia times and allows the placement of osteoconductive and/or osteoinductive grafts directly on the exposed medullary areas, with the aim of promoting integration and reducing the resorption rate in large grafts.

Shear horizontal wave propagation in inhomogeneous wedge space

In this paper, a closed-form analytical solution is presented for SH wave propagation in density radial inhomogeneous wedge space. The material parameter of this inhomogeneous wedge space with arbitrary vertex angle is given in functional form. Based on complex function method, an appropriate mapping function is introduced to transform the governing Helmholtz equation with variable coefficients into a standard one. The wave field expression satisfying zero-stress boundary condition in wedge space is derived. Finally, numerical examples are presented to analysis the influence of different parameters on displacement amplitudes.

Wedge Domains in Compactly Causal Symmetric Spaces

AbstractMotivated by constructions in Algebraic Quantum Field Theory we introduce wedge domains in compactly causal symmetric spaces $M=G/H$, which includes in particular anti-de Sitter space in all dimensions and its coverings. Our wedge domains generalize Rindler wedges in Minkowski space. The key geometric structure we use is the modular flow on $M$ defined by an Euler element in the Lie algebra of $G$. Our main geometric result asserts that three seemingly different characterizations of these domains coincide: the positivity domain of the modular vector field, the domain specified by a KMS-like analytic extension condition for the modular flow, and the domain specified by a polar decomposition in terms of certain cones. In the second half of the article we show that our wedge domains share important properties with wedge domains in Minkowski space. If $G$ is semisimple, there exist unitary representations $(U,{\mathcal {H}})$ of $G$ and isotone covariant nets of real subspaces $\textsf {H}({\mathcal {O}}) \subseteq {\mathcal {H}}$, defined for any open subset ${\mathcal {O}} \subseteq M$, which assign to connected components of the wedge domains a standard subspace whose modular group corresponds to the modular flow on $M$. This corresponds to the Bisognano–Wichmann property in Quantum Field Theory. We also show that the set of $G$-translates of the connected components of the wedge domain provides a geometric realization of the abstract wedge space introduced by the first author and V. Morinelli.

Coronal Plane Deformity and Total Ankle Replacement: When to Stage with Cement Spacer Ankle Arthroplasty for Deformity Correction

Category:Ankle ArthritisIntroduction/Purpose:Degenerative ankle joint disease is a debilitating condition that causes significant pain, adversely affects function and quality of life. Though primary arthritis of the ankle can occur without deformity, frequently soft tissue imbalances or joint deformities complicate the clinical picture. Often, additional procedures are required to balance the foot and ankle during the index total ankle replacement procedure. When large deformities exist a staged approach to first, align the ankle joint to neutral as stage one and then implantation of the TAR as stage two can be deployed. This paper will further popularize the cement spacer staged TAR technique in correction of coronal deformities, share a clinical algorithm on approach, and depict a case series demonstrating its application.Methods:A case series was performed of 7 patients and 8 ankles, who underwent staged primary TAR utilizing a cement spacer to assist with deformity correction, between the years 2016-2019.Results:Patients' mean age 58.5 yrs., preoperative varus coronal plane deformity mean 19.1 degrees, preoperative valgus coronal plane mean 10.25 degrees. Mean time from stage 1 till 2 was 163.5, +-140.2 days. Stage 1 soft tissue procedures: Chrisman-Snook procedure with synthetic ligament graft, Brostrum-Gould with synthetic graft, Brostrum-Gould without graft, FDL transfer, and isolated medial release/peel. Osteotomies performed during stage one: Dwyer, MDCO, Cotton, and MDCO with medial malleolus osteotomy. Fusions performed during stage one consisted: Subtalar joint, talonavicular joint (TNJ), and STJ with 1st Metatarsophalangeal joint (MTPJ). Seven ankles were replaced with Cadence Total Ankle System (Integra), and one with INBONE II (Wright Medical Technology). Average follow-up time for included patients was 290.75 days (9.7 months). One revision was performed following index TAR procedure.Conclusion:This paper describes a cement wedge spacer staged total ankle arthroplasty technique for correction and stabilization of deforming forces at the ankle joint. While not all ankle deformities necessitate a staged approach, the complexity of the malalignment and the extent of tissue disruption needed to achieve a neutral ankle should be considered when correcting a given deformity with a staged or non-staged approach.

Scattering of SH waves around circular canyon in inhomogeneous wedge space

SUMMARYScattering of SH waves around a circular canyon in radial inhomogeneous wedge space is investigated in this paper. Based on the complex function method, the governing equation with variable coefficients is transformed into a standard Helmholtz equation and the corresponding analytical solution to this problem is derived. The unknown coefficients in the wavefield is obtained by enforcing the stress-free condition in the circular canyon, then the incident, reflected and scattering waves in the total wavefield are all acquired. Through the calculation and analysis of the parameters that affect the ground motion, the influence of the circular canyon on the ground motion in the radial inhomogeneous wedge space is obtained. Moreover, combined with graphical results, the effects by inhomogeneous parameter on ground motion with circular canyon in wedge space are conspicuous.

Certain subgroups of groups of self-pair homotopy equivalences

Let E(X) be the set of based homotopy classes of based self-homotopy equivalences of a CW-complex X. The concept of E(X) is applied to the category of pairs and is extended to a general concept E(α) for a map α:A→B. In this study, E(α) is generalized to Eγ(α) for two objects α and γ. Several generalized subgroups of E(α) or Eγ(α) are obtained and are combined to form an exact sequence. The exactness and the split property of this sequence is investigated. In particular, the sequence of a product space or a wedge space is demonstrated to be a split exact sequence. The split property and the exactness are used to completely compute those subgroups.

Experimental and numerical study on formation mechanism of premixed hydrogen-air squish flame in wall constrained environment

The study of hydrogen-air premixed flame propagation behavior and induced accelerated combustion in a constrained environment is of great significance for realizing rapid controllable combustion and promoting the efficient use of hydrogen energy. In this work, the propagation process of hydrogen-air premixed flame and the effect of different initial conditions on flame shape and propagation velocity under the wall constraint were studied in a constant volume bomb using the schlieren method. Then, the flow field characteristics in the wedge space were studied by CFD (computational fluid dynamics) simulation, and the formation mechanism of the squish flame was revealed. The experimental results show that the flame propagation process under wall constraint includes four stages: laminar flame, cell flame, squish flame and spontaneous combustion. The squish flame tends to appear at lower initial temperature in the lean zone and tends to occur at higher initial temperatures in the rich zone. The flame propagation speed increases with the increase of the initial pressure and the initial temperature, but increases first and then decreases with the increase of equivalence ratio. The flame propagation velocity of the rich zone is more sensitive to changes in the initial temperature than the lean zone. The simulation results show that during the flame propagation process, the flow of unburned gas in the wedge-shaped space formed by the flame and the two walls forms a large velocity gradient with the wall surface, which induces strong wall turbulence. The turbulence intensity induced in the wedge-shaped space is higher than that induced by the flame and the single wall surface, and the faster the flame propagation speed, the stronger the wall turbulence generated in the wedge-shaped space. When the flame itself is unstable, the strong wall turbulence in the wedge-shaped space causes the instability or even turbulence of the near-wall flame, which accelerates the rapid propagation of the unstable flame. Therefore, the combination of strong wall turbulence formed in the wedge-shaped space and flame instability results in the formation of squish flame.

An analytical model for wedge-shaped acoustic arrays

This work presents the derivation of a 3D sound field model for the pressure field radiated from loudspeaker arrays in acoustic wedge spaces. These wedge arrays are described by their normal velocity profile at a given boundary. Using this model, a suitable beamforming technique with two different beam patterns is derived based on a mode-matching approach. The model is then used to study the beamforming performance as a function of frequency and distance from the array by analysing the Arc Radial Functions introduced in this work. The theory is tested on the basis of simulation results for different wedges and validated through holographic measurements made with a hemi-cylindrical array. It is found that for a large distance, a far-field approximation of the model can be used to drive the array, whereas for a short distance, the general model must be applied to yield accurate results.

New angle measurement device to control the posterior tibial slope angle in medial opening wedge high tibial osteotomy.

Medial opening wedge high tibial osteotomy has been associated with an unintentional increase in the posterior tibial slope angle. We aimed to evaluate the effectiveness of a novel bone spreader angle rod to maintain the native posterior tibial slope angle in medial opening wedge high tibial osteotomy. Data from 92 consecutive knees in 83 patients who underwent medial opening wedge high tibial osteotomy for knee osteoarthritis between March 2015 and June 2016 were analysed. The osteotomy was performed without the use of a bone spreader angle rod in the first 50 cases (control group) and with the use of the angle rod in the subsequent 42 cases (angle rod group). The wedge insertion angle, defined as the angle between a line drawn along the posterior aspect of the wedge spacer and a line tangential to the posterior aspect of the femoral condyles, and the posterior tibial slope angle were evaluated on pre- and postoperative lateral knee radiographs and postoperative computed tomography images. Wedge insertion angle showed that wedge spacers were inserted in a more direct horizontal direction in the angle rod group than in the control group (16.0 ± 8.8° and 23.0 ± 10.0°, respectively, P < 0.001). The pre- to postoperative change in posterior tibial slope angle was significantly smaller in the angle rod group (0.6 ± 1.6°) compared to that in the control group (3.2 ± 3.2°; P < 0.0001). A change of posterior tibial slope angle > 3° (outlier) was identified in 1 case (2.4%) in the angle rod group compared to 27 cases in the control group (54.0%). The direct horizontal insertion of wedge spacers with the assistance of our novel bone spreader angle rod maintains the native posterior tibial slope angle better than conventional methods. IV.

A general radiation model for sound fields and nearfield acoustical holography in wedge propagation spaces.

In this work an expression for the solution of the Helmholtz equation for wedge spaces is derived. Such propagation spaces represent scenarios for many acoustical problems where a free field assumption is not eligible. The proposed sound field model is derived from the general solution of the wave equation in cylindrical coordinates, using sets of orthonormal basis functions. The latter are modified to satisfy several boundary conditions representing the reflective behaviour of wedge-shaped propagation spaces. This formulation is then used in the context of nearfield acoustical holography (NAH) and to obtain the expression of the Neumann Green function. The model and its suitability for NAH is demonstrated through both numerical simulations and measured data, where the latter was acquired for the specific case of a loudspeaker on a hemi-cylindrical rigid baffle.

Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C

For the BGG category of $\mathfrak{q}(n)$-modules of half-integer weights, a Kazhdan-Lusztig conjecture \`a la Brundan is formulated in terms of categorical canonical basis of the $n$th tensor power of the natural representation of the quantum group of type $C$. For the BGG category of $\mathfrak{q}(n)$-modules of congruent non-integral weights, a Kazhdan-Lusztig conjecture is formulated in terms of canonical basis of a mixed tensor of the natural representation and its dual of the quantum group of type $A$. We also establish a character formula for the finite-dimensional irreducible $\mathfrak{q}(n)$-modules of half-integer weights in terms of type $C$ canonical basis of the corresponding $q$-wedge space.

Effect of Wedge Insertion Angle on Posterior Tibial Slope in Medial Opening Wedge High Tibial Osteotomy.

Background:Medial opening wedge high tibial osteotomy (HTO) is a well-established surgery for medial compartment knee osteoarthritis (OA) wherein the lower extremity is realigned to shift the load distribution from the medial compartment of the knee to the lateral compartment. However, this surgery is known to affect the posterior tibial slope angle (PTSA), which could lead to abnormal knee kinematics and instability, and eventually to knee OA. Although PTSA control is as important as coronal realignment, few appropriate measurements for this parameter have been reported. The placement of a wedge spacer might have an effect on PTSA.Purpose:To elucidate the relationship between the PTSA and the direction of insertion of a wedge spacer.Study Design:Case series; Level of evidence, 4.Methods:This study assessed 43 knees from 34 patients who underwent medial opening wedge HTO for knee OA. Pre- and postoperative lateral radiographs of the knee as well as postoperative computed tomography scans were performed to evaluate the relationship among PTSA, wedge insertion angle (WIA), and opening gap ratio (distance of the anterior opening gap/distance of the posterior opening gap at the osteotomy site).Results:The PTSA significantly increased from 9.0° ± 2.8° preoperatively to 13.2° ± 4.1° postoperatively (P < .001), resulting in a mean ΔPTSA of 4.7° ± 4.5°. The mean opening gap ratio was 0.86 ± 0.11, and the mean WIA was 25.9° ± 8.4°. The WIA and opening gap ratio were both highly correlated with ΔPTSA (r = 0.71 and 0.72, respectively), implying that a smaller WIA or smaller gap ratio leads to less increase in posterior slope.Conclusion:The direction of wedge insertion is highly correlated with PTSA increase, which suggests that the PTSA can be controlled for by adjusting the direction of wedge insertion during surgery.Clinical Relevance:Study results suggest that it is possible to adjust the PTSA by controlling the WIA during surgery. Proper attention to WIA can avoid an iatrogenic increase in posterior tibial slope.

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

The indirect boundary element method (IBEM) is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and efficiently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Finite element analysis of plate-screw systems used in medial opening wedge proximal tibial osteotomies

This study investigates, through finite-element analysis, different plate-screw fixation systems used for medial opening proximal tibial osteotomies (locking or non-locking with or without a medial spacer). Sulzer stainless steel non-locking without spacer, Synthes titanium locking without spacer, Smith and Nephew custom titanium locking with a wedge spacer and Arthrex stainless steel non-locking with a wedge spacer fixation systems were modelled and compared. All fixation systems were tested under static loading of 889 N applied evenly over the proximal tibia particular surface. The areas of highest stress experienced in the bone and the plate/screw interface were analysed. Tendency of the osteotomy wedge to close under loading for each fixation system was analysed. The numerical results suggest the titanium locking plate with wedge spacer block outperforms the others by achieving lower stresses (incurred by the fixation system and bone) and loss of correction. Locking screw mechanisms and wedge spacer blocks appear advantageous.

The Pressure Distribution around Particles in Fluid in Confined Wedge Space

The particle motion in fluid has attracted much attention in material engineering concerned the particle effects such as the debris in lubrication and the particles deposition in material processing. By taking the hydrodynamic effect into account, the pressure distribution around particles in fluid in confined wedge space is analyzed. The influences of the particle position, particle shape and its velocity on the pressure distribution are also investigated. Results show that in confined wedge space, the fluid pressure around the particle in the side near the upper slope plate is larger than that in another side, which may make the particle move downwards. And the pressure discrepancy between both sides of the particle increases with the particle shape, the particle velocity and the particle coordinates in both directions of x and z. These special phenomenons may be used in structured surfaces fabrication based on particle deposition by constructing special fluid field.

Wedges, cones, cosmic strings and their vacuum energy

One of J Stuart Dowker’s most significant achievements has been to observe that the theory of diffraction by wedges developed a century ago by Sommerfeld and others provided the key to solving two problems of great interest in general-relativistic quantum field theory during the last quarter of the 20th century: the vacuum energy associated with an infinitely thin, straight cosmic string, and (after an interchange of time with a space coordinate) the apparent vacuum energy of empty space as viewed by an accelerating observer. In a sense the string problem is more elementary than the wedge, since Sommerfeld’s technique was to relate the wedge problem to that of a conical manifold by the method of images. Indeed, Minkowski space, as well as all cone and wedge problems, are related by images to an infinitely sheeted master manifold, which we call Dowker space. We review the research in this area and exhibit in detail the vacuum expectation values of the energy density and pressure of a scalar field in Dowker space and the cone and wedge spaces that result from it. We point out that the (vanishing) vacuum energy of Minkowski space results, from the point of view of Dowker space, from the quantization of angular modes, in precisely the way that the Casimir energy of a toroidal closed universe results from the quantization of Fourier modes; we hope that this understanding dispels any lingering doubts about the reality of cosmological vacuum energy.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

On reductibility of the self-homotopy equivalences of wedge spaces

Reducibility of the self-homotopy equivalences of wedge spaces is studied and some conditions implying the reducibility are obtained.