Double Bundles Research Articles

Functional double-bundle anterior cruciate ligament reconstruction using hamstring tendon autografts with preserved insertions is an effective treatment for tibiofemoral instability.

The aim of this study was to introduce a modified anatomical anterior cruciate ligament reconstruction using functional double bundles (F-DBACLR), which achieved sequential tensioning at all flexion angles postoperatively, and compare its clinical outcomes with the anatomical single-bundle technique (A-SBACLR). A total of 156 patients with an ACL injury underwent ACLR (A-SB group, n = 78; F-DB group, n = 78). All operations were performed by anatomically identifying the ACL footprints and fixing the graft at a pre-determined degree of knee flexion. Two observers blinded to the patient identities examined the patients preoperatively and during follow-up (median 28.2months; range 26-31 months). Multiple subjective and objective clinical evaluation tests and assessment of clinical outcomes concerning the translational and rotational stability of the knee including the International Knee Documentation Committee (IKDC) questionnaire, Lysholm Knee Scoring Scale, Knee Injury and Osteoarthritis Outcome Score (KOOS), Tegner Activity Scale, KT-1000 laxity measurements, Lachman test and pivot-shift test were performed preoperatively and postoperatively. Preoperatively, no differences were found between the two groups. During the 2-year observation period, patients in the F-DB group revealed better clinical outcomes in terms of the Tegner Activity Scale Score, IKDC, KOOS and Lysholm Knee Scoring Scale. Similar results were shown in regard to the translational stability in both groups, while the F-DB group had more rotational stability at 2years of follow-up. The clinical outcomes indicated that F-DBACLR is clinically practicable and advantageous in the treatment of the ACL-deficient knee. II.

The rotating stretched curved planar reconstruction of 3D-FIESTA MR imaging for evaluating the anterior cruciate ligament of the knee joint

PurposeTo determine the feasibility of the rotating stretched curved planar reconstruction (CPR) of three-dimensional fast imaging with steady-state acquisition magnetic resonance imaging (3D-FIESTA MRI) for evaluating the anterior cruciate ligament of the knee joint. Materials and methodsMRI of 40 knee joints in healthy volunteers was performed on a 3.0-T MR scanner and a phased-array extremity coil. The protocol consisted of oblique sagittal spin echo (SE) T1WI, coronal FS-PDWI, axial FS-FSE-T2WI, and 3D-FIESTA sequences. The rotating stretched curved planar reconstructions (CPR) of the ACL at angles of 0°, 30°, 60°, 90°, 120°, 150°, and 180° were generated from images of 3D-FIESTA sequences. Signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of the 3D-FIESTA were compared with those of the oblique sagittal SE T1WI sequence. The presence of the tibial attachment, midportion, femoral attachment, and double bundles of the ACL on the oblique sagittal SE T1WI and CPR of 3D-FIESTA MR imaging were divided into two categories: visible and not visible. ResultsThe ACL SNR efficiency of 3D-FIESTA sequences was significantly higher than that of oblique sagittal SE T1WI sequence (P < 0.05). The 3D-FIESTA sequences produced images with a significantly higher CNR between ACL and synovial fluid than did the oblique sagittal SE T1WI sequence (P < 0.05). CPR of 3D-FIESTA MRI generated an excellent visualization of the ACL. The CPR of 3D-FIESTA MRI was rated superior to oblique sagittal SE T1WI sequence in 60% and 65% of cases with regard to the tibial attachment and midportion of ACL, respectively (P < 0.05). CPR of 3D-FIESTA MR imaging was rated superior to oblique sagittal SE T1WI sequence in 80% and 85% of cases with regard to femoral attachment and double bundles of ACL, respectively (P < 0.05). ConclusionThe rotating stretched curved planar reconstruction of 3D-FIESTA sequences is significantly better than that of conventional 2D-MRI in evaluating the native ACL and its components, AM bundle and PL bundle, in healthy volunteers.

The geometrization of N-manifolds of degree 2

This paper describes an equivalence of the canonical category of $\mathbb N$-manifolds of degree $2$ with a category of involutive double vector bundles. More precisely, we show how involutive double vector bundles are in duality with double vector bundles endowed with a linear metric. We describe then how special sections of the metric double vector bundle that is dual to a given involutive double vector bundle are the generators of a graded manifold of degree $2$ over the double base. We discuss how split Poisson $\mathbb N$-manifolds of degree $2$ are equivalent to \emph{self-dual representations up to homotopy} and so, following Gracia-Saz and Mehta, to linear splittings of a certain class of VB-algebroids. In other words, the equivalence of categories above induces an equivalence between so called \emph{Poisson involutive double vector bundles}, which are the dual objects to metric VB-algebroids, and Poisson $\mathbb N$-manifolds of degree $2$.

Graded manifolds of type $$\Delta $$ Δ and n-fold vector bundles

Vector bundles and double vector bundles, or twofold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these structures possess a unified description using the language of supergeometry and $$\mathbb {Z}$$ -graded manifolds of degree $$\le 2$$ . Indeed, a link has been established between the super and classical pictures by the geometrization process, leading to an equivalence of the category of $$\mathbb {Z}$$ -graded manifolds of degree $$\le 2$$ and the category of (double) vector bundles with additional structures. In this paper we study the geometrization process in the case of $$\mathbb {Z}^r$$ -graded manifolds of type $$\Delta $$ , where $$\Delta $$ is a certain weight system and r is the rank of $$\Delta $$ . We establish an equivalence between a subcategory of the category of n-fold vector bundles and the category of graded manifolds of type $$\Delta $$ .

γ-Tubulin has a conserved intrinsic property of self-polymerization into double stranded filaments and fibrillar networks

γ-Tubulin is essential for microtubule nucleation and also plays less understood roles in nuclear and cell-cycle-related functions. High abundancy of γ-tubulin in acentrosomal Arabidopsis cells facilitated purification and biochemical characterization of large molecular species of γ-tubulin. TEM, fluorescence, and atomic force microscopy of purified high molecular γ-tubulin forms revealed the presence of linear filaments with a double protofilament substructure, filament bundles and aggregates. Filament formation from highly purified γ-tubulin free of γ-tubulin complex proteins (GCPs) was demonstrated for both plant and human γ-tubulin. Moreover, γ-tubulin associated with porcine brain microtubules formed oligomers. Experimental evidence on the intrinsic ability of γ-tubulin to oligomerize/polymerize was supported by conservation of α- and β-tubulin interfaces for longitudinal and lateral interactions for γ-tubulins. STED (stimulated emission depletion) microscopy of Arabidopsis cells revealed fine, short γ-tubulin fibrillar structures enriched on mitotic microtubular arrays that accumulated at polar regions of acentrosomal spindles and the outer nuclear envelope before mitosis, and were also present in nuclei. Fine fibrillar structures of γ-tubulin representing assemblies of higher order were localized in cell-cycle-dependent manner at sites of dispersed γ-tubulin location in acentrosomal plant cells as well as at sites of local γ-tubulin enrichment after drug treatment. Our findings that γ-tubulin preserves the capability of prokaryotic tubulins to self-organize into filaments assembling by lateral interaction into bundles/clusters help understanding of the relationship between structure and multiple cellular functions of this protein species and suggest that besides microtubule nucleation and organization, γ-tubulin may also have scaffolding or sequestration functions.

Mid-term effects of arthroscopic anatomical reconstruction of double bundles of the anterior cruciate ligament

Objective To investigate the mid-term clinical outcomes of arthroscopic anatomical reconstruction of double bundles of the anterior cruciate ligament (ACL). Methods The clinical data of 78 patients diagnosed with ACL rupture from April 2012 to July 2014 were analyzed retrospectively. They were 60 males and 18 females, aged from 19 to 56 years (mean, 26.8 years).The time from injury to surgery ranged from one week to 23 months (mean, 5.8 months). All of them obtained positive results in anterior drawer test and Lachman test preoperatively. Their preoperative KT-1000 examinations showed an average side-to-side difference of 8.29±1.81 mm in anterior laxity.They were all treated with arthroscopic anatomical reconstruction of double bundles of the anterior cruciate ligament using autologous hamstrings. The International Knee Documentation Committee (IKDC) and Lysholm scores were used to assess their knee function at the last follow-up. Results All the 78 patients were followed up for 34.6 months on average (range, from 25 to 56 months). At the last follow-up, the IKDC and Lysholm scores were significantly increased from preoperative 42.6±9.5 and 44.4±8.5 to postoperative 92.9±2.8 and 94.2±3.4, respectively (P<0.05). The Lachman test was negative in 73 cases (93.6%) and the pivot shift test was negative in 69 cases (88.5%). The KT-1000 examinations showed that the side-to-side difference in anterior laxity averaged 1.47±0.68 mm, significantly improved from the preoperative values (P<0.05). At their last follow-up, 29 patients underwent MRI scans which showed continuity of the anteromedial and posterolateral bundles of the anterior cruciate ligament. Conclusion The arthroscopic anatomical reconstruction of double bundles of the anterior cruciate ligament can restore the knee stability and achieve fine mid-term clinical outcomes. Key words: Knee joint; Anterior cruciate ligament; Arthroscopy; Anatomical reconstruction; Double bundle

On the concept of a filtered bundle

We present the notion of a filtered bundle as a generalization of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include affine bundles and various jet bundles, both of which play fundamental roles in geometric mechanics and classical field theory. We also present the notion of double filtered bundles which provide natural generalizations of double vector bundles and double affine bundles. Furthermore, we show that the linearization of a filtered bundle — which can be seen as a partial polarization of the admissible changes of local coordinates — is well defined.

Duality for Graded Manifolds

We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different category than the initial ones, namely graded polynomial (co)algebra bundles and free graded Weil (co)algebra bundles. Our results are then applied to obtain elegant characterizations of double vector bundles and graded bundles of degree 2. All these results have their supergeometric counterparts. For instance, we give a simple proof of a nice characterisation of $N$-manifolds of degree 2, announced in the literature.

The glenocapsular ligament and the posterosuperior part of the joint capsule of the shoulder are well vascularized.

A detailed structural anatomy of the posterosuperior shoulder capsule and "glenocapsular ligament" is still rather unknown. The purpose of this study was meticulously to investigate and describe the structure and blood supply of the glenocapsular ligament on the posterosuperior shoulder joint capsule. Sixteen fixed and twelve fresh cadaveric shoulder specimens with a mean age of 73.4 (±6.4) years were analysed. Dissection without arterial injection was performed on the 16 fixed specimens-using an alcohol-formalin-glycerol solution. Before dissection, the 12 fresh specimens received of arterial injection a 10% aqueous dispersion of latex solution. After the injection, these shoulders were also fixed in an alcohol-formalin-glycerol solution. The glenocapsular ligament was found in all 28 specimens. Single or double parallel-running bundles of connective tissue fibres were found to form a capsular-ligamentous structure on the posterosuperior part of the joint capsule. One part of the ligament was mediosuperior, another posterosuperior. The mediosuperior part varied in shape, and in 12 of 28 cases, it was absent. The glenocapsular ligament arose from the supraglenoid tubercle and posterior part of the collum scapulae and inserted into the semicircular humeral ligament. The posterior ascending branch of the circumflex scapular artery directly fed small branches laterally and medially to the joint capsule, supplying the glenocapsular ligament and the deep layer of the joint capsule. The glenocapsular ligament is a constant anatomical structure that consists of one or two different parts. The glenocapsular ligament and the posterosuperior part of the joint capsule appear well vascularized via the posterior ascending branch of the circumflex scapular artery. It is the hope of the authors that this anatomical study can help surgeons who perform open or arthroscopic surgery to the posterior part of the shoulder. Knowledge of the vascular anatomy presented in this study may be especially important when incisions are made to the posterior part of the shoulder, and should minimize the risk of complications.

The effect study of arthroscopic reconstruction of posterior cruciate ligament with ligament advanced reinforcement system Y-shape double bundles artificial ligament

The effect study of arthroscopic reconstruction of posterior cruciate ligament with ligament advanced reinforcement system Y-shape double bundles artificial ligament

Linear duals of graded bundles and higher analogues of (Lie) algebroids

Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded bundle which allows us to define the notion of the linear dual of a graded bundle. They are examples of double structures, graded-linear ($\mathcal{GL}$) bundles, including double vector bundles as a particular case. On $\mathcal{GL}$-bundles we define what we shall call weighted algebroids, which are to be understood as algebroids in the category of graded bundles. They can be considered as a geometrical framework for higher order Lagrangian mechanics. Canonical examples are reductions of higher tangent bundles of Lie groupoids. Weighted algebroids represent also a generalisation of $\mathcal{VB}$-algebroids as defined by Gracia-Saz & Mehta and the $\mathcal{LA}$-bundles of Mackenzie. The resulting structures are strikingly similar to Voronov's higher Lie algebroids, however our approach does not require the initial structures to be defined on supermanifolds.

Bioreduction of nitrate in a hydrogen-based membrane biofilm reactor using CO2 for pH control and as carbon source

The hydrogen-based membrane biofilm reactor (MBfR) is efficient in removing nitrate in oligotrophic water, but pH increase due to denitrification is a tough problem in practice. To control pH, we investigated a novel MBfR with double bundles of hollow fibers (one for H2 supply and the other for CO2 supply). CO2 was used for pH control and as the carbon source. The Fick’s first law and steady state permeation tests were adopted to determine the CO2 permeability of polyvinyl chloride (PVC) hollow fibers used in this study. The CO2 diffusion coefficient in the membrane was 3.8375×10−7m2/d @ 25°C. The CO2 diffusion coefficient was verified by a nitrate bioreduction experiment in the MBfR. The calculated supply of CO2 based on the CO2 diffusion coefficient is consistent with the experimental results: The total nitrogen removal rate was more than 99% and the pH is stable at around 7.45. CO2 diffused through the membrane is sufficient to be the sole carbon source. We confirmed that the novel MBfR with double bundles was stable and efficient. This research provides direct guidance to the design and operation of this new type MBfR.

Tulczyjew triples in higher derivative field theory

The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of the variational calculus we derive Tulczyjew triples for classical field theories of arbitrary high order, i.e. depending on arbitrary high derivatives of the fields. A first triple appears as the result of considering higher order theories as first order ones with configurations being constrained to be holonomic jets. A second triple is obtained after a reduction procedure aimed at getting rid of nonphysical degrees of freedom. This picture we present is fully covariant and complete: it contains both Lagrangian and Hamiltonian formalisms, in particular the Euler-Lagrange equations. Notice that, the required Geometry of jet bundles is affine (as opposed to the linear Geometry of the tangent bundle). Accordingly, the notions of affine duality and affine phase space play a distinguished role in our picture. In particular the Tulczyjew triples in this paper consist of morphisms of double affine-vector bundles which, moreover, preserve suitable presymplectic structures.

On double vector bundles

In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.

Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings

The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration space is TM, is based on the existence of canonical symplectic isomorphisms of double vector bundles T*TM, T*TM, and TT*M. We show that there exist an analogous picture in the dynamics of objects for which the configuration space is the vector bundle of n-vectors, if we make use of certain graded bundle structures of degree n, i.e. objects generalizing vector bundles (for which n=1). For instance, the role of TT*M is played in our approach by the vector bundle of n-vectors on the bundle of n-covectors, which is canonically a graded bundle of degree n over the bundle of n-vectors. Dynamics of strings and the Plateau problem in statics are particular cases of this framework.

Knee

The October 2013 Knee Roundup360 looks at: Make it easy, release the MCL; Do patients remember clinical information in day surgery?; Osteoarthritis and arthroscopy?; How best to double your bundles; When to operate for infection; Cementless unicompartment knee replacement?; Tibial tubercle-trochlear groove confusion; Tarts, cherries and osteoarthritis

Geometry of the double tangent bundles of Banach manifolds

In this paper for a vector bundle (v.b.) (p,E,M), we show that at the presence of a (possibly nonlinear) connection on (p,E.M), TE on M admits a v.b. structure. This fact is followed by a suitable converse which asserts that a v.b. structure for TE over M yields a linear connection on the original bundle (p,E,M). Moreover we clarify the relation between v.b. structures and also the induced bundle morphisms which will be used for classification of these v.b. structures. Afterwards the concept of second order connections on a manifold M is introduced which leads us to interesting geometric tools on the bundle of accelerations. In fact by using the v.b. structure for σ:TTM⟶M, we will study the geometric tools on the second order tangent bundle. The concepts of second order covariant derivative, first and second order auto-parallel curve, the appropriate exponential mapping and second order Lie derivative are introduced.

Evolving Techniques in ACL Graft Fixation

More than 1600 techniques for ACL reconstruction have been published.1 Within recent years, most of the debate was neither the choice of graft nor the fixation, but rather the usefulness of a single-bundle or double-bundle reconstruction. Meanwhile, several studies have questioned the clinical and experimental benefits of a double-bundle reconstruction when compared with a center-to-center reconstruction technique.2 In cases with hyperextension, a double-bundle reconstruction can even limit full side-to-side extension.3 No matter if reconstructions use single or double bundles, the most important surgical goal of ACL reconstruction remains control of the tunnel placement. Following this, the choice of graft fixation is an important cornerstone that determines the fate of the transplant and may compromise the final result. Implants may be beneficial for secure fixation but can hamper the integrity of the graft and cause difficulties in tunnel-to-bone healing, allergies, postoperative MRIs, and revision surgery. This issue of Techniques in Orthopedics provides an overview of the history of graft fixation, the biomechanical strengths and weaknesses of individual types of fixation, and has a special focus on implant-free graft fixation techniques. It provides well-recognized and documented techniques with more than 10 years of experience, such as evolving techniques that can be used for any type of graft in the future. We hope that the Orthopedic Community enjoys these technical novelties and are anxious to receive your feedback.

A retrospective comparative study of remnant preservation and resection in double-bundle anterior cruciate ligament reconstruction using hamstring tendon grafts

Objective To compare the remnant preservation (RP) and the remnant resection (RR) techniques in double-bundle anterior cruciate ligament (ACL) reconstruction using hamstring tendon grafts.Methods Included in this study were 62 patients with injury to the ACL double bundles who met our criteria and had been treated from May 2003 to June 2005 in our department.They were divided into an RP group (n =31) and a RR(n =31) group.There was no significant difference between the 2 groups regarding general clinical data (P ＜ 0.05).The subjective evaluations of the patients [subjective International Knee Documentation Committee(IKDC) score,Lysholm score and Cincinnati knee score] and objective ones (objective IKDC score,pivot shift test and Kneelax3 measurement) were recorded preoperatively and postoperatively and compared between the 2 groups.Results At 2 years postoperation,the average subjective IKDC score (92.3 ± 4.3 points),Lysholm score (89.0±4.5 points) and Cincinnati knee score (91.8 ±4.4 points) for the RP group were significantly better respectively than those for the RR group (88.2 ± 5.2,85.6 ± 4.9,87.2 ± 6.2points) (P ＜ 0.05).There were,however,no significant differences at 2 years postoperation between the 2 groups regarding the average objective IKDC score,pivot shift test or Kneelax3 measurement (P ＞ 0.05).The results of all the subjective and objective evaluations improved significantly at 2 years postoperation compared with preoperation in all patients (P ＜ 0.05).Conclusion Compared with the RR technique,RP technique may have a significant advantage in the subjective clinical outcomes in the double-bundle ACL reconstruction using hamstring tendon grafts,but shows no significant difference in the postoperative mechanical stability of the knee. Key words: Anterior cruciate ligament; Knee injuries; Arthroscopy; Reconstructive surgical procedures

Q-Manifolds and Mackenzie Theory

Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie algebroids and double vector bundles. In this paper we establish a simple alternative characterization of double Lie algebroids in a supermanifold language. Namely, we show that a double Lie algebroid in Mackenzie's sense is equivalent to a double vector bundle endowed with a pair of commuting homological vector fields of appropriate weights. Our approach helps to simplify and elucidate Mackenzie's original definition; we show how it fits into a bigger picture of equivalent structures on `neighbor' double vector bundles. It also opens ways for extending the theory to multiple Lie algebroids, which we introduce here.