Spectrum of the non-commutative spherical well

We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be discussed unambiguously. Here we focus on the infinite well and solve for the eigenvalues and eigenfunctions. We find that time reversal symmetry is broken by the non-commutativity. We show that in the commutative and thermodynamic limits the eigenstates and eigenfunctions of the commutative spherical well are recovered and time reversal symmetry is restored

The Single-Particle density of States, Bound States, Phase-Shift Flip, and a Resonance in the Presence of an Aharonov-Bohm Potential

Both the nonrelativistic scattering and the spectrum in the presence of the Aharonov-Bohm potential are analyzed. The single-particle density of states (DOS) for different self-adjoint extensions is calculated. The DOS provides a link between different physical quantities and is a natural starting point for their calculation. The consequences of an asymmetry of the S matrix for the generic self-adjoint extension are examined. I. Introduction II. Impenetrable flux tube and the density of states III. Penetrable flux tube and self-adjoint extensions IV. The S matrix and scattering cross sections V. The Krein-Friedel formula and the resonance VI. Regularization VII. The R --> 0 limit and the interpretation of self-adjoint extensions VIII. Energy calculations IX. The Hall effect in the dilute vortex limit X. Persistent current of free electrons in the plane pierced by a flux tube XI. The 2nd virial coefficient of nonrelativistic interacting anyons XII. Discussion of the results and open questionsComment: 68 pages, plain latex, 7 figures, 3 references and one figure added plus a few minor text correction

Biomechanics and anterior cruciate ligament reconstruction

For years, bioengineers and orthopaedic surgeons have applied the principles of mechanics to gain valuable information about the complex function of the anterior cruciate ligament (ACL). The results of these investigations have provided scientific data for surgeons to improve methods of ACL reconstruction and postoperative rehabilitation. This review paper will present specific examples of how the field of biomechanics has impacted the evolution of ACL research. The anatomy and biomechanics of the ACL as well as the discovery of new tools in ACL-related biomechanical study are first introduced. Some important factors affecting the surgical outcome of ACL reconstruction, including graft selection, tunnel placement, initial graft tension, graft fixation, graft tunnel motion and healing, are then discussed. The scientific basis for the new surgical procedure, i.e., anatomic double bundle ACL reconstruction, designed to regain rotatory stability of the knee, is presented. To conclude, the future role of biomechanics in gaining valuable in-vivo data that can further advance the understanding of the ACL and ACL graft function in order to improve the patient outcome following ACL reconstruction is suggested

The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory

Role of biomechanics in the understanding of normal, injured, and healing ligaments and tendons

Ligaments and tendons are soft connective tissues which serve essential roles for biomechanical function of the musculoskeletal system by stabilizing and guiding the motion of diarthrodial joints. Nevertheless, these tissues are frequently injured due to repetition and overuse as well as quick cutting motions that involve acceleration and deceleration. These injuries often upset this balance between mobility and stability of the joint which causes damage to other soft tissues manifested as pain and other morbidity, such as osteoarthritis

Functional tissue engineering of ligament healing

Ligaments and tendons are dense connective tissues that are important in transmitting forces and facilitate joint articulation in the musculoskeletal system. Their injury frequency is high especially for those that are functional important, like the anterior cruciate ligament (ACL) and medial collateral ligament (MCL) of the knee as well as the glenohumeral ligaments and the rotator cuff tendons of the shoulder. Because the healing responses are different in these ligaments and tendons after injury, the consequences and treatments are tissue- and site-specific. In this review, we will elaborate on the injuries of the knee ligaments as well as using functional tissue engineering (FTE) approaches to improve their healing. Specifically, the ACL of knee has limited capability to heal, and results of non-surgical management of its midsubstance rupture have been poor. Consequently, surgical reconstruction of the ACL is regularly performed to gain knee stability. However, the long-term results are not satisfactory besides the numerous complications accompanied with the surgeries. With the rapid development of FTE, there is a renewed interest in revisiting ACL healing. Approaches such as using growth factors, stem cells and scaffolds have been widely investigated. In this article, the biology of normal and healing ligaments is first reviewed, followed by a discussion on the issues related to the treatment of ACL injuries. Afterwards, current promising FTE methods are presented for the treatment of ligament injuries, including the use of growth factors, gene delivery, and cell therapy with a particular emphasis on the use of ECM bioscaffolds. The challenging areas are listed in the future direction that suggests where collection of energy could be placed in order to restore the injured ligaments and tendons structurally and functionally

Impact of polypropylene prolapse mesh on vaginal smooth muscle in rhesus macaque

© 2019 Elsevier Inc. Background: The use of polypropylene prolapse mesh to treat pelvic organ prolapse has been limited by mesh-related complications. Gynemesh PS mesh, implanted via sacrocolpopexy in rhesus macaques, had a negative impact on the vagina with thinning of vaginal muscularis and decreased vaginal smooth muscle contractility. The negative effect was attenuated when a bioscaffold derived from urinary bladder extracellular matrix was used as a composite with Gynemesh PS. Objective: The objective of the study was to further elucidate the impact of Gynemesh PS polypropylene mesh and MatriStem extracellular matrix bioscaffolds on the vaginal smooth muscle in terms of micromorphology of vaginal smooth muscle (muscle bundles and individual myocytes), innervation, and nerve-mediated contractile function following their implantations in a rhesus macaque model via sacrocolpopexy. Study Design: Thirty-two middle-aged rhesus macaques were randomized to undergo either a sham surgery (sham, n = 8), or the implantation of Gynemesh PS alone (n = 8) vs composite mesh comprised of Gynemesh PS plus 2-ply MatriStem (n = 8) vs 6-ply MatriStem alone (n = 8) via sacrocolpopexy. The graft-vagina complexes were harvested 3 months later. Histomorphometrics of smooth muscle bundles and myocytes were performed by immunofluorescent labeling of alpha smooth muscle actin, caveolin-3 (membrane protein), and cell nuclei followed by confocal imaging. The cross-sectional diameters of smooth muscle bundles and individual myocytes were quantified using images randomly taken in at least 5 areas of each section of sample. Contractile proteins alpha smooth muscle actin and smoothelin were quantified by Western immunoblotting. Nerve density was measured by immunohistochemical labeling of a pan-neuron marker, PGP9.5. Nerve-mediated smooth muscle contractility was quantified using electrical field stimulation. One-way analysis of variance and appropriate post hoc tests were used for statistical comparisons. Results: Compared with sham, the implantation of Gynemesh PS alone resulted in a disorganized smooth muscle morphology with the number of small muscle bundles (cross-sectional diameter less than 20 μm) increased 67% (P = .004) and the myocyte diameter decreased 22% (P \u3c .001). Levels of contractile proteins were all decreased vs sham with alpha smooth muscle actin decreased by 68% (P = .009), low-molecular-weight smoothelin by 51% (P = .014), and high-molecular-weight smoothelin by 40% (P = .015). Nerve density was decreased by 48% (P = .03 vs sham) paralleled by a 63% decrease of nerve-mediated contractility (P = .02). Following the implantation of composite mesh, the results of measurements were similar to sham (all P \u3e .05), with a 39% increase in the myocyte diameter (P \u3c .001) and a 2-fold increase in the level of alpha smooth muscle actin relative to Gynemesh (P = .045). Following the implantation of MatriStem alone, the number of small muscle bundles were increased 54% vs sham (P = .002), while the other parameters were not significantly different from sham (all P \u3e .05). Conclusion: The implantation of Gynemesh PS had a negative impact on the structural and functional integrity of vaginal smooth muscle evidenced by atrophic macro- and microscopic muscle morphology, decreased innervation, and impaired contractile property, consistent with a maladaptive remodeling response. The extracellular matrix bioscaffold (MatriStem), when used with Gynemesh PS as a composite (2 ply), attenuated the negative impact of Gynemesh PS; when used alone (6 ply), it induced adaptive remodeling as evidenced by an increased fraction of small smooth muscle bundles with normal contractility