Annulus and Disk Complex Is Contractible and Quasi-convex

The annulus and disk complex is defined and researched. Especially, we prove that this complex is contractible and quasi-convex in the curve complex.

Growth of the Pulmonary Valve Annulus after the Modified Blalock-Taussig Shunt in Patients with Tetralogy of Fallot

Background:The surgical outcomes of tetralogy of Fallot(TOF)have evolved dramatically and have resulted in lower mortality rate.Currently,the many cardiac centers have a trend to early single-stage complete repair more than a staged repair.However,the patients who have an early primary repair were required transannular patch augmentation of a pulmonary valve frequently.This effect has been developed a chronic pulmonary insufficiency may lead to right ventricular dilation,dysfunction.In this era,the aim of treatment of TOF is attempted to preserve pulmonary valve annulus for prevent right ventricular dysfunction in the future.The systemic to pulmonary artery shunt is a palliative procedure or known as staged repair for symptomatic patients with TOF.The modified Blalock-Taussig shunt(mBTS)is the most useful systemic to pulmonary shunt and perform as an initial procedure before complete repair.The mBTS can provide increase pulmonary blood flow as well as improve oxygenation and also promote pulmonary artery(PA)growth.However,the effect of this procedure to promote growth of a pulmonary valve annulus is still debate.Objectives:To compare a growth of pulmonary valve annulus between after staged repair and primary repair in patients with TOF(without pulmonary atresia).Methods:A retrospective case-control study,review of patients with TOF underwent total repair at our hospitals from January 2005 and December 2017 was performed,a total number of 112 patients underwent TOF repair.Twenty-nine patients(26%)underwent a staged repair(mBTS group)and 83(74%)underwent total repair only or primary repair(PR group).We evaluated diameter of pulmonary valve annulus by using echocardiography at the time of first diagnosis and before complete repair on both groups.Results:The age of diagnosis of mBTS group were younger than PR group(p=0.011).Therefore,pulmonary valve annuls were smaller in mBTS group.(Z-score,−2.93±1.42 vs.−1.89±0.97;p=0.001).However,the growth potential of pulmonary valve annulus was increase more than PR group significantly(Z-score,−1.46±1.02 vs.−2.11±1.19;p=0.009)Even though a patent ductus arteriosus was found commonly in PR group(p=0.018).Conclusions:Our results suggest the systemic to pulmonary shunt or mBTS can promote growth of pulmonary valve annulus in patients with TOF.

The effect of the fibre orientation of electrospun scaffolds on the matrix production of rabbit annulus fibrosus-derived stem cells

Annulus fibrosus （AF） tissue engineering has recently received increasing attention as a treatment for intervertebral disc 0VD） degeneration; however, such engineering remains challenging because of the remarkable complexity of AF tissue. In order to engineer a functional AF replacement, the fabrication of cell-scaffold constructs that mimic the cellular, biochemical and structural features of native AF tissue is critical. In this study, we fabricated aligned fibroua polyurethane scaffolds using an electrospinning technique and used them for culturing AF-derived-stem/progenitor cells （AFSCs）. Random fibrous scaffolds, also prepared via electrospinningy were used as a control. We compared the morphology, proliferation, gene expression and matrix production of AFSCs on aligned scaffolds and random scaffolds. There was no apparent difference in the attachment or proliferation of cells cultured on aligned scaffolds and random scaffolds. However, compared to cells on random scaffolds, the AFSCs on aligned scaffolds were more elongated and better aligned, and they exhibited higher gene expression and matrix production of coUagen-I and aggrecan. The gene expression and protein production of coUagen-II did not appear to differ between the two groups. Together, these findings indicate that aligned fibrous scaffolds may provide a favourable microenvironment for the differentiation of AFSCs into cells similar to outer AF cells, which predominantly produce collagen-I matrix.

Rabbit Annulus Fibrosus Cell Apoptosis Induced by Mechanical Overload via a Mitochondrial Apoptotic Pathway

In order to investigate the apoptotic pathway of rabbit annulus fibrosus(AF) cells induced by mechanical overload,an experimental air-pressure model was established in this study to pressurize the rabbit AF cells in vitro.Cells were randomly divided into five groups in which the cells were exposed to a continuous pressure of 1.1 MPa for different lengths of time(0,5,12,24 and 36 h).The cell proliferation and apoptosis were detected by cell counting kit-8(CCK-8) assay and flow cytometry;the alterations in mitochondrial membrane potential were measured by fluorescence microscopy and fluorescence spectrophotometer;the activities of caspase-8 and 9 were determined by spectrophotometry.The results showed that after the cells were subjected to the pressure for 24 or 36 h,the cell proliferation was inhibited;the ratio of cell apoptosis was increased;the mitochondrial membrane potential was decreased;the activity of caspase-9 was enhanced;no activity changes were observed in caspase-8.The results suggested that treatment with a pressure of 1.1 MPa for more than 24 h can lead to the proliferation inhibition and the apoptosis of rabbit AF cells in vitro,and the mitochondrial-dependent pathway is implicated in the pressure-induced AF cell apoptosis.

Existence of Multiple solutions for semilinear elliptic equations in the annulus

The existence of radial solutions of Δu ＋ λg（｜x｜）f（u） = 0 in annuli with Dirichlet（Dirichlet/Neumann） boundary conditions is investigated.It is proved that the problems have at least two positive radial solutions on any annulus if f is superlinear at 0 and sublinear at ∞.

A Heterologous Fibrin Glue Enhances the Closure Effect of Surgical Suture on the Repair of Annulus Fibrous Defect in a Sheep Model

Improving the closure effect of surgical suture for repair of annulus fibrosus defects remains an unsolved problem.A new type of porcine fibrin glue was reported for the repair of annulus fibrous defects in sheep models in this study.Continuous axial loading test showed that this glue could effectively improve the closure effect of surgical suture for annulus fibrous defect.Magnetic resonance imaging (MRI) of the lumbar spine confirmed that,compared with nonfibrin glue treated intervertebral discs,it contributed to preservation of the nucleus pulposus and maintained the physiological hydration of the intervertebral discs.Moreover,histomorphology evaluation showed that the porcine fibrin glue could partially reverse degeneration of the injured intervertebral discs.Taken together,porcine fibrin glue can effectively enhance the closure effect of surgical suture on annulus fibrosus,improve the repair effect and slow down the degeneration of the intervertebral disc,and provide a potential therapeutic strategy for degenerative intervertebral disc disease.

Numerical Simulation of Double Diffusive Mixed Convection in a Horizontal Annulus with Finned Inner Cylinder

The present work relates to a numerical investigation of double diffusive mixed convection around a horizontal annulus with a finned inner cylinder.The solutal and thermal buoyancy forces are sustained by maintaining the inner and outer cylinders at uniform temperatures and concentrations.Buoyancy effects are also considered,with the Boussinesq approximation.The forced convection effect is induced by the outer cylinder rotating with an angular velocity(ω)in an anti-clockwise direction.The studies are made for various combinations of dimensionless numbers;buoyancy ratio number(N),Lewis number(Le),Richardson number(Ri)and Grashof number(Gr).The isotherms,isoconcentrations and streamlines as well as both average and local Nusselt and Sherwood numbers were studied.A finite volume scheme is adopted to solve the transport equations for continuity,momentum,energy and mass transfer.The results indicate that the use of fins on the inner cylinder with outer cylinder rotation,significantly improves the heat and mass transfer in the annulus.

Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation

The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H_2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The nonuniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters(thermal radiation, nonlinear convection,and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology(RSM) and the face-centered central composite design(CCD). The heat transport of the composite nanoliquid for the spacerelated heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.

Thermoelastic vibrations in a thin elliptic annulus plate with elastic supports

In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.

Acoustic focusing through two layer annuluses in air

We report an acoustic focusing lens composed of two-layer annuluses made of metal cylinders in air. We find that the cylindrical waves can be focused into a perfect point without diffraction in the centre of the annuluses, which arises from the Mie-resonance modes in the annuluses. The focusing frequencies are related to the size of the inner annulus, and the focusing effect can be applied to the annuluses with different shapes and incident positions. Interesting applications of the focusing lens in the acoustic beam splitter and directional transmitter with energy enhancement are further discussed.

Settling behavior of spherical particles in eccentric annulus filled with viscous inelastic fluid

Hole cleaning is a complex process as there are many variables affecting cuttings removal(e.g.drilling fluid type,density,flow rate and rheological properties,cuttings size,drill pipe rotation speed).With the increasing number of drilling small diameter wells(e.g.coiled tubing drilling applications,ultra-deep wells drilled for exploitations of unconventional oil and gas resources),the wall resistance of the micro annulus also emerges as one of the most critical factors affecting the cuttings accumulation in wellbore.The eccentricity of drill pipes commonly observed during the drilling process of ultra-deep well and coiled tubing well makes the wall resistance effect on the cuttings transport even more prominent.Understanding the wall resistance effect on the particle settling behavior in eccentric annuli is,therefore,crucial for hydraulic design of efficient cuttings transport operations in these wells.In this study,a total of 196 sets of particle settling experiments were carried out to investigate the particle settling behavior in eccentric annuli filled with power-law fluids.The test matrix included the eccentricity ranges of 0-0.80,the dimensionless diameter ranges of 0.13-0.75 and the particle Reynolds number ranges of 0.09-32.34.A high-speed camera was used to record the particle settling process and determine the influences of the eccentricity,the dimensionless diameter,the fluid rheological properties,and the solid particle characteristics on the wall factor and the particle settling velocity.The functional relationship among the dimensionless diameter,the particle Reynolds number,and the wall factor was determined by using the method of controlling variables.An eccentric annulus wall factor model with average relative error of 5.16%was established.Moreover,by introducing Archimedes number,an explicit model of particle settling velocity in the eccentric annulus with average relative error of 10.17%was established.A sample calculation of particle settling velocity was provided to show the application of the explicit model.Results of this study can be used as a guideline by field engineers to improve hydraulic design of cuttings transport operations in concentric and eccentric annuli.

Thermoelastic analysis of functionally graded annulus with arbitrary gradient

A thermoelastic problem of a circular annulus made of functionally graded materials with an arbitrary gradient is investigated. Different from previous works, our analysis neither requires a special form of the gradient of material properties nor demands partitioning the entire structure into a multilayered homogeneous structure. Instead, we propose a new method for solving the thermoelastic problem of a functionally graded circular annulus by transforming it to a Fredholm integral equation. The distribution of thermal stresses and radial displacement can be obtained by solving the resulting equation. Illustrative examples are given to show the effects of varying gradients on the thermal stresses and radial displacement for given temperature changes at the inner and outer surfaces. The results indicate that the thermal stresses can be relaxed for specified gradients, which is beneficial to design an inhomogeneous annulus to maintain structural integrity.

A Sufficient Condition for the Genus of an Annulus Sum of Two 3-manifolds to Be Non-degenerate

Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on a component of δMi, say Fi, i = 1, 2. Let h ： A1 → A2 be a homeomorphism, and M→M1 ∪h M2, the annulus sum of Mi and M2 along A1 and A2. Suppose that Mi has a Heegaard splitting Vi ∪Si Wi with distance d（Si） ≥ 2g（Mi） ＋ 2g（F3-i） ＋ 1, i = 1, 2. Then g（M） = g（M1） ＋ g（M2）, and the minimal Heegaard splitting of M is unique, which is the natural Heegaard splitting of M induced from Vi∪S1 Wi and V2 ∪S2 W2.

Transient Natural Convection in an Annulus with Thermal Radiation

The interaction of transient fully developed natural convection flow with thermal radiation inside a vertical annulus is analyzed both analytically and numerically. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The mathematical model capturing the present physical situation is highly non-linear due to the presence of radiation effect. The solution of transient model is obtained by implicit finite difference method. To check accuracy of the numerical solution, steady state solution for energy and momentum equations are derived analytically using perturbation series method. Skin-friction and Nusselt number at the outer surface of inner cylinder as well as inner surface of the outer cylinder are obtained. Selected sets of graphical results illustrating the effects of various controlling parameters involved in the problem on flow formation are discussed.

Multi Modality Imaging for Cardiac Masses Can Avoid Unnecessary Surgical Intervention: A Case Report of Caseous Calcification of Mitral Annulus

Mitral Annular Calcification (MAC) is a degenerative process involving the fibrous ring of the mitral valve. Caseous Calcification of Mitral Annulus (CCMA) is a rare variant of MAC. This condition is benign and usually needs no treatment. This is a case report of a 67-year-old woman with non-specific symptoms in whom a cardiac tumor was suspected by transthoracic Echocardiography. The use of multi-modality imaging strategy with transesophageal Echocardiography and cardiac MR scanning revealed however the diagnosis of CCMA and spared the patient an unnecessary operation.

Prosthetic Ring Endocarditis with Shrunken Mitral Annulus Late After Undersized Mitral Annuloplasty

We report a case of supra-annular mitral valve replacement for a patient with prosthetic ring endocarditis that developed late after undergoing undersized mitral annuloplasty (UMAP). A 58-year-old man had undergone left ventriculoplasty and UMAP with a 26-mm semi-rigid full ring for dilated cardiomyopathy and functional mitral regurgitation. The mitral valve had progressively stenosed and he developed prosthetic ring endocarditis 5 years after the operation. In the surgery, there were brownish fresh vegetations around the anterior mitral leaflet and the prosthetic ring. The mitral annulus was very small, even after removal of the infected ring prosthesis and debridement of the infected tissues. We implanted a 22-mm mechanical prosthesis in the supra-annular position using everting mattress sutures to prevent the valve leaflets from getting stuck by the thickened subannular tissue. Herein, we discuss the surgical procedures for a shrunken mitral annulus.

Surgical Method for Facilitation of Aortic Valve Replacement:Intraoperative Application of External Pressure for Increasing the Transverse Axis of Aortic Annulus

Background: Surgical method was introduced for enhancement of prosthetic valve insertion and overcoming difficulties ensourcing from prosthesis-patient mismatch. Methods: Twenty-two patients that underwent aortic valve replacement between January 2005 and July 2009 were included in this prospective study. In these patients, the insertion of prosthesis larger than the annulus diameter was attempted after the application of an external pressure that increased the transverse axis diameter of the aortic annulus. The postoperative results and complications were assessed. Results: This surgical method was performed on 22 patients (16 males, 6 females, mean age: 52.2 ± 15.8 years) during the valve replacement. In 12 patients (55%), replacement of proper sized aortic valve compliant to their surface area was accomplished, while the insertion of a proper valve could not be achieved in 10 (45%) of the patients. No perioperative mortality or complications related to the procedure were reported. Conclusion: Increasing the transverse diameter of aortic valve may not only facilitate the insertion of a prosthetic valve but also aid in overcoming prosthesis-patient mismatch. Further studies on larger series are necessary to document the actual effectively and precise selection criteria for application of this method.

Valve replacement plus reconstruction of the annulus

Objective To investigate surgical technique and clinical outcomes of reconstruction of annulus and intervalvular fibrous body during valve replacements. Methods Fifty-nine patients underwent reconstruction of annulus or intervalvular fibrous body during valve replacement. Indications for operation were small

An experimental research on surface oscillation of buoyant-thermocapillary convection in open cylindrical annuli

An experiment is carried out on the surface oscillation of buoyant-thermocapillary convection in an open cylindrical annulus. When the radial temperature difference AT reaches a critical value △Tc, a regular oscillation appears and soon disappears on the open surface, which varies when the liquid layer＇s thickness h and temperature difference △T are varied. With growth of △T, dominant frequency of the visible oscillation will grow too but is found within certain frequencies. Driving forces, buoyance and thermocapillarity, are responsible for this phenomanon and the ＂balance＂ point is considered to exist when h is between 4.5-5.0 mm. Surface oscillation region is also found restricted within a narrow gap when Bo is smaller than 3.7.

A novel rat tail disc degeneration model induced by static bending and compression

Background:A new rat tail intervertebral disc degeneration model was established to observe the morphologic and biologic changes of static bending and compression applied to the discs.Methods:In total,20 Sprague-Dawley rats with similar weight were randomly di-vided into 4 groups.Group 1 served as a control group for a baseline assessment of normal discs.Group 2 underwent a sham surgery,using an external device to bend the vertebrae of coccygeal 8-10.Groups 3 and 4 were the loaded groups,and exter-nal devices were instrumented to bend the spine with a compression level of 1.8 N and 4.5 N,respectively.Magnetic resonance imaging(MRI),histological,and quanti-tative real-time PCR(qRT-PCR)analysis were performed on all animals on day 14 of the experiment.Results:Magnetic resonance imaging and histological results showed that the changes of intervertebral disc degeneration increased with the size of compression load.Some architecture disorganizations in nucleus pulposus and annulus fibro-sus were found on both of the convex and concave side in the groups of 1.8 N and 4.5 N.An upregulation of MM-3,MM-13,and collagen 1-α1 mRNA expression and a downregulation of collagen 2-α1 and aggrecan mRNA expression were observed in the sham and loading groups.Significant changes were found between the loading groups,whereas the sham group showed similar results to the control group.Conclusions:Static bending and compression could induce progressive disc degen-eration,which could be used for biologic study on disc degeneration promoted by static complex loading.