HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.

Homeomorphisms of the annulus with a transitive lift

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the infinite strip (A) over tilde which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set B(-) subset of (A) over tilde such that B(-) is bounded to the right, the projection of B to A is dense, B - (1, 0) subset of B and (f) over tilde (B) subset of B. Moreover, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of B(-), lim sup (n ->infinity) p1((f) over tilde (n)((z) over tilde)) - p(1) ((z) over tilde)/n < - d. In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior.

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

Assessment of right ventricular systolic function: Comparison between cardiac magnetic resonance derived ejection fraction and pulsed-wave tissue Doppler imaging of the tricuspid annulus

Systolic right ventricular (RV) function is an important predictor in the course of various congenital and acquired heart diseases. Its practical determination by echocardiography remains challenging. We compared routine assessment of lateral tricuspid annular systolic motion velocity (TV(lat), cm/s) using pulsed-wave tissue Doppler imaging from the apical 4-chamber view with cardiac magnetic resonance (CMR) as reference method.

Accuracy and reproducibility of aortic annulus sizing using a dedicated three-dimensional computed tomography reconstruction tool in patients evaluated for transcatheter aortic valve replacement

Aims: To evaluate the accuracy and reproducibility of aortic annulus sizing using a multislice computed tomography (MSCT) based aortic root reconstruction tool compared with conventional imaging among patients evaluated for transcatheter aortic valve replacement (TAVR). Methods and results: Patients referred for TAVR underwent standard preprocedural assessment of aortic annulus parameters using MSCT, angiography and transoesophageal echocardiography (TEE). Three-dimensional (3-D) reconstruction of MSCT images of the aortic root was performed using 3mensio (3mensio Medical Imaging BV, Bilthoven, The Netherlands), allowing for semi-automated delineation of the annular plane and assessment of annulus perimeter, area, maximum, minimum and virtual diameters derived from area and perimeter (aVD and pVD). A total of 177 patients were enrolled. We observed a good inter-observer variability of 3-D reconstruction assessments with concordance coefficients for agreement of 0.91 (95% CI: 0.87-0.93) and 0.91 (0.88-0.94) for annulus perimeter and area assessments, respectively. 3-D derived pVD and aVD correlated very closely with a concordance coefficient of 0.97 (0.96-0.98) with a mean difference of 0.5±0.3 mm (pVD-aVD). 3-D derived pVD showed the best, but moderate concordance with diameters obtained from coronal MSCT (0.67, 0.56-0.75; 0.3±1.8 mm), and the lowest concordance with diameters obtained from TEE (0.42, 0.31-0.52; 1.9±1.9 mm). Conclusions: MSCT-based 3-D reconstruction of the aortic annulus using the 3mensio software enables accurate and reproducible assessment of aortic annulus dimensions.

Challenges and strategies in the repair of ruptured annulus fibrosus

Lumbar discectomy is the surgical procedure most frequently performed for patients suffering from low back pain and sciatica. Disc herniation as a consequence of degenerative or traumatic processes is commonly encountered as the underlying cause for the painful condition. While discectomy provides favourable outcome in a majority of cases, there are conditions where unmet requirements exist in terms of treatment, such as large disc protrusions with minimal disc degeneration; in these cases, the high rate of recurrent disc herniation after discectomy is a prevalent problem. An effective biological annular repair could improve the surgical outcome in patients with contained disc herniations but otherwise minor degenerative changes. An attractive approach is a tissue-engineered implant that will enable/stimulate the repair of the ruptured annulus. The strategy is to develop three-dimensional scaffolds and activate them by seeding cells or by incorporating molecular signals that enable new matrix synthesis at the defect site, while the biomaterial provides immediate closure of the defect and maintains the mechanical properties of the disc. This review is structured into (1) introduction, (2) clinical problems, current treatment options and needs, (3) biomechanical demands, (4) cellular and extracellular components, (5) biomaterials for delivery, scaffolding and support, (6) pre-clinical models for evaluation of newly developed cell- and material-based therapies, and (7) conclusions. This article highlights that an interdisciplinary approach is necessary for successful development of new clinical methods for annulus fibrosus repair. This will benefit from a close collaboration between research groups with expertise in all areas addressed in this review.

Human intervertebral disc stiffness correlates better with the Otsu threshold computed from axial T2 map of its posterior annulus fibrosus than with clinical classifications

Degeneration of the intervertebral disc, sometimes associated with low back pain and abnormal spinal motions, represents a major health issue with high costs. A non-invasive degeneration assessment via qualitative or quantitative MRI (magnetic resonance imaging) is possible, yet, no relation between mechanical properties and T2 maps of the intervertebral disc (IVD) has been considered, albeit T2 relaxation time values quantify the degree of degeneration. Therefore, MRI scans and mechanical tests were performed on 14 human lumbar intervertebral segments freed from posterior elements and all soft tissues excluding the IVD. Degeneration was evaluated in each specimen using morphological criteria, qualitative T2 weighted images and quantitative axial T2 map data and stiffness was calculated from the load-deflection curves of in vitro compression, torsion, lateral bending and flexion/extension tests. In addition to mean T2, the OTSU threshold of T2 (TOTSU), a robust and automatic histogram-based method that computes the optimal threshold maximizing the distinction of two classes of values, was calculated for anterior, posterior, left and right regions of each annulus fibrosus (AF). While mean T2 and degeneration schemes were not related to the IVDs' mechanical properties, TOTSU computed in the posterior AF correlated significantly with those classifications as well as with all stiffness values. TOTSU should therefore be included in future degeneration grading schemes.

Co-culture of Notochordal Cells with Nucleus pulposus and Annulus fibrosus cells under normoxia and hypoxia

Introduction Notochordal cells (NC) are shifted back into focus due to their apparent action of activating other disc cells via indirect release of yet unknown factors into the medium (conditioned medium = CM).1,2 Recent evidence confirms the results from the late 1990s.3,4 Here, we test porcine (p) NC cultured in 3D and the influence of adding serum or using serum-free medium onto the culture on NC cells and its stimulating effects for subsequent coculture with primary bovine (b) nucleus pulposus (bNPC) and annulus fibrous cells (bAFC). Materials and Methods Primary pNC, bNPC, and bAFC were isolated from porcine tails (< 6-12 months age) or bovine tails (∼1 year age), which were obtained from the food chain (N = 4 repeats) within 4 hours postmortem. All cells were seeded into 1.2% alginate, each with a density of 4 × 106/mL. NC were then either cultured for 7 days in serum free medium (SFM = Dulbecco modified eagle medium [DMEM] supplied with ITS+, 50 µg/mL vitamin C and nonessential amino acids) or DMEM + 10% fetal calf serum (FCS). CM was produced from NC collecting 4 mL SFM and keeping approximately 30 beads for 7 days. Then, a coculture was set up in SFM for 14 days using indirect cell-cell contact (culture insert, high density pore, 0.4 µm) using a 50:50% ratio5 of pNC:bNP or bAF, or by addition of CM, respectively. The cell activity, glycosaminoglycan per DNA (GAG/DNA) ratio, and real-time RT-PCR of IVD relevant genes were monitored. Mass spectrometry was performed on the SFM and the cocultured medium as well as the CM of the pNC to identify possible key cytokines to the stimulatory effects. Results The results for cell activity confirmed that pNC are highly responsive on the nutritional condition in the culture (K-W test, p = 0.048) after 7 days of coculture. bNPC and bAFC did not respond significantly different to coculture or addition of CM with respect to cell activity. However, GAG/DNA ratio of pNC was significantly upregulated if they were initially pre-exposed to FCS and in coculture with bNPC after 14 days, for both normoxia and hypoxia (K-W, p = 0.03). The bNPC were stimulated by both, 1:1 coculture with pNC but also by addition of CM only, which resulted in approximately 200% increased GAG/DNA values relative to the day 0 state. However, this doubling of the GAG/DNA ratio was nonsignificant after 14 days. The aggrecan/collagen type 2 ratio as quantified from real-time RT-PCR pointed to a beneficial state of the bNPC if cultured either in indirect coculture with pNC or by the addition of CM (Fig. 1). The mass spectrometric analysis of the CM revealed that there was connecting tissue growth factor present (CTGF) among the cytokine CLC11, a cytokine that has been found to be expressed in skeletal tissues including bone marrow and chondrocytes among other factors that might have immunoregulatory and cell proliferative functions.

Extent and distribution of calcification of both the aortic annulus and the left ventricular outflow tract predict aortic regurgitation after transcatheter aortic valve replacement

Aims: We sought to analyse local distribution of aortic annulus and left ventricular outflow tract (LVOT) calcification in patients undergoing transcatheter aortic valve replacement (TAVR) and its impact on aortic regurgitation (AR) immediately after device placement. Methods and results: A group of 177 patients with severe aortic stenosis undergoing multislice computed tomography of the aortic root followed by TAVR were enrolled in this single-centre study. Annular and LVOT calcifications were assessed per cusp using a semi-quantitative grading system (0: none; 1 [mild]: small, non-protruding calcifications; 2 [moderate]: protruding [>1 mm] or extensive [>50% of cusp sector] calcifications; 3 [severe]: protruding and extensive calcifications). Any calcification of the annulus or LVOT was present in 107 (61%) and 63 (36%) patients, respectively. Prevalence of annulus/LVOT calcifications in the left coronary cusp was 42% and 25%, respectively, in the non-coronary cusp 28% and 13%, in the right coronary cusp 13% and 5%. AR grade 2 to 4 assessed by the method of Sellers immediately after TAVR device implantation was observed in 55 patients (31%). Multivariate regression analysis revealed that the overall annulus calcification (OR [95% CI] 1.48 [1.10-2.00]; p=0.0106), the overall LVOT calcification (1.93 [1.26-2.96]; p=0.0026), any moderate or severe LVOT calcification (5.37 [1.52-18.99]; p=0.0092), and asymmetric LVOT calcification were independent predictors of AR. Conclusions: Calcifications of the aortic annulus and LVOT are frequent in patients undergoing TAVR, and both the distribution and the severity of calcifications appear to be independent predictors of aortic regurgitation after device implantation. - See more at: http://www.pcronline.com/eurointervention/77th_issue/126/#sthash.Hzodgju5.dpuf

Mechanical restoration and failure analyses of a hydrogel and scaffold composite strategy for annulus fibrosus repair

Unrepaired defects in the annulus fibrosus of intervertebral disks are associated with degeneration and persistent back pain. A clinical need exists for a disk repair strategy that can seal annular defects, be easily delivered during surgical procedures, and restore biomechanics with low risk of herniation. Multiple annulus repair strategies were developed using poly(trimethylene carbonate) scaffolds optimized for cell delivery, polyurethane membranes designed to prevent herniation, and fibrin-genipin adhesive tuned to annulus fibrosus shear properties. This three-part study evaluated repair strategies for biomechanical restoration, herniation risk and failure mode in torsion, bending and compression at physiological and hyper-physiological loads using a bovine injury model. Fibrin-genipin hydrogel restored some torsional stiffness, bending ROM and disk height loss, with negligible herniation risk and failure was observed histologically at the fibrin-genipin mid-substance following rigorous loading. Scaffold-based repairs partially restored biomechanics, but had high herniation risk even when stabilized with sutured membranes and failure was observed histologically at the interface between scaffold and fibrin-genipin adhesive. Fibrin-genipin was the simplest annulus fibrosus repair solution evaluated that involved an easily deliverable adhesive that filled irregularly-shaped annular defects and partially restored disk biomechanics with low herniation risk, suggesting further evaluation for disk repair may be warranted. Statement of significance Lower back pain is the leading cause of global disability and commonly caused by defects and failure of intervertebral disk tissues resulting in herniation and compression of adjacent nerves. Annulus fibrosus repair materials and techniques have not been successful due to the challenging mechanical and chemical microenvironment and the needs to restore biomechanical behaviors and promote healing with negligible herniation risk while being delivered during surgical procedures. This work addressed this challenging biomaterial and clinical problem using novel materials including an adhesive hydrogel, a scaffold capable of cell delivery, and a membrane to prevent herniation. Composite repair strategies were evaluated and optimized in quantitative three-part study that rigorously evaluated disk repair and provided a framework for evaluating alternate repair techniques.

Repair of Annulus fibrosus with Genipin-enhanced Fibrin Hydrogel and silk membrane- fleece

Introduction Low back pain is often caused by a trauma causing disc herniation and /or disc degeneration. Although there are some promising approaches for nucleus pulposus repair, the inner tissue of the intervertebral disc (IVD) so far no treatment or repair is available for annulus fibrosus (AF) injuries. Here we aimed to develop a new method to seal and repair AF injuries by using a silk fleece composite and a genipin enhanced hydrogel. Methods Bovine (b) IVDs were harvested under aseptic conditions and kept in free swelling conditions for 24h in high-glucose DMEM containing 5% bovine serum for equilibration (1). A circular 2mm biopsy punch (Polymed Medical Center, Switzerland) was used to form a reproducible defect in the AF. For filling the defect and keeping the silk composite in place a human-derived fibrin gel (Baxter Tisseel, Switzerland) enhanced with 4.2mg/ml of the cross linker genipin (Wako Chemicals GmbH, Germany) was used. The silk composite consists of a mesh- and a membrane side (Spintec Engineering GmbH, Germany); the membrane is facing outwards to form a seal. bIVDs were cultured in vitro for 14 days either under dynamic load in a custom-built bioreactor under physiological conditions (0.2MPa load and ±2° torsion at 0.2Hz for 8h/day) or static diurnal load of 0.2MPa (2). At the end of culture discs were checked for seal failure, disc height, metabolic activity, cell death by necrosis (LDH assay), DNA content and glycosaminoglycan content. Results Silk composite maintained its position throughout the 14 days of culture under loaded conditions. Although repaired discs performed slightly lower in cell activity, DNA and GAG content were in the range of the control. Also LDH resulted in similar values compared to control discs (Fig 1). Height loss in repaired discs was in the same range as for static diurnal loaded control samples. For dynamically loaded samples the decrease was comparable to the injured, unrepaired discs. Fig 1 LDH of repaired discs compared to control disc after 24h in free swelling conditions for equilibration and first three loading cycles. Conclusions Silk-genipin-fibrin reinforced hydrogel is a promising approach to close AF defects as tested by two degree of freedom loading. In further experiments cytocompatibility of genipin has to be investigated. References 1. Chan SC, Gantenbein-Ritter B. Preparation of intact bovine tail intervertebral discs for organ culture. J Vis Exp 2012, Feb 2;60(60):e3490. 2. Walser J, Ferguson SJ, Gantenbein-Ritter B. Design of a mechanical loading device to culture intact bovine caudal motional segments of the spine under twisting motion. In: Davies J, editors. Replacing animal models: a practical guide to creating and using biomimetic alternatives. Chichester, UK: John Wiley & Sons, Ltd.; 2012. p. 89-105. Acknowledgements This project is funded by the Gerbert Rüf Stiftung project # GRS-028/13 and the Swiss National Science Project SNF #310030_153411.