The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

Influence of Clinically Invisible, but Optical Coherence Tomography Detected, Optic Disc Margin Anatomy on Neuroretinal Rim Evaluation

PURPOSE. We previously demonstrated that most eyes have regionally variable extensions of Bruch's membrane (BM) inside the clinically identified disc margin (DM) that are clinically and photographically invisible. We studied the impact of these findings on DM- and BM opening (BMO)-derived neuroretinal rim parameters. METHODS. Disc stereo-photography and spectral domain optical coherence tomography (SD-OCT, 24 radial B-scans centered on the optic nerve head) were performed on 30 glaucoma patients and 10 age-matched controls. Photographs were colocalized to SD-OCT data such that the DM and BMO could be visualized in each B-scan. Three parameters were computed: (1) DM-horizontal rim width (HRW), the distance between the DM and internal limiting membrane (ILM) along the DM reference plane; (2) BMO-HRW, the distance between BMO and ILM along the BMO reference plane; and (3) BMO-minimum rim width (MRW), the minimum distance between BMO and ILM. Rank-order correlations of sectors ranked by rim width and spatial concordance measured as angular distances between equivalently ranked sectors were derived. RESULTS. The average DM position was external to BMO in all quadrants, except inferotemporally. There were significant sectoral differences among all three rim parameters. DM- HRW and BMO-HRW sector ranks were better correlated (median rho = 0.84) than DM- HRW and BMO-MRW (median rho = 0.55), or BMO-HRW and BMO-MRW (median rho = 0.60) ranks. Sectors with the narrowest BMO-MRW were infrequently the same as those with the narrowest DM-HRW or BMO-HRW. CONCLUSIONS. BMO-MRW quantifies the neuroretinal rim from a true anatomical outer border and accounts for its variable trajectory at the point of measurement. (Invest Ophthalmol Vis Sci. 2012;53:1852-1860) DOI:10.1167/iovs.11-9309

MRI analysis of the relationship between bone changes in the temporomandibular joint and articular disc position in symptomatic patients

Objectives: The aim of this study was to investigate bone changes in the condyle, articular eminence and glenoid fossa in relation to the position of the articular disc. Methods: 148 temporomandibular joints (TMJs) of 74 symptomatic patients who underwent MRI were evaluated. The position of the disc was classified as either normal (N), disc displacement with reduction (DDwR), disc displacement without reduction (DDwoR) and posterior displacement (PD). Bone changes were investigated in the condyle and temporal components of the TMJ and classified as osteophytosis, sclerosis or erosion. Results: There were no bone changes in the glenoid fossa of the temporal bone. Of the total number of TMJs studied, 94 (63.5%) were N, 34 (23%) presented DDwoR, 19 (12.8%) presented DDwR and 1 (0.7%) presented PD. The bone changes in the condyle and posterior aspect of the articular eminence were associated with the position of the disc. The bone changes in the anterior aspect of the articular eminence were not associated with the position of the disc. Conclusion: In cases of DDwoR, bone changes in the condyles were more common. The combination of erosion and osteophytosis in the condyle and the bone changes of the posterior aspect of the articular eminence were associated with disc position. Dentomaxillofacial Radiology (2012) 41, 367-372. doi: 10.1259/dmfr/79317853

Optic Disc Margin Anatomy in Patients with Glaucoma and Normal Controls with Spectral Domain Optical Coherence Tomography

Objective: To characterize optic nerve head (ONH) anatomy related to the clinical optic disc margin with spectral domain-optical coherence tomography (SD-OCT). Design: Cross-sectional study. Participants: Patients with open-angle glaucoma with focal, diffuse, and sclerotic optic disc damage, and age-matched normal controls. Methods: High-resolution radial SD-OCT B-scans centered on the ONH were analyzed at each clock hour. For each scan, the border tissue of Elschnig was classified for obliqueness (internally oblique, externally oblique, or nonoblique) and the presence of Bruch's membrane overhanging the border tissue. Optic disc stereophotographs were co-localized to SD-OCT data with customized software. The frequency with which the disc margin identified in stereophotographs coincided with (1) Bruch's membrane opening (BMO), defined as the innermost edge of Bruch's membrane; (2) Bruch's membrane/border tissue, defined as any aspect of either outside BMO or border tissue; or (3) border tissue, defined as any aspect of border tissue alone, in the B-scans was computed at each clock hour. Main Outcome Measures: The SD-OCT structures coinciding with the disc margin in stereophotographs. Results: There were 30 patients (10 with each type of disc damage) and 10 controls, with a median (range) age of 68.1 (42-86) years and 63.5 (42-77) years, respectively. Although 28 patients (93%) had 2 or more border tissue configurations, the most predominant one was internally oblique, primarily superiorly and nasally, frequently with Bruch's membrane overhang. Externally oblique border tissue was less frequent, observed mostly inferiorly and temporally. In controls, there was predominantly internally oblique configuration around the disc. Although the configurations were not statistically different between patients and controls, they were among the 3 glaucoma groups. At most locations, the SD-OCT structure most frequently identified as the disc margin was some aspect of Bruch's membrane and border tissue external to BMO. Bruch's membrane overhang was regionally present in the majority of patients with glaucoma and controls; however, in most cases it was not visible as the disc margin. Conclusions: The clinically perceived disc margin is most likely not the innermost edge of Bruch's membrane detected by SD-OCT. These findings have important implications for the automated detection of the disc margin and estimates of the neuroretinal rim. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references. Ophthalmology 2012;119:738-747 (C) 2012 by the American Academy of Ophthalmology.

Rates of Change in the Visual Field and Optic Disc in Patients with Distinct Patterns of Glaucomatous Optic Disc Damage

Purpose: To investigate the rate of visual field and optic disc change in patients with distinct patterns of glaucomatous optic disc damage. Design: Prospective longitudinal study. Participants: A total of 131 patients with open-angle glaucoma with focal (n = 45), diffuse (n = 42), and sclerotic (n = 44) optic disc damage. Methods: Patients were examined every 4 months with standard automated perimetry (SAP, SITA Standard, 24-2 test, Humphrey Field Analyzer, Carl Zeiss Meditec, Dublin, CA) and confocal scanning laser tomography (CSLT, Heidelberg Retina Tomograph, Heidelberg Engineering GmbH, Heidelberg, Germany) for a period of 4 years. During this time, patients were treated according to a predefined protocol to achieve a target intraocular pressure (IOP). Rates of change were estimated by robust linear regression of visual field mean deviation (MD) and global optic disc neuroretinal rim area with follow-up time. Main Outcome Measures: Rates of change in MD and rim area. Results: Rates of visual field change in patients with focal optic disc damage (mean -0.34, standard deviation [SD] 0.69 dB/year) were faster than in patients with sclerotic (mean - 0.14, SD 0.77 dB/year) and diffuse (mean + 0.01, SD 0.37 dB/year) optic disc damage (P = 0.003, Kruskal-Wallis). Rates of optic disc change in patients with focal optic disc damage (mean - 11.70, SD 25.5 x 10(-3) mm(2)/year) were faster than in patients with diffuse (mean -9.16, SD 14.9 x 10(-3) mm(2)/year) and sclerotic (mean -0.45, SD 20.6 x 10(-3) mm(2)/year) optic disc damage, although the differences were not statistically significant (P = 0.11). Absolute IOP reduction from untreated levels was similar among the groups (P = 0.59). Conclusions: Patients with focal optic disc damage had faster rates of visual field change and a tendency toward faster rates of optic disc deterioration when compared with patients with diffuse and sclerotic optic disc damage, despite similar IOP reductions during follow-up. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references. Ophthalmology 2012; 119: 294-303 (C) 2012 by the American Academy of Ophthalmology.

Processing of high resolution magic angle spinning spectra of breast cancer cells by the filter diagonalization method

Proton nuclear magnetic resonance (H-1 NMR) spectroscopy for detection of biochemical changes in biological samples is a successful technique. However, the achieved NMR resolution is not sufficiently high when the analysis is performed with intact cells. To improve spectral resolution, high resolution magic angle spinning (HR-MAS) is used and the broad signals are separated by a T-2 filter based on the CPMG pulse sequence. Additionally, HR-MAS experiments with a T-2 filter are preceded by a water suppression procedure. The goal of this work is to demonstrate that the experimental procedures of water suppression and T-2 or diffusing filters are unnecessary steps when the filter diagonalization method (FDM) is used to process the time domain HR-MAS signals. Manipulation of the FDM results, represented as a tabular list of peak positions, widths, amplitudes and phases, allows the removal of water signals without the disturbing overlapping or nearby signals. Additionally, the FDM can also be used for phase correction and noise suppression, and to discriminate between sharp and broad lines. Results demonstrate the applicability of the FDM post-acquisition processing to obtain high quality HR-MAS spectra of heterogeneous biological materials.

Multi-Walled Carbon Nanotubes and Poly(lactic acid) Nanocomposite Fibrous Membranes Prepared by Solution Blow Spinning

Nanocomposite fibers based on multi-walled carbon nanotubes (MWCNT) and poly(lactic acid) (PLA) were prepared by solution blow spinning (SBS). Fiber morphology was characterized by scanning electron microscopy (SEM) and optical microscopy (OM). Electrical, thermal, surface and crystalline properties of the spun fibers were evaluated, respectively, by conductivity measurements (4-point probe), thermogravimetric analyses (TGA), differential scanning calorimetry (DSC), contact angle and X-ray diffraction (XRD). OM analysis of the spun mats showed a poor dispersion of MWCNT in the matrix, however dispersion in solution was increased during spinning where droplets of PLA in solution loaded with MWCNT were pulled by the pressure drop at the nozzle, producing PLA fibers filled with MWCNT. Good electrical conductivity and hydrophobicity can be achieved at low carbon nanotube contents. When only 1 wt% MWCNT was added to low-crystalline PLA, surface conductivity of the composites increased from 5 x 10(-8) to 0.46 S/cm. Addition of MWCNT can slightly influence the degree of crystallinity of PLA fibers as studied by XRD and DSC. Thermogravimetric analyses showed that MWCNT loading can decrease the onset degradation temperature of the composites which was attributed to the catalytic effect of metallic residues in MWCNT. Moreover, it was demonstrated that hydrophilicity slightly increased with an increase in MWCNT content. These results show that solution blow spinning can also be used to produce nanocomposite fibers with many potential applications such as in sensors and biosensors.

Comparison of disc diffusion, Etest and broth microdilution for testing susceptibility of carbapenem-resistant P. aeruginosa to polymyxins

Abstract Background Considering the increasing use of polymyxins to treat infections due to multidrug resistant Gram-negative in many countries, it is important to evaluate different susceptibility testing methods to this class of antibiotic. Methods Susceptibility of 109 carbapenem-resistant P. aeruginosa to polymyxins was tested comparing broth microdilution (reference method), disc diffusion, and Etest using the new interpretative breakpoints of Clinical and Laboratory Standards Institute. Results Twenty-nine percent of isolates belonged to endemic clone and thus, these strains were excluded of analysis. Among 78 strains evaluated, only one isolate was resistant to polymyxin B by the reference method (MIC: 8.0 μg/mL). Very major and major error rates of 1.2% and 11.5% were detected comparing polymyxin B disc diffusion with the broth microdilution (reference method). Agreement within 1 twofold dilution between Etest and the broth microdilution were 33% for polymyxin B and 79.5% for colistin. One major error and 48.7% minor errors were found comparing polymyxin B Etest with broth microdilution and only 6.4% minor errors with colistin. The concordance between Etest and the broth microdilution (reference method) was respectively 100% for colistin and 90% for polymyxin B. Conclusion Resistance to polymyxins seems to be rare among hospital carbapenem-resistant P. aeruginosa isolates over a six-year period. Our results showed, using the new CLSI criteria, that the disc diffusion susceptibility does not report major errors (false-resistant results) for colistin. On the other hand, showed a high frequency of minor errors and 1 very major error for polymyxin B. Etest presented better results for colistin than polymyxin B. Until these results are reproduced with a large number of polymyxins-resistant P. aeruginosa isolates, susceptibility to polymyxins should be confirmed by a reference method.

Experimental and numerical analysis of dry contact in the pin on disc test

The reduction of friction and wear in systems presenting metal-to-metal contacts, as in several mechanical components, represents a traditional challenge in tribology. In this context, this work presents a computational study based on the linear Archard's wear law and finite element modeling (FEM), in order to analyze unlubricated sliding wear observed in typical pin on disc tests. Such modeling was developed using finite element software Abaqus® with 3-D deformable geometries and elastic–plastic material behavior for the contact surfaces. Archard's wear model was implemented into a FORTRAN user subroutine (UMESHMOTION) in order to describe sliding wear. Modeling of debris and oxide formation mechanisms was taken into account by the use of a global wear coefficient obtained from experimental measurements. Such implementation considers an incremental computation for surface wear based on the nodal displacements by means of adaptive mesh tools that rearrange local nodal positions. In this way, the worn track was obtained and new surface profile is integrated for mass loss assessments. This work also presents experimental pin on disc tests with AISI 4140 pins on rotating AISI H13 discs with normal loads of 10, 35, 70 and 140 N, which represent, respectively, mild, transition and severe wear regimes, at sliding speed of 0.1 m/s. Numerical and experimental results were compared in terms of wear rate and friction coefficient. Furthermore, in the numerical simulation the stress field distribution and changes in the surface profile across the worn track of the disc were analyzed. The applied numerical formulation has shown to be more appropriate to predict mild wear regime than severe regime, especially due to the shorter running-in period observed in lower loads that characterizes this kind of regime.