On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

Analyzing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling

The unstable rock slope, Stampa, above the village of Flåm, Norway, shows signs of both active and postglacial gravitational deformation over an area of 11 km2. Detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, as well as geomorphic analysis of high-resolution digital elevation models based on airborne and terrestrial laser scanning indicate that slope deformation is complex and spatially variable. Numerical modeling was used to investigate the influence of former rockslide activity and to better understand the failure mechanism. Field observations, kinematic analysis and numerical modeling indicate a strong structural control of the unstable area. Based on the integration of the above analyses, we propose that the failure mechanism is dominated by (1) a toppling component, (2) subsiding bilinear wedge failure and (3) planar sliding along the foliation at the toe of the unstable slope. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points have an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks with volumes smaller than 300,000 m3. Large fractures indicate deep-seated gravitational deformation of volumes reaching several 100 million m3, but the movement rates in these areas are below 2 mm/year. Two different lobes of prehistoric rock slope failures were dated with terrestrial cosmogenic nuclides. While the northern lobe gave an average age of 4,300 years BP, the southern one resulted in two different ages (2,400 and 12,000 years BP), which represent most likely multiple rockfall events. This reflects the currently observable deformation style with unstable blocks in the northern part in between Joasete and Furekamben and no distinct blocks but a high rockfall activity around Ramnanosi in the south. With a relative susceptibility analysis it is concluded that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes > 100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A larger collapse involving several million m3 is presently considered of very low likelihood.

Numerical simulation of left ventricular assist device implantations: comparing the ascending and the descending aorta cannulations.

In this work we present numerical simulations of continuous flow left ventricle assist device implantation with the aim of comparing difference in flow rates and pressure patterns depending on the location of the anastomosis and the rotational speed of the device. Despite the fact that the descending aorta anastomosis approach is less invasive, since it does not require a sternotomy and a cardiopulmonary bypass, its benefits are still controversial. Moreover, the device rotational speed should be correctly chosen to avoid anomalous flow rates and pressure distribution in specific location of the cardiovascular tree. With the aim of assessing the differences between these two approaches and device rotational speed in terms of flow rate and pressure waveforms, we set up numerical simulations of network of one-dimensional models where we account for the presence of an outflow cannula anastomosed to different locations of the aorta. Then, we use the resulting network to compare the results of the two different cannulations for several stages of heart failure and different rotational speed of the device. The inflow boundary data for the heart and the cannulas are obtained from a lumped parameters model of the entire circulatory system with an assist device, which is validated with clinical data. The results show that ascending and descending aorta cannulations lead to similar waveforms and mean flow rate in all the considered cases. Moreover, regardless of the anastomosis region, the rotational speed of the device has an important impact on wave profiles; this effect is more pronounced at high RPM.

An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Imputation in data fusion of heterogeneous data sets a model-based numerical experiment

Given the very large amount of data obtained everyday through population surveys, much of the new research again could use this information instead of collecting new samples. Unfortunately, relevant data are often disseminated into different files obtained through different sampling designs. Data fusion is a set of methods used to combine information from different sources into a single dataset. In this article, we are interested in a specific problem: the fusion of two data files, one of which being quite small. We propose a model-based procedure combining a logistic regression with an Expectation-Maximization algorithm. Results show that despite the lack of data, this procedure can perform better than standard matching procedures.

An electronic portfolio for quantitative assessment of surgical skills in undergraduate medical education.

BACKGROUND We evaluated a newly designed electronic portfolio (e-Portfolio) that provided quantitative evaluation of surgical skills. Medical students at the University of Seville used the e-Portfolio on a voluntary basis for evaluation of their performance in undergraduate surgical subjects. METHODS Our new web-based e-Portfolio was designed to evaluate surgical practical knowledge and skills targets. Students recorded each activity on a form, attached evidence, and added their reflections. Students self-assessed their practical knowledge using qualitative criteria (yes/no), and graded their skills according to complexity (basic/advanced) and participation (observer/assistant/independent). A numerical value was assigned to each activity, and the values of all activities were summated to obtain the total score. The application automatically displayed quantitative feedback. We performed qualitative evaluation of the perceived usefulness of the e-Portfolio and quantitative evaluation of the targets achieved. RESULTS Thirty-seven of 112 students (33%) used the e-Portfolio, of which 87% reported that they understood the methodology of the portfolio. All students reported an improved understanding of their learning objectives resulting from the numerical visualization of progress, all students reported that the quantitative feedback encouraged their learning, and 79% of students felt that their teachers were more available because they were using the e-Portfolio. Only 51.3% of students reported that the reflective aspects of learning were useful. Individual students achieved a maximum of 65% of the total targets and 87% of the skills targets. The mean total score was 345 ± 38 points. For basic skills, 92% of students achieved the maximum score for participation as an independent operator, and all achieved the maximum scores for participation as an observer and assistant. For complex skills, 62% of students achieved the maximum score for participation as an independent operator, and 98% achieved the maximum scores for participation as an observer or assistant. CONCLUSIONS Medical students reported that use of an electronic portfolio that provided quantitative feedback on their progress was useful when the number and complexity of targets were appropriate, but not when the portfolio offered only formative evaluations based on reflection. Students felt that use of the e-Portfolio guided their learning process by indicating knowledge gaps to themselves and teachers.

Operator algebras: an informal overview

This article is an informal introduction to some classical results of the theory of operator algebras. It aims to illustrate the richness and diversity of possible applications of this topic.

Segmentation and grid generation for numerical simulations of vad connections with patient-specific data

Objectives: We are interested in the numerical simulation of the anastomotic region comprised between outflow canula of LVAD and the aorta. Segmenta¬tion, geometry reconstruction and grid generation from patient-specific data remain an issue because of the variable quality of DICOM images, in particular CT-scan (e.g. metallic noise of the device, non-aortic contrast phase). We pro¬pose a general framework to overcome this problem and create suitable grids for numerical simulations.Methods: Preliminary treatment of images is performed by reducing the level window and enhancing the contrast of the greyscale image using contrast-limited adaptive histogram equalization. A gradient anisotropic diffusion filter is applied to reduce the noise. Then, watershed segmentation algorithms and mathematical morphology filters allow reconstructing the patient geometry. This is done using the InsightToolKit library (www.itk.org). Finally the Vascular Model¬ing ToolKit (www.vmtk.org) and gmsh (www.geuz.org/gmsh) are used to create the meshes for the fluid (blood) and structure (arterial wall, outflow canula) and to a priori identify the boundary layers. The method is tested on five different patients with left ventricular assistance and who underwent a CT-scan exam.Results: This method produced good results in four patients. The anastomosis area is recovered and the generated grids are suitable for numerical simulations. In one patient the method failed to produce a good segmentation because of the small dimension of the aortic arch with respect to the image resolution.Conclusions: The described framework allows the use of data that could not be otherwise segmented by standard automatic segmentation tools. In particular the computational grids that have been generated are suitable for simulations that take into account fluid-structure interactions. Finally the presented method features a good reproducibility and fast application.

An electronic portfolio for quantitative assessment of surgical skills in undergraduate medical education.

BACKGROUND We evaluated a newly designed electronic portfolio (e-Portfolio) that provided quantitative evaluation of surgical skills. Medical students at the University of Seville used the e-Portfolio on a voluntary basis for evaluation of their performance in undergraduate surgical subjects. METHODS Our new web-based e-Portfolio was designed to evaluate surgical practical knowledge and skills targets. Students recorded each activity on a form, attached evidence, and added their reflections. Students self-assessed their practical knowledge using qualitative criteria (yes/no), and graded their skills according to complexity (basic/advanced) and participation (observer/assistant/independent). A numerical value was assigned to each activity, and the values of all activities were summated to obtain the total score. The application automatically displayed quantitative feedback. We performed qualitative evaluation of the perceived usefulness of the e-Portfolio and quantitative evaluation of the targets achieved. RESULTS Thirty-seven of 112 students (33%) used the e-Portfolio, of which 87% reported that they understood the methodology of the portfolio. All students reported an improved understanding of their learning objectives resulting from the numerical visualization of progress, all students reported that the quantitative feedback encouraged their learning, and 79% of students felt that their teachers were more available because they were using the e-Portfolio. Only 51.3% of students reported that the reflective aspects of learning were useful. Individual students achieved a maximum of 65% of the total targets and 87% of the skills targets. The mean total score was 345 ± 38 points. For basic skills, 92% of students achieved the maximum score for participation as an independent operator, and all achieved the maximum scores for participation as an observer and assistant. For complex skills, 62% of students achieved the maximum score for participation as an independent operator, and 98% achieved the maximum scores for participation as an observer or assistant. CONCLUSIONS Medical students reported that use of an electronic portfolio that provided quantitative feedback on their progress was useful when the number and complexity of targets were appropriate, but not when the portfolio offered only formative evaluations based on reflection. Students felt that use of the e-Portfolio guided their learning process by indicating knowledge gaps to themselves and teachers.

Iowa Motorcycle Operator's Manual, 2002

The rules and regualtions for owning and operating a motorcycle in Iowa

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Methodology for studying the numerical speed of sound in finite differences schemes

The space and time discretization inherent to all FDTD schemesintroduce non-physical dispersion errors, i.e. deviations ofthe speed of sound from the theoretical value predicted bythe governing Euler differential equations. A generalmethodologyfor computing this dispersion error via straightforwardnumerical simulations of the FDTD schemes is presented.The method is shown to provide remarkable accuraciesof the order of 1/1000 in a wide variety of twodimensionalfinite difference schemes.

Total knee arthroplasty - a clinical and numerical study of the micromovements of the tibial implant

Introduction The importance of the micromovements in the mechanism of aseptic loosening is clinically difficult to evaluate. To complete the analysis of a series of total knee arthroplasties (TKA), we used a tridimensional numerical model to study the micromovements of the tibial implant.Material and Methods Fifty one patients (with 57 cemented Porous Coated Anatomic TKAs) were reviewed (mean follow-up 4.5 year). Radiolucency at the tibial bone-cement interface was sought on the AP radiographs and divided in 7 areas. The distribution of the radiolucency was then correlated with the axis of the lower limb as measured on the orthoradiograms.The tridimensional numerical model is based on the finite element method. It allowed the measurement of the cemented prosthetic tibial implant's displacements and the microvements generated at bone-ciment interface. A total load (2000 Newton) was applied at first vertically and asymetrically on the tibial plateau, thereby simulating an axial deviation of the lower limbs. The vector's posterior inclination then permitted the addition of a tangential component to the axial load. This type of effort is generated by complex biomechanical phenomena such as knee flexion.Results 81 per cent of the 57 knees had a radiolucent line of at least 1 mm, at one or more of the tibial cement-epiphysis jonctional areas. The distribution of these lucent lines showed that they came out more frequently at the periphery of the implant. The lucent lines appeared most often under the unloaded margin of the tibial plateau, when axial deviation of lower limbs was present.Numerical simulations showed that asymetrical loading on the tibial plateau induced a subsidence of the loaded margin (0-100 microns) and lifting off at the opposite border (0-70 microns). The postero-anterior tangential component induced an anterior displacement of the tibial implant (160-220 microns), and horizontal micromovements with non homogenous distribution at the bone-ciment interface (28-54 microns).Discussion Comparison of clinical and numerical results showed a relation between the development of radiolucent lines and the unloading of the tibial implant's margin. The deleterious effect of lower limbs' axial deviation is thereby proven. The irregular distribution of lucent lines under the tibial plateau was similar of the micromovements' repartition at the bone-cement interface when tangential forces were present. A causative relation between the two phenomenaes could not however be established.Numerical simulation is a truly useful method of study; it permits to calculate micromovements which are relative, non homogenous and of very low amplitude. However, comparative clinical studies remain as essential to ensure the credibility of results.