The Standard Biplot

Biplots are graphical displays of data matrices based on the decomposition of a matrix as the product of two matrices. Elements of these two matrices are used as coordinates for the rows and columns of the data matrix, with an interpretation of the joint presentation that relies on the properties of the scalar product. Because the decomposition is not unique, there are several alternative ways to scale the row and column points of the biplot, which can cause confusion amongst users, especially when software packages are not united in their approach to this issue. We propose a new scaling of the solution, called the standard biplot, which applies equally well to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. The standard biplot also handles data matrices with widely different levels of inherent variance. Two concepts taken from correspondence analysis are important to this idea: the weighting of row and column points, and the contributions made by the points to the solution. In the standard biplot one set of points, usually the rows of the data matrix, optimally represent the positions of the cases or sample units, which are weighted and usually standardized in some way unless the matrix contains values that are comparable in their raw form. The other set of points, usually the columns, is represented in accordance with their contributions to the low-dimensional solution. As for any biplot, the projections of the row points onto vectors defined by the column points approximate the centred and (optionally) standardized data. The method is illustrated with several examples to demonstrate how the standard biplot copes in different situations to give a joint map which needs only one common scale on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot readable. The proposal also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important.

Speculation, risk premia and expectations in the yield curve

An affine asset pricing model in which traders have rational but heterogeneous expectations aboutfuture asset prices is developed. We use the framework to analyze the term structure of interestrates and to perform a novel three-way decomposition of bond yields into (i) average expectationsabout short rates (ii) common risk premia and (iii) a speculative component due to heterogeneousexpectations about the resale value of a bond. The speculative term is orthogonal to public informationin real time and therefore statistically distinct from common risk premia. Empirically wefind that the speculative component is quantitatively important accounting for up to a percentagepoint of yields, even in the low yield environment of the last decade. Furthermore, allowing for aspeculative component in bond yields results in estimates of historical risk premia that are morevolatile than suggested by standard Affine Gaussian term structure models which our frameworknests.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

Necrophagous diptera associated with wild animal carcasses in southern Brazil

Necrophagous Diptera associated with wild animal carcasses in southern Brazil. The aim of this study was to acquire a better knowledge concerning the diversity of necrophagous Diptera that develop on wild animal carcasses. For this purpose, the decomposition of six wild animal carcasses was observed in order to collect and identify the main species of necrophagous flies associated with the decomposition process. The carcasses were found on highways near the cities of Pelotas and Capão do Leão in the initial stage of decomposition, with no significant injuries or prior larval activity. Four wild animal models were represented in this study: two specimens of Didelphis albiventris Lund, 1840; two Tupinambis merianae Linnaeus, 1758; one Nothura maculosa Temminck, 1815; and one Cerdocyon thous Linnaeus, 1766. A total of 16,242 flies from 14 species were reared in the laboratory, where Muscidae presented the greatest diversity of necrophagous species. Overall, (i) carcasses with larger biomass developed a higher abundance of flies and (ii) the necrophagous community was dominated by Calliphoridae, two patterns that were predicted from published literature; and (iii) the highest diversity was observed on the smaller carcasses exposed to the lowest temperatures, a pattern that may have been caused by the absence of the generalist predator Chrysomya albiceps (Wiedemann, 1819). (iv) An UPGMA analysis revealed a similar pattern of clusters of fly communities, where the same species were structuring the groupings.

Feminist Perspectives on Motherhood and Reproduction

Motherhood and reproduction have been at the core of the feminist discourse about women's rights ever since its onset. For the first and second feminist movements, the right to abortion and the public recognition of motherhood have been main issues in the discourse on reproduction. Since the last two dec- ades of the 20th century, the potentials of assisted reproductive technologies (ART) have opened up new venues of feminist discourse.In this paper we sketch the main feminist lines of argumentation regarding motherhood and reproduction since the 1970s, and we identify specific shifts in their recurrent issues. We argue that an essential contribution of feminism to the understanding of motherhood as a structuring category has been its insis- tence on the distinction between biological and social motherhood. Feminist discourse shows how ART has further decomposed biological motherhood and has altered the meaning of motherhood and reproduction. Feminist analysis maintains that despite the rhetoric of choice surrounding ART, these technolo- gies have not increased women's reproductive freedom. The decomposition of biological motherhood, the medical, legal, and commercial development of re- production, and the change in the social perception of motherhood have rather established new forms of control over female reproduction.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Decomposing Cross-Country Gaps in Obesity and Overweight: Does the Social Environment Matter?

[cat] Una qüestió clau sobre la producció de salut relativament poc explorada es refereix a la influència dels factors socioeconòmics i mediambientals sobre el pes i l’obesitat. Aquesta problemàtica adquireix particular rellevància quan es comparen dos països Mediterranis com Itàlia i Espanya. És interessant adonar-se que l’obesitat a Espanya és 5 punts percentual més elevada al 2003 mentre que a l’any 1990 era aproximadament la mateixa en ambdós països. Aquesta article presenta una descomposició no lineal dels gaps o diferencials en taxes de sobrepès (índex de massa corporal – IMC- entre 25 i 29.9 9 kg/m2), obesitat classe 1 (IMC≥30 kg/m2) i classe 2 (IMC≥35 kg/m2) entre Espanya i Itàlia per gènere i grups d’edat. En explicar aquests gaps entre països aïllem les influències dels estils de vida, els efectes socioeconòmics i els mediambientals. Els nostres resultats indiquen que quan no es controla pels efectes mediambientals (efectes de grup o ‘peer effects’) els hàbits alimentaris i el nivell educatiu són els principals predictors del gaps totals entre països (36-52%), si bé aquests dos factors exerceixen un impacte diferenciat segons gènere i edat. Un tant paradoxalment, quan controlem pels efectes de grup aquests predictors perden la seva capacitat explicativa i els efectes de grup passen a explicar entre el 46-76% dels gaps en sobrepès i obesitat i mostren un patró creixent amb l’edat.

A fully automated hot-wall multiplasma-monochamber reactor for thin film deposition

We present a study on the development and the evaluation of a fully automated radio-frequency glow discharge system devoted to the deposition of amorphous thin film semiconductors and insulators. The following aspects were carefully addressed in the design of the reactor: (1) cross contamination by dopants and unstable gases, (2) capability of a fully automated operation, (3) precise control of the discharge parameters, particularly the substrate temperature, and (4) high chemical purity. The new reactor, named ARCAM, is a multiplasma-monochamber system consisting of three separated plasma chambers located inside the same isothermal vacuum vessel. Thus, the system benefits from the advantages of multichamber systems but keeps the simplicity and low cost of monochamber systems. The evaluation of the reactor performances showed that the oven-like structure combined with a differential dynamic pumping provides a high chemical purity in the deposition chamber. Moreover, the studies of the effects associated with the plasma recycling of material from the walls and of the thermal decomposition of diborane showed that the multiplasma-monochamber design is efficient for the production of abrupt interfaces in hydrogenated amorphous silicon (a-Si:H) based devices. Also, special attention was paid to the optimization of plasma conditions for the deposition of low density of states a-Si:H. Hence, we also present the results concerning the effects of the geometry, the substrate temperature, the radio frequency power and the silane pressure on the properties of the a-Si:H films. In particular, we found that a low density of states a-Si:H can be deposited at a wide range of substrate temperatures (100°C

Charged AdS black holes and catastrophic holography

We compute the properties of a class of charged black holes in antide Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der WaalsMaxwell liquid-gas system. In that case, the phases are controlled by the universal cusp and swallowtail shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.

Vestibulo-ocular reflex characteristics in patients with unilateral Ménière's disease.

OBJECTIVE: The pathophysiologic concept of Ménière's disease assumes that endolymphatic hydrops is the cause of the symptoms via increased pressure in the endolymphatic space and/or ionic disorder due to ruptured membrane. The goal of this study was to assess whether the vestibulo-ocular reflex (VOR) properties in patients with Ménière's disease were consistent with the classical theory. MATERIAL AND METHODS: We studied 34 patients (19 women, 15 men) presenting with unilateral Ménière's disease divided into 2 groups according to the duration of the disease: 18 were in the early stage (< 12 mo), and 16 were in the late stage (> or = 12 mo). Nineteen patients were examined during an attack. Eight of them and the 15 other patients were tested during the interval between attacks. Their characteristics were compared with those of a group of 22 normal subjects. The VOR function was evaluated via standard caloric and impulse rotatory tests (velocity step). A mathematic model of vestibular function was used to characterize the VOR response to rotational stimulation. Dynamic VOR parameters (sensitivity coefficient, time constant, gain, and asymmetries between the 2 directions of rotation) were statistically compared between the 2 groups of patients during and between attacks and between the patients and controls. RESULTS: All dynamic VOR parameters showed no statistically significant difference both with normal controls and among the patients during and between attacks (p > 0.05) except for gain asymmetry (p < or = 0.008). During attacks, patients with early Ménière's disease displayed a higher gain in rotation toward the affected ear, the opposite being observed in patients with late disease. Caloric test revealed a moderate canal paresis on the affected side during the crisis and a slight asymmetry between attacks. CONCLUSION: During attacks in patients with early Ménière's disease, the VOR gain toward the affected side is higher than that toward the intact side, supporting the fact that that the sensitivity of the cupuloendolymphatic system on the affected ear is increased. This observation is in agreement with a mechanical pressure effect of hydrops on the vestibular organs.

Supraclavicular flap in head and neck reconstruction: experience in 50 consecutive patients.

The supraclavicular flap (SCF) is a fasciocutaneous flap used to cover head, oral, and neck region defects after tumor resection. Its main vascular supply is the supraclavicular artery and accompanying veins and it can be harvested as a vascularised pedicled flap. The SCF serves as an excellent outer skin cover as well as a good inner mucosal lining after oral cavity and head-neck tumor resections. The flap has a wide arc of rotation and matches the skin colour and texture of the face and neck. Between March 2006 and March 2011, the pedicled supraclavicular flap was used for reconstruction in 50 consecutive patients after head and neck tumor resections and certain benign conditions in a tertiary university hospital setting. The flaps were tunnelized under the neck skin to cover the external cervicofacial defects or passed medial to the mandible to give an inner epithelial lining after the oral cavity and oropharyngeal tumor excision. Forty-four of the 50 patients had 100% flap survival with excellent wound healing. All the flaps were harvested in less than 1 h. There were four cases of distal tip desquamation and two patients had complete flap necrosis. Distal flap desquamation was observed in SCFs used for resurfacing the external skin defects after oral cavity tumor ablation and needed only conservative treatment measures. Total flap failure was encountered in two patients who had failed in previous chemoradiotherapy for squamous cell cancer of the floor of mouth and tonsil, respectively, and the SCF was used in mucosal defect closure after tumor ablation. The benefits of a pedicled fasciocutaneous supraclavicular flap are clear; it is thin, reliable, easy, and quick to harvest. In head, face and neck reconstructions, it is a good alternative to free fasciocutaneous flaps, regional pedicled myocutaneous flaps, and the deltopectoral flap.

Decomposing Cross-Country Gaps in Obesity and Overweight: Does the Social Environment Matter?

[cat] Una qüestió clau sobre la producció de salut relativament poc explorada es refereix a la influència dels factors socioeconòmics i mediambientals sobre el pes i l’obesitat. Aquesta problemàtica adquireix particular rellevància quan es comparen dos països Mediterranis com Itàlia i Espanya. És interessant adonar-se que l’obesitat a Espanya és 5 punts percentual més elevada al 2003 mentre que a l’any 1990 era aproximadament la mateixa en ambdós països. Aquesta article presenta una descomposició no lineal dels gaps o diferencials en taxes de sobrepès (índex de massa corporal – IMC- entre 25 i 29.9 9 kg/m2), obesitat classe 1 (IMC≥30 kg/m2) i classe 2 (IMC≥35 kg/m2) entre Espanya i Itàlia per gènere i grups d’edat. En explicar aquests gaps entre països aïllem les influències dels estils de vida, els efectes socioeconòmics i els mediambientals. Els nostres resultats indiquen que quan no es controla pels efectes mediambientals (efectes de grup o ‘peer effects’) els hàbits alimentaris i el nivell educatiu són els principals predictors del gaps totals entre països (36-52%), si bé aquests dos factors exerceixen un impacte diferenciat segons gènere i edat. Un tant paradoxalment, quan controlem pels efectes de grup aquests predictors perden la seva capacitat explicativa i els efectes de grup passen a explicar entre el 46-76% dels gaps en sobrepès i obesitat i mostren un patró creixent amb l’edat.

Perdida toda coherencia: El Descubrimiento de América en la 'crisis de la conciencia europea'

Este trabajo estudia de qué modo el Descubrimiento del Nuevo Mundo contribuyó no sólo a la descomposición del Viejo Mundo, sino, más aún, a la desaparición del"mundo" o"cosmos" mismo, entendido como un todo definido y ordenado jerárquicamente según valores trascendentes. ABSTRACT: This paper studies how the Discovery of the New World contributed not only to the decomposition of the Old World, but moreover to the disappearance of the"world" or"cosmos" itself, understood as a whole defined and ordered hierarchically according to trascendent values

Radiographic total disc replacement angle measurement accuracy using the Oxford Cobbometer: precision and bias.

Total disc replacement (TDR) clinical success has been reported to be related to the residual motion of the operated level. Thus, accurate measurement of TDR range of motion (ROM) is of utmost importance. One commonly used tool in measuring ROM is the Oxford Cobbometer. Little is known however on its accuracy (precision and bias) in measuring TDR angles. The aim of this study was to assess the ability of the Cobbometer to accurately measure radiographic TDR angles. An anatomically accurate synthetic L4-L5 motion segment was instrumented with a CHARITE artificial disc. The TDR angle and anatomical position between L4 and L5 was fixed to prohibit motion while the motion segment was radiographically imaged in various degrees of rotation and elevation, representing a sample of possible patient placement positions. An experienced observer made ten readings of the TDR angle using the Cobbometer at each different position. The Cobbometer readings were analyzed to determine measurement accuracy at each position. Furthermore, analysis of variance was used to study rotation and elevation of the motion segment as treatment factors. Cobbometer TDR angle measurements were most accurate (highest precision and lowest bias) at the centered position (95.5%), which placed the TDR directly inline with the x-ray beam source without any rotation. In contrast, the lowest accuracy (75.2%) was observed in the most rotated and off-centered view. A difference as high as 4 degrees between readings at any individual position, and as high as 6 degrees between all the positions was observed. Furthermore, the Cobbometer was unable to detect the expected trend in TDR angle projection with changing position. Although the Cobbometer has been reported to be reliable in different clinical applications, it lacks the needed accuracy to measure TDR angles and ROM. More accurate ROM measurement methods need to be developed to help surgeons and researchers assess radiological success of TDRs.