Optimal Consensus set for nD Fixed Width Annulus Fitting

International audienceThis paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N) for dimension n, N being the number of points. Our algorithm guarantees optimal solution(s) and has lower complexity than previous known methods

Digital hyperplane fitting

International audienceThis paper addresses the hyperplane fitting problem of discrete points in any dimension (i.e. in Z d). For that purpose, we consider a digital model of hyperplane, namely digital hyperplane, and present a combinatorial approach to find the optimal solution of the fitting problem. This method consists in computing all possible digital hyperplanes from a set S of n points, then an exhaustive search enables us to find the optimal hyperplane that best fits S. The method has, however, a high complexity of O(n d), and thus can not be applied for big datasets. To overcome this limitation, we propose another method relying on the Delaunay triangulation of S. By not generating and verifying all possible digital hyperplanes but only those from the elements of the triangula-tion, this leads to a lower complexity of O(n d 2 +1). Experiments in 2D, 3D and 4D are shown to illustrate the efficiency of the proposed method

The Young, Massive, Star Cluster Sandage-96 After the Explosion of SN 2004dj in NGC 2403

The bright Type II-plateau supernova (SN) 2004dj occurred within the young, massive stellar cluster Sandage-96 in a spiral arm of NGC 2403. New multi-wavelength observations obtained with several ground-based and space-based telescopes are combined to study the radiation from Sandage-96 after SN 2004dj faded away. Sandage-96 started to dominate the flux in the optical bands starting September 2006 (~800 d after explosion). The optical fluxes are equal to the pre-explosion ones within the observational uncertainties. An optical Keck spectrum obtained ~900 d after explosion shows the dominant blue continuum from the cluster stars shortward of 6000 \AA as well as strong SN nebular emission lines redward. The integrated spectral energy distribution (SED) of the cluster has been extended into the ultraviolet region by archival XMM-Newton and new Swift observations, and compared with theoretical models. The outer parts of the cluster have been resolved by the Hubble Space Telescope, allowing the construction of a color-magnitude diagram. The fitting of the cluster SED with theoretical isochrones results in cluster ages between 10--40 Myr, depending on metallicity and the model family. The isochrone fitting indicates that the resolved part of the cluster has a bimodal age distribution: a younger population at ~10--16 Myr, and an older one at ~32--100 Myr which is similar to the age distribution of the nearby field stars. These stars may have been captured from the field during the cluster formation. The young age of Sandage-96 suggest 12 < M_prog < 20 M_\odot as the most probable mass range for the progenitor of SN 2004dj. This is consistent with, but perhaps slightly higher than, most of the other Type II-plateau SN progenitor masses determined so far.Comment: accepted in Ap

Biomechanical study of intervertebral disc degeneration

Degeneration and age affect the biomechanics of the intervertebral disc, by reducing its stiffness, flexibility and shock absorption capacities against daily movement and spinal load. The biomechanical characterization of intervertebral discs is achieved by conducting mechanical testing to vertebra-disc-vertebra segments and applying axial, shear, bend and torsion loads, statically or dynamically, with load magnitudes corresponding to the physiological range. However, traditional testing does not give a view of the load and deformation states of the disc components: nucleus pulposus, annulus fibrosus and endplate. Thus, the internal state of stress and strains of the disc can only be predicted by numerical methods, one of which is the finite element method. The objective of this thesis was, to study the biomechanics of degenerated intervertebral discs to load conditions in compression, bending and torsion, by using mechanical testing and a finite element model of disc degeneration, based on magnetic resonance imaging (MRI). Therefore, lumbar discs obtained from cadavers corresponding to spinal levels L2-L3 and L4-L5 with mild to severe degeneration were used. Intervertebral osteochondrosis and spondylosis deformans were identified, being the disc space collapse, the most striking feature. Next, all discs were tested to static and dynamic load conditions, the results gained corresponded to the disc stiffness (in compression, bending and torsion), stress relaxation and dynamic response. Of these, the stiffness response was used to validate the disc model. The testing results suggest that discs with advanced degeneration over discs with mild degeneration are, less rigid in compression, less stiffer under bending and torsion, showed less radial bulge, and reduce their viscoelastic and damping properties. This study shows that degeneration has an impact on the disc biomechanical properties which can jeopardize normal functionality. Development of one finite element model of disc degeneration started by choosing a MRI of a L2-L3 disc. Segmentation of vertebra bone and disc materials followed, and were based on pixel brightness and radiology fundamentals, then a finite element mesh was created to account for the disc irregular shape. The disc materials were modeled as hyperelastic and the bone materials were modeled as orthotropic and isotropic. Adjustment of material properties was based on integrity of the annulus fibrosus, giving a stiffness value matching that of a mild degeneration disc. Then, validation of the model was performed, and included a study of the distributions of stress and strain under loads of compression, bending and torsion. The results from all load simulations show that the disc undergoes large deformations. In contrast, the vertebrae are subjected to higher stress but with negligible deformations. In compression, the model predicted formation of symmetrical disc bulge which agree with the testing behavior. The nucleus pulposus showed to be the principal load carrier with negative principal stresses and strains. In bending and torsion, the annulus fibrosus showed to be the principal load carrier with large symmetrical principal strains and stresses for the former loading and large shearing for the latter. The study showed the importance of soft tissue deformation, mostly noticed in advanced degeneration. In contrast, the higher stresses in the vertebra over those of the intervertebral disc showed the relevance of bone predisposition to fracture. Such kind of studies, should contribute to the understanding of the biomechanics of the intervertebral disc.La degeneración y edad afectan la biomecánica del disco intervertebral, reduciendo la capacidad de rigidez, flexibilidad y atenuación de impactos, contra el movimiento y carga del raquis. La caracterización biomecánica del disco se realiza con ensayos mecánicos a segmentos de vértebra-disco-vértebra y aplicando cargas axiales, cortantes, flexión y torsión, estáticas ó dinámicas, con magnitudes de carga según el intervalo fisiológico. Sin embargo, las pruebas tradicionales no dan una visión de los estados de carga y deformación de los componentes del disco: núcleo pulposo, anillo fibroso y placa terminal. Por lo tanto, el estado interno de esfuerzos y deformaciones del disco, solo puede ser predicho con métodos numéricos, uno de los cuales es el método de elemento finito. El objetivo de esta tesis fue, estudiar la biomecánica de discos intervertebrales degenerados a las condiciones de carga en compresión, flexión y torsión, mediante el uso de ensayos mecánicos y de un modelo de elementos finitos de la degeneración de disco, basado en imágenes con resonancia magnética (MRI). Por lo tanto, se usaron discos lumbares L2-L3 y L4-L5 obtenidos de cadáveres, con degeneración leve a severa. Se identificó osteocondrosis intervertebral y espondilosis deformante, siendo el colapso del espacio intervertebral el aspecto más relevante. Luego, todos los discos fueron ensayados a condiciones de carga estática y dinámica, y los resultados correspondieron a la rigidez del disco (a compresión, flexión y torsión), a la relajación de tensiones y a la respuesta dinámica. De éstos, la rigidez fue usada para validar el modelo de disco. Los resultados de los ensayos sugieren que los discos con degeneración avanzada sobre aquellos con degeneración leve son, menos rigidos a compresión, menos rigidos a flexión y torsión, presentan menor protuberancia radial, y reducen sus propiedades viscoelásticas y de amortiguamiento. El estudio muestra que la degeneración impacta las propiedades biomecánicas del disco, poniendo en riesgo la funcionalidad normal. El desarollo de un modelo de elementos finitos de la degeneración de disco inició eligiendo una secuencia de resonancia magnética de un disco L2-L3. La segmentación de los materiales del disco y de las vértebras se realizó basado en intensidad de brillo del pixel y en fundamentos de radiología, y se creó una malla de elementos finitos correspondiente a la forma irregular del disco. Los materiales del disco se modelaron como hiperelásticos y los tejidos óseos se modelaron como materiales ortotrópicos e isotrópicos. El ajuste de propiedades de los materiales fue basado en la integridad del anillo fibroso, y dio una rigidez correspondiente a la de un disco con degeneración leve. Luego, se realizó la validación del modelo, e incluyó un estudio de las distribuciones de esfuerzo y deformación a las condiciones de carga en compresión, flexión y torsión. Los resultados de todas las simulaciones de carga mostraron que el disco es sometido a grandes deformaciones. En contraste, las vértebras fueron sometidas a mayores esfuerzos pero con deformaciones insignificantes. En compresión, el modelo predijo la formación de una protuberancia radial simétrica, en concordancia con la experimentación. El núcleo pulposo mostró ser el portador principal de carga, con tensiones y deformaciones principales negativas. En flexión y torsión, el anillo fibroso mostró ser el portador principal de carga, con grandes deformaciones y tensiones principales simétricas para la primera carga, y con grandes tensiones cortantes para la segunda carga. El estudio mostró la importancia de las deformaciones de los tejidos blandos, principalmente notados en la degeneración avanzada. Por el contrario, las tensiones mayores en los cuerpos vertebrales sobre aquellas del disco intervertebral mostraron la relevancia de la predisposición a las fracturas óseas. Este tipo de estudio debe contribuir a la comprensión de la biomecánica del disco intervertebral

Image Quality Modeling and Optimization for Non-Conventional Aperture Imaging Systems

The majority of image quality studies have been performed on systems with conventional aperture functions. These systems have straightforward aperture designs and well-understood behavior. Image quality for these systems can be predicted by the General Image Quality Equation (GIQE). However, in order to continue pushing the boundaries of imaging, more control over the point spread function of an imaging system may be necessary. This requires modifications in the pupil plane of a system, causing a departure from the realm of most image quality studies. Examples include sparse apertures, synthetic apertures, coded apertures and phase elements. This work will focus on sparse aperture telescopes and the image quality issues associated with them, however, the methods presented will be applicable to other non-conventional aperture systems. \\ In this research, an approach for modeling the image quality of non-conventional aperture systems will be introduced. While the modeling approach is based in previous work, a novel validation study will be performed, which accounts for the effects of both broadband illumination and wavefront error. One of the key image quality challenges for sparse apertures is post-processing ringing artifacts. These artifacts have been observed in modeled data, but a validation study will be performed to observe them in measured data and to compare them to model predictions. Once validated, the modeling approach will be used to perform a small set of design studies for sparse aperture systems, including spectral bandpass selection and aperture layout optimization

Reverberation Mapping of the Accretion Discs in the Quasars 3C 273 and 1H 2106-099

The main aim of this thesis is to perform the first accretion disc reverberation mapping analysis on the AGN 3C 273 and 1H 2106-099 using the modern reverberation mapping algorithms Javelin, PyceCREAM and PyROA. This is with the intention of obtaining useful physical insights into these AGN and to compare the performance of the algorithms. Through spectral, photometric and reverberation mapping measurements we find evidence to suggest the accretion disc spectrum in 3C 273 follows a power law with a slightly shallower exponent β ∼ 1 than expected from the approximated thin disc model (β = 4/3 ). However the difference does not seem very significant and good agreement was found with the more physically meaningful unapproximated thin disc model simulated with a boundary condition at the radius of innermost stable circular orbit. We therefore conclude 3C 273 likely conforms to the thin disc model and displays the ’accretion disc size problem’ with a scale ∼ 2 − 3 larger than expected. For 1H 2106-099, we found an unexpected discontinuity in the PyROA and Javelin lag estimates which is reflected in the spectrum and which we cannot identify with any specific contamination. Investigating the possibility that the discontinuity is anomalous, we obtain corrected Javelin and PyROA lag estimates in near perfect agreement with the thin disc model without an up-scaled accretion disc. Our PyceCREAM RM results also indicate that the discontinuity is anomalous but differ from PyROA and Javelin in suggesting the accretion disc in 1H 2106-099 is up-scaled by a factor ∼ 2. A secondary aim of the thesis was to investigate how the uncertainties on lag estimates returned by the algorithms depends on the length of the observing period and cadence of the light-curve data. Analysis on two dust reverberation mapping campaigns returned results which suggest that the length of the light-curve relative to the expected lag has a more significant effect on the size of the uncertainties than the cadence relative to the lag. We then estimate the optimum light-curve length to be ∼ 10× the expected lag and the optimum cadence to be ∼ 6× smaller than the expected lag which had associated lag uncertainties of ∼ 11% and ∼ 10% respectively

Four years of Type Ia Supernovae Observed by TESS: Early Time Light Curve Shapes and Constraints on Companion Interaction Models

We present 307 Type Ia supernova (SN) light curves from the first four years of the TESS mission. We use this sample to characterize the shapes of the early time light curves, measure the rise times from first light to peak, and search for companion star interactions. Using simulations, we show that light curves must have noise $<$10% of the peak to avoid biases in the early time light curve shape, restricting our quantitative analysis to 74 light curves. We find that the mean power law index $t^{\beta_1}$ of the early time light curves is 1.83$\pm$ 0.57 and the mean rise time to peak is 15.7 $\pm$ 3.5 days. We also estimate the underlying population distribution and find a Gaussian component with mean $\beta_1 = 2.29$, width 0.34, and a tail extending to values less than 1.0. We use model comparison techniques to test for the presence of companion interactions. In contrast to recent results in the literature, we find that the data can rarely distinguish between models with and without companion interactions, and caution is needed when claiming detections of early time flux excesses. Nevertheless, we find three high-quality SN light curves that tentatively prefer the addition of a companion interaction model, but the statistical evidence is not robust. We also find two SNe that disfavor the addition of a companion interaction model to a curved power law model. Taking the 74 SNe together, we calculate 3$\sigma$ upper limits on the presence of companion signatures to control for orientation effects that can hide companions in individual light curves. Our results rule out common progenitor systems with companions having Roche lobe radii $>$ 31 R$_{\odot}$ (99.9% confidence level) and disfavor companions having Roche lobe radii $>$ 10 R$_{\odot}$ (95% confidence level). Lastly, we discuss the implications of our results for the intrinsic fraction of single degenerate progenitor systems.Comment: 40 pages, 23 figures, resubmitted to ApJ. Figure sets for all 307 objects in Figures 3, 13, 14, and 16, can be viewed at https://space.mit.edu/home/faus/snIa_fig_sets/ in advance of the online journal articl

A Parametric Model for the Analysis and Quantification of Foveal Shapes

Recently, the advance of OCT enables a detailed examination of the human retina in-vivo for clinical routine and experimental eye research. One of the structures inside the retina of immense scientific interest is the fovea, a small retinal pit located in the central region with extraordinary visual resolution. Today, only a few investigations captured foveal morphology based on a large subject group by a detailed analysis employing mathematical models. In this work, we develop a parametric model function to describe the shape of the human fovea. Starting with a detailed discussion on the history and present of fovea research, we define the requirements for a suitable model and derive a function which can represent a broad range of foveal shapes. The model is one-dimensional in its basic form and can only account for the shape of one particular section through a fovea. Therefore, we apply a radial fitting scheme in different directions which can capture a fovea in its full three-dimensional appearance. Highly relevant foveal characteristics, derived from the model, provide valuable descriptions to quantify the fovea and allow for a detailed analysis of different foveal shapes. To put the theoretical model into practice, we develop a numerical scheme to compute model parameters from retinal \ac{oct} scans and to reconstruct the shape of an entire fovea. For the sake of scientific reproducibility, this section includes implementation details, examples and a discussion of performance considerations. Finally, we present several studies which employed the fovea model successfully. A first feasibility study verifies that the parametric model is suitable for foveal shapes occurring in a large set of healthy human eyes. In a follow-up investigation, we analyse foveal characteristics occurring in healthy humans in detail. This analysis will concern with different aspects including, e.g. an investigation of the fovea's asymmetry, a gender comparison, a left versus right eye correlation and the computation of subjects with extreme foveal shapes. Furthermore, we will show how the model was used to support investigations unrelated to the direct quantification of the fovea itself. In these investigations we employed the model to compute anatomically correct regions of interest in an analysis of the OCB and the calculation of an average fovea for an optical simulation of light rays. We will conclude with currently unpublished data that shows the fovea modelling of hunting birds which have unusual, funnel-like foveal shapes

Haemodynamic alterations after percutaneous valve implantation

Many patients who suffer from aortic valve dysfunction are too weak to be eligible for valve replacement via surgery, due to co-morbidities and old age. Transcatheter aortic valve (TAV) implantation has been developed as an alternative to surgery, enabling replacement of the dysfunctional valve percutaneously. However, the inability to remove the native leaflets leads to the bioprosthetic being held in place inside a pseudo-cylindrical structure. The passive nature of heart valves means the surrounding fluid environment’s dynamics are critical in producing optimum performance, and would ideally be returned to the healthy, physiological state. The association of TAVs with thrombotic events, such as strokes, has not yet been fully explained. A pulse duplicator and particle image velocimetry were used to model and characterise the flow fields of a healthy, physiological aortic root and valve, which was then compared to those resulting from a number of typical post- surgical outcomes, identifying the fluid mechanisms promoted by the root geometry to optimise the ejection and closing phases of the cardiac cycle, and revealing the importance of an optimal integration of valve and root architecture, and characterising common post-surgical environments. The same techniques were then used to examine the flow dynamics of the region following TAV implantation, revealing the effect of TAV alignment with its hosts’ commissures, and how the presence of native leaflets, commonly omitted from in vitro TAV testing, affect the valve performance. Slow and stagnant flow was observed within the sinuses due to the native leaflets, whilst global valve performance was broadly unaffected, and omission of the native leaflets resulted in improved haemodynamic performance. A model of coronary arteries was incorporated into the benchtop simulation, revealing increase of flow in the upper coronary sinuses, but flow at the base of all sinuses remained very slow following TAV implantation. The elucidation of this stagnation, associated with thrombotic events, provides an explanation for the increased levels of thrombotic-associated pathologies following TAV implantation