Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

Three-dimensional electrical impedance, tomography: A topology optimization approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

Space-time Measurements of Oceanic Sea States

Stereo video techniques are effective for estimating the space–time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. We present an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea and near the southern seashore of the Crimean peninsula, in the Black Sea. We use classical epipolar techniques to reconstruct the sea surface from the stereo pairs sequentially in time, viz. a sequence of spatial snapshots. We also present a variational approach that exploits the entire data image set providing a global space–time imaging of the sea surface, viz. simultaneous reconstruction of several spatial snapshots of the surface in order to guarantee continuity of the sea surface both in space and time. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics at a point in time that agrees well with probabilistic models. In particular, WASS stereo imaging is able to capture typical features of the wave surface, especially the crest-to-trough asymmetry due to second order nonlinearities, and the observed shape of large waves are fairly described by theoretical models based on the theory of quasi-determinism (Boccotti, 2000). Further, we investigate space–time extremes of the observed stationary sea states, viz. the largest surface wave heights expected over a given area during the sea state duration. The WASS analysis provides the first experimental proof that a space–time extreme is generally larger than that observed in time via point measurements, in agreement with the predictions based on stochastic theories for global maxima of Gaussian fields.

Simultaneous two-wavelength holographic interferometry in a superorbital expansion tube facility

A new variation of holographic interferometry has been utilized to perform simultaneous two-wavelength measurements, allowing quantitative analysis of the heavy particle and electron densities in a superorbital facility. An air test gas accelerated to 12 km/s was passed over a cylindrical model, simulating reentry conditions encountered by a space vehicle on a superorbital mission. Laser beams with two different wavelengths have been overlapped, passed through the test section, and simultaneously recorded on a single holographic plate. Reconstruction of the hologram generated two separate interferograms at different. angles from which the quantitative measurements were made. With this technique, a peak electron concentration of (5.5 +/- 0.5) x 10(23) m(-3) was found behind a bow shock on a cylinder. (C) 1997 Optical Society of America.

Double-bundle transtibial posterior cruciate ligament reconstruction with a tendon-patellar bone-semitendinosus tendon autograft: clinical results with a minimum of 2 years' follow-up.

PURPOSE: The purpose of this study was to evaluate the clinical and subjective outcomes after arthroscopic-assisted double-bundle posterior cruciate ligament (PCL) reconstruction. METHODS: A series of 15 patients with grade III isolated chronic PCL tears underwent double-bundle PCL reconstruction. Of these patients, 8 (53%) had simultaneous fractures. The mean time from accident to surgery was 10.8 months (range, 8 to 15 months). The mean age at the time of surgery was 28.2 years (range, 17 to 43 years). All of the patients reported knee insecurity during activities of daily living or light sporting activities, with associated anterior knee pain in 5 patients. Preoperatively, posterolateral or posteromedial corner injuries were ruled out through accurate clinical examination. The knees were assessed before surgery and at a mean follow-up of 3.2 years (range, 2 to 5 years) with a physical examination, 4 different rating scales, and stress radiographs obtained with a Telos device (Telos, Marburg, Germany). RESULTS: Postoperative physical examination revealed a reduction of the posterior drawer and tibial step-off in all cases, although the posterior laxity was not completely normalized. Nevertheless, the patients were subjectively better after surgery. The subjective International Knee Documentation Committee score was significantly ameliorated. With regard to the objective International Knee Documentation Committee score, 6 knees (40%) were graded as abnormal because of posterior displacement of 6 mm or greater on follow-up stress radiographs with the Telos device. On the Lysholm knee scoring scale, the score was excellent in 13% of patients and good in 87%. The mean score on the Hospital for Special Surgery knee ligament rating scale was 85.8. The Tegner activity score showed an amelioration after surgery, but no patient resumed his or her preinjury level of activities. The postoperative stress radiographs revealed an improvement in posterior instability of 50% or more in all but 3 knees (20%). CONCLUSIONS: Our technique of double-bundle PCL reconstruction produced a significant reduction in knee symptoms and allowed the patients to return to moderate or strenuous activity, although the posterior tibial translation was not completely normalized and our results appear to be no better than the results of single-bundle PCL reconstruction. LEVEL OF EVIDENCE: Level IV, therapeutic case series.

Precision of tibial tunnel placement under arthroscopic control alone in posterior cruciate ligament reconstruction: A radiological study

Introduction: Accurate and reproducible tibial tunnel placement minimizing the risk of neurovascular damage is a crucial condition for successful arthroscopic reconstruction of the posterior cruciate ligament (PCL). This step is commonly performed under fluoroscopic control. Hypothesis: Performing the tibial tunnel under exclusive arthroscopic control allows accurate and reliable tunnel placement according to recommendations in the literature. Materials and Methods: Between February 2007 and December 2009, 108 arthroscopic single bundle PCL reconstructions in tibial tunnel technique were performed. The routine postoperative radiographs were screened according to previously defined quality criterions. After critical analysis, the radiographs of 48 patients (48 knees) were enrolled in the study. 10 patients had simultaneous ACL reconstruction and 7 had PCL revision surgery. The tibial tunnel was placed under direct arthroscopic control through a posteromedial portal using a standard tibial aming device. Key anatomical landmarks were the exposed tibial insertion of the PCL and the posterior horn of the medial meniscus. First, the centre of the posterior tibial tunnel outlet on the a-p view was determined by digital analysis of the postoperative radiographes. Its distance to the medial tibial spine was measured parallel to the tibia plateau. The mediolateral position was expressed by the ratio between the distance of the tunnel outlet to the medial border and the total width of the tibial plateau. On the lateral view the vertical tunnel position was measured perpendicularly to a tangent of the medial tibial plateau. All measurement were repeated at least twice and carried out by two examiners. Results: The mean mediolateral tunnel position was 49.3 ± 4.6% (ratio), 6.7 ± 3.6 mm lateral to the medial tibial spine. On the lateral view the tunnel centre was 10.1 ± 4.5 mm distal to the bony surface of the medial tibial plateau. Neurovascular damage was observed in none of our patients. Conclusion: The results of this radiological study confirm that exclusive arthroscopic control for tibial tunnel placement in PCL reconstruction yields reproducible and accurate results according to the literature. Our technique avoids radiation, facilitates the operation room setting and enables the surgeon to visualize the anatomic key landmarks for tibial tunnel placement.

3D Simultaneous Inversion for Seismic Structure and Local Hypocenters in Germany under Consideration of Seismic Anisotropy in the Upper Mantel

The main task of this work has been to investigate the effects of anisotropy onto the propagation of seismic waves along the Upper Mantle below Germany and adjacent areas. Refraction- and reflexion seismic experiments proved the existence of Upper Mantle anisotropy and its influence onto the propagation of Pn-waves. By the 3D tomographic investigations that have been done here for the crust and the upper mantle, considering the influence of anisotropy, a gap for the investigations in Europe has been closed. These investigations have been done with the SSH-Inversionprogram of Prof. Dr. M. Koch, which is able to compute simultaneously the seismic structure and hypocenters. For the investigation, a dataset has been available with recordings between the years 1975 to 2003 with a total of 60249 P- and 54212 S-phase records of 10028 seismic events. At the beginning, a precise analysis of the residuals (RES, the difference between calculated and observed arrivaltime) has been done which confirmed the existence of anisotropy for Pn-phases. The recognized sinusoidal distribution has been compensated by an extension of the SSH-program by an ellipse with a slow and rectangular fast axis with azimuth to correct the Pn-velocities. The azimuth of the fast axis has been fixed by the application of the simultaneous inversion at 25° - 27° with a variation of the velocities at +- 2.5 about an average value at 8 km/s. This new value differs from the old one at 35°, recognized in the initial residual analysis. This depends on the new computed hypocenters together with the structure. The application of the elliptical correction has resulted in a better fit of the vertical layered 1D-Model, compared to the results of preceding seismological experiments and 1D and 2D investigations. The optimal result of the 1D-inversion has been used as initial starting model for the 3D-inversions to compute the three dimensional picture of the seismic structure of the Crust and Upper Mantle. The simultaneous inversion has showed an optimization of the relocalization of the hypocenters and the reconstruction of the seismic structure in comparison to the geology and tectonic, as described by other investigations. The investigations for the seismic structure and the relocalization have been confirmed by several different tests. First, synthetic traveltime data are computed with an anisotropic variation and inverted with and without anisotropic correction. Further, tests with randomly disturbed hypocenters and traveltime data have been proceeded to verify the influence of the initial values onto the relocalization accuracy and onto the seismic structure and to test for a further improvement by the application of the anisotropic correction. Finally, the results of the work have been applied onto the Waldkirch earthquake in 2004 to compare the isotropic and the anisotropic relocalization with the initial optimal one to verify whether there is some improvement.

Scene Reconstruction And Understanding By RGB-D Sensors

This thesis investigates interactive scene reconstruction and understanding using RGB-D data only. Indeed, we believe that depth cameras will still be in the near future a cheap and low-power 3D sensing alternative suitable for mobile devices too. Therefore, our contributions build on top of state-of-the-art approaches to achieve advances in three main challenging scenarios, namely mobile mapping, large scale surface reconstruction and semantic modeling. First, we will describe an effective approach dealing with Simultaneous Localization And Mapping (SLAM) on platforms with limited resources, such as a tablet device. Unlike previous methods, dense reconstruction is achieved by reprojection of RGB-D frames, while local consistency is maintained by deploying relative bundle adjustment principles. We will show quantitative results comparing our technique to the state-of-the-art as well as detailed reconstruction of various environments ranging from rooms to small apartments. Then, we will address large scale surface modeling from depth maps exploiting parallel GPU computing. We will develop a real-time camera tracking method based on the popular KinectFusion system and an online surface alignment technique capable of counteracting drift errors and closing small loops. We will show very high quality meshes outperforming existing methods on publicly available datasets as well as on data recorded with our RGB-D camera even in complete darkness. Finally, we will move to our Semantic Bundle Adjustment framework to effectively combine object detection and SLAM in a unified system. Though the mathematical framework we will describe does not restrict to a particular sensing technology, in the experimental section we will refer, again, only to RGB-D sensing. We will discuss successful implementations of our algorithm showing the benefit of a joint object detection, camera tracking and environment mapping.

Decoupling surface reconstruction and perchlorate adsorption on Au(111)

On Au(111) electrodes, the investigation of ClO4− adsorption is hampered by a simultaneous surface reconstruction. We demonstrate that these two processes can be decoupled in cyclic voltammograms by a proper choice of the scan rate and of the initial potential. Our approach allowed the establishment of a relation between potentials of zero charge for the reconstructed and unreconstructed Au(111) surfaces.

Space-time Reconstruction of Oceanic Sea States via Variational Stereo Methods

We present a remote sensing observational method for the measurement of the spatio-temporal dynamics of ocean waves. Variational techniques are used to recover a coherent space-time reconstruction of oceanic sea states given stereo video imagery. The stereoscopic reconstruction problem is expressed in a variational optimization framework. There, we design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal regularizers. A nested iterative scheme is devised to numerically solve, via 3-D multigrid methods, the system of partial differential equations resulting from the optimality condition of the energy functional. The output of our method is the coherent, simultaneous estimation of the wave surface height and radiance at multiple snapshots. We demonstrate our algorithm on real data collected off-shore. Statistical and spectral analysis are performed. Comparison with respect to an existing sequential method is analyzed.

POSE ESTIMATION AND 3D RECONSTRUCTION USING SENSOR FUSION

A camera maps 3-dimensional (3D) world space to a 2-dimensional (2D) image space. In the process it loses the depth information, i.e., the distance from the camera focal point to the imaged objects. It is impossible to recover this information from a single image. However, by using two or more images from different viewing angles this information can be recovered, which in turn can be used to obtain the pose (position and orientation) of the camera. Using this pose, a 3D reconstruction of imaged objects in the world can be computed. Numerous algorithms have been proposed and implemented to solve the above problem; these algorithms are commonly called Structure from Motion (SfM). State-of-the-art SfM techniques have been shown to give promising results. However, unlike a Global Positioning System (GPS) or an Inertial Measurement Unit (IMU) which directly give the position and orientation respectively, the camera system estimates it after implementing SfM as mentioned above. This makes the pose obtained from a camera highly sensitive to the images captured and other effects, such as low lighting conditions, poor focus or improper viewing angles. In some applications, for example, an Unmanned Aerial Vehicle (UAV) inspecting a bridge or a robot mapping an environment using Simultaneous Localization and Mapping (SLAM), it is often difficult to capture images with ideal conditions. This report examines the use of SfM methods in such applications and the role of combining multiple sensors, viz., sensor fusion, to achieve more accurate and usable position and reconstruction information. This project investigates the role of sensor fusion in accurately estimating the pose of a camera for the application of 3D reconstruction of a scene. The first set of experiments is conducted in a motion capture room. These results are assumed as ground truth in order to evaluate the strengths and weaknesses of each sensor and to map their coordinate systems. Then a number of scenarios are targeted where SfM fails. The pose estimates obtained from SfM are replaced by those obtained from other sensors and the 3D reconstruction is completed. Quantitative and qualitative comparisons are made between the 3D reconstruction obtained by using only a camera versus that obtained by using the camera along with a LIDAR and/or an IMU. Additionally, the project also works towards the performance issue faced while handling large data sets of high-resolution images by implementing the system on the Superior high performance computing cluster at Michigan Technological University.

Phylogenetics, Ancestral State Reconstruction, And A New Infrafamilial Classification Of The Pantropical Ochnaceae (medusagynaceae, Ochnaceae S.str., Quiinaceae) Based On Five Dna Regions.

Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.

Paired Evaluation Of Calvarial Reconstruction With Prototyped Titanium Implants With And Without Ceramic Coating.

To investigate the osseointegration properties of prototyped implants with tridimensionally interconnected pores made of the Ti6Al4V alloy and the influence of a thin calcium phosphate coating. Bilateral critical size calvarial defects were created in thirty Wistar rats and filled with coated and uncoated implants in a randomized fashion. The animals were kept for 15, 45 and 90 days. Implant mechanical integration was evaluated with a push-out test. Bone-implant interface was analyzed using scanning electron microscopy. The maximum force to produce initial displacement of the implants increased during the study period, reaching values around 100N for both types of implants. Intimate contact between bone and implant was present, with progressive bone growth into the pores. No significant differences were seen between coated and uncoated implants. Adequate osseointegration can be achieved in calvarial reconstructions using prototyped Ti6Al4V Implants with the described characteristics of surface and porosity.

Simultaneous determination of B-Group vitamins in enriched cookies

The objective of this research was to determine the levels of enrichment of vitamins B1, B2, B6 and B3 in different types and brands of enriched cookies. The chromatographic separation was performed in a C18 column with gradient elution and UV detection at 254 and 287 nm. The results show that only 5 of the 24 brands evaluated are in accordance with the Brazilian legislation with respect to the vitamin content declared on the labels. However, consumption of approximately 100-150 g of most of the brands supplies the recommended dietary intake for children and adults of the vitamins evaluated.