Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Denoising Your Monte Carlo Renders: Recent Advances in Image Space-Adaptive Sampling and Reconstruction

With the ongoing shift in the computer graphics industry toward Monte Carlo rendering, there is a need for effective, practical noise-reduction techniques that are applicable to a wide range of rendering effects and easily integrated into existing production pipelines. This course surveys recent advances in image-space adaptive sampling and reconstruction algorithms for noise reduction, which have proven very effective at reducing the computational cost of Monte Carlo techniques in practice. These approaches leverage advanced image-filtering techniques with statistical methods for error estimation. They are attractive because they can be integrated easily into conventional Monte Carlo rendering frameworks, they are applicable to most rendering effects, and their computational overhead is modest.

Rapid estimation of cartilage T2 based on double echo at steady state (DESS) with 3 Tesla

The double-echo-steady-state (DESS) sequence generates two signal echoes that are characterized by a different contrast behavior. Based on these two contrasts, the underlying T2 can be calculated. For a flip-angle of 90 degrees , the calculated T2 becomes independent of T1, but with very low signal-to-noise ratio. In the present study, the estimation of cartilage T2, based on DESS with a reduced flip-angle, was investigated, with the goal of optimizing SNR, and simultaneously minimizing the error in T2. This approach was validated in phantoms and on volunteers. T2 estimations based on DESS at different flip-angles were compared with standard multiecho, spin-echo T2. Furthermore, DESS-T2 estimations were used in a volunteer and in an initial study on patients after cartilage repair of the knee. A flip-angle of 33 degrees was the best compromise for the combination of DESS-T2 mapping and morphological imaging. For this flip angle, the Pearson correlation was 0.993 in the phantom study (approximately 20% relative difference between SE-T2 and DESS-T2); and varied between 0.429 and 0.514 in the volunteer study. Measurements in patients showed comparable results for both techniques with regard to zonal assessment. This DESS-T2 approach represents an opportunity to combine morphological and quantitative cartilage MRI in a rapid one-step examination.

Estimation of tool pose based on force-density correlation during robotic drilling

The application of image-guided systems with or without support by surgical robots relies on the accuracy of the navigation process, including patient-to-image registration. The surgeon must carry out the procedure based on the information provided by the navigation system, usually without being able to verify its correctness beyond visual inspection. Misleading surrogate parameters such as the fiducial registration error are often used to describe the success of the registration process, while a lack of methods describing the effects of navigation errors, such as those caused by tracking or calibration, may prevent the application of image guidance in certain accuracy-critical interventions. During minimally invasive mastoidectomy for cochlear implantation, a direct tunnel is drilled from the outside of the mastoid to a target on the cochlea based on registration using landmarks solely on the surface of the skull. Using this methodology, it is impossible to detect if the drill is advancing in the correct direction and that injury of the facial nerve will be avoided. To overcome this problem, a tool localization method based on drilling process information is proposed. The algorithm estimates the pose of a robot-guided surgical tool during a drilling task based on the correlation of the observed axial drilling force and the heterogeneous bone density in the mastoid extracted from 3-D image data. We present here one possible implementation of this method tested on ten tunnels drilled into three human cadaver specimens where an average tool localization accuracy of 0.29 mm was observed.

Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

Next-generation sequencing of HIV-1 RNA genomes: determination of error rates and minimizing artificial recombination.

Next-generation sequencing (NGS) is a valuable tool for the detection and quantification of HIV-1 variants in vivo. However, these technologies require detailed characterization and control of artificially induced errors to be applicable for accurate haplotype reconstruction. To investigate the occurrence of substitutions, insertions, and deletions at the individual steps of RT-PCR and NGS, 454 pyrosequencing was performed on amplified and non-amplified HIV-1 genomes. Artificial recombination was explored by mixing five different HIV-1 clonal strains (5-virus-mix) and applying different RT-PCR conditions followed by 454 pyrosequencing. Error rates ranged from 0.04-0.66% and were similar in amplified and non-amplified samples. Discrepancies were observed between forward and reverse reads, indicating that most errors were introduced during the pyrosequencing step. Using the 5-virus-mix, non-optimized, standard RT-PCR conditions introduced artificial recombinants in a fraction of at least 30% of the reads that subsequently led to an underestimation of true haplotype frequencies. We minimized the fraction of recombinants down to 0.9-2.6% by optimized, artifact-reducing RT-PCR conditions. This approach enabled correct haplotype reconstruction and frequency estimations consistent with reference data obtained by single genome amplification. RT-PCR conditions are crucial for correct frequency estimation and analysis of haplotypes in heterogeneous virus populations. We developed an RT-PCR procedure to generate NGS data useful for reliable haplotype reconstruction and quantification.

Non-invasive and non-occlusive blood pressure estimation via a chest sensor

The clinical demand for a device to monitor Blood Pressure (BP) in ambulatory scenarios with minimal use of inflation cuffs is increasing. Based on the so-called Pulse Wave Velocity (PWV) principle, this paper introduces and evaluates a novel concept of BP monitor that can be fully integrated within a chest sensor. After a preliminary calibration, the sensor provides non-occlusive beat-by-beat estimations of Mean Arterial Pressure (MAP) by measuring the Pulse Transit Time (PTT) of arterial pressure pulses travelling from the ascending aorta towards the subcutaneous vasculature of the chest. In a cohort of 15 healthy male subjects, a total of 462 simultaneous readings consisting of reference MAP and chest PTT were acquired. Each subject was recorded at three different days: D, D+3 and D+14. Overall, the implemented protocol induced MAP values to range from 80 ± 6 mmHg in baseline, to 107 ± 9 mmHg during isometric handgrip maneuvers. Agreement between reference and chest-sensor MAP values was tested by using intraclass correlation coefficient (ICC = 0.78) and Bland-Altman analysis (mean error = 0.7 mmHg, standard deviation = 5.1 mmHg). The cumulative percentage of MAP values provided by the chest sensor falling within a range of ±5 mmHg compared to reference MAP readings was of 70%, within ±10 mmHg was of 91%, and within ±15mmHg was of 98%. These results point at the fact that the chest sensor complies with the British Hypertension Society (BHS) requirements of Grade A BP monitors, when applied to MAP readings. Grade A performance was maintained even two weeks after having performed the initial subject-dependent calibration. In conclusion, this paper introduces a sensor and a calibration strategy to perform MAP measurements at the chest. The encouraging performance of the presented technique paves the way towards an ambulatory-compliant, continuous and non-occlusive BP monitoring system.

Image registration for triggered and non-triggered DTI of the human kidney: Reduced variability of diffusion parameter estimation

BACKGROUND: To investigate if non-rigid image-registration reduces motion artifacts in triggered and non-triggered diffusion tensor imaging (DTI) of native kidneys. A secondary aim was to determine, if improvements through registration allow for omitting respiratory-triggering. METHODS: Twenty volunteers underwent coronal DTI of the kidneys with nine b-values (10-700 s/mm2 ) at 3 Tesla. Image-registration was performed using a multimodal nonrigid registration algorithm. Data processing yielded the apparent diffusion coefficient (ADC), the contribution of perfusion (FP ), and the fractional anisotropy (FA). For comparison of the data stability, the root mean square error (RMSE) of the fitting and the standard deviations within the regions of interest (SDROI ) were evaluated. RESULTS: RMSEs decreased significantly after registration for triggered and also for non-triggered scans (P < 0.05). SDROI for ADC, FA, and FP were significantly lower after registration in both medulla and cortex of triggered scans (P < 0.01). Similarly the SDROI of FA and FP decreased significantly in non-triggered scans after registration (P < 0.05). RMSEs were significantly lower in triggered than in non-triggered scans, both with and without registration (P < 0.05). CONCLUSION: Respiratory motion correction by registration of individual echo-planar images leads to clearly reduced signal variations in renal DTI for both triggered and particularly non-triggered scans. Secondarily, the results suggest that respiratory-triggering still seems advantageous.J. Magn. Reson. Imaging 2014. (c) 2014 Wiley Periodicals, Inc.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Localization and Segmentation of 3D Intervertebral Discs in MR Images by Data Driven Estimation

This paper addresses the problem of fully-automatic localization and segmentation of 3D intervertebral discs (IVDs) from MR images. Our method contains two steps, where we first localize the center of each IVD, and then segment IVDs by classifying image pixels around each disc center as foreground (disc) or background. The disc localization is done by estimating the image displacements from a set of randomly sampled 3D image patches to the disc center. The image displacements are estimated by jointly optimizing the training and test displacement values in a data-driven way, where we take into consideration both the training data and the geometric constraint on the test image. After the disc centers are localized, we segment the discs by classifying image pixels around disc centers as background or foreground. The classification is done in a similar data-driven approach as we used for localization, but in this segmentation case we are aiming to estimate the foreground/background probability of each pixel instead of the image displacements. In addition, an extra neighborhood smooth constraint is introduced to enforce the local smoothness of the label field. Our method is validated on 3D T2-weighted turbo spin echo MR images of 35 patients from two different studies. Experiments show that compared to state of the art, our method achieves better or comparable results. Specifically, we achieve for localization a mean error of 1.6-2.0 mm, and for segmentation a mean Dice metric of 85%-88% and a mean surface distance of 1.3-1.4 mm.

Computer Vision-Based Carbohydrate Estimation for Type 1 Diabetic Patients Using Smartphones

Background: Individuals with type 1 diabetes (T1D) have to count the carbohydrates (CHOs) of their meal to estimate the prandial insulin dose needed to compensate for the meal’s effect on blood glucose levels. CHO counting is very challenging but also crucial, since an error of 20 grams can substantially impair postprandial control. Method: The GoCARB system is a smartphone application designed to support T1D patients with CHO counting of nonpacked foods. In a typical scenario, the user places a reference card next to the dish and acquires 2 images with his/her smartphone. From these images, the plate is detected and the different food items on the plate are automatically segmented and recognized, while their 3D shape is reconstructed. Finally, the food volumes are calculated and the CHO content is estimated by combining the previous results and using the USDA nutritional database. Results: To evaluate the proposed system, a set of 24 multi-food dishes was used. For each dish, 3 pairs of images were taken and for each pair, the system was applied 4 times. The mean absolute percentage error in CHO estimation was 10 ± 12%, which led to a mean absolute error of 6 ± 8 CHO grams for normal-sized dishes. Conclusion: The laboratory experiments demonstrated the feasibility of the GoCARB prototype system since the error was below the initial goal of 20 grams. However, further improvements and evaluation are needed prior launching a system able to meet the inter- and intracultural eating habits.