Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.

Designing three-dimensional transformation optical media using quasiconformal coordinate transformations.

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.

Flow stabilization with active hydrodynamic cloaks

We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5-119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder. © 2012 American Physical Society.

Far-field analysis of axially symmetric three-dimensional directional cloaks.

Axisymmetric radiating and scattering structures whose rotational invariance is broken by non-axisymmetric excitations present an important class of problems in electromagnetics. For such problems, a cylindrical wave decomposition formalism can be used to efficiently obtain numerical solutions to the full-wave frequency-domain problem. Often, the far-field, or Fraunhofer region is of particular interest in scattering cross-section and radiation pattern calculations; yet, it is usually impractical to compute full-wave solutions for this region. Here, we propose a generalization of the Stratton-Chu far-field integral adapted for 2.5D formalism. The integration over a closed, axially symmetric surface is analytically reduced to a line integral on a meridional plane. We benchmark this computational technique by comparing it with analytical Mie solutions for a plasmonic nanoparticle, and apply it to the design of a three-dimensional polarization-insensitive cloak.

A comparison of dimensional models of emotion: evidence from emotions, prototypical events, autobiographical memories, and words.

The intensity and valence of 30 emotion terms, 30 events typical of those emotions, and 30 autobiographical memories cued by those emotions were each rated by different groups of 40 undergraduates. A vector model gave a consistently better account of the data than a circumplex model, both overall and in the absence of high-intensity, neutral valence stimuli. The Positive Activation - Negative Activation (PANA) model could be tested at high levels of activation, where it is identical to the vector model. The results replicated when ratings of arousal were used instead of ratings of intensity for the events and autobiographical memories. A reanalysis of word norms gave further support for the vector and PANA models by demonstrating that neutral valence, high-arousal ratings resulted from the averaging of individual positive and negative valence ratings. Thus, compared to a circumplex model, vector and PANA models provided overall better fits.

Intracardiac acoustic radiation force impulse imaging: a novel imaging method for intraprocedural evaluation of radiofrequency ablation lesions.

BACKGROUND: Arrhythmia recurrence after cardiac radiofrequency ablation (RFA) for atrial fibrillation has been linked to conduction through discontinuous lesion lines. Intraprocedural visualization and corrective ablation of lesion line discontinuities could decrease postprocedure atrial fibrillation recurrence. Intracardiac acoustic radiation force impulse (ARFI) imaging is a new imaging technique that visualizes RFA lesions by mapping the relative elasticity contrast between compliant-unablated and stiff RFA-treated myocardium. OBJECTIVE: To determine whether intraprocedure ARFI images can identify RFA-treated myocardium in vivo. METHODS: In 8 canines, an electroanatomical mapping-guided intracardiac echo catheter was used to acquire 2-dimensional ARFI images along right atrial ablation lines before and after RFA. ARFI images were acquired during diastole with the myocardium positioned at the ARFI focus (1.5 cm) and parallel to the intracardiac echo transducer for maximal and uniform energy delivery to the tissue. Three reviewers categorized each ARFI image as depicting no lesion, noncontiguous lesion, or contiguous lesion. For comparison, 3 separate reviewers confirmed RFA lesion presence and contiguity on the basis of functional conduction block at the imaging plane location on electroanatomical activation maps. RESULTS: Ten percent of ARFI images were discarded because of motion artifacts. Reviewers of the ARFI images detected RFA-treated sites with high sensitivity (95.7%) and specificity (91.5%). Reviewer identification of contiguous lesions had 75.3% specificity and 47.1% sensitivity. CONCLUSIONS: Intracardiac ARFI imaging was successful in identifying endocardial RFA treatment when specific imaging conditions were maintained. Further advances in ARFI imaging technology would facilitate a wider range of imaging opportunities for clinical lesion evaluation.

Component-wise gradient boosting and false discovery control in survival analysis with high-dimensional covariates.

MOTIVATION: Technological advances that allow routine identification of high-dimensional risk factors have led to high demand for statistical techniques that enable full utilization of these rich sources of information for genetics studies. Variable selection for censored outcome data as well as control of false discoveries (i.e. inclusion of irrelevant variables) in the presence of high-dimensional predictors present serious challenges. This article develops a computationally feasible method based on boosting and stability selection. Specifically, we modified the component-wise gradient boosting to improve the computational feasibility and introduced random permutation in stability selection for controlling false discoveries. RESULTS: We have proposed a high-dimensional variable selection method by incorporating stability selection to control false discovery. Comparisons between the proposed method and the commonly used univariate and Lasso approaches for variable selection reveal that the proposed method yields fewer false discoveries. The proposed method is applied to study the associations of 2339 common single-nucleotide polymorphisms (SNPs) with overall survival among cutaneous melanoma (CM) patients. The results have confirmed that BRCA2 pathway SNPs are likely to be associated with overall survival, as reported by previous literature. Moreover, we have identified several new Fanconi anemia (FA) pathway SNPs that are likely to modulate survival of CM patients. AVAILABILITY AND IMPLEMENTATION: The related source code and documents are freely available at https://sites.google.com/site/bestumich/issues. CONTACT: yili@umich.edu.

PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.

Investigation and Development of a Fully 3D Tilt Capable Hybrid SPECT - CT System for Dedicated Breast Imaging

X-ray mammography has been the gold standard for breast imaging for decades, despite the significant limitations posed by the two dimensional (2D) image acquisitions. Difficulty in diagnosing lesions close to the chest wall and axilla, high amount of structural overlap and patient discomfort due to compression are only some of these limitations. To overcome these drawbacks, three dimensional (3D) breast imaging modalities have been developed including dual modality single photon emission computed tomography (SPECT) and computed tomography (CT) systems. This thesis focuses on the development and integration of the next generation of such a device for dedicated breast imaging. The goals of this dissertation work are to: [1] understand and characterize any effects of fully 3-D trajectories on reconstructed image scatter correction, absorbed dose and Hounsifeld Unit accuracy, and [2] design, develop and implement the fully flexible, third generation hybrid SPECT-CT system capable of traversing complex 3D orbits about a pendant breast volume, without interference from the other. Such a system would overcome artifacts resulting from incompletely sampled divergent cone beam imaging schemes and allow imaging closer to the chest wall, which other systems currently under research and development elsewhere cannot achieve.

The dependence of x-ray scatter radiation on object shape, size, material composition and the CT acquisition trajectory, was investigated with a well-established beam stop array (BSA) scatter correction method. While the 2D scatter to primary ratio (SPR) was the main metric used to characterize total system scatter, a new metric called ‘normalized scatter contribution’ was developed to compare the results of scatter correction on 3D reconstructed volumes. Scatter estimation studies were undertaken with a sinusoidal saddle (±15° polar tilt) orbit and a traditional circular (AZOR) orbit. Clinical studies to acquire data for scatter correction were used to evaluate the 2D SPR on a small set of patients scanned with the AZOR orbit. Clinical SPR results showed clear dependence of scatter on breast composition and glandular tissue distribution, otherwise consistent with the overall phantom-based size and density measurements. Additionally, SPR dependence was also observed on the acquisition trajectory where 2D scatter increased with an increase in the polar tilt angle of the system.

The dose delivered by any imaging system is of primary importance from the patient’s point of view, and therefore trajectory related differences in the dose distribution in a target volume were evaluated. Monte Carlo simulations as well as physical measurements using radiochromic film were undertaken using saddle and AZOR orbits. Results illustrated that both orbits deliver comparable dose to the target volume, and only slightly differ in distribution within the volume. Simulations and measurements showed similar results, and all measured dose values were within the standard screening mammography-specific, 6 mGy dose limit, which is used as a benchmark for dose comparisons.

Hounsfield Units (HU) are used clinically in differentiating tissue types in a reconstructed CT image, and therefore the HU accuracy of a system is very important, especially when using non-traditional trajectories. Uniform phantoms filled with various uniform density fluids were used to investigate differences in HU accuracy between saddle and AZOR orbits. Results illustrate the considerably better performance of the saddle orbit, especially close to the chest and nipple region of what would clinically be a pedant breast volume. The AZOR orbit causes shading artifacts near the nipple, due to insufficient sampling, rendering a major portion of the scanned phantom unusable, whereas the saddle orbit performs exceptionally well and provides a tighter distribution of HU values in reconstructed volumes.

Finally, the third generation, fully-suspended SPECT-CT system was designed in and developed in our lab. A novel mechanical method using a linear motor was developed for tilting the CT system. A new x-ray source and a custom made 40 x 30 cm2 detector were integrated on to this system. The SPECT system was nested, in the center of the gantry, orthogonal to the CT source-detector pair. The SPECT system tilts on a goniometer, and the newly developed CT tilting mechanism allows ±15° maximum polar tilting of the CT system. The entire gantry is mounted on a rotation stage, allowing complex arbitrary trajectories for each system, without interference from the other, while having a common field of view. This hybrid system shows potential to be used clinically as a diagnostic tool for dedicated breast imaging.