[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

Solitons in Exciton-Polariton System: Reduced Modelling, Analysis, and Numerical Studies

In this dissertation, we study the behavior of exciton-polariton quasiparticles in semiconductor microcavities, under the sourceless and lossless conditions.

First, we simplify the original model by removing the photon dispersion term, thus effectively turn the PDEs system to an ODEs system,

and investigate the behavior of the resulting system, including the equilibrium points and the wave functions of the excitons and the photons.

Second, we add the dispersion term for the excitons to the original model and prove that the band of the discontinuous solitons now become dark solitons.

Third, we employ the Strang-splitting method to our sytem of PDEs and prove the first-order and second-order error bounds in the $H^1$ norm and the $L_2$ norm, respectively.

Using this numerical result, we analyze the stability of the steady state bright soliton solution. This solution revolves around the $x$-axis as time progresses

and the perturbed soliton also rotates around the $x$-axis and tracks closely in terms of amplitude but lags behind the exact one. Our numerical result shows orbital

stability but no $L_2$ stability.

Expression in aneuploid Drosophila S2 cells.

Extensive departures from balanced gene dose in aneuploids are highly deleterious. However, we know very little about the relationship between gene copy number and expression in aneuploid cells. We determined copy number and transcript abundance (expression) genome-wide in Drosophila S2 cells by DNA-Seq and RNA-Seq. We found that S2 cells are aneuploid for >43 Mb of the genome, primarily in the range of one to five copies, and show a male genotype ( approximately two X chromosomes and four sets of autosomes, or 2X;4A). Both X chromosomes and autosomes showed expression dosage compensation. X chromosome expression was elevated in a fixed-fold manner regardless of actual gene dose. In engineering terms, the system "anticipates" the perturbation caused by X dose, rather than responding to an error caused by the perturbation. This feed-forward regulation resulted in precise dosage compensation only when X dose was half of the autosome dose. Insufficient compensation occurred at lower X chromosome dose and excessive expression occurred at higher doses. RNAi knockdown of the Male Specific Lethal complex abolished feed-forward regulation. Both autosome and X chromosome genes show Male Specific Lethal-independent compensation that fits a first order dose-response curve. Our data indicate that expression dosage compensation dampens the effect of altered DNA copy number genome-wide. For the X chromosome, compensation includes fixed and dose-dependent components.

Global Rates of Free Hydrogen (H2) Production by Serpentinization and other Abiogenic Processes within Young Ocean Crust

The main conclusion of this dissertation is that global H2 production within young ocean crust (<10 Mya) is higher than currently recognized, in part because current estimates of H2 production accompanying the serpentinization of peridotite may be too low (Chapter 2) and in part because a number of abiogenic H2-producing processes have heretofore gone unquantified (Chapter 3). The importance of free H2 to a range of geochemical processes makes the quantitative understanding of H2 production advanced in this dissertation pertinent to an array of open research questions across the geosciences (e.g. the origin and evolution of life and the oxidation of the Earth’s atmosphere and oceans).

The first component of this dissertation (Chapter 2) examines H2 produced within young ocean crust [e.g. near the mid-ocean ridge (MOR)] by serpentinization. In the presence of water, olivine-rich rocks (peridotites) undergo serpentinization (hydration) at temperatures of up to ~500°C but only produce H2 at temperatures up to ~350°C. A simple analytical model is presented that mechanistically ties the process to seafloor spreading and explicitly accounts for the importance of temperature in H2 formation. The model suggests that H2 production increases with the rate of seafloor spreading and the net thickness of serpentinized peridotite (S-P) in a column of lithosphere. The model is applied globally to the MOR using conservative estimates for the net thickness of lithospheric S-P, our least certain model input. Despite the large uncertainties surrounding the amount of serpentinized peridotite within oceanic crust, conservative model parameters suggest a magnitude of H2 production (~1012 moles H2/y) that is larger than the most widely cited previous estimates (~1011 although previous estimates range from 1010-1012 moles H2/y). Certain model relationships are also consistent with what has been established through field studies, for example that the highest H2 fluxes (moles H2/km2 seafloor) are produced near slower-spreading ridges (<20 mm/y). Other modeled relationships are new and represent testable predictions. Principal among these is that about half of the H2 produced globally is produced off-axis beneath faster-spreading seafloor (>20 mm/y), a region where only one measurement of H2 has been made thus far and is ripe for future investigation.

In the second part of this dissertation (Chapter 3), I construct the first budget for free H2 in young ocean crust that quantifies and compares all currently recognized H2 sources and H2 sinks. First global estimates of budget components are proposed in instances where previous estimate(s) could not be located provided that the literature on that specific budget component was not too sparse to do so. Results suggest that the nine known H2 sources, listed in order of quantitative importance, are: Crystallization (6x1012 moles H2/y or 61% of total H2 production), serpentinization (2x1012 moles H2/y or 21%), magmatic degassing (7x1011 moles H2/y or 7%), lava-seawater interaction (5x1011 moles H2/y or 5%), low-temperature alteration of basalt (5x1011 moles H2/y or 5%), high-temperature alteration of basalt (3x1010 moles H2/y or <1%), catalysis (3x108 moles H2/y or <<1%), radiolysis (2x108 moles H2/y or <<1%), and pyrite formation (3x106 moles H2/y or <<1%). Next we consider two well-known H2 sinks, H2 lost to the ocean and H2 occluded within rock minerals, and our analysis suggests that both are of similar size (both are 6x1011 moles H2/y). Budgeting results suggest a large difference between H2 sources (total production = 1x1013 moles H2/y) and H2 sinks (total losses = 1x1011 moles H2/y). Assuming this large difference represents H2 consumed by microbes (total consumption = 9x1011 moles H2/y), we explore rates of primary production by the chemosynthetic, sub-seafloor biosphere. Although the numbers presented require further examination and future modifications, the analysis suggests that the sub-seafloor H2 budget is similar to the sub-seafloor CH4 budget in the sense that globally significant quantities of both of these reduced gases are produced beneath the seafloor but never escape the seafloor due to microbial consumption.

The third and final component of this dissertation (Chapter 4) explores the self-organization of barchan sand dune fields. In nature, barchan dunes typically exist as members of larger dune fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in external forcing. To explore the possibility that observed structures emerge spontaneously as a collective result of many dunes interacting with each other, we built a numerical model that treats barchans as discrete entities that interact with one another according to simplified rules derived from theoretical and numerical work, and from field observations: Dunes exchange sand through the fluxes that leak from the downwind side of each dune and are captured on their upstream sides; when dunes become sufficiently large, small dunes are born on their downwind sides (“calving”); and when dunes collide directly enough, they merge. Results show that these relatively simple interactions provide potential explanations for a range of field-scale phenomena including isolated patches of dunes and heterogeneous arrangements of similarly sized dunes in denser fields. The results also suggest that (1) dune field characteristics depend on the sand flux fed into the upwind boundary, although (2) moving downwind, the system approaches a common attracting state in which the memory of the upwind conditions vanishes. This work supports the hypothesis that calving exerts a first order control on field-scale phenomena; it prevents individual dunes from growing without bound, as single-dune analyses suggest, and allows the formation of roughly realistic, persistent dune field patterns.

Advanced Techniques for Image Quality Assessment of Modern X-ray Computed Tomography Systems

X-ray computed tomography (CT) imaging constitutes one of the most widely used diagnostic tools in radiology today with nearly 85 million CT examinations performed in the U.S in 2011. CT imparts a relatively high amount of radiation dose to the patient compared to other x-ray imaging modalities and as a result of this fact, coupled with its popularity, CT is currently the single largest source of medical radiation exposure to the U.S. population. For this reason, there is a critical need to optimize CT examinations such that the dose is minimized while the quality of the CT images is not degraded. This optimization can be difficult to achieve due to the relationship between dose and image quality. All things being held equal, reducing the dose degrades image quality and can impact the diagnostic value of the CT examination.

A recent push from the medical and scientific community towards using lower doses has spawned new dose reduction technologies such as automatic exposure control (i.e., tube current modulation) and iterative reconstruction algorithms. In theory, these technologies could allow for scanning at reduced doses while maintaining the image quality of the exam at an acceptable level. Therefore, there is a scientific need to establish the dose reduction potential of these new technologies in an objective and rigorous manner. Establishing these dose reduction potentials requires precise and clinically relevant metrics of CT image quality, as well as practical and efficient methodologies to measure such metrics on real CT systems. The currently established methodologies for assessing CT image quality are not appropriate to assess modern CT scanners that have implemented those aforementioned dose reduction technologies.

Thus the purpose of this doctoral project was to develop, assess, and implement new phantoms, image quality metrics, analysis techniques, and modeling tools that are appropriate for image quality assessment of modern clinical CT systems. The project developed image quality assessment methods in the context of three distinct paradigms, (a) uniform phantoms, (b) textured phantoms, and (c) clinical images.

The work in this dissertation used the “task-based” definition of image quality. That is, image quality was broadly defined as the effectiveness by which an image can be used for its intended task. Under this definition, any assessment of image quality requires three components: (1) A well defined imaging task (e.g., detection of subtle lesions), (2) an “observer” to perform the task (e.g., a radiologists or a detection algorithm), and (3) a way to measure the observer’s performance in completing the task at hand (e.g., detection sensitivity/specificity).

First, this task-based image quality paradigm was implemented using a novel multi-sized phantom platform (with uniform background) developed specifically to assess modern CT systems (Mercury Phantom, v3.0, Duke University). A comprehensive evaluation was performed on a state-of-the-art CT system (SOMATOM Definition Force, Siemens Healthcare) in terms of noise, resolution, and detectability as a function of patient size, dose, tube energy (i.e., kVp), automatic exposure control, and reconstruction algorithm (i.e., Filtered Back-Projection– FPB vs Advanced Modeled Iterative Reconstruction– ADMIRE). A mathematical observer model (i.e., computer detection algorithm) was implemented and used as the basis of image quality comparisons. It was found that image quality increased with increasing dose and decreasing phantom size. The CT system exhibited nonlinear noise and resolution properties, especially at very low-doses, large phantom sizes, and for low-contrast objects. Objective image quality metrics generally increased with increasing dose and ADMIRE strength, and with decreasing phantom size. The ADMIRE algorithm could offer comparable image quality at reduced doses or improved image quality at the same dose (increase in detectability index by up to 163% depending on iterative strength). The use of automatic exposure control resulted in more consistent image quality with changing phantom size.

Based on those results, the dose reduction potential of ADMIRE was further assessed specifically for the task of detecting small (<=6 mm) low-contrast (<=20 HU) lesions. A new low-contrast detectability phantom (with uniform background) was designed and fabricated using a multi-material 3D printer. The phantom was imaged at multiple dose levels and images were reconstructed with FBP and ADMIRE. Human perception experiments were performed to measure the detection accuracy from FBP and ADMIRE images. It was found that ADMIRE had equivalent performance to FBP at 56% less dose.

Using the same image data as the previous study, a number of different mathematical observer models were implemented to assess which models would result in image quality metrics that best correlated with human detection performance. The models included naïve simple metrics of image quality such as contrast-to-noise ratio (CNR) and more sophisticated observer models such as the non-prewhitening matched filter observer model family and the channelized Hotelling observer model family. It was found that non-prewhitening matched filter observers and the channelized Hotelling observers both correlated strongly with human performance. Conversely, CNR was found to not correlate strongly with human performance, especially when comparing different reconstruction algorithms.

The uniform background phantoms used in the previous studies provided a good first-order approximation of image quality. However, due to their simplicity and due to the complexity of iterative reconstruction algorithms, it is possible that such phantoms are not fully adequate to assess the clinical impact of iterative algorithms because patient images obviously do not have smooth uniform backgrounds. To test this hypothesis, two textured phantoms (classified as gross texture and fine texture) and a uniform phantom of similar size were built and imaged on a SOMATOM Flash scanner (Siemens Healthcare). Images were reconstructed using FBP and a Sinogram Affirmed Iterative Reconstruction (SAFIRE). Using an image subtraction technique, quantum noise was measured in all images of each phantom. It was found that in FBP, the noise was independent of the background (textured vs uniform). However, for SAFIRE, noise increased by up to 44% in the textured phantoms compared to the uniform phantom. As a result, the noise reduction from SAFIRE was found to be up to 66% in the uniform phantom but as low as 29% in the textured phantoms. Based on this result, it clear that further investigation was needed into to understand the impact that background texture has on image quality when iterative reconstruction algorithms are used.

To further investigate this phenomenon with more realistic textures, two anthropomorphic textured phantoms were designed to mimic lung vasculature and fatty soft tissue texture. The phantoms (along with a corresponding uniform phantom) were fabricated with a multi-material 3D printer and imaged on the SOMATOM Flash scanner. Scans were repeated a total of 50 times in order to get ensemble statistics of the noise. A novel method of estimating the noise power spectrum (NPS) from irregularly shaped ROIs was developed. It was found that SAFIRE images had highly locally non-stationary noise patterns with pixels near edges having higher noise than pixels in more uniform regions. Compared to FBP, SAFIRE images had 60% less noise on average in uniform regions for edge pixels, noise was between 20% higher and 40% lower. The noise texture (i.e., NPS) was also highly dependent on the background texture for SAFIRE. Therefore, it was concluded that quantum noise properties in the uniform phantoms are not representative of those in patients for iterative reconstruction algorithms and texture should be considered when assessing image quality of iterative algorithms.

The move beyond just assessing noise properties in textured phantoms towards assessing detectability, a series of new phantoms were designed specifically to measure low-contrast detectability in the presence of background texture. The textures used were optimized to match the texture in the liver regions actual patient CT images using a genetic algorithm. The so called “Clustured Lumpy Background” texture synthesis framework was used to generate the modeled texture. Three textured phantoms and a corresponding uniform phantom were fabricated with a multi-material 3D printer and imaged on the SOMATOM Flash scanner. Images were reconstructed with FBP and SAFIRE and analyzed using a multi-slice channelized Hotelling observer to measure detectability and the dose reduction potential of SAFIRE based on the uniform and textured phantoms. It was found that at the same dose, the improvement in detectability from SAFIRE (compared to FBP) was higher when measured in a uniform phantom compared to textured phantoms.

The final trajectory of this project aimed at developing methods to mathematically model lesions, as a means to help assess image quality directly from patient images. The mathematical modeling framework is first presented. The models describe a lesion’s morphology in terms of size, shape, contrast, and edge profile as an analytical equation. The models can be voxelized and inserted into patient images to create so-called “hybrid” images. These hybrid images can then be used to assess detectability or estimability with the advantage that the ground truth of the lesion morphology and location is known exactly. Based on this framework, a series of liver lesions, lung nodules, and kidney stones were modeled based on images of real lesions. The lesion models were virtually inserted into patient images to create a database of hybrid images to go along with the original database of real lesion images. ROI images from each database were assessed by radiologists in a blinded fashion to determine the realism of the hybrid images. It was found that the radiologists could not readily distinguish between real and virtual lesion images (area under the ROC curve was 0.55). This study provided evidence that the proposed mathematical lesion modeling framework could produce reasonably realistic lesion images.

Based on that result, two studies were conducted which demonstrated the utility of the lesion models. The first study used the modeling framework as a measurement tool to determine how dose and reconstruction algorithm affected the quantitative analysis of liver lesions, lung nodules, and renal stones in terms of their size, shape, attenuation, edge profile, and texture features. The same database of real lesion images used in the previous study was used for this study. That database contained images of the same patient at 2 dose levels (50% and 100%) along with 3 reconstruction algorithms from a GE 750HD CT system (GE Healthcare). The algorithms in question were FBP, Adaptive Statistical Iterative Reconstruction (ASiR), and Model-Based Iterative Reconstruction (MBIR). A total of 23 quantitative features were extracted from the lesions under each condition. It was found that both dose and reconstruction algorithm had a statistically significant effect on the feature measurements. In particular, radiation dose affected five, three, and four of the 23 features (related to lesion size, conspicuity, and pixel-value distribution) for liver lesions, lung nodules, and renal stones, respectively. MBIR significantly affected 9, 11, and 15 of the 23 features (including size, attenuation, and texture features) for liver lesions, lung nodules, and renal stones, respectively. Lesion texture was not significantly affected by radiation dose.

The second study demonstrating the utility of the lesion modeling framework focused on assessing detectability of very low-contrast liver lesions in abdominal imaging. Specifically, detectability was assessed as a function of dose and reconstruction algorithm. As part of a parallel clinical trial, images from 21 patients were collected at 6 dose levels per patient on a SOMATOM Flash scanner. Subtle liver lesion models (contrast = -15 HU) were inserted into the raw projection data from the patient scans. The projections were then reconstructed with FBP and SAFIRE (strength 5). Also, lesion-less images were reconstructed. Noise, contrast, CNR, and detectability index of an observer model (non-prewhitening matched filter) were assessed. It was found that SAFIRE reduced noise by 52%, reduced contrast by 12%, increased CNR by 87%. and increased detectability index by 65% compared to FBP. Further, a 2AFC human perception experiment was performed to assess the dose reduction potential of SAFIRE, which was found to be 22% compared to the standard of care dose.

In conclusion, this dissertation provides to the scientific community a series of new methodologies, phantoms, analysis techniques, and modeling tools that can be used to rigorously assess image quality from modern CT systems. Specifically, methods to properly evaluate iterative reconstruction have been developed and are expected to aid in the safe clinical implementation of dose reduction technologies.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.