Tissue Equivalent Phantom Design for Optimization of a Coherent Scatter Imaging System

Scatter in medical imaging is typically cast off as image-related noise that detracts from meaningful diagnosis. It is therefore typically rejected or removed from medical images. However, it has been found that every material, including cancerous tissue, has a unique X-ray coherent scatter signature that can be used to identify the material or tissue. Such scatter-based tissue-identification provides the advantage of locating and identifying particular materials over conventional anatomical imaging through X-ray radiography. A coded aperture X-ray coherent scatter spectral imaging system has been developed in our group to classify different tissue types based on their unique scatter signatures. Previous experiments using our prototype have demonstrated that the depth-resolved coherent scatter spectral imaging system (CACSSI) can discriminate healthy and cancerous tissue present in the path of a non-destructive x-ray beam. A key to the successful optimization of CACSSI as a clinical imaging method is to obtain anatomically accurate phantoms of the human body. This thesis describes the development and fabrication of 3D printed anatomical scatter phantoms of the breast and lung.

The purpose of this work is to accurately model different breast geometries using a tissue equivalent phantom, and to classify these tissues in a coherent x-ray scatter imaging system. Tissue-equivalent anatomical phantoms were designed to assess the capability of the CACSSI system to classify different types of breast tissue (adipose, fibroglandular, malignant). These phantoms were 3D printed based on DICOM data obtained from CT scans of prone breasts. The phantoms were tested through comparison of measured scatter signatures with those of adipose and fibroglandular tissue from literature. Tumors in the phantom were modeled using a variety of biological tissue including actual surgically excised benign and malignant tissue specimens. Lung based phantoms have also been printed for future testing. Our imaging system has been able to define the location and composition of the various materials in the phantom. These phantoms were used to characterize the CACSSI system in terms of beam width and imaging technique. The result of this work showed accurate modeling and characterization of the phantoms through comparison of the tissue-equivalent form factors to those from literature. The physical construction of the phantoms, based on actual patient anatomy, was validated using mammography and computed tomography to visually compare the clinical images to those of actual patient anatomy.

Analytic-domain lens design with proximate ray tracing.

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.

Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.

Protein and Drug Design Algorithms Using Improved Biophysical Modeling

This thesis focuses on the development of algorithms that will allow protein design calculations to incorporate more realistic modeling assumptions. Protein design algorithms search large sequence spaces for protein sequences that are biologically and medically useful. Better modeling could improve the chance of success in designs and expand the range of problems to which these algorithms are applied. I have developed algorithms to improve modeling of backbone flexibility (DEEPer) and of more extensive continuous flexibility in general (EPIC and LUTE). I’ve also developed algorithms to perform multistate designs, which account for effects like specificity, with provable guarantees of accuracy (COMETS), and to accommodate a wider range of energy functions in design (EPIC and LUTE).