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Full-Text Articles in Biomedical Engineering and Bioengineering

Development Of A Statistical Shape-Function Model Of The Implanted Knee For Real-Time Prediction Of Joint Mechanics, Kalin Gibbons Aug 2019

Development Of A Statistical Shape-Function Model Of The Implanted Knee For Real-Time Prediction Of Joint Mechanics, Kalin Gibbons

Boise State University Theses and Dissertations

Outcomes of total knee arthroplasty (TKA) are dependent on surgical technique, patient variability, and implant design. Non-optimal design or alignment choices may result in undesirable contact mechanics and joint kinematics, including poor joint alignment, instability, and reduced range of motion. Implant design and surgical alignment are modifiable factors with potential to improve patient outcomes, and there is a need for robust implant designs that can accommodate patient variability. Our objective was to develop a statistical shape-function model (SFM) of a posterior stabilized implant knee to instantaneously predict output mechanics in an efficient manner. Finite element methods were combined with Latin ...


Investigation Of Fundamental Principles Of Rigid Body Impact Mechanics, Khalid Alluhydan Jul 2019

Investigation Of Fundamental Principles Of Rigid Body Impact Mechanics, Khalid Alluhydan

Mechanical Engineering Research Theses and Dissertations

In impact mechanics, the collision between two or more bodies is a common, yet a very challenging problem. Producing analytical solutions that can predict the post-collision motion of the colliding bodies require consistent modeling of the dynamics of the colliding bodies. This dissertation presents a new method for solving the two and multibody impact problems that can be used to predict the post-collision motion of the colliding bodies. Also, we solve the rigid body collision problem of planar kinematic chains with multiple contacts with external surfaces.

In the first part of this dissertation, we study planar collisions of Balls and ...


Feedforward And Feedback Signals In The Olfactory System, Srimoy Chakraborty May 2019

Feedforward And Feedback Signals In The Olfactory System, Srimoy Chakraborty

Theses and Dissertations

The conglomeration of myriad activities in neural systems often results in prominent oscillations. The primary goal of the research presented in this thesis was to study effects of sensory stimulus on the olfactory system of rats, focusing on the olfactory bulb (OB) and the anterior piriform cortex (aPC). Extracellular electrophysiological measurements revealed distinct frequency bands of oscillations in OB and aPC. However, how these oscillatory fluctuations help the animal to process sensory input is not clearly understood. Here we show high frequency oscillations in olfactory bulb carry feedforward signals to anterior piriform cortex whereas feedback from the aPC is predominantly ...


Development Of In Situ Forming Hydrogels For Intra-Articular Drug Delivery, Andy Prince Feb 2019

Development Of In Situ Forming Hydrogels For Intra-Articular Drug Delivery, Andy Prince

Electronic Thesis and Dissertation Repository

Hydrogels are 3-dimensional crosslinked polymer networks that can absorb significant amounts of water. The physical properties associated with hydrogels affords them resemblance to biological tissues making them good candidates for biomedical applications. Many pharmaceuticals, specifically non-steroidal anti-inflammatory drugs (NSAIDs), have poor aqueous solubility, which limits their bioavailability and efficacy. People suffering from chronic osteoarthritis (OA) are required to frequently take large doses to mitigate pain, which can lead to serious side effects. Hydrogels are good strategies to deliver NSAIDs via articular injection because they can form solid gels in situ. This thesis describes the synthesis, formulation, mechanical testing, in vitro ...


Foodlocker: An Online Marketplace For Automated Meals, Josiah Buxton Jan 2019

Foodlocker: An Online Marketplace For Automated Meals, Josiah Buxton

Computer Science Graduate Theses & Dissertations

Food waste is a major problem for the human race, particularly in "rich" industrial countries.

We propose a creative, partial solution to this problem through the development of an online marketplace for left-over food and a physical infrastructure to secure the food throughout each transaction.

The software platform will consist of three separate portions: a mobile food consumer application, a mobile food provider application, and a web food provider application. Restaurants and other licensed food distributors can utilize the food provider applications to broadcast available left-over meals, which can be purchased at a discounted price. The hardware infrastructure will be ...


Nanoscale Stiffness Cues Influence Valvular Interstitial Cell Activation To Myofibroblasts, Michaela Wenning Jan 2019

Nanoscale Stiffness Cues Influence Valvular Interstitial Cell Activation To Myofibroblasts, Michaela Wenning

Undergraduate Honors Theses

Surgery is currently the primary treatment option for aortic valve stenosis (AVS) patients, many of whom are ineligible for surgery and are left untreated. AVS is progression is known to differ between males and females, and an understanding of sex-specific mechanisms of disease progression is imperative in developing accurate treatment options for men and women. The development of a nonsurgical therapy for AVS patients requires a deeper understanding of the molecular and cellular mechanisms of AVS progression. Currently, the role of calcium phosphate nanoparticles detected in the aortic valve during early stages of AVS in influencing disease progression and valvular ...


Optical Vortex And Poincaré Analysis For Biophysical Dynamics, Anindya Majumdar Jan 2019

Optical Vortex And Poincaré Analysis For Biophysical Dynamics, Anindya Majumdar

Dissertations, Master's Theses and Master's Reports

Coherent light - such as that from a laser - on interaction with biological tissues, undergoes scattering. This scattered light undergoes interference and the resultant field has randomly added phases and amplitudes. This random interference pattern is known as speckles, and has been the subject of multiple applications, including imaging techniques. These speckle fields inherently contain optical vortices, or phase singularities. These are locations where the intensity (or amplitude) of the interference pattern is zero, and the phase is undefined.

In the research presented in this dissertation, dynamic speckle patterns were obtained through computer simulations as well as laboratory setups involving scattering ...


Relaxed Mental State Detection Using The Emotiv Epoc And Adaptive Threshold Algorithms, Olin L. Anderson Jan 2019

Relaxed Mental State Detection Using The Emotiv Epoc And Adaptive Threshold Algorithms, Olin L. Anderson

EWU Masters Thesis Collection

The electroencephalogram (EEG) has proven to be useful in a wide variety of applications, including: diagnosis of mental disorders, psychological research, neurofeedback, and brain-computer interfacing. Most such applications of the EEG benefit from an ability to automatically detect when the subject is in a relaxed state. Recently, inexpensive and relatively easy to use EEG systems, with multiple electrodes, have become available at prices comparable to cellular phones or game machines. This project’s purpose is to investigate the feasibility of real-time classification of a subject's relaxation state using one such consumer-grade EEG system, the Emotiv Epoc. The subject's ...


Multiscale Mathematical Modelling Of Nonlinear Nanowire Resonators For Biological Applications, Rosa Fallahpourghadikolaei Jan 2019

Multiscale Mathematical Modelling Of Nonlinear Nanowire Resonators For Biological Applications, Rosa Fallahpourghadikolaei

Theses and Dissertations (Comprehensive)

Nanoscale systems fabricated with low-dimensional nanostructures such as carbon nanotubes, nanowires, quantum dots, and more recently graphene sheets, have fascinated researchers from different fields due to their extraordinary and unique physical properties. For example, the remarkable mechanical properties of nanoresonators empower them to have a very high resonant frequency up to the order of giga to terahertz. The ultra-high frequency of these systems attracted the attention of researchers in the area of bio-sensing with the idea to implement them for detection of tiny bio-objects. In this thesis, we originally propose and analyze a mathematical model for nonlinear vibrations of nanowire ...


Radiolabeled Nanohydroxyapatite As A Platform For The Development Of New Pet Imaging Agents, Stacy Lee Queern Dec 2018

Radiolabeled Nanohydroxyapatite As A Platform For The Development Of New Pet Imaging Agents, Stacy Lee Queern

Arts & Sciences Electronic Theses and Dissertations

Positron emission tomography (PET) imaging utilizes drugs labeled with positron emitters to target and evaluate different biological processes occurring in the body. Tailoring medicine to the individual allows for higher quality of care with better diagnosis and treatment and is a key purpose for advancing research into developing new platforms for PET imaging agents. A PET nuclide of high interest for the development of these agents is 89Zr. This can be attributed to the long half-life of 3.27 days and low positron energy of 89Zr.

In this work, we developed a production method for 89Zr using Y sputtered coins ...


Assessing Biofiltration Without Ozonation For Removal Of Trihalomethane Precursors In Drinking Water At The Beaver Water District Drinking Water Treatment Plant, Sana Ajaz Dec 2018

Assessing Biofiltration Without Ozonation For Removal Of Trihalomethane Precursors In Drinking Water At The Beaver Water District Drinking Water Treatment Plant, Sana Ajaz

Theses and Dissertations

Biofiltration without pre-ozonation has the capability to remove natural organic matter (NOM) fractions that serve as precursors of disinfection byproducts (DBPs), which include the four regulated trihalomethanes (THMs) and dichloroacetonitrile (DCAN). Rapid small-scale column tests (RSSCTs) and Pilot Plant filters operated at empty-bed contact times (EBCTs) of 4, 8, and 16 minutes were used to evaluate the performance of nutrient-amended (free ammonia and phosphorus) biofiltration for THM and DCAN precursor removal, as measured using formation potential (FP) tests. NOM surrogates – which include dissolved organic carbon (DOC), specific ultraviolet absorbance (SUVA254) and fluorescence-PARAFAC components – were measured weekly throughout the 30-week study ...


In Vivo Vascular Imaging With Photoacoustic Microscopy, Hsun-Chia Hsu Aug 2018

In Vivo Vascular Imaging With Photoacoustic Microscopy, Hsun-Chia Hsu

Engineering and Applied Science Theses & Dissertations

Photoacoustic (PA) tomography (PAT) has received extensive attention in the last decade for its capability to provide label-free structural and functional imaging in biological tissue with highly scalable spatial resolution and penetration depth. Compared to modern optical modalities, PAT offers speckle-free images and is more sensitive to optical absorption contrast (with 100% relative sensitivity). By implementing different regimes of optical wavelength, PAT can be used to image diverse light-absorbing biomolecules. For example, hemoglobin is of particular interest in the visible wavelength regime owing to its dominant absorption, and lipids and water are more commonly studied in the near-infrared regime.

In ...


A Discrete-Event Simulation Approach For Modeling Human Body Glucose Metabolism, Buket Aydas Aug 2018

A Discrete-Event Simulation Approach For Modeling Human Body Glucose Metabolism, Buket Aydas

Theses and Dissertations

This dissertation describes CarbMetSim (Carbohydrate Metabolism Simulator), a discrete-event simulator that tracks the blood glucose level of a person in response to a timed sequence of diet and exercise activities. CarbMetSim implements broader aspects of carbohydrate metabolism in human beings with the objective of capturing the average impact of various diet/exercise activities on the blood glucose level. Key organs (stomach, intestine, portal vein, liver, kidney, muscles, adipose tissue, brain and heart) are implemented to the extent necessary to capture their impact on the production and consumption of glucose. Key metabolic pathways (glucose oxidation, glycolysis and gluconeogenesis) are accounted for ...


Evaluation Of Drug-Loaded Gold Nanoparticle Cytotoxicity As A Function Of Tumor Tissue Heterogeneity., Hunter Allan Miller Aug 2018

Evaluation Of Drug-Loaded Gold Nanoparticle Cytotoxicity As A Function Of Tumor Tissue Heterogeneity., Hunter Allan Miller

Electronic Theses and Dissertations

The inherent heterogeneity of tumor tissue presents a major challenge to nanoparticle-medicated drug delivery. This heterogeneity spans from the molecular to the cellular (cell types) and to the tissue (vasculature, extra-cellular matrix) scales. Here we employ computational modeling to evaluate therapeutic response as a function of vascular-induced tumor tissue heterogeneity. Using data with three-layered gold nanoparticles loaded with cisplatin, nanotherapy is simulated with different levels of tissue heterogeneity, and the treatment response is measured in terms of tumor regression. The results show that tumor vascular density non-trivially influences the nanoparticle uptake and washout, and the associated tissue response. The drug ...


Preparation Of Supramolecular Amphiphilic Cyclodextrin Bilayer Vesicles For Pharmaceutical Applications, Kate E. Frischkorn Jun 2018

Preparation Of Supramolecular Amphiphilic Cyclodextrin Bilayer Vesicles For Pharmaceutical Applications, Kate E. Frischkorn

Master's Theses and Project Reports

Recent pharmaceutical developments have investigated using supramolecular nanoparticles in order to increase the bioavailability and solubility of drugs delivered in various methods. Modification of the carbohydrate cyclodextrin increases the ability to encapsulate hydrophobic pharmaceutical molecules by forming a carrier with a hydrophobic core and hydrophilic exterior. Guest molecules are commonly added to these inclusion complexes in order to add stability and further increase targeting abilities of the carriers. One such guest molecule is adamantine combined with a poly(ethylene glycol) chain. Vesicles are formed by hydrating a thin film of amphiphilic cyclodextrin and guest molecules in buffer solution that mimics ...


A 3d Simulation Of Leukocyte Adhesion In Blood Flow, Tai-Hsien Wu Jun 2018

A 3d Simulation Of Leukocyte Adhesion In Blood Flow, Tai-Hsien Wu

Dissertations

It has been widely acknowledged that further understanding about the dynamics between blood cells and blood flow can help us gain more knowledge about the causes of diseases and discover more effective treatments. Examples of such dynamics include red blood cell (RBC, or erythrocyte) aggregation, white blood cell (WBC, or leukocyte) margination, and WBC extravasation. WBC extravasation is an important multiple-step process in the inflammatory response and therefore has drawn considerable attention over the past two decades. In this multiple-step process, a WBC undergoes at least four steps, including capture, rolling, firm adhesion, and transmigration, and each step is influenced ...


Radical Social Ecology As Deep Pragmatism: A Call To The Abolition Of Systemic Dissonance And The Minimization Of Entropic Chaos, Arielle Brender May 2018

Radical Social Ecology As Deep Pragmatism: A Call To The Abolition Of Systemic Dissonance And The Minimization Of Entropic Chaos, Arielle Brender

Student Theses 2015-Present

This paper aims to shed light on the dissonance caused by the superimposition of Dominant Human Systems on Natural Systems. I highlight the synthetic nature of Dominant Human Systems as egoic and linguistic phenomenon manufactured by a mere portion of the human population, which renders them inherently oppressive unto peoples and landscapes whose wisdom were barred from the design process. In pursuing a radical pragmatic approach to mending the simultaneous oppression and destruction of the human being and the earth, I highlight the necessity of minimizing entropic chaos caused by excess energy expenditure, an essential feature of systems that aim ...


Developing Photoacoustic Tomography Devices For Translational Medicine And Basic Science Research, Tsz Wai Wong May 2018

Developing Photoacoustic Tomography Devices For Translational Medicine And Basic Science Research, Tsz Wai Wong

Engineering and Applied Science Theses & Dissertations

Photoacoustic (PA) tomography (PAT) provides volumetric images of biological tissue with scalable spatial resolutions and imaging depths, while preserving the same imaging contrast—optical absorption. Taking the advantage of its 100% sensitivity to optical absorption, PAT has been widely applied in structural, functional, and molecular imaging, with both endogenous and exogenous contrasts, at superior depths than pure optical methods. Intuitively, hemoglobin has been the most commonly studied biomolecule in PAT due to its strong absorption in the visible wavelength regime.

One of the main focuses of this dissertation is to investigate an underexplored wavelength regime—ultraviolet (UV), which allows us ...


Design & Delivery Of Automated Winston-Lutz Test For Isocentric & Off-Axis Delivery Stability Utilizing Truebeam Developer Mode & Electronic Portal Imaging Device, Mahmoud Mohammad Yaqoub May 2018

Design & Delivery Of Automated Winston-Lutz Test For Isocentric & Off-Axis Delivery Stability Utilizing Truebeam Developer Mode & Electronic Portal Imaging Device, Mahmoud Mohammad Yaqoub

UNLV Theses, Dissertations, Professional Papers, and Capstones

The uncertainties in treatment delivery cannot be ignored in radiation therapy. Thus, the quality assurance QA tests are very important task of the medical physicist in clinical practice. Assuring the coincidence between the mechanical isocenter of the Linear Accelerator (LINAC) and its radiation beams isocenter is one of the most important qualities need to be tested, and the Winston Lust (WL) test is the

most popular technique to perform this task, especially for the treatment modalities which need high precision in beam delivery such as the stereotactic radiosurgery/stereotactic body radiotherapy (SRS/SBRT). The linear accelerator-based SRS/SBRT is a ...


Developing Wavefront Shaping Techniques For Focusing Through Highly Dynamic Scattering Media, Ashton Hemphill May 2018

Developing Wavefront Shaping Techniques For Focusing Through Highly Dynamic Scattering Media, Ashton Hemphill

Engineering and Applied Science Theses & Dissertations

One of the prime limiting factors of optical imaging in biological applications is the diffusion of light by tissue, which prevents focusing at depths greater than the optical diffusion limit of ~1 mm in soft tissue. This greatly restricts the utility of optical diagnostic and therapeutic techniques, such as optogenetics, microsurgery, optical tweezing, and phototherapy of deep tissue, which require focused light in order to function. Wavefront shaping extends the depth at which optical focusing may be achieved by compensating for phase distortions induced by scattering, allowing for focusing through constructive interference.

However, due to physiological motion, scattering of light ...


Fluorescence Guided Tumor Imaging: Foundations For Translational Applications, Jessica P. Miller May 2018

Fluorescence Guided Tumor Imaging: Foundations For Translational Applications, Jessica P. Miller

Engineering and Applied Science Theses & Dissertations

Optical imaging for medical applications is a growing field, and it has the potential to improve medical outcomes through its increased sensitivity and specificity, lower cost, and small instrumentation footprint as compared to other imaging modalities. The method holds great promise, ranging from direct clinical use as a diagnostic or therapeutic tool, to pre-clinical applications for increased understanding of pathology. Additionally, optical imaging uses non-ionizing radiation which is safe for patients, so it can be used for repeated imaging procedures to monitor therapy, guide treatment, and provide real-time feedback. The versatile features of fluorescence-based optical imaging make it suited for ...


Sex Differences In Lower Limb Biomechanics During A Single-Leg Cut With Body Borne Load, Auralea Carylon Fain May 2018

Sex Differences In Lower Limb Biomechanics During A Single-Leg Cut With Body Borne Load, Auralea Carylon Fain

Boise State University Theses and Dissertations

Introduction: Musculoskeletal injuries are ever-increasing in military personnel, particularly females. These musculoskeletal injuries are attributed to adaptations in lower limb biomechanics while performing routine military tasks, such as a single-leg cut, with the addition of body borne load. However, it is unknown if females and males exhibit similar lower limb biomechanics with the addition of body borne load during these tasks. This study sought to compare the lower limb biomechanical adaptations exhibited by females and males performing a single-leg cut with body borne load. Methods: Eleven females and 17 males had lower limb biomechanics quantified during a single-leg cut with ...


Longitudinal Tracking Of Physiological State With Electromyographic Signals., Robert Warren Stallard May 2018

Longitudinal Tracking Of Physiological State With Electromyographic Signals., Robert Warren Stallard

Electronic Theses and Dissertations

Electrophysiological measurements have been used in recent history to classify instantaneous physiological configurations, e.g., hand gestures. This work investigates the feasibility of working with changes in physiological configurations over time (i.e., longitudinally) using a variety of algorithms from the machine learning domain. We demonstrate a high degree of classification accuracy for a binary classification problem derived from electromyography measurements before and after a 35-day bedrest. The problem difficulty is increased with a more dynamic experiment testing for changes in astronaut sensorimotor performance by taking electromyography and force plate measurements before, during, and after a jump from a small ...


Characterization Of Computed Tomography Radiomic Features Using Texture Phantoms, Muhammad Shafiq Ul Hassan Apr 2018

Characterization Of Computed Tomography Radiomic Features Using Texture Phantoms, Muhammad Shafiq Ul Hassan

Graduate Theses and Dissertations

Radiomics treats images as quantitative data and promises to improve cancer prediction in radiology and therapy response assessment in radiation oncology. However, there are a number of fundamental problems that need to be solved in order to potentially apply radiomic features in clinic. The first basic step in computed tomography (CT) radiomic analysis is the acquisition of images using selectable image acquisition and reconstruction parameters. Radiomic features have shown large variability due to variation of these parameters. Therefore, it is important to develop methods to address these variability issues in radiomic features due to each CT parameter. To this end ...


Elastin-Like Polypeptide Fusion Tag As A Protein-Dependent Solubility Enhancer Of Cysteine-Knot Growth Factors, Tamina L. Johnson Apr 2018

Elastin-Like Polypeptide Fusion Tag As A Protein-Dependent Solubility Enhancer Of Cysteine-Knot Growth Factors, Tamina L. Johnson

Graduate Theses and Dissertations

Elastin-like peptide (ELP) fusions promote therapeutic delivery and efficacy. Recombinant proteins, like neurotrophins, lack bioavailability, have short in vivo half-lives, and require high manufacturing costs. Fusing recombinant proteins with genetically encodable ELPs will increase bioavailability, enhance in vivo solubilization, as well as provide a cost-effective method for purification without the need for chromatography. During expression of neurotrophin-ELP (N-ELP) fusions, dense water-insoluble aggregates known as inclusion bodies (IBs) are formed. Inclusion bodies are partially and misfolded proteins that usually require denaturants like Urea for solubilization. Strong denaturants arrest ELPs stimuli-responsive property and increase unwanted aggregation, making purification difficult, yet possible. The ...


Diatomaceous Solar Cells, Jesse Granger Apr 2018

Diatomaceous Solar Cells, Jesse Granger

Undergraduate Honors Theses

An experiment was conducted at the college of William and Mary to explore the ability of wild type diatoms to enhance the abilities of a Dye-Sensitized Solar Cell (DSSC). The goal was to see if the efficiency of a solar cell could be enhanced by the addition of wild-type diatoms in the active layer of the cell, and if there was any notable advantage to using diatoms where the frustule material had been altered. For this purpose, diatoms were cleaned using near-boiling baths of hydrogen peroxide and then coated in Titanium Dioxide using a peptide-mediated deposition [1]. Diatoms were tested ...


Development And Characterization Of Improved Red Fluorescent Protein Variants, Premashis Manna Jan 2018

Development And Characterization Of Improved Red Fluorescent Protein Variants, Premashis Manna

Chemistry & Biochemistry Graduate Theses & Dissertations (1986-2018)

Aequorea victoria-based green fluorescent proteins and their blue, cyan and red counterparts offer unprecedented advantage as biological markers owing to their genetic encodability and straightforward expression in different organisms. Fluorescent proteins are characterized with complex photo-kinetics due to the presence of light-induced non-fluorescent or dark states which are responsible for their fluorescence intermittency or 'blinking'. We developed time- and frequency-domain techniques for probing the kinetics involving dark state conversion (DSC) and ground state recovery (GSR) in red fluorescent proteins (RFPs). Ensemble-level DSC and GSR kinetics in FPs were presented in the context of their single molecule fluorescence behaviors. Although ...


Application Of Advances In Synthetic Biology To Modular Megasynthase Design And Scalable Combinatorial Biosynthesis, William Clifford Grau Jan 2018

Application Of Advances In Synthetic Biology To Modular Megasynthase Design And Scalable Combinatorial Biosynthesis, William Clifford Grau

Chemistry & Biochemistry Graduate Theses & Dissertations (1986-2018)

The diversity in structure and biological activity of natural products has long captured the imagination of chemists and molecular biologists alike. Natural products are synthesized by elaborate secondary metabolic pathways or enzymes. For example, modular megasynthases such as Type I Polyketide Synthases (PKSs), Non-ribosomal Peptide Synthetases (NRPSs), and PKS-NRPS hybrids, produce an array of quintessential natural products. The apparent modularity, defined architecture, and predictable chemistry of modular megasynthases make them especially attractive for combinatorial biosynthesis, which has long been a focus of biotechnology. Combinatorial biosynthetic libraries are of particular interest due to the high value of many natural products and ...


Can A Comprehensive Transition Plan To Barefoot Running Be The Solution To The Injury Epidemic In American Endurance Runners?, Michael A. Scarlett Jan 2018

Can A Comprehensive Transition Plan To Barefoot Running Be The Solution To The Injury Epidemic In American Endurance Runners?, Michael A. Scarlett

CMC Senior Theses

Fossils belonging to the genus Homo, dating as far back as two million years ago, exhibit uniquely efficient features suggesting that early humans had evolved to become exceptional endurance runners. Although they did not have the cushion or stability-control features provided in our modern day running shoes, our early human ancestors experienced far less of the running-related injuries we experience today. The injury rate has been estimated as high as 90% annually for Americans training for a marathon and as high as 79% annually for all American endurance runners. There is an injury epidemic in conventionally shod populations that does ...


An Area Based Fan Beam Projection Model, Richard E. Steele, Jiehua Zhu Jan 2018

An Area Based Fan Beam Projection Model, Richard E. Steele, Jiehua Zhu

University Honors Program Theses

Area based projection models for computed tomography mitigate raw data errors by treating X-Rays as beams, whereas traditional line based projection models treat an X-Ray like a line, thus generating significant error. In an existing area based fan beam projection model, a rotation matrix, Q, simulates the rotation of the emitter detector pair to reduce computational load, but this introduces approximations by using an approximated rotation matrix. We eliminate approximations by deriving an exact formula for the entries of Q. Using a rotation of axes and by considering the neighboring cells' contributions to the area, the result has formulations for ...