Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

CALR mutation profile in Irish patients with myeloproliferative neoplasms

Insertion and/or deletion mutations of the CALR gene have recently been demonstrated to be the second most common driver mutations in the myeloproliferative neoplasms (MPNs) of essential thrombocythemia (ET) and primary myelofibrosis (PMF). Given the diagnostic and emerging prognostic significance of these mutations, in addition to the geographical heterogeneity reported, the incidence of CALR mutations was determined in an Irish cohort of patients with MPNs with a view to incorporate this analysis into a prospective screening program. A series of 202 patients with known or suspected ET and PMF were screened for the presence of CALR mutations. CALR mutations were detected in 58 patients. Type 1 and Type 1-like deletion mutations were the most common (n = 40) followed by Type 2 and Type 2-like insertion mutations (n = 17). The CALR mutation profile in Irish ET and PMF patients appears similar to that in other European populations. Establishment of this mutational profile allows the introduction of a rational, molecular diagnostic algorithm in cases of suspected ET and PMF that will improve clinical management.

The development of an algorithm to track blood pressure accurately based on the pulse transit time method

Oscillometric blood pressure (BP) monitors are currently used to diagnose hypertension both in home and clinical settings. These monitors take BP measurements once every 15 minutes over a 24 hour period and provide a reliable and accurate system that is minimally invasive. Although intermittent cuff measurements have proven to be a good indicator of BP, a continuous BP monitor is highly desirable for the diagnosis of hypertension and other cardiac diseases. However, no such devices currently exist. A novel algorithm has been developed based on the Pulse Transit Time (PTT) method, which would allow non-invasive and continuous BP measurement. PTT is defined as the time it takes the BP wave to propagate from the heart to a specified point on the body. After an initial BP measurement, PTT algorithms can track BP over short periods of time, known as calibration intervals. After this time has elapsed, a new BP measurement is required to recalibrate the algorithm. Using the PhysioNet database as a basis, the new algorithm was developed and tested using 15 patients, each tested 3 times over a period of 30 minutes. The predicted BP of the algorithm was compared to the arterial BP of each patient. It has been established that this new algorithm is capable of tracking BP over 12 minutes without the need for recalibration, using the BHS standard, a 100% improvement over what has been previously identified. The algorithm was incorporated into a new system based on its requirements and was tested using three volunteers. The results mirrored those previously observed, providing accurate BP measurements when a 12 minute calibration interval was used. This new system provides a significant improvement to the existing method allowing BP to be monitored continuously and non-invasively, on a beat-to-beat basis over 24 hours, adding major clinical and diagnostic value.

The development of new methods for high resolution radio astronomy imaging

Very Long Baseline Interferometry (VLBI) polarisation observations of the relativistic jets from Active Galactic Nuclei (AGN) allow the magnetic field environment around the jet to be probed. In particular, multi-wavelength observations of AGN jets allow the creation of Faraday rotation measure maps which can be used to gain an insight into the magnetic field component of the jet along the line of sight. Recent polarisation and Faraday rotation measure maps of many AGN show possible evidence for the presence of helical magnetic fields. The detection of such evidence is highly dependent both on the resolution of the images and the quality of the error analysis and statistics used in the detection. This thesis focuses on the development of new methods for high resolution radio astronomy imaging in both of these areas. An implementation of the Maximum Entropy Method (MEM) suitable for multi-wavelength VLBI polarisation observations is presented and the advantage in resolution it possesses over the CLEAN algorithm is discussed and demonstrated using Monte Carlo simulations. This new polarisation MEM code has been applied to multi-wavelength imaging of the Active Galactic Nuclei 0716+714, Mrk 501 and 1633+382, in each case providing improved polarisation imaging compared to the case of deconvolution using the standard CLEAN algorithm. The first MEM-based fractional polarisation and Faraday-rotation VLBI images are presented, using these sources as examples. Recent detections of gradients in Faraday rotation measure are presented, including an observation of a reversal in the direction of a gradient further along a jet. Simulated observations confirming the observability of such a phenomenon are conducted, and possible explanations for a reversal in the direction of the Faraday rotation measure gradient are discussed. These results were originally published in Mahmud et al. (2013). Finally, a new error model for the CLEAN algorithm is developed which takes into account correlation between neighbouring pixels. Comparison of error maps calculated using this new model and Monte Carlo maps show striking similarities when the sources considered are well resolved, indicating that the method is correctly reproducing at least some component of the overall uncertainty in the images. The calculation of many useful quantities using this model is demonstrated and the advantages it poses over traditional single pixel calculations is illustrated. The limitations of the model as revealed by Monte Carlo simulations are also discussed; unfortunately, the error model does not work well when applied to compact regions of emission.

Development and reliability of a direct access sensor using flip chip on flex technology with anisotropic conductive adhesive

Technological developments in biomedical microsystems are opening up new opportunities to improve healthcare procedures. Swallowable diagnostic sensing capsules are an example of these. In none of the diagnostic sensing capsules, is the sensor’s first level packaging achieved via Flip Chip Over Hole (FCOH) method using Anisotropic Conductive Adhesive (ACA). In a capsule application with direct access sensor (DAS), ACA not only provides the electrical interconnection but simultaneously seals the interconnect area and the underlying electronics. The development showed that the ACA FCOH was a viable option for the DAS interconnection. Adequate adhesive formed a strong joint that withstood a shear stress of 120N/mm2 and a compressive stress of 6N required to secure the final sensor assembly in place before encapsulation. Electrical characterization of the ACA joint in a fluid environment showed that the ACA was saturated with moisture and that the ions in the solution actively contributed to the leakage current, characterized by the varying rate of change of conductance. Long term hygrothermal aging of the ACA joint showed that a thermal strain of 0.004 and a hygroscopic strain of 0.0052 were present and resulted in a fatigue like process. In-vitro tests showed that high temperature and acidity had a deleterious effect of the ACA and its joint. It also showed that the ACA contact joints positioned at around or over 1mm would survive the gastrointestinal (GI) fluids and would be able to provide a reliable contact during the entire 72hr of the GI transit time. A final capsule demonstrator was achieved by successfully integrating the DAS, the battery and the final foldable circuitry into a glycerine capsule. Final capsule soak tests suggested that the silicone encapsulated system could survive the 72hr gut transition.

Iterative reconstruction as a novel method of radiation dose reduction at computed tomography in patients with Crohn's disease

Prior work of our research group, that quantified the alarming levels of radiation dose to patients with Crohn’s disease from medical imaging and the notable shift towards CT imaging making these patients an at risk group, provided context for this work. CT delivers some of the highest doses of ionising radiation in diagnostic radiology. Once a medical imaging examination is deemed justified, there is an onus on the imaging team to endeavour to produce diagnostic quality CT images at the lowest possible radiation dose to that patient. The fundamental limitation with conventional CT raw data reconstruction was the inherent coupling of administered radiation dose with observed image noise – the lower the radiation dose, the noisier the image. The renaissance, rediscovery and refinement of iterative reconstruction removes this limitation allowing either an improvement in image quality without increasing radiation dose or maintenance of image quality at a lower radiation dose compared with traditional image reconstruction. This thesis is fundamentally an exercise in optimisation in clinical CT practice with the objectives of assessment of iterative reconstruction as a method for improvement of image quality in CT, exploration of the associated potential for radiation dose reduction, and development of a new split dose CT protocol with the aim of achieving and validating diagnostic quality submillisiever t CT imaging in patients with Crohn’s disease. In this study, we investigated the interplay of user-selected parameters on radiation dose and image quality in phantoms and cadavers, comparing traditional filtered back projection (FBP) with iterative reconstruction algorithms. This resulted in the development of an optimised, refined and appropriate split dose protocol for CT of the abdomen and pelvis in clinical patients with Crohn’s disease allowing contemporaneous acquisition of both modified and conventional dose CT studies. This novel algorithm was then applied to 50 patients with a suspected acute complication of known Crohn’s disease and the raw data reconstructed with FBP, adaptive statistical iterative reconstruction (ASiR) and model based iterative reconstruction (MBIR). Conventional dose CT images with FBP reconstruction were used as the reference standard with which the modified dose CT images were compared in terms of radiation dose, diagnostic findings and image quality indices. As there are multiple possible user-selected strengths of ASiR available, these were compared in terms of image quality to determine the optimal strength for this modified dose CT protocol. Modified dose CT images with MBIR were also compared with contemporaneous abdominal radiograph, where performed, in terms of diagnostic yield and radiation dose. Finally, attenuation measurements in organs, tissues, etc. with each reconstruction algorithm were compared to assess for preservation of tissue characterisation capabilities. In the phantom and cadaveric models, both forms of iterative reconstruction examined (ASiR and MBIR) were superior to FBP across a wide variety of imaging protocols, with MBIR superior to ASiR in all areas other than reconstruction speed. We established that ASiR appears to work to a target percentage noise reduction whilst MBIR works to a target residual level of absolute noise in the image. Modified dose CT images reconstructed with both ASiR and MBIR were non-inferior to conventional dose CT with FBP in terms of diagnostic findings, despite reduced subjective and objective indices of image quality. Mean dose reductions of 72.9-73.5% were achieved with the modified dose protocol with a mean effective dose of 1.26mSv. MBIR was again demonstrated superior to ASiR in terms of image quality. The overall optimal ASiR strength for the modified dose protocol used in this work is ASiR 80%, as this provides the most favourable balance of peak subjective image quality indices with less objective image noise than the corresponding conventional dose CT images reconstructed with FBP. Despite guidelines to the contrary, abdominal radiographs are still often used in the initial imaging of patients with a suspected complication of Crohn’s disease. We confirmed the superiority of modified dose CT with MBIR over abdominal radiographs at comparable doses in detection of Crohn’s disease and non-Crohn’s disease related findings. Finally, we demonstrated (in phantoms, cadavers and in vivo) that attenuation values do not change significantly across reconstruction algorithms meaning preserved tissue characterisation capabilities with iterative reconstruction. Both adaptive statistical and model based iterative reconstruction algorithms represent feasible methods of facilitating acquisition diagnostic quality CT images of the abdomen and pelvis in patients with Crohn’s disease at markedly reduced radiation doses. Our modified dose CT protocol allows dose savings of up to 73.5% compared with conventional dose CT, meaning submillisievert imaging is possible in many of these patients.

Development and optimisation of photonic crystal based nanosensors

This thesis involved the development of two Biosensors and their associated assays for the detection of diseases, namely IBR and BVD for veterinary use and C1q protein as a biomarker to pancreatic cancer for medical application, using Surface Plasmon Resonance (SPR) and nanoplasmonics. SPR techniques have been used by a number of groups, both in research [1-3] and commercially [4, 5] , as a diagnostic tool for the detection of various biomolecules, especially antibodies [6-8]. The biosensor market is an ever expanding field, with new technology and new companies rapidly emerging on the market, for both human [8] and veterinary applications [9, 10]. In Chapter 2, we discuss the development of a simultaneous IBR and BVD virus assay for the detection of antibodies in bovine serum on an SPR-2 platform. Pancreatic cancer is the most lethal cancer by organ site, partially due to the lack of a reliable molecular signature for diagnostic testing. C1q protein has been recently proposed as a biomarker within a panel for the detection of pancreatic cancer. The third chapter discusses the fabrication, assays and characterisation of nanoplasmonic arrays. We will talk about developing C1q scFv antibody assays, clone screening of the antibodies and subsequently moving the assays onto the nanoplasmonic array platform for static assays, as well as a custom hybrid benchtop system as a diagnostic method for the detection of pancreatic cancer. Finally, in chapter 4, we move on to Guided Mode Resonance (GMR) sensors, as a low-cost option for potential use in Point-of Care diagnostics. C1q and BVD assays used in the prior formats are transferred to this platform, to ascertain its usability as a cost effective, reliable sensor for diagnostic testing. We discuss the fabrication, characterisation and assay development, as well as their use in the benchtop hybrid system.