State Variable Model for Unsteady Two Dimensional Axial Vortex Flow with Pressure Relaxation

This research has utilized a state variable model for unsteady two dimensional axial vortex flows experiencing non-equilibrium pressure gradient forces. The model was developed successfully using perturbed radial and azimuthal momentum equations and a pressure Poisson\u27s equations. Three main regions of the axial vortex flow were highlighted in this study including: a laminar core region, a non-equilibrium pressure envelope, and an outer potential vortex. Linear stability theory was utilized to formulate the model and the perturbation functions were assumed to be of the Fourier type. The flow parameters considered were the Reynolds numbers, ranging between 6,000 and 14,000, and a new non-equilibrium swirl parameter, Np determining the area of significant non-equilibrium pressure forces. Two other state variable parameters were imposed-complex frequency and associated azimuthal mode number. Perturbation outputs included primary Reynolds stress, radial and azimuthal velocity amplitudes, and radial pressure gradient amplitudes. Maximum perturbation growth occurred inside the non-equilibrium pressure zone between one and five core radii from the rotational axis, while the inner core remained laminar. The maximum amplitudes and critical radii depended on the four physical and state variable parameters. Increases in Np resulted in lower perturbation pressure gradient amplitudes, moving the critical radius closer to the vortex core, and expanding the non-equilibrium pressure zone. Increasing the frequency resulted in steady increases in the perturbation amplitudes until a particular dimensionless frequency was reached. Beyond that frequency, additional perturbation growth was insignificant or the amplitude decayed because of a high damping factor. Two types of azimuthal modes were unstable, the ±½ modes inside the non-equilibrium pressure zone, causing the pressure gradient amplitudes to peak even though the azimuthal velocity profile remained stable, and ± 1 helical modes associated with growing pressure gradient amplitudes in the outer potential region. The symmetrical azimuthal modes were globally stable. The state variable model was stable numerically inside the non-equilibrium pressure zone, even though the perturbation amplitudes exhibited instability. Inside that region, unstable pressure eigenmodes were detected in the form of relaxation Reynolds stresses in response to perturbations in the flow. The width of the non-equilibrium pressure zone was again determined using eigenmode plots for different Np. The positive real parts of the unstable modes were slightly larger in the outer potential region causing slow growth profiles. The current vortex state variable model can be utilized to explore the development of small perturbations in the non-equilibrium zone as the flow becomes turbulent, via a bifurcation cycle study where coherent structures can be identified. Experimental verification using hot-wire probes is needed to validate the theory and adjust the state variable model parameters. A side effect of the non-equilibrium pressure model for this vortical flow is the likely sound propagation causing small density perturbations that are balanced by the contracted pressure gradient-velocity tensor terms in the pressure relaxation equations. This non-equilibrium balance process appears to vanish in the outer potential vortex region

Segmentation-Free Statistical Image Reconstruction for Polyenergetic X-Ray Computed Tomography

This paper describes a statistical iterative reconstruction method for X-ray CT based on a physical model that accounts for the polyenergetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. The algorithm accommodates mixtures of tissues with known mass attenuation coefficients but unknown densities. We formulate a penalized-likelihood approach for this polyenergetic model based on Poisson statistics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85881/1/Fessler173.pd

Statistical X-Ray-Computed Tomography Image Reconstruction with Beam- Hardening Correction

This paper describes two statistical iterative reconstruction methods for X-ray CT. The rst method assumes a mono-energetic model for X-ray attenuation. We approximate the transmission Poisson likelihood by a quadratic cost function and exploit its convexity to derive a separable quadratic surrogate function that is easily minimized using parallelizable algorithms. Ordered subsets are used to accelerate convergence. We apply this mono-energetic algorithm (with edge-preserving regularization) to simulated thorax X-ray CT scans. A few iterations produce reconstructed images with lower noise than conventional FBP images at equivalent resolutions. The second method generalizes the physical model and accounts for the poly-energetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume the object consists of a given number of nonoverlapping tissue types. The attenuation coeÆcient of each tissue is the product of its unknown density and a known energy-dependent mass attenuation coeÆcient. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown densities in each voxel. Applying this method to simulated X-ray CT measurements of a phantom containing both bone and soft tissue yields images with signi cantly reduced beam hardening artifacts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85939/1/Fessler165.pd

Efficient and Accurate Llikelihood for Iterative Image Reconstruction in X-Ray Computed Tomography

We report a novel approach for statistical image reconstruction in X-ray CT. Statistical image reconstruction depends on maximizing a likelihood derived from a statistical model for the measurements. Traditionally, the measurements are assumed to be statistically Poisson, but more recent work has argued that CT measurements actually follow a compound Poisson distribution due to the polyenergetic nature of the X-ray source. Unlike the Poisson distribution, compound Poisson statistics have a complicated likelihood that impedes direct use of statistical reconstruction. Using a generalization of the saddle-point integration method, we derive an approximate likelihood for use with iterative algorithms. In its most realistic form, the approximate likelihood we derive accounts for polyenergetic X-rays and Poisson light statistics in the detector scintillator, and can be extended to account for electronic additive noise. The approximate likelihood is closer to the exact likelihood than is the conventional Poisson likelihood, and carries the promise of more accurate reconstruction, especially in low X-ray dose situations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85924/1/Fessler182.pd

Advances on Dientamoeba fragilis Infections

Dientamoeba fragilis is an enteric protozoan parasite that remains neglected, probably due to the misconception that it is uncommon and non-pathogenic. As more information became available and antimicrobial agents were developed with activity against this parasite, it became clear that D. fragilis is responsible of an active infection, associated with symptoms such as abdominal pain and diarrhea. The clinical presentation of dientamoebiasis varies from asymptomatic carriage to symptoms ranging from altered bowel motions, abdominal discomfort, nausea and diarrhea with associated eosinophilia reported in up to 50% of paediatric and 10% of adult patients. Moreover, controversy exists over the protective role of the parasite in priming the immune system in a beneficial way such as in selecting beneficial bacteria, keeping potential harmful microbial intruders at bay or producing metabolites beneficial to the host. Thus, a number of ambiguities and obscurities surrounding D. fragilis infections exist. Moreover, the means by which this parasite is transmitted has not been fully defined. The diagnostic recognition of this parasite in fecal examinations requires specific processing and expertise; thus, it is possible that many infections with D. fragilis may go undiagnosed. A number of studies conducted on small numbers of case reports have demonstrated parasite clearance, as well as resolution of clinical symptoms following treatment with various antiparasitic compounds such as paromomycin, hydroxyquinolines and the 5-nitroimidazoles, including metronidazole and tinidazole. In addition there is very little in vitro susceptibility data available for the organism making some current treatment options questionable. This chapter reviews the scientific literature relating to Dientamoeba\u27s life cycle, prevalence, diagnosis and pathogenicity

Statistical Image Reconstruction for Polyenergetic X-Ray Computed Tomography

This paper describes a statistical image reconstruction method for X-ray computed tomography (CT) that is based on a physical model that accounts for the polyenergetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume that the object consists of a given number of nonoverlapping materials, such as soft tissue and bone. The attenuation coefficient of each voxel is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this polyenergetic model and develop an ordered-subsets iterative algorithm for estimating the unknown densities in each voxel. The algorithm monotonically decreases the cost function at each iteration when one subset is used. Applying this method to simulated X-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85895/1/Fessler74.pd

Segmentation-Free Statistical Image Reconstruction for Polyenergetic X-Ray Computed Tomography with Experimental Validation

This paper describes a statistical image reconstruction method for x-ray CT that is based on a physical model that accounts for the polyenergetic x-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. Unlike our earlier work, the proposed algorithm does not require pre-segmentation of the object into the various tissue classes (e.g., bone and soft tissue) and allows mixed pixels. The attenuation coefficient of each voxel is modelled as the product of its unknown density and a weighted sum of energy-dependent mass attenuation coefficients. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown density of each voxel. Applying this method to simulated x-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artefacts relative to conventional beam hardening correction methods. We also apply the method to real data acquired from a phantom containing various concentrations of potassium phosphate solution. The algorithm reconstructs an image with accurate density values for the different concentrations, demonstrating its potential for quantitative CT applications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85911/1/Fessler66.pd

Interval Estimates for Parameters of Discrete Sampling Distributions

Well recommended methods of forming confidence intervals for discrete distributions parameter give interval estimates that do not actually meet the definition of a confidence interval, in that their coverage is sometimes lower than the nominal confidence level. The methods are favored because their intervals have a shorter average length than the exact method, whose intervals really are confidence intervals. Comparison of such methods is tricky as the best method should perhaps be the one that gives the shortest intervals (on average), but when is the coverage of a method so poor it should not be classed as a means of forming confidence interval. As the definition of a confidence interval is being flouted, a better criterion for forming interval estimates for discrete distributions parameters is needed. The aim of this thesis is to suggest a new criterion: methods that meet the criterion are said to yield locally correct confidence intervals. We propose a method that yields such intervals and proves that its intervals have a shorter average length than those of any other method that meets the criterion. We refer to the new estimator as the optimal locally correct method or just the OLC method. The thesis begins by applying the new criterion and method to the binomial parameter. Then we extend the method so as to obtain locally correct confidence intervals for parameters of the Poisson distribution and the negative binomial distribution

Maximum-Likelihood Dual-Energy TomographicImage Reconstruction

Dual-energy (DE) X-ray computed tomography (CT) has shown promise for material characterization and for providing quantitatively accurate CT values in a variety of applications. However, DE-CT has not been used routinely in medicine to date, primarily due to dose considerations. Most methods for DE-CT have used the filtered backprojection method for image reconstruction, leading to suboptimal noise/dose properties. This paper describes a statistical (maximum-likelihood) method for dual-energy X-ray CT that accommodates a wide variety of potential system configurations and measurement noise models. Regularized methods (such as penalized-likelihood or Bayesian estimation) are straightforward extensions. One version of the algorithm monotonically decreases the negative log-likelihood cost function each iteration. An ordered-subsets variation of the algorithm provides a fast and practical version.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85934/1/Fessler172.pd