Understanding the gas phase flow and transport of volatile organic compounds (VOCs) in unsaturated zones is indispensable to develop effective environmental remediation strategies, to create precautions for fresh water protection, and to provide guidance for land and water resources management. Atmospheric pressure and water table fluctuations are two important natural processes at the upper and lower boundaries of the unsaturated zone, respectively. However, their significance has been neglected in previous studies. This dissertation systematically investigates their influence on the gas phase flow and transport of VOCs in soil and ground water remediation processes using analytically and numerically mathematical modeling. New semi-analytical and numerical solutions are developed to calculate the subsurface gas flow field and the gas phase transport of VOCs in active soil vapor extraction (SVE), barometric pumping (BP) and natural attenuation taking into account the atmospheric pressure and the water table fluctuations. The accuracy of the developed solutions are checked by comparing with published analytical solutions under extreme conditions, newly developed numerical solutions in COMSOL Multiphysics and field measured data. Results indicate that both the atmospheric pressure and the tidal-induced water table fluctuations significantly change the gas flow field in active SVE, especially when the vertical gas permeability is small (less than 0.4 Darcy). The tidal-induced downward moving water table increases the depth-averaged radius of influence (ROI) for the gas pumping well. However, this downward moving water table leads to a greater vertical pore gas velocity away from the gas pumping well, which is unfavorable for removing VOCs. The gas flow rate to/from the barometric pumping well can be accurately calculated by our newly developed solutions in both homogeneous and multi-layered unsaturated zones. Under natural unsaturated zone conditions, the time-averaged advective flux of the gas phase VOCs induced by the atmospheric pressure and water table fluctuations is one to three orders of magnitude less than the diffusive flux. The time-averaged advective flux is comparable with the diffusive flux only when the gas-filled porosity is very small (less than 0.05). The density-driven flux is negligible.

Single frame ultrasound B-mode image quality is largely governed by the ability to focus the ultrasound beam over a range in depths both in transmission and reception. By developing a comprehensive understanding of acoustic wave propagation two signal processing methods were identified for solving the transmission problem. We made use of both the impulse response using the classical point spread function (PSF) and the spatial sensitivity function (SSF) which describes the spatial distribution at a particular time. Using the angular spectrum method, an accurate analytical model was developed for the field distribution arising from a finite geometry, apodized and focused, plane piston transducer. While there is a thorough understanding of the radiated field arising from uniformly excited plane piston transducers, the focused equivalent (i.e., one that allows a continuous change in phase over the plane piston surface) is incomplete and assumes the Fresnel approximation. Our model addresses the effects of diffraction and evanescent waves without the use of the Fresnel approximation and is applicable at all near- and far-field locations in a lossless medium. The model was analyzed to identify new insights into wave propagation and compared with the Fresnel approximation and the spherically-focused, concave transducer. The piston transducer model was then extended to an attenuating and dispersive medium. After analysing existing models of power-law frequency dependent attenuation, a causal, spherical wave Green’s function was derived from the Navier-Stokes equation for a classical viscous medium. Modifications to the angular spectrum method were presented and used to analyze the radiated field of a focused, planar piston transducer. Finally, after presenting our signal processing strategy for improving imaging spatial resolution through minimization of the SSF, two signal processing methods were derived and analysed in simulation: a deconvolution technique to remove the effects of the ultrasound excitation wave and suppress additive noise from the received ultrasound signal, and a retrospective transmit focusing method that changed the response from a predefined transmit focus to an arbitrary transmit focal depth. Proof-of-concept simulations were presented using a variable number of scatterers and compared with the traditional matched filtering and envelope detection technique.

Although higher correlation between gauge and radar at hourly or daily accumulations are reported, it is rarely observed at higher time resolution (e.g. 10 -minute). This study investigates six major rainfall events in year 2000 in the greater Winnipeg area with durations varying from four to nine hours. The correlation between gauge and radar measurements of precipitation is found to be only 0.3 at 10-minute resolution and 0.55 at hourly resolution using Marshall-Palmer’s Z-R relationship (Z=200R1.6). The rainfalls are classified into convective and stratiform regions using Steiner et al. (1995)’s algorithm and two different Z-R relationships are tested to minimize the error associated with the variability of drop-size-distribution, however no improvement is observed. The performance of the artificial neural network is explored as a reflectivity-rainfall mapping function. Three different types of neural networks are explored: the back propagation network, the radial basis function network, and the generalized regression neural network. It is observed that the neural network’s performance is better than the Z-R relationship to estimate the rainfall events which was used for training and validation (correlation 0.67). When this network is tested on a new rainfall its performance is found quite similar to that obtained from the Z-R relationship (correlation 0.33). Based on this observation neural network may be recommended as a post-processing tool but may not be very useful for operational purposes - at least as used in this study. Variability in weather and precipitation scenarios affects the radar measurements which apparently makes it impossible for the neural network or the Z-R relationship to show consistent performance at every rainfall event. To account for variability in weather and rainfall scenarios conventional correction schemes for attenuation and hail contamination are applied and a trajectory model is developed to account for rainfall advection due to wind drift. The trajectory model uses velocity obtained from the single-doppler observation. A space-time interpolation technique is applied to generate reflectivity maps at one-minute resolution based on the direction obtained from the correlation based tracking algorithm. The trajectory model uses the generated reflectivity maps having one-minute resolution which help to account for the travel time by the rainfall mass to reach to the ground. It was found that the attenuation correction algorithm adversely increases the reflectivity. This study assumes that the higher reflectivity caused by hail contaminated regions is one reason for the overestimation in the attenuation correction process. It was observed that the hail capping method applied prior to the attenuation correction algorithm helps to improve the situation. A statistical expression to account for radome attenuation is also developed. It is observed that the correlation between the gauge and the radar measurement is 0.81 after applying the various algorithms. Although Marshall-Palmer’s relationship is recommended for stratiform precipitation only, this study found it suitable for both convective and stratiform precipitation when attenuation is properly taken into account. The precipitation processing model developed in this study generates more accurate rainfall estimates at the surface from radar observations and may be a better choice for rainfall-runoff modellers.

The purpose of this study is to develop probabilistic hazard maps for EskiSehir including &lsquo / Peak Ground Acceleration&rsquo / values for 10% probability of exceedance in 50-year and 100-year periods at different site classes. A seismotectonic map has been prepared in the Geographical Information Systems environment by compiling instrumental seismicity and neotectonic data for the study area. The seismic sources have been defined spatially in six areal zones, characterized by a commonly used recurrence law and a maximum magnitude value. Four attenuation relationships have been selected being one of them totaly developed from the strong-motion records of Turkey. After the implementation of a seismic hazard model by using SEISRISK software, the probabilistic seismic hazard curves and maps were developed based on the selected attenuation relationships, at &lsquo / rock&rsquo / and &lsquo / soil&rsquo / sites, with a probability of exceedance of 10% in 50-year and 100-year periods. At rock sites the highest levels of hazard were calculated based on the predictive relationship of Abrahamson and Silva (1996), whereas the lowest ones based on the one of Boore et al. (1996). On the other hand the highest hazard levels were determined at soil sites based on the attenuation relationship of Ambraseys et al. (1996), whereas the lowest ones based on the one of Boore et al. (1997). For EskiSehir, the peak ground acceleration values calculated based on attenuation relationship by Boore et al. (1997) were found to be applicable for 10% probability of exceedance in 50 and 100 years, taking into consideration the fact that a considerable portion of the city is founded over alluviums.

Natural Attenuation can be an effective cleanup option for remediation of Groundwater contamination by BTEX. One of the important aspects of the methodology that has been recognized recently is that mass removal rates, the most important parameters used to determine effectiveness of the methodology, is controlled by groundwater flow regime, which to a large extent controlled by aquifer heterogeneity. Considering this recognition, the primary objective of this research is to quantitatively describe the relationship between natural attenuation rates of BTEX and aquifer heterogeneity using numerical solution techniques. To represent different levels of aquifer heterogeneity, hydraulic conductivity distributions are simulated using Turning Bands Algorithm, changing statistical parameters Coefficient of Variation (CV) and correlation length (h). Visual MODFLOW is used to model the transport of BTEX contamination, at different hydraulic conductivity fields. Degradation rates are calculated by Buscheck&amp / Alcantar and Conservative Tracer Methods. The results show that, for a given h, as CV increases, the plume slows down and stays longer at the domain, so areal extent of plume decreases. For anisotropic field, plumes are more dispersed along x and y-direction, and areal extents of the plumes are greater. During MNA feasibility studies, for the aquifer heterogeneity level of CV and h smaller than 100 % and 10 m, respectively, a minimum recommended biodegradation rate constant of 0.02 d-1 can be used, whereas for the aquifer heterogeneity level of CV and h greater than 100 % and 10 m, respectively, using a minimum biodegradation rate constant of 0.06 d-1 can be recommended.

Monitored natural attenuation has been particularly used at sites where petroleum hydrocarbons and chlorinated solvents have contaminated soil and groundwater. One of the important aspects of the methodology that has been recognized recently is that the mass removal rates, the most important parameter to determine effectiveness of the methodology, is controlled by the groundwater flow regime and the aquifer heterogeneity. Considering this recognition, the primary objective of this study is to quantitatively describe the relationship between the natural attenuation rates and aquifer heterogeneity using numerical simulation techniques. To represent different levels of aquifer heterogeneity, the hydraulic conductivity distribution (ln K) is statistically simulated with the numerical algorithm, Turning Bands Random Field Generator, by changing the statistical parameters, Coefficient of Variation (CV) and correlation length (h) and Visual MODFLOW and RT3D software programs are used for the simulation of groundwater flow and chlorinated solvent transport. Simulation results showed that degradation rates and the shape of the contaminant plumes show variations for different heterogeneity levels. Increasing CV resulted in the decrease in the transport of the plume and shrinkage in the areal extend. On the other hand, &ldquo / h&rdquo / determined the shape and the size of the plume through its affect on mechanical dispersion. For a given &ldquo / h&rdquo / , degradation rates increased with increasing CV, but change in &ldquo / h&rdquo / did not show a regular trend. Such findings are expected to be beneficial when assessing the effectiveness of natural attenuation process for a selected site during the feasibility studies without need for detailed site characterization.

The goal of this thesis is to investigate the biophysical basis underlying the nonlinear relationship between firing response and current stimulation in single motor neurons. After reviewing the relevant motoneuron physiology and theories that describe complex dendritic signaling properties, I hypothesize that at least five passive electrical properties must be considered to better understand the physiological input-output properties of motor neurons in vivo: input resistance, system time constant, and three signal propagation properties between the soma and dendrites that depend on the signal direction (i.e. soma to dendrites or vice versa) and type (i.e. direct (DC) or alternating (AC) current). To test my hypothesis, I begin with characterizing the signal propagation of the dendrites, by directly measuring voltage attenuations along the path of dendrites of the type-identified anatomical neuron models. Based on this characterization of dendritic signaling, I develop the novel realistic reduced modeling approach by which the complex geometry and passive electrical properties of anatomically reconstructed dendrites can be analytically mapped into simple two-compartment modeling domain without any restrictive assumptions. Combining mathematical analysis and computer simulations of my new reduced model, I show how individual biophysical properties (system input resistance, time constant and dendritic signaling) contribute to the local excitability of the dendrites, which plays an essential role in activating the plateau generating membrane mechanisms and subsequent nonlinear input-output relations in a single neuron. The biophysical theories and computer simulations in this thesis are primarily applied to motor neurons that compose the motor neuron pool for control of movement. However, the general features of the new reduced neuron modeling approach and important insights into neuronal computations are not limited to this area. My findings can be extended to other areas including artificial neural networks consisting of single compartment processors. / Medical Sciences – Biomedical Engineering

The images in positron emission tomography (PET) represent three dimensional dynamic distributions of biologically interesting molecules labelled with positron emitting radionuclides (radiotracers). Spatial localisation of the radio-tracers is achieved by detecting in coincidence two collinear photons which are emitted when the positron annihilates with an ordinary electron. In order to obtain quantitatively accurate images in PET, it is necessary to correct for the effects of photon attenuation within the subject being imaged. These corrections can be obtained using singles-mode photon transmission scanning. Although suitable for small animal PET, these scans are subject to high amounts of contamination from scattered photons. Currently, no accurate correction exists to account for scatter in these data. The primary purpose of this work was to implement and validate an analytical scatter correction for PET transmission scanning. In order to isolate the effects of scatter, we developed a simulation tool which was validated using experimental transmission data. We then presented an analytical scatter correction for singles-mode transmission data in PET. We compared our scatter correction data with the previously validated simulation data for uniform and non-uniform phantoms and for two different transmission source radionuclides. Our scatter calculation correctly predicted the contribution from scattered photons to the simulated data for all phantoms and both transmission sources. We then applied our scatter correction as part of an iterative reconstruction algorithm for simulated and experimental PET transmission data for uniform and non-uniform phantoms. We also tested our reconstruction and scatter correction procedure using transmission data for several animal studies (mice, rats and primates). For all studies considered, we found that the average reconstructed linear attenuation coefficients for water or soft-tissue regions of interest agreed with expected values to within 4%. Using a 2.2 GHz processor, the scatter correction required between 6 to 27 minutes of CPU time (without any code optimisation) depending on the phantom size and source used. This extra calculation time does not seem unreasonable considering that, without scatter corrections, errors in the reconstructed attenuation coefficients were between 18 to 45% depending on the phantom size and transmission source used.

Aim: The past two decades have seen a large body of work dedicated to the development of a three dimensional gel dosimetry system for the recording of radiation dose distributions in radiation therapy. The purpose of much of the work to date has been to improve methods by which the absorbed dose information is extracted. Current techniques include magnetic resonance imaging (MRI), optical tomography, Raman spectroscopy, x-ray computed tomography (CT) and ultrasound. This work examines CT imaging as a method of evaluating polymer gel dosimeters. Apart from publications resulting from this work, there has been only two other journal articles to date reporting results of CT gel dosimetry. This indicates that there is still much work required to develop the technique. Therefore, the aim of this document is to develop CT gel dosimetry to the extent that it is of use to clinical and research physicists. Scope: Each chapter in this document describes an aspect of CT gel dosimetry which was examined; with Chapters 2 to 7 containing brief technical backgrounds for each aspect. Chapter 1 contains a brief review of gel dosimetry. The first step in the development of any method for reading a signal is to determine whether the signal can actually be obtained. However, before polymer gel dosimeters can be imaged using a CT scanner, imaging techniques are required which are employable to obtain reliable readings. Chapter 2 examines the various artifacts inherent in CT which interfere with the quantitative analysis of gel dosimeters and a method for their removal is developed. The method for artifact reduction is based on a subtraction technique employed previously in a feasibility study and a system is designed to greatly simplify the process. The simplification of the technique removes the requirement for accurate realignment of the phantom within the scanner and the imaging of calibration vials is enabled. Having established a method by which readings of polymer gel dosimeters can be obtained with CT, Chapter 3 examines the CT dose response. A number of formulations of polymer gel dosimeter are studied by varying the constituent chemicals and their concentrations. The results from this chapter can be employed to determine the concentration of chemicals when manufacturing a polymer gel dosimeter with a desired CT dose response. With the CT dose response characterised in Chapter 3, the macroscopic cause of the CT signal is examined in Chapter 4. To this end direct measurement of the linear attenuation coefficient is obtained with a collimated radiation source and detector. Density is measured by Archimedes' principle. Comparison of the two results shows that the cause of the CT signal is a density change and the implications for polymer gel dosimetry are discussed. The CT scanner is revisited in Chapter 5 to examine the CT imaging techniques required for optimal performance. The main limitation of the use of CT in gel dosimetry to date has been image noise. In Chapter 5 stochastic noise is investigated and reduced. The main source of non-stochastic noise in CT is found and imaging techniques are examined which can greatly reduce this residual noise. Predictions of computer simulations are verified experimentally. Although techniques for the reduction of noise are developed in Chapter 5, there may be situations where the noise must be further reduced. An image processing algorithm is designed in Chapter 6 which employs a combination of commonly available image filters. The algorithm and the filters are tested for their suitability in gel dosimetry through the use of a simulated dose distribution and by performing a pilot study on an irradiated polymer gel phantom. Having developed CT gel dosimetry to the point where a suitable image can be obtained, the final step is to investigate the uncertainty in the dose calibration. Methods used for calibration uncertainty in MRI gel dosimetry to date have either assumed a linear response up to a certain dose, or have removed the requirement for linearity but incorrectly ignored the reliability of the data and fit of the calibration function. In Chapter 7 a method for treatment of calibration data in CT gel dosimetry is proposed which allows for non-linearity of the calibration function, as well as the goodness of its fit to the data. Alternatively, it allows for the reversion to MRI techniques if linearity is assumed in a limited dose range. Conclusion: The combination of the techniques developed in this project and the newly formulated normoxic gels (not extensively studied here) means that gel dosimetry is close to becoming viable for use in the clinic. The only capital purchase required for a typical clinic is a suitable water tank, which is easily and inexpensively producible if the clinic has access to a workshop.

Partial saturation of porous rock by two fluids substantially affects compressional wave propagation. In particular, partial saturation causes significant attenuation and dispersion due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. When partial saturation is mesoscopic, i.e. existing on a length scale much greater than pore scale but less than wavelength scale, significant attenuation can arise for frequencies 10-1000 Hz. Models for attenuation and dispersion due to mesoscale heterogeneities mostly assume fluids are distributed in a regular way. Recent experiments indicate mesoscopic heterogeneities have less idealised distributions and distribution affects attenuation/dispersion. Thus, theoretical models are required to simulate effects due to realistic fluid distributions. / The thesis focus is to model attenuation and dispersion due to realistic mesoscopic fluid distributions and fluid contrasts. First X-ray tomographic images of partially saturated rock are analysed statistically to identify spatial measures useful for describing fluid distribution patterns. The correlation function and associated correlation length for a specific fluid type are shown to be of greatest utility. Next a new model, called 3DCRM (CRM stands for continuous random media) is derived, utilizing a correlation function to describe the fluid distribution pattern. It is a random media model, is accurate for small fluid contrast and approximate for large fluid contrast. Using 3DCRM attenuation and dispersion are shown to depend on fluid distribution. / Next a general framework for partial saturation called APS (acoustics of partial saturation) is extended enabling estimation of attenuation and dispersion due to arbitrary 1D/3D fluid distributions. The intent is to construct a versatile model enabling attenuation and dispersion to be estimated for arbitrary fluid distributions, contrasts and saturations. Two crucial parameters within APS called shape and frequency scaling parameters are modified via asymptotic analysis using several random media models (which are accurate for only certain contrasts in fluid bulk moduli and percent saturation). For valid fluid contrasts and saturations, which satisfy certain random media conditions there is good correspondence between modified APS and the random media models, hence showing that APS can be utilized to model attenuation and dispersion due to more realistic fluid distributions. / Finally I devise a numerical method to test the accuracy of the analytical shape parameters for a range of fluid distributions, saturations and contrasts. In particular, the analytical shape parameter for randomly distributed spheres was shown to be accurate for a large range of saturations and fluid contrasts.