Computational Electromagnetic Methods for Transcranial Magnetic Stimulation.

Transcranial magnetic stimulation (TMS) is a noninvasive technique used both as a research tool for cognitive neuroscience and as a FDA approved treatment for depression. During TMS, coils positioned near the scalp generate electric fields and activate targeted brain regions. In this thesis, several computational electromagnetics methods that improve the analysis, design, and uncertainty quantification of TMS systems were developed. Analysis: A new fast direct technique for solving the large and sparse linear system of equations (LSEs) arising from the finite difference (FD) discretization of Maxwell’s quasi-static equations was developed. Following a factorization step, the solver permits computation of TMS fields inside realistic brain models in seconds, allowing for patient-specific real-time usage during TMS. The solver is an alternative to iterative methods for solving FD LSEs, often requiring run-times of minutes. A new integral equation (IE) method for analyzing TMS fields was developed. The human head is highly-heterogeneous and characterized by high-relative permittivities (10^7). IE techniques for analyzing electromagnetic interactions with such media suffer from high-contrast and low-frequency breakdowns. The novel high-permittivity and low-frequency stable internally combined volume-surface IE method developed. The method not only applies to the analysis of high-permittivity objects, but it is also the first IE tool that is stable when analyzing highly-inhomogeneous negative permittivity plasmas. Design: TMS applications call for electric fields to be sharply focused on regions that lie deep inside the brain. Unfortunately, fields generated by present-day Figure-8 coils stimulate relatively large regions near the brain surface. An optimization method for designing single feed TMS coil-arrays capable of producing more localized and deeper stimulation was developed. Results show that the coil-arrays stimulate 2.4 cm into the head while stimulating 3.0 times less volume than Figure-8 coils. Uncertainty quantification (UQ): The location/volume/depth of the stimulated region during TMS is often strongly affected by variability in the position and orientation of TMS coils, as well as anatomical differences between patients. A surrogate model-assisted UQ framework was developed and used to statistically characterize TMS depression therapy. The framework identifies key parameters that strongly affect TMS fields, and partially explains variations in TMS treatment responses.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111459/1/luisgo_1.pd

Coating Thickness Measurements and Defect Characterization in Non-Metallic Composite Materials by Using Thermography

Thermography is a non-destructive testing method (NDT), which is widely used to guarantee the quality of non-metallic materials, such as carbon fiber composite, anti-reflection (AR) film, and coatings. As other NDT methods do, thermography determines a defective area based on the signal difference between suspected defective areas and defective-free areas. Two unavoidable effects are decreasing the credibility of thermography detection: one is uneven heating, and the other is lateral diffusion of heat. To solve this problem, researchers have developed various reconstruction methods. Restoring methods are known to have the capacity to reduce the effect of heat-flux lateral diffusion by de-convoluting a point spread function either along a temporal profile or a spatial profile to process captured thermal images. These methods either require pre-knowledge with depth or are not effective in detecting deep defects. Here we propose a spatial-temporal profile-based reconstruction method to reduce the effect of uneven heating and lateral diffusion. The method evaluates the heat flux deposited onto tested samples based on surface temperature gathered under ideal conditions. Then the proposed method is tested in three real applications – in defect detection on semi-transparent materials, on semi-infinite defects (coatings) and anisotropic materials. The method is evaluated against existing methods. Results suggest that the proposed method is effective and computationally efficiently over all the reconstruction methods reviewed. It reduces the effect of uneven heating by providing a good approximation to the input heat flux at the ending image of the sequence

The Application of Tomographic Reconstruction Techniques to Ill-Conditioned Inverse Problems in Atmospheric Science and Biomedical Imaging

A methodology is presented for creating tomographic reconstructions from various projection data, and the relevance of the results to applications in atmospheric science and biomedical imaging is analyzed. The fundamental differences between transform and iterative methods are described and the properties of the imaging configurations are addressed. The presented results are particularly suited for highly ill-conditioned inverse problems in which the imaging data are restricted as a result of poor angular coverage, limited detector arrays, or insufficient access to an imaging region. The class of reconstruction algorithms commonly used in sparse tomography, the algebraic reconstruction techniques, is presented, analyzed, and compared. These algorithms are iterative in nature and their accuracy depends significantly on the initialization of the algorithm, the so-called initial guess. A considerable amount of research was conducted into novel initialization techniques as a means of improving the accuracy. The main body of this paper is comprised of three smaller papers, which describe the application of the presented methods to atmospheric and medical imaging modalities. The first paper details the measurement of mesospheric airglow emissions at two camera sites operated by Utah State University. Reconstructions of vertical airglow emission profiles are presented, including three-dimensional models of the layer formed using a novel fanning technique. The second paper describes the application of the method to the imaging of polar mesospheric clouds (PMCs) by NASA’s Aeronomy of Ice in the Mesosphere (AIM) satellite. The contrasting elements of straight-line and diffusive tomography are also discussed in the context of ill-conditioned imaging problems. A number of developing modalities in medical tomography use near-infrared light, which interacts strongly with biological tissue and results in significant optical scattering. In order to perform tomography on the diffused signal, simulations must be incorporated into the algorithm, which describe the sporadic photon migration. The third paper presents a novel Monte Carlo technique derived from the optical scattering solution for spheroidal particles designed to mimic mitochondria and deformed cell nuclei. Simulated results of optical diffusion are presented. The potential for improving existing imaging modalities through continual development of sparse tomography and optical scattering methods is discussed

Aging concrete structures: a review of mechanics and concepts

The safe and cost-efficient management of our built infrastructure is a challenging task considering the expected service life of at least 50 years. In spite of time-dependent changes in material properties, deterioration processes and changing demand by society, the structures need to satisfy many technical requirements related to serviceability, durability, sustainability and bearing capacity. This review paper summarizes the challenges associated with the safe design and maintenance of aging concrete structures and gives an overview of some concepts and approaches that are being developed to address these challenges

Numerical and Analytical Methods in Electromagnetics

Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics

Microstructure design of magneto-dielectric materials via topology optimization

Engineered materials, such as new composites, electromagnetic bandgap and periodic structures have attracted considerable interest in recent years due to their remarkable and unique electromagnetic behavior. As a result, an extensive literature on the theory and application of artificially modified materials exists. Examples include photonic crystals (regular, degenerate or magnetic) illustrating that extraordinary gain and high transmittance can be achieved at specific frequencies. Of importance is that recent investigations of material loading demonstrate that substantial improvements in antenna performance (smaller size, larger bandwidth, higher gain etc.) can be attained by loading bulk materials such as ferrites or by simply grading the material subject to specific design objectives. Multi-tone ceramic materials have also been used for miniaturization and pliable polymers offer new possibilities in three dimensional antenna design and multilayer printed structures, including 3D electronics. However, as the variety of examples in the literature shows, the perfect combination of materials is unique and extremely difficult to determine without optimization. In addition, existing artificial dielectrics are mostly based on intuitive studies, i.e. a formal design framework to predict the exact spatial combination of dielectrics, magnetics and conductors does not exist. In the first part of this thesis, an inverse design framework integrating FE based analysis tool (COMSOL MULTIPHYSICS-PDE Coefficient Module) with an optimization technique (MATLAB-Genetic Algorithm and Direct Search toolbox) suitable for designing the microstructure of artificial magneto-dielectrics from isotropic material phases is proposed. Homogenizing Maxwell's Equations (MEQ) in order to estimate the effective material parameters of the desired composite made of periodic microstructures is the initial task of the framework. The FE analysis tool is used to evaluate intermediate fields at the "micro-scale" level of a unit cell that is integrated with the homogenized MEQ's in order to estimate the "macro-scale" effective constitutive parameters of the overall bulk periodic structure. Simulation of the periodic structure is an extremely challenging task due to the mesh at micro-level (inclusions much smaller than the periodic cell dimension) that spans over the entire bulk structure turning the computational problem into a very intensive one. Therefore, the proposed framework based on the solution of homogenized MEQ's via the micro-macro approach, allows topology design capabilities of microstructures with desired properties. The goal is to achieve predefined material constitutive parameters via artificial electromagnetic substrates. Physical material bounds on the attainable properties are studied to avoid infeasible effective parameter requirements via available multi-constituents. The proposed framework is applied on examples such as microstructure layers of non-reciprocal magnetic photonic crystals. Results show that the homogenization technique along with topology optimization is able to design non-intuitive material compositions with desired electromagnetic properties. In the second part of the thesis, approximation techniques to speed-up large scale topology optimization studies of devices with complex frequency responses are investigated. Miniaturization of microstrip antennas via topology optimization of both the conductor and material substrate via multi-tone ceramic shades is a typical example treated here. Long computational times required for both the electromagnetic analysis over a frequency range and the need for a heuristic based optimization tool to locate the global minima for complex devices present themselves as two important bottlenecks for practical design studies. In this thesis, two new techniques for speeding up the optimization process by reducing the number of frequency calls needed to accurately predict a multi-resonance type response of a candidate design are proposed. The proposed techniques employ adaptive sampling methods along with novel rational function interpolations. The first technique relies on a heuristic based rational interpolation using Bayes' theory and rational functions. Second, a rational function interpolation employing a new adaptive path based on Stoer-Bulirsch algorithm is used. Both techniques prove to efficiently predict resonances and significantly reduce the computational time by at least three folds

High Frequency Characterization of Carbon Nanotube Networks for Device Applications

This work includes the microwave characterization of carbon nanotubes (CNTs) to design new CNTs-based high frequency components. A novel developed method to extract the electrical properties over a broad microwave frequency band from 10 MHz to 50 GHz of carbon nanotubes (CNTs) in a powder form is performed. The measured scattering parameters (S-parameters) with a performance network analyzer are compared to the simulated one obtained from an in-house computed mode matching technique (MMT). An optimized first order gradient method iteratively changes the unknown complex permittivity parameters to map the simulated S-parameters with the measured one until convergence criteria are satisfied. The mode matching technique accurately describes waveguide discontinuities as both propagating and evanescent modes are considered allowing an error less than 5% on the extracted permittivity over a broad frequency range. The very large values obtained at low frequencies of carbon nanotubes permittivity are explained theoretically and experimentally based on the percolation theory. The powder composed of semiconducting and conducting CNTs illuminated by an electromagnetic field is seen as series of nano-resistance-capacitance which significantly increase the real and imaginary parts of the complex effective permittivity until the percolation threshold is reached. Based on experimental results different CNTs-based composites material are engineered to design novel microwave components for possible electromagnetic compatibility (EMC) applications. As the extraordinary properties of the carbon nanotubes exist along their axis, the second part of this work is oriented on the alignment and the deposition of carbon nanotubes using a dielectrophoresis (DEP) technique. Micro/nano-electrodes are fabricated using a lift-off process consisting of photo-lithography and electron-beam lithography techniques where the carbon nanotubes suspended in an aqueous solution are attracted in the gap between the electrodes by applying an AC bias voltage. After burning the conducting carbon nanotubes an observed photocurrent with aligned semiconducting CNTs is used to develop high frequency photo-device prototypes

Bi-directional evolutionary structural optimization (BESO) for topology optimization of material’s microstructure

It is known that composite materials with improved properties can be achieved through modifications to the topology of their microstructures. Structural topology optimization approaches can be utilized as a systematic way for finding the best spatial distribution of constituent phases within the microstructures of materials/composites. This study presents a new approach for designing material’s microstructures based on the Bi-directional Evolutionary Structural Optimization (BESO) methodology. It is assumed that the materials/composites are composed of repeating microstructures known as periodic base cells (PBC). The goal is to find the best spatial distribution of constituent phases within the PBC, in such a way that materials with desired or improved functional properties are achieved. To this end, the Homogenization theory is applied to establish a relationship between properties of materials microstructure and their macroscopic characteristics. As the first step of this study, the optimization problem is formulated to find microstructures for materials with maximum stiffness, in the form of bulk or shear modulus, or thermal conductivity. Cellular materials, which are composed of one solid phase and one void phase, are considered at this stage. By conducting finite element analysis of the PBC, and applying the Homogenization theory, elemental sensitivity numbers are derived. By gradual removing and adding elements in an iterative process, the optimal topology of the solid phase within the PBC is found. In the next stage of this study, the aim is to combine additional performance constraint to the above procedure. Maximization of bulk or shear modulus is selected as the objective of the material design, subject to the constraint on the isotropy of material and volume constraint. The methodology is extended into topology optimization of microstructures for composites of two or more non-zero constituent phases. For design of material with maximum stiffness or thermal conductivity, the constituent phases are divided into groups and sensitivity analysis is performed between different groups. The developed methodology is also applied in designing functionally graded material (FGM), in which the mechanical property of material gradually changes. It is assumed that the microstructure of the FGM is composed of a series of cellular base cells in the direction of gradation and self-repeated in other directions. Finally, an approach is proposed for the topological design of FGMs with two non-zero constituent phases and multi graded properties. The objective of optimization is defined to find the stiffest materials with prescribed gradation of thermal conductivity. Similar to the approach used for cellular FGMs, the connectivity of base cells is maintained by considering three base cells at each stage. The effectiveness and computational efficiency of the proposed approaches are numerically tested, through designing a range of 2D and 3D microstructures for materials. A series of new and interesting microstructures of materials are presented. The results clearly indicate the advantages of BESO utilization in terms of computational costs and convergence speed, quality of generated microstructures, and ease of implementation as a post processing algorithm