Doctor of Philosophy

dissertationMagnetic Resonance Imaging (MRI) is one of the most important medical imaging technologies in use today. Unlike other imaging tools, such as X-ray imaging or computed tomography (CT), MRI is noninvasive and without ionizing radiation. A major limitation of MRI, however, is its relatively low imaging speed and low spatial-temporal resolution, as in the case of dynamic contrast enhanced magnetic resonance imaging (DCE-MRI). These hinder the clinical use of MRI. In this thesis, we aim to develop novel signal processing techniques to improve the imaging quality and reduce the imaging time of MRI. This thesis consists of two parts, corresponding to our work on parallel MRI and dynamic MRI, respectively. In the first part, we address an important problem in parallel MRI that the coil sensitivities functions are not known exactly and the estimation error often leads to artifacts in the reconstructed image. First, we develop a new framework based on multichannel blind deconvolution (MBD) to jointly estimate the image and the sensitivity functions. For fully sampled MRI, the proposed approach yields more uniform image reconstructions than that of the sum-of-squares (SOS) and other existing methods. Second, we extend this framework to undersampled parallel MRI and develop a new algorithm, termed Sparse BLIP, for blind iterative parallel image reconstruction using compressed sensing (CS). Sparse BLIP reconstructs both the sensitivity functions and the image simultaneously from the undersampled data, while enforcing the sparseness constraint in the image and sensitivities. Superior image constructions can be obtained by Sparse BLIP when compared to other state-of-the-art methods. In the second part of the thesis, we study highly accelerated DCE-MRI and provide a comparative study of the temporal constraint reconstruction (TCR) versus model-based reconstruction. We find that, at high reduction factors, the choice of baseline image greatly affects the convergence of TCR and the improved TCR algorithm with the proposed baseline initialization can achieve good performance without much loss of temporal or spatial resolution for a high reduction factor of 30. The model-based approach, on the other hand, performs inferior to TCR with even the best phase initialization

Optimization of a boundary element approach to electromagnet design with application to a host of current problems in Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) has proven to be a valuable methodological approach in both basic research and clinical practice. However, significant hardware advances are still needed in order to further improve and extend the applications of the technique. The present dissertation predominantly addresses gradient and shim coil design (sub-systems of the MR system). A design study to investigate gradient performance over a set of surface geometries ranging in curvature from planar to a full cylinder using the boundary element (BE) method is presented. The results of this study serve as a guide for future planar and pseudo-planar gradient systems for a range of applications. Additions to the BE method of coil design are developed, including the direct control of the magnetic field uniformity produced by the final electromagnet and the minimum separation between adjacent wires in the final design. A method to simulate induced eddy currents on thin conducting surfaces is presented. The method is used to predict the time-dependent decay of eddy currents induced on a cylindrical copper bore within a 7 T MR system and the induced heating on small conducting structures; both predictions are compared against experiment. Next, the method is extended to predict localized power deposition and the spatial distribution of force due to the Lorentz interaction of the eddy current distribution with the main magnetic field. New methods for the design of actively shielded electromagnets are presented and compared with existing techniques for the case of a whole-body transverse gradient coil. The methods are judged using a variety of shielding performance parameters. A novel approach to eliminate the interactions between the MR gradient system and external, non-MR specific, active devices is presented and its feasibility is discussed. A completely new approach to shimming is presented utilizing a network of current pathways that can be adaptively changed on a subject-by-subject basis and dynamically controlled. The potential benefits of the approach are demonstrated using computer simulations and a prototype coil is constructed and tested as a proof-of-principle

3D simulation of magneto-mechanical coupling in MRI scanners using high order FEM and POD

Magnetic Resonance Imaging (MRI) scanners have become an essential tool in the medi-cal industry due to their ability to produce high resolution images of the human body. To generate an image of the body, MRI scanners combine strong static magnetic fields with transient gradient magnetic fields. The interaction of these magnetic fields with the con-ducting components present in superconducting MRI scanners gives rise to an important problem in the design of new MRI scanners. The transient magnetic fields give rise to the appearance of eddy currents in conducting components. These eddy currents, in turn, result in electromagnetic stresses, which cause the conducting components to deform and vibrate. The vibrations are undesirable as they lead to a deterioration in image quality (with image artefacts) and to the generation of noise, which can cause patient discomfort. The eddy currents, in addition, lead to heat being dissipated and deposited into the cryo-stat, which is filled with helium in order to maintain the coils in a superconducting state. This deposition of heat can cause helium boil off and potentially result in a costly magnet quench. Understanding the mechanisms involved in the generation of these vibrations and the heat being deposited into the cryostat are, therefore, key for a successful MRI scanner design. This involves the solution of a coupled magneto-mechanical problem, which is the focus of this work.In this thesis, a new computational methodology for the solution of three-dimensional (3D) magneto-mechanical coupled problems with application to MRI scanner design is presented. To achieve this, first an accurate mathematical description of the magneto-mechanical coupling is presented, which is based on a Lagrangian formulation and the assumption of small displacements. Then, the problem is linearised using an AC-DC splitting of the fields, and a variational formulation for the solution of the linearised prob-lem in a time-harmonic setting is presented. The problem is then discretised using high order finite elements, where a combination of hierarchical H1 and H(curl) basis func-tions is used. An efficient staggered algorithm for the solution of the coupled system is proposed, which combines the DC and AC stages and makes use of preconditioned iter-ative solvers when appropriate. This finite element methodology is then applied to a set of challenging academic and industrially relevant problems in order to demonstrate its accuracy and efficiency.This finite element methodology results in the accurate and efficient solution of the magneto-mechanical problem of interest. However, in the design stage of a new MRI scanner, this coupled problem must be solved repeatedly for varying model parameters such as frequency or material properties. Thus, even if an efficient finite element solver is available for the solution of the coupled problem, the need for these repeated simulations result in a bottleneck in terms of computational cost, which leads to an increase in design time and its associated financial implications. Therefore, in order to optimise this process, the application of Reduced Order Modelling (ROM) techniques is considered. A ROM based on the Proper Orthogonal Decomposition (POD) method is presented and applied to a series of challenging MRI configurations. The accuracy and efficiency of this ROM is demonstrated by performing comparisons against the full order or high fidelity finite element software, showing great performance in terms of computational speed-up, which has major benefits in the optimisation of the design process of new MRI scanners

Advanced methods for mapping the radiofrequency magnetic fields in MRI

As MRI systems have increased in static magnetic field strength, the radiofrequency (RF) fields that are used for magnetisation excitation and signal reception have become significantly less uniform. This can lead to image artifacts and errors when performing quantitative MRI. A further complication arises if the RF fields vary substantially in time. In the first part of this investigation temporal variations caused by respiration were explored on a 3T scanner. It was found that fractional changes in transmit field amplitude between inhalation and expiration ranged from 1% to 14% in the region of the liver in a small group of normal subjects. This observation motivated the development of a pulse sequence and reconstruction method to allow dynamic observation of the transmit field throughout the respiratory cycle. However, the proposed method was unsuccessful due to the inherently time-consuming nature of transmit field mapping sequences. This prompted the development of a novel data reconstruction method to allow the acceleration of transmit field mapping sequences. The proposed technique posed the RF field reconstruction as a nonlinear least-squares optimisation problem, exploiting the fact that the fields vary smoothly. It was shown that this approach was superior to standard reconstruction approaches. The final component of this thesis presents a unified approach to RF field calibration. The proposed method uses all measured data to estimate both transmit and receive sensitivities, whilst simultaneously insisting that they are smooth functions of space. The resulting maps are robust to both noise and imperfections in regions of low signal

Mathematical methods for magnetic resonance based electric properties tomography

Magnetic resonance-based electric properties tomography (MREPT) is a recent quantitative imaging technique that could provide useful additional information to the results of magnetic resonance imaging (MRI) examinations. Precisely, MREPT is a collective name that gathers all the techniques that elaborate the radiofrequency (RF) magnetic field B1 generated and measured by a MRI scanner in order to map the electric properties inside a human body. The range of uses of MREPT in clinical oncology, patient-specific treatment planning and MRI safety motivates the increasing scientific interest in its development. The main advantage of MREPT with respect to other techniques for electric properties imaging is the knowledge of the input field inside the examined body, which guarantees the possibility of achieving high-resolution. On the other hand, MREPT techniques rely on just the incomplete information that MRI scanners can measure of the RF magnetic field, typically limited to the transmit sensitivity B1+. In this thesis, the state of art is described in detail by analysing the whole bibliography of MREPT, started few years ago but already rich of contents. With reference to the advantages and drawbacks of each technique proposed for MREPT, the particular implementation based on the contrast source inversion method is selected as the most promising approach for MRI safety applications and is denoted by the symbol csiEPT. Motivated by this observation, a substantial part of the thesis is devoted to a thoroughly study of csiEPT. Precisely, a generalised framework based on a functional point of view is proposed for its implementation. In this way, it is possible to adapt csiEPT to various physical situations. In particular, an original formulation, specifically developed to take into account the effects of the conductive shield always employed in RF coils, shows how an accurate modelling of the measurement system leads to more precise estimations of the electric properties. In addition, a preliminary study for the uncertainty assessment of csiEPT, an imperative requirement in order to make the method reliable for in vivo applications, is performed. The uncertainty propagation through csiEPT is studied using the Monte Carlo method as prescribed by the Supplement 1 to GUM (Guide to the expression of Uncertainty in Measurement). The robustness of the method when measurements are performed by multi-channel TEM coils for parallel transmission confirms the eligibility of csiEPT for MRI safety applications

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