«by Sung Man Moon A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of ...»
METHODS FOR THE DESIGN, OPTIMIZATION, AND IMAGE
CORRECTION OF LOCAL INSERT GRADIENT SYSTEM
IN MAGNETIC RESONANCE IMAGING
Sung Man Moon
A dissertation submitted to the faculty of
The University of Utah
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Electrical and Computer Engineering
The University of Utah
December 2010 i Copyright © Sung Man Moon 2010 All Rights Reserved i The University of Utah Graduate School
STATEMENT OF DISSERTATION APPROVALSung Man Moon The dissertation of
has been approved by the following supervisory committee members:
Cynthia Furse 10/12/2010 Chair ' _______ bate Approved Dennis L. Parker 10/11/2010, Member
-----Date Approved Gengsheng L. Zeng 10/11/2010 Member ' ______ Date Approved Rong-Rong Chen 10/12/2010 Member ' ______ Date Approved Michael Zhdanov 10/12/2010, Member
-----Date Approved Gianluca Lazzi and by Chair of ' _______ Electrical and Computer Engineering the Department of and by Charles A. Wight, Dean of The Graduate School.
This limitation can be reduced by designing proper local gradient coils. In this dissertation, various types of local insert gradient coil designs, as well as their optimization and image correction techniques are investigated.
Conventional method of designing planar gradient systems that uses twodimensional stream functions can be more computationally intensive than optimizing the one dimensional stream functions required for cylindrical gradients. In this dissertation, a novel planar gradient design method, which simplifies the twodimensional planar gradient coil design problem to a faster and easier one-dimensional problem by using a conformal mapping technique. The simulated gradient filed maps prove that the proposed gradient design technique creates same homogeneous gradient and works well throughout the imaging volume.
Many MRI applications such as DCE-MRI of the breast require high spatial and temporal resolution. The planar gradient systems as currently designed cannot create an imaging volume large enough to accommodate both breasts. A new concept for designing planar gradient systems, which has a superellipse shape and the addition of a field-modifying layer, has been presented. Homogeneous gradient volumes (HGVs) of the proposed superelliptical coil are increased as much as 182 % (x-gradient) over those of the original planar system. In addition, adding an extra field-modifying layer allows the further enlargement of the HGVs by 214 % (z-gradient).
Gradient homogeneity of the flat gradient systems is worse compared to cylindrical gradient systems, because the magnetic field and gradient strength drop nearly exponentially with distance from the coil surface. As a result, imaging with a planar insert gradient coil is challenging and prone to image distortions. A new concept of image de-warping has been demonstrated that calculates the nonlinear gradient field as an analytical function, and applies to de-warp collected image data. The simulated results indicate that the usable imaging region (in plane) has improved by 450% over the conventional linear gradient imaging.
I would like to thank my research advisor Dr. Dennis L. Parker for his constant encouragement, deliberate consideration, and patience throughout my Ph.D. study. His profound understanding and mastery of medical imaging science made my research work in this field possible and worthwhile.
I would also like to thank academic advisor Dr. Cynthia Furse for her thoughtful advice during my Ph.D. study and for being my committee chair.
I give special thanks to Craig, Rock, Adam, Sathya, and Nelly for their friendship, kindness, encouragement, and helpful advice.
My gratitude also goes to all of my committee members as well as the faculty, staff, and student colleagues in the Utah Center for Advanced Imaging Research (UCAIR) for their friendship and advice.
Finally, I would like to express my deepest appreciation to my family and Namkoong’s family. Their endless love, selfless caring, warm encouragement and
Magnetic resonance imaging (MRI) is one of the most widely used medical imaging techniques to produce high quality images of the inside of the human body.
This unique imaging method is noninvasive and requires no radioactivity. In addition, MRI has superior soft tissue contrast over other imaging modalities, as it utilizes various physical parameters of tissues to achieve optimal contrast between normal and abnormal tissues. As a result, MRI has become the imaging modality of choice in many clinical and research studies especially when extremely high contrast between soft tissues is needed.
MRI creates a strong magnetic field in the main bore of the system, where the patient is placed. This main magnetic field establishes net magnetization when the patient is placed within the bore. In order to generate an MRI image from a specific region of interest (ROI) of the body, extra magnetic fields are needed. The extra magnetic fields, which are superimposed on the main magnetic field, allow the spatial encoding of the nuclear magnetic resonance (NMR) signals, which in turn, form the image. Gradient coils, also known as gradient arrays, are the part of the MRI system that generates these extra magnetic fields.
In spite of its crucial role for MR imaging (MRI), only a small number of researchers made contributions to gradient coil development until the mid 1980’s .
This is partly because MRI image acquisition times were much longer than they are now, and did not involve rapid switching gradients.
Since then, more efficient, highly homogeneous, and faster switching gradient coils have been developed to meet the needs of faster image acquisition time. Among these, there are several outstanding developments such as the introduction of the stream function (SF) for cylindrical surface current density [2-4], the use of distributed current loops , the development of minimization methods to reduce power dissipation , and the improvement of fabrication methods and the introduction of high-current gradient drivers.
Developing a faster gradient system is very demanding but is desirable for fast imaging pulse sequences. Body gradient systems are limited in performance due to the large size, reduced efficiency, and high inductance. These limitations can be at least partly overcome using local gradient coils to improve image quality and speed.
A local gradient system is smaller than conventional whole body gradient systems and is used as an insert to fit in the magnet bore. Local gradient coils have many advantages over body gradient systems including high efficiency and low inductance (high slew rate), which result in higher spatial and temporal resolution. Also, less patient body volume is required inside the highly changing magnetic field (dB/dt) resulting in less peripheral nerve stimulation (PNS) [7, 8]. Therefore, local gradient systems can be used very effectively when specific areas of the body such as head, neck, breasts or knee are imaged. In this dissertation, various types of local insert gradient coil designs, as well as their optimization and image correction techniques, are investigated.
This dissertation is composed of seven chapters, including this introductory chapter. In Chapter 2, the basic principles of MR imaging are reviewed including a brief description of data acquisition and reconstruction techniques, as well as the hardware of MRI.
In Chapter 3, details of the gradient coil development method is described. The concepts, performance parameters, and various types of gradient coils are covered followed by design and optimization methods, and practical considerations for the gradient coil.
Chapter 4 presents a novel planar gradient design method using conformal mapping and simulated annealing optimization. The improved gradient performance required to achieve high spatial and temporal resolution in MRI may be achieved by using local gradient coils such as planar gradient inserts. Although the wire patterns for planar gradients can be designed using two-dimensional stream functions [9-11], optimization of the two-dimensional stream functions can be much more computationally intensive and time consuming than optimizing the one-dimensional stream functions required for cylindrical gradients. To address this problem, a simple and rapid method for designing planar gradient inserts to produce a high strength local gradient field and a reasonably uniform imaging region has been developed. This method reduces the two-dimensional planar gradient coil design problem to a faster and easier one-dimensional problem using conformal mapping. This work has been published [12, 13].
Many MRI applications such as DCE-MRI of the breast require high spatial and temporal resolution, and can benefit from improved gradient performance (increased gradient strength and reduced gradient rise time) especially when they are designed for a target anatomy such as breasts. Chapter 5 describes a new concept for designing planar gradient systems, which consists of transformation of cylindrical gradients to a superellipse shape and the addition of a field-modifying layer. Even though there have been a few attempts to design flat gradient systems for breast imaging , these systems have not created an imaging volume large enough to accommodate both breasts. Furthermore, the gradient field produced is not homogeneous, dropping rapidly with distance from the gradient coil surface. To attain an imaging volume adequate for breast MRI, a conventional local planar gradient design has been transformed into a segment of a superellipse shape to create homogeneous gradient volumes (HGVs) that are bigger than those of the original planar local gradient system. In addition, adding an extra field-modifying (FM) layer also allowed the further enlargement of the homogeneous gradient volume near the gradient coil surface compared to the already enlarged HGVs of the superelliptical gradients. This work has been published as a conference publication and submitted to Magnetic Resonance in Medicine [15, 16].
In Chapter 6, a new concept of imaging planar insert gradient system is presented. Insert gradient coils can generate high strength gradient fields over a small HGV because of their small size. With higher gradient strength and slew rate, the insert gradient coils can achieve high spatial and temporal resolution with less peripheral nerve stimulation (PNS) . However, the insert gradient coils typically suffer from relatively larger deviations in gradient strength over their smaller HGVs. Gradient homogeneity is especially bad with flat insert gradients because the magnetic field and gradient strength drop nearly exponentially with distance from the coil surface. As a result, imaging with a planar insert gradient coil is more challenging and prone to image distortions. Calibration and image correction methods such as Gradwarp can de-warp field distortion from the images , but require a cumbersome and time-consuming pre-scan calibration. In this chapter, a new concept of image de-warping is presented that calculates the nonlinear gradient field of the planar insert gradient coil as an analytical function, and use this to de-warp collected image data.
Chapter 7 is a summary describing the accomplishments achieved over the course of this dissertation. Some directions of future work are also suggested.
 W. A. Edelstein and J. F. Schenck, "Current streamline method for coil construction," US Patent 4,840,700, July 13 1987.
 R. J. Sutherland, "Selective excitation in NMR and considerations for its application in three-demensional imaging," University of Aberdeen, vol. Ph.D.
Thesis, 1980. J. F. Schenck, M. A. Hussein, and W. A. Edelstein, "Transverse gradient field coils for nuclear magnetic resonance imaging," US Patent 4,646,024, November 2 1983.
 M. W. Garrett, "Axially symmetric systems for generating and measuring magnetic field," J Appl Phys, vol. Part 1, pp. 1091-1171, 1951.
 R. Turner, "Minimum Inductance Coils," J Phys E:Sci Instrum, vol. 23, pp. 948B. Zhang, Y. F. Yen, B. A. Chronik, B. C. McKinnon, D. J. Schaefer, and B. K.
Rutt, "Peripheral nerve stimulation properties of head and body gradient coils of various sizes," Magn Reson Med, vol. 50, pp. 50-58, 2003.
 R. E. Feldman, C. J. Hardy, B. Aksel, J. Schenck, and B. A. Chronik, "Experimental determination of human peripheral nerve stimulation thresholds in a 3-axis planar gradient system," Magn Reson Med, vol. 62, pp. 763-770, 2009.
 M. A. Martens, L. S. Petropoulos, R. W. Brown, and J. H. Andrews, "Insertable biplanar gradient coils for magnetic resonance imaging," Rev Sci Instrum, vol.
62, pp. 2639-2645, 1991.
 K. Yoda, "Analytical design of self-shielded planar coils," J Appl Phys, vol. 67, pp. 4349-4353, 1990.
 E. C. Caparelli, D. Tomasi, and H. Panepucci, "Shielded biplanar gradient coil design," J Magn Reson Imaing, vol. 9, pp. 725-731, 1999.
 S. M. Moon, K. C. Goodrich, J. R. Hadley, and D. L. Parker, "Local uni-planar gradient array design using conformal mapping and simulated annealing," Concepts Magn Reson B, vol. 35B, pp. 23-31, Feb. 2009 2009.
 S. M. Moon, K. C. Goodrich, J. R. Hadley, and D. L. Parker, "Local uni-planar gradient array design using conformal mapping and simulated annealing," 16th ISMRM Proceedings, p. 1168, 2008.
 C. F. Maier, H. N. Nikolov, K. C. Chu, B. A. Chronik, and B. K. Rutt, "Practical design of a high-strength breast gradient coil," Magn Reson Med, vol. 39, pp.
 S. M. Moon, K. C. Goodrich, J. R. Hadley, G. L. Zeng, G. R. Morrell, M.
McAlpine, B. Chronik, and D. L. Parker, "Superelliptical insert gradient coil with a field modifying layer for breast imaging," Magn Reson Med, vol. in review, 2009.