Development of Magnetic Resonance-Based Susceptibility Imaging Applications

Transcription

1 Development of Magnetic Resonance-Based Susceptibility Imaging Applications Sung-Min Gho The Graduate School Yonsei University

2 Development of Magnetic Resonance-Based Susceptibility Imaging Applications A Dissertation Submitted to the Department of Electrical and Electronic Engineering and the Graduate School of Yonsei University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Sung-Min Gho February 2015

3 This certifies that the dissertation of Sung-Min Gho is approved. Thesis Supervisor: Dong-Hyun Kim Sanghoon Lee Dosik Hwang Eung Yeop Kim Chunlei Liu The Graduate School Yonsei University February 2015

4 감사의글 지난 2008 년자기공명영상이라는생소한분야를접하며시작한저의연구자로서의삶이, 그간의고민과노력끝에마침내조그만결실을맺게되었습니다. 지난시간동안많은분들로부터받았던도움과격려가제작은성과의큰힘이되었습니다. 본지면을통해서저를도와주시고격려해주신고마운분들께감사의마음을전하고자합니다. 먼저저의지도교수님이신김동현교수님께감사드립니다. 교수님께서는제가자기공명영상분야의연구자로성장할수있도록많은지원과지도를해주셨습니다. 특히, 따뜻한관심과조언을통해저의부족한점을보완하고, 독립적인연구자로성장할수있도록도와주셨습니다. 또한가끔씩인생의선배로서해주신좋은말씀들은제가앞으로삶을살아가면서사회생활을하는데큰도움이될것입니다. 아울러 교수님께서보내주신미국의 Duke University 와중국의칭화대학교해외파견은 세계적인연구그룹과함께공부하고, 새로운사람들을만나다양한분야를접해볼수있는소중한경험이되었습니다. 이경험은제가연구를지속하고, 연구분야를넓힐수있는큰자산이될것입니다. 바쁘신와중에도학위논문심사를맡아주신이상훈교수님, 황도식교수님, 가천길병원김응엽교수님, 그리고 Duke University 의 Chunlei Liu 교수님께도감사드립니다. 이상훈교수님께서해주신말씀을통해깊이있는분석과고찰의필요성, 그리고정량적비교와검증의중요성을깨달을수있었습니다. 황도식교수님께서해주신따뜻한격려와세심한조언은제연구분야의큰그림을그려보고자신감을가질수있는좋은계기가되었습니다. 김응엽교수님께서영상의학과의사의입장에서말씀해주신조언과지적은제가미처생각지못했던실제임상에서의적용가능성에대해생각해볼수있는계기가되었을뿐만아니라, 새로운임상적용분야에대해배울수있는기회가되었습니다. 그리고 Chunlei Liu 교수님께서는제가잠시 Duke University 에서공부하게된것을인연으로제가좀더성숙한연구자로성장할수있도록도와주셨습니다. 특히, MR susceptibility imaging 에대한깊이있는가르침과제가수행하였던연구들에대한세심한지도와조언은제가 MR susceptibility imaging 연구를수행하는데큰도움이되었습니다. 연구실에서함께생활했던모든분들께도감사드립니다. 생활패턴이남들과달랐지만누구보다 MRI 에대한열정이있는상영이형, 요즘아들자랑에정신없는곧두아이의

5 아빠이준성박사님, 이번에같이졸업하는카리스마있는한성이형, 항상친절하게후배를챙겨주던에이스윤호, 연구실의대표모범생이자나와 ISMRM 숙소를늘함께쓴진짜사나이민오, 항상웃는얼굴로연구실분위기를밝게만들어주는이번에같이졸업하게된나래, 누구보다독창적이고자기색깔강한은혜, 재치있고뛰어난영어 실력으로많은이들을도와주는 American idol 승욱이, 항상능동적으로연구하고 연구실사람들사이의윤활유가되어주는성격좋은나이스가이동엽이, 누구보다성실하고착하며항상다른사람을잘배려해주는 MILAB 마스코트재욱이, 송도에서연구하느라자주보진못하지만항상긍정적이고에너지넘치는신국이, 항상유쾌하고자유롭지만열심히노력하는은근히허당홍표, 몇안되는 MILAB 아침형인간이자연구와운동모두잘하고인기도많은능력자태화, 묵묵히자기일을성실히잘하는조성민, MILAB 막내이자게임최고수한솔이, 심심할때연락하면기꺼이술친구가되어준준형이, 멀리이란에서온 MILAB 야야투레 Saeed, 풋풋한신입재은이등좋은사람들과함께생활하며같이연구할수있었던것은저에게큰행운이었습니다. 바쁘다는핑계로자주연락하지못하지만, 만나면늘반갑고즐거운나의베스트프렌드준석이와승훈이에게도감사의인사를전합니다. 앞으로도서로격려하며돈독한우정을지켜나가면좋겠습니다. 그리고오랜시간함께활동한한국문화표현단동아리사람들에게도고마움을전합니다. 늘바쁘지만세심하고사람좋은상헌이형, 행복한신혼부부정욱이와지윤이, 리액션이너무좋은소미, 센스있는세은이, 새신부아림이, 사람들잘챙기는지용이와민경이등등. 지금은각자의자리에서바쁘게살아가느라자주만나지는못하지만, 앞으로도좋은인연오래도록함께하면좋겠습니다. 마지막으로, 넉넉지못한형편에서도제가학위과정을무사히마칠수있도록지원해주시고격려해주신사랑하는부모님께가장큰감사를전하고싶습니다. 부모님께서주신큰사랑이제가더성장하고, 성숙한사람이될수있는밑바탕이되었습니다. 그리고어느새저보다빨리사회에나가가족을챙겨주고있는동생경민이에게도감사의인사를전합니다. 또, 항상저를위해기도해주고, 언제나저를잘챙겨주는사랑하는제연인민지에게도감사하다는말전하고싶습니다 년 1 월 고성민드림

6 Content List of Figures...iii List of Tables... v Abstract Introduction Thesis outline MRI Basics and Background Knowledge MRI Basics Bloch Equation Static Magnetic Field B Radiofrequency Field B Receive Coils and Signal Reception Spatial Encoding Gradients Relaxation Spin-Lattice Relaxation Spin-Spin Relaxation T 2 * Relaxation in External Magnetic Field Inhomogeneity Spin Echo sequence Gradient Recalled Echo sequence Susceptibility Imaging Magnetic Susceptibility Phase Imaging Susceptibility Weighted Imaging Quantitative Susceptibility Mapping Background Phase Removal Susceptibility Map-Weighted Imaging (SMWI) for Neuroimaging Introduction Methods Brain MR Imaging i

7 3.2.2 Multi-echo Denoising Image Reconstruction Optimization of the Susceptibility Mask Multiplication: Simulation Optimization of the Threshold Value: Simulation Results Simulation: Optimal Number of Multiplications Simulation: Optimal Threshold Value Multi-echo Denoising Method In vivo Anisotropic High-Resolution Data of Healthy Volunteers Clinical Data Discussion Simultaneous Neuro Imaging of Susceptibility and Conductivity Introduction Materials and Methods Simulation Phantom Experiment In vitro Hematoma Phantom Experiments Data Acquisition QSM Reconstruction QCM Reconstruction Results Simulation of Brain phantom QCM using UTE phase In vivo Brain Results In vitro Hematoma Phantom Experiments Discussion Summary References 국문요약 ii

8 List of Figures Figure 2.1 Pulse sequence diagram of two dimensional SE imaging...10 Figure 2.2 Pulse sequence diagram of two dimensional GRE imaging...11 Figure 2.3 Flowchart of the SWI process...14 Figure 2.4 Reconstructed magnitude image and SWI...15 Figure 2.5 Flowchart of the QSM process...17 Figure 2.6 Limitations of QSM...18 Figure 3.1 Optimizing the number of multiplications...28 Figure 3.2 Optimizing the threshold values...30 Figure 3.3 The effects of the number of multiplications by the susceptibility mask and the threshold values on in vivo data...32 Figure 3.4 Multi-echo reconstruction results...33 Figure 3.5 Two illustrative figures of SMWI...35 Figure 3.6 One example of comparison among the magnitude images, SWI and SMWI...36 Figure 3.7 Comparative results of SWI, QSM, and SMWI in vivo...38 Figure 3.8 Three successive slices of the reconstructed data obtained from a hemorrhagic stroke patient...39 Figure 4.1 3D double-echo UTE pulse sequence diagram and corresponding radial k-space trajectory...47 Figure 4.2 Reconstructed QCM images at different TEs and corresponding difference maps...49 Figure 4.3 Verification of conductivity mapping using the UTE phase...50 Figure 4.4 In vivo reconstructed images of the proposed method...52 Figure 4.5 A representative reconstruction results of one volunteer case...54 iii

9 Figure 4.6 Line plots of the estimated quantitative values...55 iv

10 List of Tables Table 3.1 The estimated CNR values of several regions obtained from eight healthy volunteers Table 4.1 The NRMSE values from ROIs at different TE values Table 4.2 QCM values estimated from the literatures and the proposed method Table 4.3 The average of the measured conductivity and susceptibility values that were obtained from four healthy volunteer v

11 Abstract Development of Magnetic Resonance-Based Susceptibility Imaging Applications Sung-Min Gho Dept. of Electrical and Electronic Eng. The Graduate School Yonsei University Magnetic resonance imaging (MRI) is a non-invasive imaging modality without ionizing radiation. MRI provides a large number of flexible contrast images using various properties. One important source of the contrast is the magnetic susceptibility of tissues. Since the development of MRI, various susceptibility-related imaging techniques (such as T 2 * mapping, phase imaging, susceptibility weighted imaging (SWI), and quantitative susceptibility mapping (QSM)) have been developed and applied to both clinical and scientific fields. However, there are still many requirements in susceptibility imaging to improve its imaging techniques and expand its applications. This dissertation focuses on the development of these requirements so as to extent the application of susceptibility-based imaging. The development of two MR based susceptibility-related imaging are presented in this thesis: susceptibility map-weighted imaging (SMWI), and simultaneous imaging of susceptibility 1

12 and conductivity. The aims of presented methods are to propose an alternative susceptibilitybased imaging method, and develop a simultaneous magnetic and electric property (i.e. susceptibility and conductivity) imaging method. Both methods are aimed to extent the applications of susceptibility imaging for neurologic applications. The SMWI method is shown to alleviate the phase based artifacts in conventional SWI by combining magnitude image information with a weighting factor determined by the QSM. The results shows that different features can be emphasized compared to present imaging techniques using magnitude image, QSM, and original SWI. In the second development, QSM and quantitative conductivity maps (QCM) were acquired simultaneously using a single scan double-echo ultrashort echo (UTE) imaging sequence. The use of UTE phase as the source for QCM is verified by simulation and phantom experiments. Furthermore, as an example of this technique for neuroimaging application, the temporal variations of the quantitative information (i.e. QSM and QCM) for venous blood during coagulation were investigated. Results demonstrate that simultaneous QSM and QCM can be successfully acquired and the information content can be complementary. Keywords: magnetic resonance imaging, susceptibility imaging, susceptibility-map weighted imaging, simultaneous imaging of susceptibility and conductivity 2

13 Chapter 1 Introduction Magnetic resonance imaging (MRI) is a biomedical imaging technique utilized in radiology to investigate the anatomy and physiology of the body. MRI is a non-invasive imaging modality without exposure to ionizing radiation by using strong magnetic fields and radiofrequency to form images. MRI can provide various types of qualitative and quantitative information such as relaxation properties, tissue structure and anatomies, motional properties, temperature and mechanical properties, and neuronal activities. The images in MRI are mostly shown in magnitude images although phase images are typically discarded with the exception of a limited number of cases such as the measuring of flow in angiography [1], enhancing image contrast in susceptibility weighted images (SWI) [2, 3] and temperature mapping [4]. Recently, methods for estimating and mapping the quantitative magnetic susceptibility and electric conductivity values using phase information were introduced and applied for various applications [5-8]. The contributions of this thesis are two methods (one for a qualitative imaging method and the other for quantitative imaging technique) for MR magnetic property imaging, i.e. susceptibility imaging which are closely related to the phase information. As a qualitative application of MR susceptibility imaging, the susceptibility map-weighted imaging (SMWI) which is an alternative susceptibility contrast imaging method [9] is proposed. The idea behind it is that quantitative susceptibility mapping (QSM) can be useful as the weighting factors of SWI instead of phase image to alleviate the limitations of the original SWI. The other contribution is simultaneous susceptibility and conductivity mapping method as a quantitative application of susceptibility imaging. The susceptibility and conductivity imaging are usually used independently. This may induce several drawbacks, therefore, three 3

14 dimensional (3D) quantitative susceptibility and conductivity mapping were acquired by single acquisition using the double-echo ultrashort TE (UTE) sequence. 1.1 Thesis outline Chapter 2 gives a brief overview of MRI and existing susceptibility related imaging methods. It provides the necessary backgrounds for the following chapters by covering brief basic MR physics, and the introduction of phase imaging, SWI, and QSM. In chapter 3, a SMWI method by combining a magnitude image with a QSM based weighting factor is proposed to provide an alternative contrast compare to magnitude image, SWI and QSM. A 3D gradient echo sequence is used to acquire the data and temporal domain denoising method is applied to enhance the signal to noise ratio. Optimal reconstruction processes of the SMWI are determined from simulations. The validity of this method is demonstrated using in vivo data from healthy volunteers and a stroke patient. In chapter 4, a method of the simultaneous imaging of magnetic and electric property (i.e. magnetic susceptibility and electric conductivity) is suggested. 3D quantitative susceptibility and conductivity mapping are obtained concurrently by double-echo UTE sequence. The possibility of UTE phase is verified as the source of conductivity mapping through the simulation and NaCl phantom studies. Furthermore, the proposed method is applied to in vitro blood coagulation experiments for investigating the evolution of hematoma using quantitative information and proposing a potential clinical application. 4

15 Chapter 2 MRI Basics and Background Knowledge 2.1 MRI Basics Bloch Equation The interaction of the magnetization M with an external magnetic field B is governed by the Bloch equation, dm ( M M ) k + = M γ B dt T T Mi z 0 x M y j 1 2 (2.1) where M 0, M z, M x and M y are the equilibrium, longitudinal, transverse magnetization of x and y directions and γ, T 1 and T 2 are the gyromagnetic ratio, and time constants for relaxation properties of specific tissues (i.e. spin-lattice relaxation, and spin-spin relaxation), respectively Static Magnetic Field B 0 B 0 field is the constant, homogeneous magnetic field utilized to polarize spins, and creating magnetization. This field points in the longitudinal direction (z-direction) and its strength determines the net magnetization and the resonance frequency. The field homogeneity is very important for imaging. Inhomogeneity often results in image distortion artifacts Radiofrequency Field B 1 5

16 B 1 field is a transverse radio-frequency (RF) field generated by coils tuned to the resonance frequency (Larmor frequency). This field is applied perpendicular to the longitudinal axis for exciting the magnetization from equilibrium by tipping it from the longitudinal direction to the transverse plane (xy-plane) Receive Coils and Signal Reception Magnetization that is excited to the transverse plane precesses at the Larmor frequency. The precession creates a changing magnetic flux, which in turn induces a changing voltage according to the Faraday's Law in a receiver coil tuned to the Larmor frequency. This voltage is the MR signal that is used for MR imaging. The received signal is the cumulative contribution from all the excited magnetization in the volume. The system does not contain any spatial information with the homogeneous B 0 field present. The received signal is a complex harmonic with a single frequency peak centered at the Larmor frequency Spatial Encoding Gradients The spatial distribution information comes from three additional spatially varying fields. Three orthogonal gradient coils, Gx, Gy, and Gz generate a linear variation in the magnetic field as a function of spatial position. As a result, the resonance frequency of the magnetization will vary in proportion to the gradient field. This variation is used to resolve the spatial distribution by Fourier transform. In MRI, image resolution is determined by the method of spatial encoding and is typically proportional to the number of encoding steps having different combination of linear field gradients. 6

17 2.1.6 Relaxation Spin-Lattice Relaxation After the longitudinal magnetization M z has been flipped by a B 1 field into the xy-plane, it starts to return back to the B 0 axis (i.e. realigned to the B 0 axis). T 1 is referred to as the longitudinal relaxation time because it indicates the time it takes for the spins to realign along the longitudinal axis. This process can be described by a first order linear differential equation dm z M0 M z dt = (2.2) T 1 The change of the longitudinal magnetization dm z /dt depends on the difference to the equilibrium magnetization M 0 - M z and the relaxation constant R 1 = 1/T 1. Solving Eq. (2.2) leads to T Mz ( t) = M0 1 e + Mzt ( 0) e = t t 1 T1 (2.3) where M z(t=0) is the longitudinal magnetization immediately after the excitation RF pulse Spin-Spin Relaxation After B 1 excitation pulse, the transverse magnetization M xy precesses within the xy-plane, oscillating around the z-axis with all spins rotating in phase. After the magnetization has been flipped into xy-plane, the RF pulse is turned off. Then, the excited spins interact with each other by sampling local magnetic field inhomogeneities on the micro- and nano-scales, their respective accumulated phases are diverged. 7

18 T 2 is called the transverse relaxation time because it represents the time it takes for the spins to dephase and decrease its transverse magnetization components. It results in decay or loss of coherent transverse magnetization. This process can be described by dm dt xy M xy = (2.4) T 2 where the change of the magnetization dm xy /dt only depends on the transverse relaxation constant R 2 = 1/T 2. Solving this first order linear differential equation leads to xy ( ) xy( t= 0) t T2 M t = M e (2.5) where M xy(t=0) denotes the transverse magnetization immediately after excitation. Both spin-lattice and spin-spin relaxations occur independently of each other and the T 2 relaxation time is always smaller than the T 1. These differences in the relaxation times of different tissues are one of the most important image contrast mechanisms in MRI T 2 * Relaxation in External Magnetic Field Inhomogeneity External magnetic field inhomogeneity makes protons in different locations to precess at different frequencies because each spin is exposed to a slightly different magnetic field strength. These varying frequencies are very close to each other and very close to the Larmor frequency, however, these tiny differences in frequency result in spin dephasing. An additional signal loss of transverse magnetization is caused by this spin dephasing. The loss of transverse magnetization is described by xy ( ) xy( t= 0) t * T2 M t = M e (2.6) 8

19 where T 2 * (= 1/R 2 *) is given by = + (2.7) T T T * ' T 2 ' (= 1/R 2 ') denotes the signal decay associated with the external magnetic field inhomogeneities Spin Echo sequence In the beginning of MRI, the applied main magnetic field was limited in its spatial homogeneity, and the transverse magnetization of the imaged volume dephased quickly. Hahn proposed the spin echo (SE) technique to overcome this problem [10]. After the magnetization is flipped to the xy-plane (90 o -pulse), it dephases quickly and the detectable signal drops with the T 2 * decay time constant. Then, after a certain time (TE/2), a refocusing pulse with 180 o flips the transverse magnetization within the xy-plane which causes a rephasing of the magnetization. After the same time which elapsed between the excitation and the refocusing RF pulse, the magnetization is recovered and the SE occurs at echo time (TE). The signal measured at TE is still limited by the spin-spin relaxation but the effects of static field inhomogeneities (resulting in T 2 ') are compensated. The repetition time (TR) for the next phase encoding step has to be in the order of hundreds of milliseconds to allow sufficient time for longitudinal magnetization recovery, therefore, this causes long imaging times and makes 3D measurements not feasible. Figure 2.1 shows a simple SE pulse sequence diagram. In Figure 2.1, Gz enables slice selective RF excitation with desired thickness. Gy and Gx encode two dimensional (2D) spatial information and are called the phase encoding and the frequency encoding gradients, respectively. 9

20 Figure 2.1 Pulse sequence diagram of two dimensional SE imaging. Pulse sequence diagram illustrates the instruction for RF pulses and three orthogonal linear magnetic field gradients in each encoding step. (TR: repetition time is the time between two excitation RF pulses, TE: echo time is the time between the 90 o RF pulse and MR signal sampling, corresponding to maximum of echo) Gradient Recalled Echo sequence With continuous development of MRI hardware, in particular with a homogeneous main magnetic field over a large field of view (FOV), the signal echo can be acquired only by the imaging gradients. The gradient echo (GRE) is generated by the frequency encoding gradient (Gx), it is used in opposite directions, i.e. the Gx is used in reverse at first to enforce transverse dephasement of spins and then right after, it is used as a readout gradient to realign the dephased spins and hence acquire echo signal. Due to the missing refocusing pulse, the TE and TR can be much smaller. 10

21 Furthermore, it is possible to flip the longitudinal magnetization a few degrees in the xyplane. As an advantage imaging time can be shortened dramatically due to the reduced TR, which makes 3D imaging practically feasible. To prevent the detection of previously excited spins in the following echoes, the residual transverse magnetization can be removed by an additional spoiling gradient. Figure 2.2 represents the 2D GRE pulse sequence diagram. The dotted line shows the spoiling gradient for removing the residual transverse magnetization prior to the next excitation pulse. The spoiling gradient can be used with any spatial encoding gradient. Figure 2.2 Pulse sequence diagram of two dimensional GRE imaging. 2.2 Susceptibility Imaging Magnetic Susceptibility 11

22 Magnetic susceptibility is a physical property of a material characterizing its degree of magnetization in response to an external magnetic field. This physical parameter is useful for deriving physiological or pathological parameters when its value can be accurately measured. Every material acquires a magnetic moment when it is put in a magnetic field H. Magnetic susceptibility χ, defined as χ = M/H, with M being the magnetic moment per unit volume (magnetization), is an intrinsic property of the material, reflecting its electronic perturbation by the applied magnetic field. For some materials such as gadolinium and iron compounds, the strong intrinsic magnetic moment of unpaired electrons give rise to paramagnetism (χ > 0). For some other materials such as calcification and myelin, the precession of the paired electron spins create a magnetic field opposing the external field, giving rise to diamagnetism (χ < 0) Phase Imaging In the past, phase information normally discarded even though the complex data (i.e. magnitude and phase data) was obtained. Because the phase images were usually noisy and lack of tissue contrast, hence had limited applications. The phase images, however, could show excellent contrast and reveal anatomic structures, such as the deep nuclei, white matter structures, and layered structure within gray matter with improved phase processing [11, 12]. Despite these advantages, phase image has several limitations. One is that phase contrast is not easily reproducible due to its non-local, orientation dependent property, and image phase is not an intrinsic tissue property. The other is that image phase requires complicated reconstruction process such as phase unwrapping [13-15] and background phase removing [16, 17]. 12

23 2.2.3 Susceptibility Weighted Imaging Susceptibility weighted imaging (SWI) is a technique to enhance contrast in magnitude imaging, which uses tissue magnetic susceptibility differences to produce a unique contrast, different from that of proton density, T 1, T 2, and T 2 *. The phase images contain a wealth of information about local susceptibility changes between tissues, therefore, the phase and the magnitude images are combined for creating a susceptibility weighted magnitude imaging. Figure 2.3 represents the flowchart of the SWI process. First, a high-pass filter (ex. homodyne filter) is employed to the phase images for removing the low-spatial frequency components of the backgrounds (the effects of high-pass filtering for background phase are shown in Ref.[18]). Second, this high-pass filtered phase image is used to make a phase mask. The phase mask is designed to suppress the voxels that have certain phases and this phase mask is multiplied to the original magnitude image to create the SWI. (more details are represented in Ref.[2] ) 13

24 Figure 2.3 Flowchart of the SWI process. The insets are representative images of each process. SWI is a phase based method, however, SWI has some image artifacts from phase wrapping (shown in Figure 2.4) and nonlocal property of phase. Furthermore, SWI may not allow the extraction of quantitative information in a straightforward manner. 14

25 Figure 2.4 Reconstructed magnitude image and SWI. SWI shows enhanced contrast compare to magnitude image such as red nucleus, and substantia nigra (dotted circle). Phase wrapping artifacts are pointed by an arrow. There are various scientific studies for improving the SWI method such as improving signal to noise ratio using combination of multi-echo data [19] or applying a temporal denosing method [20], reducing the artifacts from background field inhomogeneity [21-23]. Also, SWI has been used for many clinical applications such as venous malformations [24], multiple sclerosis [25, 26], tumors [27, 28], and traumatic brain injuries [29] Quantitative Susceptibility Mapping As mentioned above, phase image is not the intrinsic property of the tissue. It is of great interest to determine the magnetic susceptibility (i.e. the intrinsic property of the tissue) from 15

26 the measured signal phase. As a solution, quantitative susceptibility mapping (QSM) has been proposed [30-33]. Given a susceptibility distribution χ(r), and the applied magnetic field B 0, the resonance frequency offset f(r) can be determined using the following equation [34-36]. δ ( r) FT D( k ) FT χ( r) = (2.8) 1 { } δ ( r) ( ) D k ( r) f ( r) ϕ = = γ B TE γ B k = 3 k k k 2 z x + y + z (2.9) (2.10) where δ is the normalized magnetic field shift, φ is the image phase, γ is the gyromagnetic ratio, D is the dipole response kernel, k is the spatial frequency vector, and r is the spatial coordinate vector. Susceptibility distribution, therefore, can be acquired by solving the inverse problem (Eq. (2.8)) and the solution is as follows: χ 1 ( k) D( k) δ ( k) = (2.11) However, at the conical surface in the frequency domain defined by D(k) = 0, the inversion for susceptibility calculation is ill-posed. To solve this problem, various methods have been suggested [30-33, 37]. 16

27 Figure 2.5 Flowchart of the QSM process. The insets are representative images of each process. Figure 2.5 represents the flowchart of the QSM process. QSM utilizes phase images, unwraps the phase wrapping, removes the background phase (more details are shown in the chapter ), and solves the magnetic field to susceptibility source inverse problem, and generates 3D susceptibility distribution. The voxel intensity in QSM is linearly proportional to the underlying tissue apparent magnetic susceptibility. Diamagnetic substances represent negative QSM values and paramagnetic represent positive QSM values. Although QSM is still in research phase, however, QSM has been applied to many clinical studies [6, 7, 38, 39]. QSM can also be used for quantification of the contrast agent [40] and identification of biomarkers [41, 42]. There are some limitations in QSM. One is the streaking artifacts from the ill-posed reconstruction problem. Another is the loss of information at the outer border regions and B 0 17

28 inhomogeneity regions (Figure 2.6). Voxels are inevitably removed at the border due to the processing of the phase data to remove background field contributions. The other is that QSM requires relatively long reconstruction time. Recently, several studies are performed to resolve these limitations [43-46]. Figure 2.6 Limitations of QSM. Streaking artifacts are pointed by arrows and loss of information at the outer border regions of the brain are shown (The blue boundary in the QSM image represents boundary of the magnitude image) Background Phase Removal For accurate susceptibility quantification in QSM, it is necessary to separate the local phase in a given region of interest (ROI) from the background phase. This background phase arises from various sources including imperfect shimming and magnetic susceptibility sources outside the ROI. Recently, novel approaches to eliminating the background phase have been published such as the sophisticated harmonic artifact reduction for phase data (SHARP) and projection-ontodipole fields [16, 17]. In this section, the SHARP method is briefly introduced. 18

29 The unwrapped phase in Eq. (2.9) yields an estimate of the relative field perturbation B (r) along the direction of the applied field. This quantity can be understood as a superposition of fields due to different sources: ( ) ( ) ( ) B r = B r + B r (2.12) internal background B internal and B background are the fields due to magnetic susceptibility variation occurring inside and outside of the volume of interest (VOI), respectively. Starting from Maxwell s equations, it can be shown that the static magnetic induction B is harmonic (i.e., satisfies Laplace s equation: 2 B = 0) [47]. In other words, B background is harmonic within the VOI. The harmonic mean value theorem states that a harmonic function u is preserved under convolution transform with any nonnegative, radially symmetric, normalized (total integral equals one) function ρ( r ), i.e., u(r) = (ρ u)(r), where the symbol denotes the 3D convolution operator. The mean value property thus enables the elimination of any information from the background fields in B Δ, as shown in the following [17]: B = B ρ B = B + B ρ B ρ B internal background internal background = B ρ B internal internal (2.13) Rewriting Eq. (2.13) yields ρ ( δ ρ) B = B B = B (2.14) internal internal internal where δ is a unit impulse at the center of the radial function. Therefore, B internal can be reconstructed from the interim data, B, by deconvolution ( -1 ) of B using the kernel (δ 1 ρ). i.e. ( ) B internal = δ ρ B. 19

30 Chapter 3 Susceptibility Map-Weighted Imaging (SMWI) for Neuroimaging 3.1 Introduction MR image phases contain unique information regarding local susceptibility changes between tissues, which can be useful in measuring iron content [48] and depicting venous information. The phase information is not only meaningful itself but is the basis for other applications such as quantitative susceptibility mapping (QSM) and susceptibility-weighted imaging (SWI). QSM provides a novel contrast in MR imaging, with the voxel intensity representing the apparent magnetic susceptibility of the underlying tissue. It has been used for chemical identification and quantification of specific biomarkers [42, 49-51] along with various clinical applications [6, 7]. Quantitative susceptibility can also be used to map white matter fiber orientations [52-54]. SWI, on the other hand, uses phase images to enhance contrast of the magnitude image [2, 3]. It is also widely used for many clinical applications [2, 3, 55, 56]. However, image phase is not an intrinsic tissue property and may not be easily reproducible due to its nonlocal and orientation-dependent properties. This particular nature of phase has thus restricted the resolution achievable and has required processing for different imaging orientations in SWI [57]. These limitations have not been completely resolved. 20

31 The purpose of this study is to suggest a susceptibility map-weighted imaging (SMWI) method by combining the magnitude image with a QSM-based weighting factor to provide an alternative contrast for susceptibility imaging. This combination with the magnitude image provides an image that can be represented more like a conventional T 2 * image, as is in SWI. The QSM-based weighting also resolves issues of nonlocal and orientation-dependence of phase. The QSM-based weighting factor was determined using phantom simulations. A multi-echo denoising method was further implemented to enhance the signal-to-noise ratio (SNR), which was used to obtain high-resolution images. The method was evaluated on healthy volunteers and on a stroke patient to evaluate the clinical feasibility. Magnitude images, SWI, and/or QSM images were also obtained for visual comparisons. 3.2 Methods Brain MR Imaging For in vivo brain imaging, healthy adult volunteers (eight male, 28 ± 4 years old) were scanned with a standard flow-compensated three-dimensional (3D) multi-gradient echo (MGRE) sequence. Isotropic and anisotropic high-resolution MGRE sequences using a 3 Tesla scanner (Tim Trio, Siemens Medical Solutions, Erlangen, Germany) with an eightchannel head coil were used to cover the whole brain. The isotropic MGRE sequence parameters were as follows: repetition time (TR) = 95 ms, first echo time (TE) = 5.67 ms, echo spacing = 5.51 ms, flip angle = 27 o, field of view (FOV) = mm 2, number of slices = 128, number of echoes = 16, voxel size = mm 3. The anisotropic highresolution MGRE sequence parameters were as follows: TR = 80 ms, first TE = 15 ms, echo spacing = 2.3 ms, flip angle = 20 o, FOV = mm 2, number of slices = 120, number of echoes = 10, voxel size = mm 3. 21

32 For each subject, contrast-to-noise ratio (CNR) values as defined in Eq.(3.5) were measured from six ROIs in the magnitude image, SWI, and SMWI. The ROIs chosen were the globus pallidus, putamen, substantia niagra, red nucleus, lateral ventricle, and optic radiation since most of these regions are studied for various applications such as estimating iron concentration and visualizing brain anatomic structures [49, 58, 59]. The background regions were selected near each selected ROIs. The estimated CNR values were averaged across all subjects and compared for each reconstruction method. A hemorrhagic stroke patient (male, 63 years old) was scanned with the following parameters: TR = 35 ms, first TE = 4.92 ms, echo spacing = 4.92 ms, flip angle = 20 o, FOV = mm 2, number of slices = 55, number of echoes = 6, voxel size = mm 3, scan time = 8 min 13 sec. All images were obtained with axial orientation Multi-echo Denoising To further improve the image quality, a model-based temporal domain denoising method was applied to both the magnitude and phase image [20, 60]. This denoising procedure was especially needed for the late echo data because the late echo images have low SNR. The magnitude signal was assumed to follow the tissue-specific multicomponent T 2 * decay. A model, based on the multicomponent T 2 * decay curve, was applied for denoising the magnitude images in the temporal domain. The phase signal increases (for paramagnetic tissues) or decreases (for diamagnetic tissues) linearly with echo times. Therefore, a linear function was fitted to denoise the phase images in the temporal domain Image Reconstruction 22

33 Brain images were reconstructed with 3D Fast Fourier transform using the complex k-space data for each of the eight receiver coils. The magnitude image was obtained using the sum of square method from the eight magnitude images, while the phase image was obtained following the method outlined in Li et al [31]. The denoising schemes were applied afterward. Although the original magnitude images could be used for generating SWI and/or SMWI, the denoised images were used to enhance the SNR in this study. The SWIs were reconstructed from the magnitude and phase images of each echo, while the SMWIs were reconstructed from the magnitude and QSM images of each echo. To obtain the high-pass filtered phase for SWI, a hamming window was applied to the k- space data. The resulting low-frequency phase images were then subtracted from the original phase images using complex division [2, 3, 61]. Because some structures have negative phase and other structures have positive phase, a negative phase mask and a positive phase mask was created individually to enhance the contrast of specific tissues. The masked phase was raised by a power of four to generate the weighting factors as proposed in the original SWI [2]. To obtain the QSM used for generating the SMWI, a Laplacian method for phase unwrapping was used [31]. The background phase was removed with a projection onto-dipole fields method [16]. The frequency map was then calculated from the resultant local phase image. QSM was calculated from the frequency map using the LSQR method [31]. The process of obtaining SMWI is similar to the SWI process except for the base of the weighting factors. The susceptibility mask was designed to suppress pixels that have certain susceptibility values. Mathematically, the SMWI is defined as: m { mask } ( ) ( ) ( ) SMWI x = S x mag x (3.1) where S mask (x) and mag(x) are the susceptibility mask and the original magnitude image at location x, respectively. 23

34 The susceptibility mask was applied in the following manner: if the diamagnetic susceptibility of interest is, e.g., in the -th values ~ 0 ppm range, then the susceptibility mask was designed as follows: ( ) 0 Svalue x < thvalue Smask ( x) = ( Svalue ( x) + thvalue ) / thvalue thvalue Svalue ( x) < 0 1 otherwise (3.2) where S value (x) is the quantitative susceptibility value at location x and th values is the threshold value bigger than zero. From Eq. (3.2), those pixels with a susceptibility of -th values or less will be completely suppressed and those with a value between -th values and zero susceptibility values will be only partly suppressed. This S mask (x) then takes on values that lie between zero and one and is referred to as diamagnetic susceptibility mask. It can be applied any number of times (integer m in Eq. (3.1)) to mag(x) to create a new image with different contrasts. Similarly, if the paramagnetic susceptibility of interest is, for example, 0 ~ th values ppm, then the susceptibility mask is designed as follows, which is referred to as a paramagnetic susceptibility mask: 0 thvalue < Svalue x S ( x) = ( th S ( x) ) / th 0< S ( x) th 1 otherwise ( ) mask value value value value value (3.3) In this work, either negative or positive phase mask for SWI (nswi or pswi) was used to improve the contrast of the specific tissues in the magnitude image. In the SMWI case, either diamagnetic (dsmwi) or paramagnetic susceptibility masks (psmwi) from above was used. Simulations were conducted to determine the optimal number of susceptibility mask multiplication and threshold value (details in the next sections). All the post-processing methods were implemented on a PC (Intel Pentium Processor 2.4 GHz, 8 GB of RAM) operating on a Microsoft Windows 7 operating system using MATLAB R2009b (Mathworks, Natick, MA, USA ). 24

35 3.2.4 Optimization of the Susceptibility Mask Multiplication: Simulation Simulations were performed to determine the optimal number of susceptibility mask multiplication using estimated CNR values. This approach is similar to the method of Haacke [2]. A series of circles with radius varying from 1 to 16 pixels (i.e. 1, 2, 4, 6, 8, 10, 12, 14, and, 16) within a matrix was created (Figure 3.1). The susceptibility value of the circles was set at 0.3 ppm. Various background susceptibility values (i.e. 0, 0.05, 0.1, 0.2 ppm) were set to simulate different situations. The initial signal intensity of all pixels within the images was set to A Gaussian noise with various standard deviations (SD) was added to the real and imaginary parts of the k-space data to simulate different SNR cases (i.e. SNR = 5, 10, 15, and 20). A region of interest (ROI) was drawn inside each circle to obtain the averaged CNR between the ROI and background (Figure 3.1. (A)). The averaged CNR was defined as: CNR = CNR n n i (3.4) i=1 { ( )- ( )} CNR = abs mean S mean S σ i i background background (3.5) where n is the number of the ROI, S i is the signal intensity of each ROI, S background is the signal intensity of the background and σ background is the SD of the background Optimization of the Threshold Value: Simulation Figure 3.2 (A) and (B) show a series of simulated circles (i.e. ROIs) that were created for determining the optimal threshold value. The radius of the circles was set to 16 pixels within a matrix. Various susceptibility values (i.e. 0.01, 0.02, 0.03, 0.04, 0.1, 0.17, 0.18, 0.19, and 0.2 ppm) were assumed to the individual ROIs with background set at 0.1 ppm. The 25

36 initial signal intensity of all pixels within the image was set to A Gaussian noise with SD of 100 was added to the real and imaginary k-space data to simulate SNR = 10 case. The purpose of this simulation was to estimate the contrast between ROIs which have similar susceptibility values. The relative contrast (RC), therefore, was used to estimate contrast as a metric. The RC was defined as follows: { ( ROI ) ( )} ( ) ( ) a ROIb ROIa ROIb RC = abs mean S mean S mean S + mean S / { } (3.6) where S ROI a, SROI b are the signal intensity of ROI a and ROI b, respectively. 3.3 Results Simulation: Optimal Number of Multiplications Simulation results to determine the optimal multiplication number are shown in Figure 3.1. The reconstructed SMW images in Figure 3.1 (B) (E) demonstrate that the best CNR was obtained when the number of multiplications was approximately 4 (m = 4) for the case of 0.3 ppm objects using the threshold value of 1 ppm (details of the threshold value are presented in the next section). Figure 3.1 (F) represents the estimated CNR for various SNR and number of multiplications with a background susceptibility value of 0.1 ppm. The estimated CNR values steadily increased until the number of multiplications reaches approximately 4, afterward, the CNR values decreases for a given SNR. The estimated CNRs for the various background susceptibility values are represented in Figure 3.1 (G) (SNR fixed to 10). A higher CNR was obviously obtained with lower background susceptibility values. The optimal number of multiplications is still around 4, as shown. Figure 3.1 (H) shows estimated CNRs using different threshold values (SNR and background susceptibility values were fixed to 10 and 0.1 ppm, respectively). It is known that the noise level will increase with the number of multiplications. Hence, the peak of the CNR decreases with multiplications. The 26

37 number of multiplications to reach the peak CNR increases with the threshold value. For threshold values between 0.8 to 1.2 ppm, however, the obtained peak CNR values showed little differences. For these cases, m = 4 seemed to be a reasonable multiplication number. In this figure, a specific case (i.e., SNR = 10 and/or background susceptibility value = 0.1 ppm) was only represented as one example, but other cases show similar results (not shown here). 27

38 Figure 3.1 Optimizing the number of multiplications. A E: Illustrative example of the reconstructed SMWI. Reference susceptibility map (A) and simulated images with the susceptibility mask multiplied once (B), 4 times (C), 8 times (D), and 16 times (E). All circles have the same susceptibility value of 0.3 ppm with background susceptibility of 0.1 ppm (threshold value = 1 ppm). F: Estimated CNR with different SNR cases (background susceptibility value = 0.1 ppm, threshold value = 1 ppm). G,H: Estimated CNR using different background susceptibility values (SNR = 10, threshold value = 1 ppm) (G), and estimated CNR using various threshold values for making susceptibility masks (SNR = 10, background susceptibility value = 0.1 ppm) (H). 28

39 3.3.2 Simulation: Optimal Threshold Value Simulation phantom images and estimated RC values of the simulated data are presented in Figure 3.2. Figure 3.2 (C) represents measured RC values between selected ROIs using the optimal multiplication number for each corresponding threshold value estimated in Figure 3.1 (H). The estimated RC values of similar susceptibility regions increase until the threshold value reaches around 1 ppm, afterward the values decrease. The simulation indicates that a threshold value of 1 ppm is a reasonable value to maximize contrast between tissues of various susceptibility. In this figure, only several specific cases are represented as examples, but other cases show similar results (not shown). Although the peak CNR is low compared with the values at 0.4 and 0.6 ppm, we chose the threshold value of 1 ppm because it displayed the highest RC value. 29

40 Figure 3.2 Optimizing the threshold values. A, B: Reference ROI map (A) with its susceptibility map (B). C: Several examples of the estimated RC values between the ROIs are chosen. The estimated RC values were obtained using the optimal number of multiplications corresponding to each threshold value as measured in Figure 3.1 (H). 30

41 Figure 3.3 represents one example of in vivo psmwi reconstruction. Images in the first row show the magnitude image, and reconstructed SMWI with varying susceptibility mask multiplication numbers, with the threshold value fixed to 1 ppm. Images in the second row demonstrate the reconstructed SMWI using different threshold values with the susceptibility mask multiplication number fixed at 4. In vivo results show similar features to the simulated phantom case. The increasing number of multiplications by the susceptibility mask and the decreasing threshold values resulted in dark patches due to excessive weighting. From these in vivo and phantom results, the optimal number of multiplications and threshold value were found to be around 4 and 1 ppm, respectively. 31

42 Figure 3.3 The effects of the number of multiplications by the susceptibility mask and the threshold values on in vivo data. The first row shows the magnitude images, and reconstructed psmwi with various number of multiplications by the susceptibility mask (threshold value = 1 ppm). The second row shows the reconstructed psmwi using different threshold values (number of multiplications by susceptibility mask = 4). 32

43 3.3.3 Multi-echo Denoising Method The reconstructed isotropic resolution images of the multi-echo SMWI, and denoised multiecho SMWI for the 6th, 8th, and 10th echo are shown in Figure 3.4. Comparison between the predenoised images and denoised images showed that the temporal domain denoising method enhanced the SNR without spatial artifacts, such as blurring especially, at the late echo image. The enlarged region in Figure 3.4 shows this clear SNR improvement. Through these denoising methods, high quality multiple-echo images could be obtained, which were subsequently used in the SMWI process. Figure 3.4 Multi-echo reconstruction results. Each row represents the SMWI, and denoised SMWI at the 6th, 8th, and 10th echo of the MGRE sequence. Multi-echo imaging shows different T 2 * weightings at multiple time points. Through the temporal domain denoising method, suppression of noise in the spatial domain and increase of SNR of each echo image 33

44 is accomplished especially at the late echoes. All images are displayed with the same intensity range. The SD values are also noted In vivo Anisotropic High-Resolution Data of Healthy Volunteers Figure 3.5 shows example images of SMWI using the data (TE = 22 ms). Images in the first row represent one example of the reconstructed dsmwi and psmwi using the same magnitude image and QSM. These two images show different features: dsmwi enhances the contrast of diamagnetic susceptibility tissues such as optic radiations and psmwi enhances the contrast of paramagnetic susceptibility tissues such as substantia niagra. In the second row, a comparison with QSM is provided from images obtained a healthy volunteer. It is seen that the dsmwi better depicts the Meyer s loop (pointed by an arrow) compared to magnitude image and QSM. The estimated CNR values were 3.08, 1.27, and 3.98 for corresponding magnitude image, QSM, and SMW images. 34

45 Figure 3.5 Two illustrative figures of SMWI. The images in the first row represent differences of dsmwi and psmwi from the same magnitude and QSM images. The images in the second row compare the magnitude, QSM, and dsmw images. The Meyer s loop (pointed by an arrow) is more conspicuously visualized in dsmwi compared to magnitude and QSM images. The CNR values of this structure are noted, which were obtained from the solid line (as the ROI) and dotted circle (as the background). 35

46 Figure 3.6 One example of comparison among the magnitude images, SWI and SMWI. The SMWI shows alternative contrasts compared with the magnitude and SW images. In the first row, psmwi more clearly depicts a high iron concentration region such as the red nucleus (RN). In the second row, dsmwi noticeably depicts the posterior limbs of the internal capsule (PLIC) on both sides. Reconstructed magnitude images, SWI, and SMWI using the data at TE of 20 ms from a healthy volunteer are shown in Figure 3.6. SMWI presents an alternative contrast compared to magnitude and SW images. The red nucleus, i.e. high iron deposition region is depicted with high contrast in psmwi. Also, dsmwi provides depicted the posterior limbs of the 36

47 internal capsule clearly. The estimated CNR values from several brain structures are listed in Table 3.1. These regions were selected from ROIs used in other studies which are closely related to the diagnosis of neurodegenerative disorders and determination of surgical planning [59, 62-64]. For these regions, the SMWI shows increased CNR values compared to the other images. Table 3.1 The estimated CNR values of several regions obtained from 8 healthy volunteers Structure CNR (Mean ± SD) Magnitude SWI SMWI Globus Pallidus 7.3 ± ± ± 4.9 Putamen 2.9 ± ± ± 3.2 Substantia nigra 4.8 ± ± ± 2.8 Red nucleus 5.6 ± ± ± 2.9 Lateral ventricle 2.6 ± ± ± 1.6 Optic radiation 3.8 ± ± ± 1.0 Additional features of the SMWI are presented in Figure 3.7. Simple high-pass filtering in SWI generates irregular weighting (shown in the second row), even in the same structure. This can cause enhancement in edge regions, especially for large structures such as globus pallidus, and putamen [65]. On the other hand, susceptibility mask have a relatively uniform weighting (Figure 3.7). One limitation of SMWI is a remaining streaking artifact especially in coronal or sagittal planes induced from QSM that is the weighting factor of the SMWI. Nevertheless, SMWI is 37

48 relatively insensitive to the streaking artifacts compared with QSM (arrows in Figure 3.7), because SMWI uses one side of susceptibility values (i.e. dsmwi only uses diamagnetic susceptibility values and psmwi only uses paramagnetic susceptibility values). Figure 3.7 Comparative results of SWI, QSM, and SMWI in vivo. The first row shows reconstructed SWI with different filtering sizes and SMWI. The matrix size in SWI represents the size of the central low-pass filtered region. The second row shows the corresponding phase and susceptibility masks used for the SWI and SMWI, respectively. The third and fourth rows compare QSM and corresponding SMWI. The blue boundaries in the QSM and SMWI images represent boundaries of the magnitude images. 38

49 Figure 3.8 Three successive slices of the reconstructed data obtained from a hemorrhagic stroke patient. Each column represents the magnitude image, phase image, QSM, SWI, and SMWI, respectively. The regions pointed by arrows represent the artifacts due to the nonlocal property of phase, which is reduced in the SMWI Clinical Data The reconstructed magnitude, phase, QSM, nsw, and psmw images obtained from a stroke patient with micro-hemorrhage and calcification over three successive slices using one specific echo data are shown in Figure 3.8 (TE = 19.7 ms). Both SWI and SMWI enhance the contrast of the cortical gray/white matter, high iron deposition region such as red nucleus (first row) and micro-hemorrhage (second and third rows). SWI that is based on phase images, 39

50 however, has the possibility to produce artifacts due to its nonlocal property. Artifacts in SWI by excessive phase weighting in huge blood vessels and the lower part of the thalamus can be observed (arrows in the first row). Also, blooming artifact in phase and SW images due to the nonlocal property of the phase at the edge of the red nucleus can be seen, which is due to the high iron concentration of the red nucleus making strong dipole fields (arrows in the second row). These nonlocal effects have been previously reported [66, 67] and may lead to erroneous identification of anatomic structures as shown here. In contrast to the SWI, SMWI shows significantly reduced artifacts. 3.4 Discussion In this work, a new susceptibility imaging method using QSM, which we termed SMWI was proposed and developed. The reconstruction algorithm to produce SMWI based on the magnitude image and QSM was optimized. With a denoising method added, high-quality human brain in vivo SMWI was produced. Image phase contains unique information regarding tissue composition. However, it is difficult to estimate and reproduce tissue-specific phases due to its nonlocal and orientationdependent properties. On the other hand, QSM represents quantitative susceptibility values of the tissue composition and removes blooming artifacts and the orientation-dependence of the dipole field. Furthermore, SWI may contain artifacts from remaining phase wrapping even when the phase images were high-pass filtered, especially at the long TE. SMWI, therefore, may have some advantages such as avoiding artifacts induced by phase using QSM as its weighting factor. In addition to these benefits, the combination with magnitude images further increases the contrast. Also, unlike QSM, the combination produces images with overall features similar to those of conventional GRE images. 40

51 One limitation of QSM is the loss of information at the outer border regions of the brain (blue boundaries in Figure 3.7). Voxels are inevitably removed at the border due to the processing of the phase data to remove background field contributions, making it difficult to detect lesions in these regions. An added benefit of SMWI is that magnitude images are replaced in these regions, albeit if no weighting factors from QSM are used. The key requirement to generate high-quality SMW images is obtaining accurate and reliable QSM. Obtaining QSM requires solving an inverse problem that has zero coefficients on a pair of cone surfaces in the Fourier domain at the magic angle with respect to main magnetic field B 0. Consequently, spatial frequencies on the cone surface are underdetermined, which often leads to severe streaking artifacts in the reconstructed QSM. Many algorithms have been developed to compensate the streaking artifacts and acquire accurate susceptibility values [30, 31, 50]. Also, noise in QSM is approximately inversely proportional to the product of the B 0, TE, and SNR of the magnitude image [68]. Increasing the SNR of the magnitude image would, therefore, decrease the noise level of QSM. Several methods can be applied to improve SNR, for example by applying higher order shims or local shims [69, 70]. Producing SMWI needs relatively long reconstruction times compared to SWI, because it requires generating the QSM. However, new methods to facilitate QSM reconstruction in seconds were recently developed [71] that can overcome this limitation. In addition to improving the SNR of magnitude images, improving the CNR and SNR of the phase images would also improve the quality of SMWI. To accumulate sufficient phase contrast, long TEs are typically needed. This will increase the data acquisition time especially for high-resolution and whole-brain 3D phase image. There are several possible solutions for accelerating the data acquisition, such as fast imaging methods [72-74] and efficient readout trajectories [75-77]. In SMWI, when diamagnetic is used as the weighting factor (i.e., dsmwi), white matter and 41

52 other diamagnetic materials such as calcium compounds appear hypointense. This dsmwi is, therefore, useful for studying white matter diseases and calcifications in the tumors. In regions of calcification, the strong diamagnetic susceptibility of calcium compounds would enhance the hypointensity as shown in the stroke patient case. On the other hand, loss of myelination or accumulation of iron in diseases such as multiple sclerosis will manifest as reduced hypointensity in SMWI. When paramagnetic susceptibility is used as the weighing factor (i.e., psmwi), veins and deep nuclei appear hypointense. One potential application of the psmwi is venography, which has been one main application of SWI. QSM eliminates the nonlocal property of the phase. Therefore, SMWI can depict the vein with accurate width and sharp edges, especially for small vessels [78, 79]. In addition, SMWI can also be useful for depicting hemorrhage in stroke and micro-hemorrhages in traumatic brain injuries and small vessel disease. In cases of localized high concentrations of iron deposits, SMWI could be advantageous in defining their boundaries and locations. One potential limitation of SMWI in studying white matter is the complication caused by anisotropic magnetic susceptibility [53, 80]. It has been shown that the susceptibility of white matter is anisotropic. Therefore, although QSM removes the dipole field variation, it is still susceptible to the intrinsic susceptibility orientation variations. Nevertheless, the SMWI technique also can be combined with susceptibility tensor imaging by using the mean magnetic susceptibility as the weighting function, thus completely eliminating the anisotropic effect. 42

53 Chapter 4 Simultaneous Neuro Imaging of Susceptibility and Conductivity 4.1 Introduction MRI can offer various types of qualitative and/or quantitative information. Magnetic susceptibility is an intrinsic property of tissue and can be used for qualitative and quantitative MR imaging (e.g. phase imaging [11, 12] and susceptibility weighted imaging [2, 3] for qualitative imaging, quantitative susceptibility mapping (QSM) [30, 31, 37] and susceptibility tensor imaging [53, 54, 81] for quantitative imaging). QSM represents the apparent magnetic susceptibility of the underlying tissue in the voxel and provides a novel contrast in MR imaging. Some of the usage of QSM includes chemical identification of specific biomarkers [40, 42, 49], and for clinical applications [6, 7, 82]. While QSM can be used for mapping the magnetic properties, the counterpart electric property also has been shown to be of use (e.g. quantitative conductivity mapping (QCM) [83-87] and conductivity tensor imaging [88-90]). QCM extracts the electrical property of tissue from the spatial variation of radiofrequency (RF) field distribution (i.e. B 1 field). The electrical conductivity value measured by QCM reveals in part the physiological characteristic of the tissue associated with ion concentration [91], diffusivity [92], ph [93]. Therefore, QCM has the potential to be employed for diagnosis such as tumor [5, 94]. Although electric and magnetic properties are naturally linked through Maxwell s equations, conductivity and susceptibility have usually been measured independently. This situation 43

54 involves several drawbacks such as lengthened scan time, mis-registered images, and different physiological noise and other distortions. To resolve these drawbacks a recent study has shown that simultaneous imaging can be possible using multi-echo gradient echo sequence [95]. The purpose of this chapter is to propose a method for simultaneous quantitative threedimensional (3D) mapping of susceptibility and conductivity. A double-echo ultrashort echo time (UTE) imaging was used for the study. In other words, ultrashort echo was included in the general 3D gradient echo sequence and the UTE phase was assumed the TE = 0 phase (i.e. RF induced phase). While QSM using long TE has been used routinely, QCM using UTE has not been previously validated. Hence, UTE based conductivity mapping was verified using simulation study and NaCl phantom experiments. The simultaneous imaging method was furthermore evaluated on healthy volunteers and the feasibility for clinical applications through in vitro hematoma experiments is demonstrated. The determination of hematoma aging has yet to be studied quantitatively, hence this method could provide useful information which can be important for monitoring and treating intracranial hemorrhage patients. 4.2 Materials and Methods This study was approved by institutional review board. Written informed consent was obtained from all human subjects Simulation A brain model was simulated to observe whether the UTE data can be used to determine the conductivity. Using an electro-magnetic (EM) simulation software (REMCOM XFDTD ver.7.1), a D simulation brain model composed of 3 regions (cerebral spinal fluid 44

55 (CSF), gray matter (GM), and white matter (WM)) was built. The phase effects due to RF pulse were simulated assuming dielectric properties (assigned conductivity values were: CSF = 2.3 S/m, GM = 0.3 S/m, and WM = 0.6 S/m, assigned relative permittivity values were: CSF = 84.04, GM = 52.53, and WM = 73.52). A 16-rung birdcage head coil was assumed for the simulations. The phase distribution at TE = 0 was determined by the EM simulator while phase distribution afterwards (i.e. TE = 40 us, 100 us, 500 us, 1 ms, and 5ms) were implemented using a Fourier based rapid approach under a given susceptibility distribution [36] (The susceptibility values of the above mentioned regions were assigned -9.04, , and ppm, respectively. The susceptibility values were quoted in Ref. [66]). The normalized root mean square error (NRMSE) criteria was used for quantitative comparison of reconstructed QCM images Phantom Experiment The experiment was to validate the UTE conductivity mapping with RF induced phase by performing conductivity quantification with different concentrations of NaCl. The phantom was composed with 2% and 3% concentration of NaCl (Figure 4.3). The reference conductivity values were measured using a conductivity meter In vitro Hematoma Phantom Experiments The experiments were to simulate temporal EM property variations of human blood using simultaneous susceptibility and conductivity mapping. Two 10 ml venous blood was extracted from four healthy volunteers and 1 ml of heparin was injected into one blood sample to prevent coagulation. The extracted blood in the syringe was embedded in a 1.5% agarose gel phantom, individually. Physiological saline solution was added to eliminate the 45

56 remaining air inside the phantoms. The normal blood phantoms were scanned every hour during the first 6 hours, then at 24 hours, 120 hours, and 192 hours. The heparinized blood samples were scanned at 24 hour Data Acquisition All experiments were conducted on a 3T clinical scanner (Tim Trio, Siemens Medical Solutions, Erlangen, Germany). A 3D radial double-echo UTE sequence was designed to acquire the data. After a hard-pulse excitation, two radial center-out projections were acquired for sampling the each echo data. A simple pulse sequence diagram is shown in Figure 4.1. For phantom imaging, a four channel Rx coil was used for signal reception. The scan parameters of the 3D radial double-echo UTE sequence were as follows: TR = 20 ms, first TE = 0.04 ms, second TE = 15 ms, flip angle = 8, FOV = mm 2, number of spokes = 28223, voxel size = mm 3 For in vivo brain imaging, healthy adult volunteers were scanned with four channel Rx head coil to cover the whole-brain. The 3D radial double-echo UTE scan parameters were as follows: TR = 25 ms, first TE = 0.04 ms, second TE = 20 ms, flip angle = 8, FOV = mm 2, number of spokes = 65535, voxel size = mm 3. 46

57 Figure 4.1 3D double-echo UTE pulse sequence diagram and corresponding radial k-space trajectory. The first echo data was used for obtaining the QCM, and the second echo data was used for creating the QSM QSM Reconstruction To obtain the QSM, the frequency map in each voxel was estimated using a complex-value linear fitting of the temporal data which can remove RF induced phase effects [32, 96, 97]. Afterwards, a Laplacian method was applied for spatial phase unwrapping [31] followed by projection-onto-dipole fields method to remove the background phase [16]. Finally, the morphology enabled dipole inversion method was used for reconstructing the QSM [32, 98] QCM Reconstruction For conductivity mapping, the phase-based electric properties tomography (EPT) [83, 86, 87] was employed using the UTE phase (i.e. first echo data). A 3D weighted polynomial fitting technique was applied to calculate the second order spatial derivative of phase. Magnitude image at the second echo was used to produce weighting factors for polynomial fitting. After 47

58 polynomial fitting, a bilateral filtering was applied. In this work, data from multi Rx coils were used for enhancing the SNR compare to the data from single Tx/Rx channel [99, 100]. All post-processing methods were implemented on a PC (Intel Pentium Processor 2.4 GHz, 8 GB of RAM) operating on a Microsoft Windows 7 operating system using MATLAB R2009b (Mathworks, Natick, MA, USA ). 4.3 Results Simulation of Brain phantom Figure 4.2 represents the reconstructed QCM images at different TE values and corresponding difference maps. As the TE values increase, the difference between the reference and the reconstructed QCM also increase due to susceptibility induced phase effect. Clear differences are shown in the difference maps after 100 us of TE especially near the structure boundary regions which are due to the second order differential calculation of EPT. The NRMSE values from region of interests (ROIs) are listed in Table 4.1. The NRMSE value from the CSF shows the highest error compared to other ROIs because the CSF region is composed of many small structures in this brain phantom and this makes severe boundary artifacts in the EPT processing. Overall, the NRMSE was within 1 % for TE values below 100us. 48

59 Figure 4.2 Reconstructed QCM images at different TEs and corresponding difference maps. The images in the first row show the results of QCM reconstruction. The second row shows the difference maps between the reconstructed QCM images and reference QCM. As the TE values increase, the errors increase. The third row represents the phantom design, masks of three substructures, and the total mask for calculating the NRMSE. The NRMSE values were listed in Table

60 Table 4.1 The NRMSE values from ROIs at different TE values. TE ROI 40 us 100 us 500 us 1 ms 5 ms CSF 1.76 % 2.44 % % % % GM 0.31 % 0.44 % 7.14 % 9.02 % % WM 0.21 % 0.29 % 1.32 % 2.34 % 5.44 % Total 0.62 % 0.86 % 6.90 % 8.67 % % QCM using UTE phase Figure 4.3 shows the NaCl phantom design, reconstructed magnitude, and QCM image using UTE data. The estimated conductivity values from the reconstructed conductivity map (ROI 1 = 1.43 ± 0.04 S/m, ROI 2 = 0.90 ± 0.02 S/m) show similar results compared to the values obtained by the conductivity meter (ROI 1 = 1.5 S/m, ROI 2 = 0.9 S/m). This result agree with a previous report that propose the possibility of using UTE phase as a source of conductivity mapping [101]. Figure 4.3 Verification of conductivity mapping using the UTE phase. A: NaCl phantom design. B, C: Reconstructed magnitude image (B) and QCM (C). 50

61 4.3.3 In vivo Brain Results Reconstructed in vivo 3D brain images are shown in Figure 4.4. From the first echo data, QCM was acquired, and from the second echo data, QSM was obtained. The 3D whole brain quantitative electric and magnetic property images, therefore, can be acquired at the same time. The second row in Figure 4.4 shows representative slice from the reconstructed images. For one volunteer, the estimated quantitative maps for 18 slices are shown in Appendix A4-1. Table 4.2 shows the estimated QCM values for the literatures [87, 102] and the proposed method in three ROIs (i.e. CSF, GM and WM) from the three subjects. The QCM values measured by the proposed method shows similar results compared to the previous studies. Table 4.2 QCM values estimated from the literatures and the proposed method. ROI Method CSF GM WM van Lier 2.26 ± ± ± 0.1 Voigt 2.19 ± ± ± 0.04 *Proposed method 2.20 ± ± ± 0.05 * : estimated mean and standard deviation value of the three subjects 51

62 Figure 4.4 In vivo reconstructed images of the proposed method. The first row shows 3D visualization of the reconstructed images and the second row illustrates one representative single slice images of each data. 52

63 4.3.4 In vitro Hematoma Phantom Experiments Representative image reconstruction results from the in vitro hematoma phantom experiments are shown in Figure 4.5. The measured quantitative values are listed in Table 4.3 and corresponding temporal plots are given in Figure 4.6. The estimated conductivity and susceptibility values monotonically increased over time. However, conductivity values maintained steady after 24 hours although susceptibility values increased continuously. The measured quantitative values of heparinized blood showed the similar results of 24 hours normal venous blood case (QCM: s/m, QSM: ppm). A possible explanation of the variation of quantitative values within the first 24 hour maybe due to the effects of sedimentation of erythrocytes including the coagulation process. It has been reported that the sedimentation of erythrocytes is a source of variation in conductivity of blood [103, 104], however, finding the specific mechanism of conductivity increment in blood is not completely known. The increase in susceptibility value is caused by the sedimentation of erythrocytes and the underlining hemoglobin (Hb) pathway from oxyhb, to deobyhb, then to methb which agrees with a previous study [105]. 53

64 Figure 4.5 A representative reconstruction results of one volunteer case. Venous blood coagulation process was represented using three types images and two quantitative information was measured over time. The quantitative values were measured from the solid line and the estimated values were listed in Table

65 Figure 4.6 Line plots of the estimated quantitative values. Average and standard deviations of data which are obtained from four volunteers are plotted. Dotted line represents the heparinized case which is estimated at the 24 hours later from venous blood extraction. 55

66 Table 4.3 The average of the measured conductivity and susceptibility values that were obtained from four healthy volunteers. Time [hour] Conductivity [S/m] (0.289) (0.242) (0.399) (0.427) (0.427) (0.349) (0.406) (0.379) (0.463) (0.400) Susceptibility [ppm] (0.090) (0.098) (0.105) (0.106) (0.112) (0.130) (0.152) (0.163) (0.093) (0.120) (): standard deviation of the estimated values. 56

67 4.4 Discussion In this work, a new simultaneous QSM and QCM imaging method using a double-echo UTE sequence was proposed. The possibility of UTE phase as the source of QCM was verified and the proposed method was applied to in vivo imaging. Also, the variation of quantitative information was investigated during the blood coagulation process by an in vitro venous blood experiment. The proposed method has several advantages compared to previous simultaneous susceptibility and conductivity imaging using a multi-echo gradient echo sequence [95]. One is the reduced QCM reconstruction time. The previous study required time consuming phase unwrapping and extrapolation processes to obtain the RF induced phase at TE = 0. Another advantage is the motion insensitivity due to the radial k-space sampling pattern. However, there are several limitations. One limitation of this method is the relatively long data acquisition time for whole brain data acquisition due to the non-selective RF excitation pulse used. The acquisition of the long TE data prevents TR to be shortened. A possible solution is to apply fast imaging methods such as parallel imaging [72, 73] and compressed sensing [74]. Other limitation is the streaking artifacts inherent in the radial acquisition. A 3D radial trajectory was used for data acquisition however Nyquist sampling ratio is not satisfied at the k-space edge regions. This causes streaking artifacts, especially at the outer edge regions of the FOV. Flow compensation gradients were not applied in the proposed method so as to be able to acquire minimum TE which can induce quantification error in flow related regions [106, 107]. The key requirement to generate high-quality QCM and QSM images are obtaining accurate and reliable phase images. Increasing the data SNR would therefore be required. Including additional echoes and applying temporal domain denosing method can be helpful for enhancing the phase SNR [20]. 57

68 Intracranial hemorrhages can be distinguished into several stages such as hyperacute, acute, early subacute, late subacute, and chronic by using conventional T 1 and T 2 weighted imaging. The proposed method can be helpful for further providing accurate and elaborate distinction of hemorrhage stage by offering additional quantitative conductivity and susceptibility information as shown. Although, the estimated QCM values measured by current MR EPT is limited in representing the variations during the blood coagulation process, it seems to reflect the separation of blood composition, i.e. separation of plasma and erythrocytes by sedimentation process of erythrocytes. On the other hand, estimated QSM values would reflect variation of Hb in the coagulation process including the sedimentation effects. There are several limitations in the hematoma evolution experiments. The electrical properties are known to change with temperature [108], however, the results of venous blood phantoms were not obtained in body temperature but in MR scanner room temperature (i.e. lower temperature compared to body temperature) and environments of the in vitro experiments were different to human in vivo (i.e. absence of some enzymes and cells that participate in coagulation process). These may induce some quantification errors compared to the real in vivo situations. There was a recent study demonstrating mapping of regions with high susceptibility values such as the sinuses, bones and teeth using short echo time [109]. These regions are generally lost in the magnitude images and QSM methods due to their very short T 2 * values. These regions can be a potential application of the proposed method using UTE data. Furthermore, it may also be possible to estimate the conductivity values using UTE phase in the regions such as skulls and bones. 58

69 Chapter 5 Summary This chapter summarizes the MR based susceptibility related imaging schemes which are presented in this dissertation. 5.1 Susceptibility Map-Weighted Imaging A susceptibility map-weighted imaging (SMWI) method was proposed by combining a magnitude image with a quantitative susceptibility mapping (QSM)-based weighting factor thereby providing an alternative contrast compared with magnitude image, susceptibilityweighted imaging, and QSM. A 3D multi-echo gradient echo sequence is used to obtain the data. The QSM was transformed to a susceptibility mask and this mask was multiplied several times with the original magnitude image to create alternative contrasts between tissues with different susceptibilities. A temporal domain denoising method to enhance the signal to noise ratio was further applied. Reconstructed SMWI created different contrasts based on its weighting factors made from paramagnetic or diamagnetic susceptibility tissue and provided an excellent delineation of micro-hemorrhage without blooming artifacts typically caused by the nonlocal property of phase. 59

70 As a future work, volumetric study of substantia nigra or red nucleus (i.e. high iron concentration regions) using SMWI for neurodegenerative disease diagnosis and aging related studies can be possible. 5.2 Simultaneous Neuro Imaging of Susceptibility and Conductivity A method for simultaneous quantitative 3D mapping of susceptibility and conductivity using double-echo ultrashort echo time (UTE) imaging was proposed and the evolution of hematoma was investigated using in vitro models though the quantitative information for demonstrating the feasibility of clinical applications. The first TE was chosen to UTE for the quantitative conductivity mapping (QCM) and the second TE was relatively long for the QSM. The QCM method using UTE phase data was verified through the simulation and NaCl phantom experiment. The investigation of QSM and QCM variations during the coagulating process can be helpful in distinguishing the hematoma evolution stages. QSM and QCM of skull and bones can be a future work using UTE data. Furthermore, simultaneous neuro imaging of quantitative susceptibility and conductivity including additional information such as T 2 * and T 2 ' mapping can be possible by combining the spinecho with multiple gradient echo data. 60

71 References 1. Gatehouse, P.D., et al., Applications of phase-contrast flow and velocity imaging in cardiovascular MRI. Eur Radiol, (10): p Haacke, E.M., et al., Susceptibility weighted imaging (SWI). Magn Reson Med, (3): p Haacke, E.M., et al., Susceptibility-weighted imaging: technical aspects and clinical applications, part 1. AJNR Am J Neuroradiol, (1): p Ishihara, Y., et al., A precise and fast temperature mapping using water proton chemical shift. Magn Reson Med, (6): p van Lier, A.L., et al. Electrical conductivity imaging of brain tumours. Proceedings of the 19th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Montréal, Canada, 2011, p Liu, T., et al., Cerebral microbleeds: burden assessment by using quantitative susceptibility mapping. Radiology, (1): p Lotfipour, A.K., et al., High resolution magnetic susceptibility mapping of the substantia nigra in Parkinson's disease. J Magn Reson Imaging, (1): p Balidemaj, E., et al., Feasibility of Electric Property Tomography of pelvic tumors at 3T. Magn Reson Med, E-pub. 9. Gho, S.M., et al., Susceptibility map-weighted imaging (SMWI) for neuroimaging. Magn Reson Med, (2): p Hahn, E.L., Spin echoes. Physical Review, : p Rauscher, A., et al., Magnetic susceptibility-weighted MR phase imaging of the human brain. AJNR Am J Neuroradiol, (4): p Duyn, J.H., et al., High-field MRI of brain cortical substructure based on signal phase. Proc Natl Acad Sci U S A, (28): p Jenkinson, M., Fast, automated, N-dimensional phase-unwrapping algorithm. Magn Reson Med, (1): p Abdul-Rahman, H.S., et al., Fast and robust three-dimensional best path phase unwrapping algorithm. Appl Opt, (26): p Witoszynskyj, S., et al., Phase unwrapping of MR images using Phi UN--a fast and robust region growing algorithm. Med Image Anal, (2): p Liu, T., et al., A novel background field removal method for MRI using projection onto dipole fields (PDF). NMR Biomed, (9): p Schweser, F., et al., Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: an approach to in vivo brain iron metabolism? Neuroimage, (4): p Haacke, E.M., et al., Susceptibility mapping as a means to visualize veins and quantify oxygen saturation. J Magn Reson Imaging, (3): p Denk, C. and A. Rauscher, Susceptibility weighted imaging with multiple echoes. J Magn Reson Imaging, (1): p

72 20. Jang, U., et al., Improvement of the SNR and resolution of susceptibility-weighted venography by model-based multi-echo denoising. Neuroimage, : p Rauscher, A., et al., Improved elimination of phase effects from background field inhomogeneities for susceptibility weighted imaging at high magnetic field strengths. Magn Reson Imaging, (8): p Lee, Y., Y. Han, and H. Park, A new susceptibility-weighted image reconstruction method for the reduction of background phase artifacts. Magn Reson Med, (3): p Oh, S.S., et al., Improved susceptibility weighted imaging method using multi-echo acquisition. Magn Reson Med, (2): p Essig, M., et al., High-resolution MR venography of cerebral arteriovenous malformations. Magn Reson Imaging, (10): p Tan, I.L., et al., MR venography of multiple sclerosis. AJNR Am J Neuroradiol, (6): p Haacke, E.M., et al., Characterizing iron deposition in multiple sclerosis lesions using susceptibility weighted imaging. J Magn Reson Imaging, (3): p Reichenbach, J.R., et al., High-resolution blood oxygen-level dependent MR venography (HRBV): a new technique. Neuroradiology, (5): p Barth, M., et al., High-resolution three-dimensional contrast-enhanced blood oxygenation level-dependent magnetic resonance venography of brain tumors at 3 Tesla: first clinical experience and comparison with 1.5 Tesla. Invest Radiol, (7): p Ashwal, S., et al., Susceptibility-weighted imaging and proton magnetic resonance spectroscopy in assessment of outcome after pediatric traumatic brain injury. Arch Phys Med Rehabil, (12 Suppl 2): p. S Liu, T., et al., Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI. Magn Reson Med, (1): p Li, W., B. Wu, and C. Liu, Quantitative susceptibility mapping of human brain reflects spatial variation in tissue composition. Neuroimage, (4): p Liu, T., et al., Morphology enabled dipole inversion (MEDI) from a single-angle acquisition: comparison with COSMOS in human brain imaging. Magn Reson Med, (3): p Wu, B., et al., Whole brain susceptibility mapping using compressed sensing. Magn Reson Med, (1): p Salomir, R., B.D. De Senneville, and C.T.W. Moonen, A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility. Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering, B(1): p Marques, J.P. and R. Bowtell, Application of a fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility. Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering, B(1): p

73 36. Koch, K.M., et al., Rapid calculations of susceptibility-induced magnetostatic field perturbations for in vivo magnetic resonance. Phys Med Biol, (24): p Shmueli, K., et al., Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data. Magn Reson Med, (6): p Deistung, A., et al., Quantitative susceptibility mapping differentiates between blood depositions and calcifications in patients with glioblastoma. PLoS One, (3): p. e Langkammer, C., et al., Quantitative susceptibility mapping in multiple sclerosis. Radiology, (2): p de Rochefort, L., et al., In vivo quantification of contrast agent concentration using the induced magnetic field for time-resolved arterial input function measurement with MRI. Med Phys, (12): p Liu, T., et al., Unambiguous identification of superparamagnetic iron oxide particles through quantitative susceptibility mapping of the nonlinear response to magnetic fields. Magn Reson Imaging, (9): p Wong, R., et al., Visualizing and quantifying acute inflammation using ICAM-1 specific nanoparticles and MRI quantitative susceptibility mapping. Ann Biomed Eng, (6): p Schweser, F., et al., Toward online reconstruction of quantitative susceptibility maps: superfast dipole inversion. Magn Reson Med, (6): p Bilgic, B., et al., Fast quantitative susceptibility mapping with L1-regularization and automatic parameter selection. Magn Reson Med, (5): p Topfer, R., et al., SHARP edges: Recovering cortical phase contrast through harmonic extension. Magn Reson Med, E-pub. 46. Wen, Y., et al., An iterative spherical mean value method for background field removal in MRI. Magn Reson Med, (4): p Li, L. and J.S. Leigh, High-precision mapping of the magnetic field utilizing the harmonic function mean value property. J Magn Reson, (2): p Haacke, E.M., et al., Imaging iron stores in the brain using magnetic resonance imaging. Magn Reson Imaging, (1): p Bilgic, B., et al., MRI estimates of brain iron concentration in normal aging using quantitative susceptibility mapping. Neuroimage, (3): p de Rochefort, L., et al., Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: validation and application to brain imaging. Magn Reson Med, (1): p Schweser, F., et al. Quantitative magnetic susceptibility mapping (QSM) in breast disease reveals additional information for MR-based characterization of carcinoma and calcification. Proceedings of the 19th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Montréal, Canada, 2011, p Lee, J., et al., Sensitivity of MRI resonance frequency to the orientation of brain tissue microstructure. Proc Natl Acad Sci U S A, (11): p Liu, C., Susceptibility tensor imaging. Magn Reson Med, (6): p Liu, C., et al., 3D fiber tractography with susceptibility tensor imaging. Neuroimage, (2): p

74 55. Thomas, B., et al., Clinical applications of susceptibility weighted MR imaging of the brain - a pictorial review. Neuroradiology, (2): p Mittal, S., et al., Susceptibility-weighted imaging: technical aspects and clinical applications, part 2. AJNR Am J Neuroradiol, (2): p Xu, Y. and E.M. Haacke, The role of voxel aspect ratio in determining apparent vascular phase behavior in susceptibility weighted imaging. Magn Reson Imaging, (2): p Ogg, R.J., et al., The correlation between phase shifts in gradient-echo MR images and regional brain iron concentration. Magn Reson Imaging, (8): p Mori, N., et al., Susceptibility-weighted imaging at 3 Tesla delineates the optic radiation. Invest Radiol, (3): p Jang, U. and D. Hwang, High-quality multiple T(2)(*) contrast MR images from low-quality multi-echo images using temporal-domain denoising methods. Med Phys, (1): p Wang, Y., et al., Artery and vein separation using susceptibility-dependent phase in contrast-enhanced MRA. J Magn Reson Imaging, (5): p Kitajima, M., et al., MR signal intensity of the optic radiation. AJNR Am J Neuroradiol, (7): p Rodriguez-Oroz, M.C., et al., Neuronal activity of the red nucleus in Parkinson's disease. Mov Disord, (6): p Kwon, D.H., et al., Seven-Tesla magnetic resonance images of the substantia nigra in Parkinson disease. Ann Neurol, (2): p Walsh, A.J. and A.H. Wilman, Susceptibility phase imaging with comparison to R2* mapping of iron-rich deep grey matter. Neuroimage, (2): p Schafer, A., et al., Using magnetic field simulation to study susceptibility-related phase contrast in gradient echo MRI. Neuroimage, (1): p Deistung, A., et al., Toward in vivo histology: a comparison of quantitative susceptibility mapping (QSM) with magnitude-, phase-, and R2*-imaging at ultrahigh magnetic field strength. Neuroimage, : p Liu, T., et al. A theoretical analysis of the morphology enabled dipole inversion (MEDI) method: using anatomical information to improve the calculation of susceptibility. in Proceedings of the 19th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Montréal, Canada, 2011, p Kim, D.H., et al., Regularized higher-order in vivo shimming. Magn Reson Med, (4): p Hsu, J.J. and G.H. Glover, Mitigation of susceptibility-induced signal loss in neuroimaging using localized shim coils. Magn Reson Med, (2): p Bilgic, B., et al. Regularized QSM in seconds. Proceedings of the 21st Annual Meeting of the International Society of Magnetic Resonance in Medicine. Salt Lake City, Utah, USA, p Pruessmann, K.P., et al., SENSE: sensitivity encoding for fast MRI. Magn Reson Med, (5): p Griswold, M.A., et al., Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med, (6): p

75 74. Lustig, M., D. Donoho, and J.M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med, (6): p Ahn, C.B., J.H. Kim, and Z.H. Cho, High-speed spiral-scan echo planar NMR imaging-i. IEEE Trans Med Imaging, (1): p Zur, Y., S. Stokar, and P. Bendel, An analysis of fast imaging sequences with steady-state transverse magnetization refocusing. Magn Reson Med, (2): p McKinnon, G.C., Ultrafast interleaved gradient-echo-planar imaging on a standard scanner. Magn Reson Med, (5): p Gho, S.M., W. Li, and D.H. Kim. Quantitative susceptibility based susceptibility weighted imaging (QSWI) for venography. Proceedings of the 20th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Melbourne, Australia, 2012, p Mok, K., et al. Generating susceptibility weighted images using susceptibility maps. Proceedings of the 20th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Melbourne, Australia, 2012, p Li, T.Q., et al., Extensive heterogeneity in white matter intensity in high-resolution T2*-weighted MRI of the human brain at 7.0 T. Neuroimage, (3): p Li, X. and P.C. van Zijl, Mean magnetic susceptibility regularized susceptibility tensor imaging (MMSR-STI) for estimating orientations of white matter fibers in human brain. Magn Reson Med, (3): p Schweser, F., et al., Differentiation between diamagnetic and paramagnetic cerebral lesions based on magnetic susceptibility mapping. Med Phys, (10): p Haacke, E.M., et al., Extraction of Conductivity and Permittivity Using Magnetic- Resonance-Imaging. Physics in Medicine and Biology, (6): p Seo, J.K., et al., Reconstruction of conductivity and current density images using only one component of magnetic field measurements. IEEE Trans Biomed Eng, (9): p Woo, E.J. and J.K. Seo, Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging. Physiol Meas, (10): p. R Katscher, U., et al., Determination of electric conductivity and local SAR via B1 mapping. IEEE Trans Med Imaging, (9): p Voigt, T., U. Katscher, and O. Doessel, Quantitative conductivity and permittivity imaging of the human brain using electric properties tomography. Magn Reson Med, (2): p Degirmenci, E. and B.M. Eyuboglu, Image reconstruction in magnetic resonance conductivity tensor imaging (MRCTI). IEEE Trans Med Imaging, (3): p Degirmenci, E. and B.M. Eyuboglu, Practical realization of magnetic resonance conductivity tensor imaging (MRCTI). IEEE Trans Med Imaging, (3): p

76 90. Kwon, O.I., et al., Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules. Phys Med Biol, (12): p Pethig, R. and D.B. Kell, The passive electrical properties of biological systems: their significance in physiology, biophysics and biotechnology. Phys Med Biol, (8): p Hancu, I., et al., On conductivity, permittivity, apparent diffusion coefficient, and their usefulness as cancer markers at MRI frequencies. Magn Reson Med, E- pub. 93. Doneva, M., et al. 3D fast spin echo acquisition for combined amide proton transfer and elecric properties tomography. Proceedings of the 21th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Salt Lake City, USA, 2013, p Sha, L., E.R. Ward, and B. Story, A Review of Dielectric Properties of Normal and Malignant Breast Tissue, in IEEE SoutheastCon2002: Columbia, USA. p Kim, D.H., et al., Simultaneous imaging of in vivo conductivity and susceptibility. Magn Reson Med, (3): p de Rochefort, L., et al., Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field. Magn Reson Med, (4): p Gho, S.M., N. Choi, and D.H. Kim. Radio Frequency (RF) effects in Quantitative susceptibility mapping (QSM). 2nd International Workshop on MRI Phase Contrast & Quantitative Susceptibility Mapping (QSM). Itaca, USA, 2013, p Liu, J., et al., Morphology enabled dipole inversion for quantitative susceptibility mapping using structural consistency between the magnitude image and the susceptibility map. Neuroimage, (3): p Shin, J., et al. Subject-specific multi-rx data combination using two-stage optimization for phase-based EPT. Proceedings of the 22nd Annual Meeting of the International Society of Magnetic Resonance in Medicine. Milan, Italy, 2014, p Shin, J., et al., Initial study on in vivo conductivity mapping of breast cancer using MRI. J Magn Reson Imaging, E-pub Schweser, F., et al. Conductivity mapping using Ultrashort Echo Time (UTE) imaging. Proceedings of the 21th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Salt Lake City, USA, 2013, p van Lier, A.L., et al., Electrical properties tomography in the human brain at 1.5, 3, and 7T: a comparison study. Magn Reson Med, (1): p Hirsch, F.G., et al., The electrical conductivity of blood. I: Relationship to erythrocyte concentration. Blood, (11): p Texter, E.C., Jr., et al., The electrical conductivity of blood. II. Relation to red cell count. Blood, (11): p Zhang, J., et al. Hematoma Evolution Measured by Quantitative MRI. Proceedings of the 22nd Annual Meeting of the International Society of Magnetic Resonance in Medicine. Milan, Italy, 2014, p

77 106. Choi, N., et al. In vivo conductivity mapping using double spin echo for flow effect removal. Proceedings of the 19th Annual Meeting of the International Society of Magnetic Resonance in Medicine. Montréal, Canada, 2011, p Xu, B., et al., Flow compensated quantitative susceptibility mapping for venous oxygenation imaging. Magn Reson Med, (2): p Foster, K.R. and H.P. Schwan, Dielectric properties of tissues and biological materials: a critical review. Crit Rev Biomed Eng, (1): p Buch, S., et al., Susceptibility mapping of air, bone, and calcium in the head. Magn Reson Med, E-pub. 67

78 Appendix A3-1. Reconstructed SWI and SMWI images for representative 12 slices of one volunteer A4-1 Reconstructed magnitude images and corresponding estimated quantitative maps (i.e. QSM and QCM) of representative 18 slices of one volunteer 68

79 A3-1. Reconstructed SWI and SMWI images for representative 12 slices of one volunteer 69

80 A4-1. Reconstructed magnitude images and corresponding estimated quantitative maps (i.e. QSM and QCM) of representative 18 slices of one volunteer. 70