Spatially Varying Saturation Pulse (SVSP) for Fat Suppression in Breast MRI

Transcription

1 Spatially Varying Saturation Pulse (SVSP) for Fat Suppression in Breast MRI by Tse Chiang Chen A thesis submitted in conformity with the requirements for the degree of Master of Science Department of Medical Biophysics University of Toronto Copyright by Tse Chiang Chen 2016

2 Spatially Varying Saturation Pulse (SVSP) for Fat Suppression in Breast MRI Tse Chiang Chen Master of Science Department of Medical Biophysics University of Toronto 2016 Abstract Achieving reliable fat suppression with high water signal in a clinically acceptable scan time remains a challenge in breast Magnetic Resonance Imaging (MRI). To improve fat saturation in the presence of field inhomogeneity, a spatially-varying saturation pulse (SVSP) is proposed. This work introduces a design methodology for creating SVSPs and describes a practical implementation on a clinical whole body 1.5T MRI scanner. Both simulation experiments with a virtual breast phantom and 1.5T imaging experiments using a phantom test object containing both fat and water were used to demonstrate the feasibility of the proposed method. Initial results indicate that the proposed SVSP method can improve the reliability of fat suppression compared to Spectral Fat Saturation, while using similar pulse durations and exciting similar levels of water signal. SVSP shows promise in terms of its applicability to the clinical setting. ii

3 Acknowledgments Thanks to Dr. Philip Beatty for his enormous devotion of time, incredible patience, effort, and guidance in making this thesis possible. Thanks to Dr. Chuck Cunningham for his continued support and guidance as co-supervisor and committee member throughout my project. Thanks to Dr. Graham Wright for his valuable input as a committee member. Alan, Andrea, and Rachel were incredible for their help and camaraderie. Thanks to Hirad for his guidance in the creation of the simulated field maps. Thanks to Justin Lau for his extraordinary devotion of time, kindness, and help throughout my project. iii

4 Table of Contents Acknowledgments... iii Table of Contents... iv List of Tables... vi List of Figures... vii Chapter 1 Introduction and Background Overview Background Breast Cancer Breast Screening Breast Examination Techniques Breast Cancer Diagnosis and Staging Treatment Breast MRI MRI Fundamentals Breast MRI Protocol Role of Fat Suppression Fat Suppression Techniques The Effect of Field Inhomogeneity on Spectral Fat Saturation Patient Effects on Magnetic Field Inhomogeneity Magnetic Susceptibility Techniques for Reducing Magnetic Field Inhomogeneity Spectral Spatial Selection...23 Chapter 2 Spatially Varying Saturation Pulse (SVSP) for Fat Suppression iv

5 2.1 Design of SVSP Methods Virtual Experiment Verification of Simulated Magnetization Map in Spectral-Spatial Space in Scanner Physical Phantom Experiment Results Virtual Phantom Verification of Simulated Magnetization Map Physical Phantom Experiment Discussion...53 Chapter 3 Future Work and Conclusion References...62 Appendices...68 Calculation of Maximum kx,max...68 v

6 List of Tables TABLE 1 SIMPLIFIED DESCRIPTION OF TNM SYSTEM FOR BREAST CANCER STAGING TABLE 2. COMPARISON OF PRACTICAL ASPECTS OF VARIOUS FAT SUPPRESSION TECHNIQUES vi

7 List of Figures FIGURE 1. ILLUSTRATIVE EXAMPLE OF 90 EXCITATION OF A SPIN FIGURE 2. ILLUSTRATIVE SPECTRUM OF SUBCUTANEOUS FAT AT 1.5 T FIGURE 3. ILLUSTRATIVE EXAMPLE OF FAT-WATER SPECTRAL SEPARATION FIGURE 4. NUMERICAL SIMULATION OF VIRTUAL BREAST AT DIFFERENT FIELD STRENGTHS FIGURE 5. VISUAL REPRESENTATION OF THE FOURIER ENCODING MATRIX FIGURE 6. ILLUSTRATION OF DESIRED TRAJECTORY WITH PARAMETERS LABELED FIGURE 7. VISUAL REPRESENTATION OF THE TARGET MAGNETIZATION FIGURE 8. VIRTUAL EXPERIMENT SETUP FIGURE 9. FREQUENCY MAP AT Z = 12 CM OF VIRTUAL BREAST FIGURE 10. RF VS TIME OF WINDOWED SINC PULSE USED IN FATSAT FIGURE 11. EXCITATION K-SPACE TRAJECTORY AND GRADIENT WAVEFORM FIGURE 12. SPECTRAL-SPATIAL TARGET MAGNETIZATIONS, AS DETERMINED FROM VIRTUAL PHANTOM S FREQUENCY- SHIFT MAP IN A SINGLE SLICE FIGURE 13. ILLUSTRATION OF PHYSICAL PHANTOM FILLED FIGURE 14. PHYSICAL PHANTOM FIGURE 15. ILLUSTRATION OF GRADIENT ECHO SEQUENCE USED FOR PHYSICAL EXPERIMENTS FIGURE 16. PLOTS OF WAVEFORMS FOR VIRTUAL EXPERIMENT FIGURE 17. SIMULATIONS OF MAGNETIZATION MAP OF SVSP IN VIRTUAL EXPERIMENT FIGURE 18. FREQUENCY PROFILE AT X = 9.5 CM OF SVSP FOR VIRTUAL PHANTOM45 FIGURE 19. VIRTUAL EXPERIMENTS OF FAT SUPPRESSION ON VIRTUAL BREAST PHANTOM FIGURE 20. VERIFICATION OF SIMULATED MAGNETIZATION MAP IN SCANNER FIGURE 21. PHYSICAL EXPERIMENT 1 - PHANTOM EXPERIMENT WITH PAPER CLIP ~20 CM AWAY FIGURE 22. COMPARISONS OF ROIS IN PRE-SATURATION, POST FATSAT, AND POST SVSP IMAGES IN PHYSICAL PHANTOM WITH PAPER CLIP ~20 CM AWAY FIGURE 23. PHYSICAL EXPERIMENT 2 - PHANTOM EXPERIMENT WITH PAPER CLIP ~15 CM AWAY FIGURE 24. COMPARISONS OF A REGION OF INTEREST IN PRE-SATURATION, POST FATSAT, AND POST SVSP IMAGES IN PHYSICAL PHANTOM WITH PAPER CLIP ~15 CM AWAY FIGURE 25. FREQUENCY MAP OF SAGITTAL VIEW OF VIRTUAL BREAST PHANTOM AND CROSS SECTION FIGURE 26. VISUAL REPRESENTATION OF A CYCLE IN THE FLYBACK TRAJECTORY vii

8 Chapter 1 Introduction and Background 1.1 Overview Breast cancer is one of the most common forms of cancer in women: approximately 1 in 10 women will develop breast cancer in her lifetime [1]. In Canada alone, 24,000 women were diagnosed with breast cancer in 2014 [2]. In the United States, 40,000 women are predicted to die from breast cancer in 2015 [3]. Treatment plans may include surgery (i.e. lumpectomy for partial breast tissue removal or mastectomy for full removal), chemotherapy, radiation therapy (often used together with lumpectomy and occasionally with mastectomy or chemotherapy), and hormone therapy[3]. Imaging plays important roles throughout the phases of breast cancer management, including screening, diagnosis, treatment planning and both pre and post treatment monitoring. Screening and early detection increase breast cancer survival [3].The Ontario Breast Screening Program (OBSP) has detected over 19,000 cancers in Ontario over more than 20 years, most of which are early stage cancers. This has led to a 33% decrease in breast cancer mortality rates between 1989 and 2004 [4]. Other countries such as Australia, Denmark, England and the Netherlands all report decreases in mortality rate between 19% and 32% [5]. Early detection also results in significantly less costly treatment. In a 1994 study by Salkeld and Gerard, early detection is estimated to save $22 million, reducing treatment costs for advanced breast cancer from $105 million to $83 million in Australia. However, screening is not without controversy. Screening has raised issues with regard to false-positives and overdiagnosis where the detection of nonthreatening cancers or false-positives expose women to unnecessary risks and psychological stress associated with imaging (i.e. radiation from x-rays) and treatment (such as surgical procedures, chemicals, and radiation). However, studies show that the benefits of screening (i.e. it saves lives) has been greater than the harm of overdiagnosis: on average between 2 and 2.5 lives are saved for every overdiagnosed case [6][7]. While mammography is the most common imaging tool used in breast cancer screening, magnetic resonance imaging (MRI) is also an important screening tool that offers complementary information to mammography. The benefits of MRI include its excellent soft-tissue contrast and ability to detect increased microvasculature development that is closely associated with tumours 1

9 [8]. MRI is especially valuable for screening women at high-risk of breast cancer (i.e. women who possess certain factors such as certain mutations of the BRCA1 and BRAC2 gene, a family history of breast cancer, and/or dense breasts [3]) as it is currently the most sensitive modality for detecting invasive breast cancer. The high sensitivity of MRI has been consistently reported in literature. In population studies of predominantly healthy women, the reported sensitivity for detecting breast tumours with MRI is 89% - 100% [8] compared to the reported sensitivity of 75%-90% for mammography [9]. The specificity of MRI is reported to be at range of 37%-97% [10] compared to 90%-95% for mammography [9]. However, the difference in sensitivity is significantly greater among women at high risk: in a 2005 study of a population of women at high risk by Kuhl et al., sensitivity for MRI was reported as 91% while the sensitivity for mammography was reported as 33%.The reported specificity was comparable at 97.2% and 96.8% for MRI and mammography respectively. The drastic difference in mammography sensitivity between the average population and women at high risk highlights the importance of MRI. Not only does MRI offer the highest sensitivity for tumour detection for either population, mammography is significantly less sensitive for women at high risk compared to the average population. However, some outstanding challenges faced by MRI include cost, accessibility, lack of standardization across health facilities, patient discomfort, and technical obstacles. In comparison to mammography, MRI is more costly (in terms of both money and time) and less accessible [11][12]. In MRI breast cancer screening, the requirement of staying immobile inside a large scanner for minutes is a significant inconvenience for patients. Recent research has also called into question the health risks associated with gadolinium-based contrast agents (used to boost tumour contrast) such as its correlation with nephrogenic systemic fibrosis in renal-impaired patients and the accumulation of residual gadolinium in patients who undergo repeated contrastagent injections[13].for radiologists, it is relatively time consuming and challenging to read MRI exams, which contain far more images than mammography. Technical obstacles faced by MRI include creating consistently high quality images in a challenging imaging environment that can include relatively low signal-to-noise, motion, and magnetic susceptibility across air-tissue boundaries. These challenges can lead to imaging artifacts, resulting in images that are grainy, blurry, streaked, or have unwanted elements. This work is focused on addressing one important 2

10 technical challenge for breast MRI: fat suppression. The abundance of fatty tissue in the breast may result in strong fat signals that mask tumour signals, making it difficult for radiologists to identify tumours. Fat suppression is an integral part of breast MRI as it improves radiologists ability to detect tumours by removing the abundant fat signal that may obscure the reading of images, thus improving the radiologists efficiency [10]. However, achieving reliable fat suppression with high water signal in a clinically acceptable scan time remains a challenge for currently available methods. In this work, a new fat suppression method using a spatially-varying saturation pulse (SVSP) is proposed as a way to address this challenge. The SVSP method extends the spectral fat saturation (SFS) method by enabling the fat saturation frequency to vary with spatial position. This work introduces a design methodology for creating SVSPs that can improve the reliability of fat suppression using similar pulse durations as those typically used for SFS. Numerical simulation experiments and phantom imaging experiments are used to demonstrate the feasibility of the proposed method. 1.2 Background An overview of breast cancer including screening, examination techniques, and treatment will be presented, followed by a closer look at breast MRI and relevant technical information Breast Cancer Cancer is the abnormal growth of cells that proliferate out of control. Cancer cells can invade into other tissues, disrupting their functions while using valuable resources. In many cases, they will result in the development of a tumour. If left untreated, cancer can cause death. Breast cancer is one of the most common forms of cancer in women and can be classified based on different schemes such as histopathology, grade, and protein/receptor status. Histopathology refers to the cancer cell characteristics as seen under light microscope and includes information about the cell type in which the cancer starts. Most breast cancers fall under the histopathological classification of invasive ductal carcinoma (cancer originating in the milk ducts of the breast that has invaded the surrounding tissue), which accounts for 80% of invasive 3

11 breast cancers. Also common is invasive lobular carcinoma (invasive cancer originating from the milk glands), which accounts for 10% of invasive breast cancers [3]. Another common classification is ductal carcinoma in situ (DCIS) which, although considered a non-invasive cancer, shows abnormalities in epithelial cells lining the milk ducts. DCIS is considered precancer and about 30% of untreated DCIS develops into invasive cancer [14]. Breast cancer can also be described by grade, which describes the microscopic similarities between the cancerous cells and surrounding normal tissue (i.e. the tumour s level of differentiation where a well-differentiated tumour means the cancer cells look similar to the surrounding normal tissue) and the aggressive potential of the cancer. Grades can be assigned by different grading systems, a popular one being the modified Bloom-Richardson Grading System which assigns grades based on tubule formation (indicative of structural order), pleomorphism (physical characteristics of the cell nuclei for which non-uniform appearance across many cells is indicative of abnormal cell production), and mitotic activity (indicative of how aggressively the cells are reproducing)[15]. Protein/receptor status is also important in the classification of breast cancer as certain drugs act only on breast cancer cells that express certain receptors and/or proteins. Specifically, cancer cells are evaluated for the presence of estrogen receptors, progesterone receptors, and HER2 protein. Estrogen and progesterone are hormones that enhance the proliferation of breast cancer cells that have estrogen and/or progesterone receptors (ER/PR). Hormone therapy drugs control breast cancer by lowering estrogen and/or progesterone levels and/or blocking the receptors on the tumour. HER2, a growth-inducing protein, can also increase breast cancer growth. In patients with elevated HER2 expression (referred to as HER2-positive), drugs can be used to lower HER2 expression. However, some types of breast cancer exhibit neither elevated levels of HER2 nor the presence of ER or PR; for these, methods other than hormone therapy or HER2-specific drugs would have to be used instead [3] Breast Screening Breast screening is used to search for cancers before the manifestation of symptoms. It can find cancers early on, which translates to earlier and usually easier and more effective treatments. 4

12 Screening programs exist in many countries. A typical program may include invitations to women who are registered with a general practitioner and aged 50 or older to attend a breast screening facility where mammography, ultrasound, physical breast examination, and/or selfexamination instruction are performed by a team that may consist of a radiologist, clinical nurse specialist, radiographer, and other support staff [16]. Patients deemed to be at high risk of developing breast cancer may undergo MRI. In Ontario, the OBSP provides screening for women aged 50 to 74 who are at average risk for breast cancer with mammography every two years and for high-risk women aged 30 to 69 years with mammography and breast MRI screening annually. OBSP also helps facilitate referrals for genetic assessment if appropriate [17] Breast Examination Techniques The healthcare team uses different tools to look for different features when performing a breast exam. Physical Exam In a physical exam, a trained health professional performs a manual inspection including palpation of the breast. The following signs and symptoms are assessed if found during the exam: masses, pain, unusual nipple discharge, and skin changes. Palpation may reveal the existence of masses, which may indicate the presence of tumours or cysts. Pain may be a result of hormone changes due to the menstrual cycle or malignancy. Unusual nipple discharge includes non-pregnant milk production, which may be indicative of inappropriate hormone regulation from the pituitary gland or medications, and blood, which may indicate malignancy. Skin changes include color changes that may be indicative of inflammation or infection while an orange-peel like texture (Peau d Orange) is indicative of an uncommon and aggressive malignancy. If symptoms indicative of malignancy are found, further tests such as imaging or biopsy may be performed [3][18]. Following the palpation of the breast, the axillary region should be examined as the axillary lymph nodes are among the first areas of spread in breast cancer [18]. Enlarged or firm axillary 5

13 lymph nodes may indicate malignancy. If an enlarged or firm lymph node is found, the patient may undergo lymph node biopsy where a pathologist would examine the node in a laboratory. Breast Self-Exam Breast self-exam is the regular self-examination of one s breast. This offers a way for women to monitor and report any changes to a health professional. Specific instructions can be given by a health professional or found online. It is interesting to note that with regards to breast self-examination, although it has been promoted for the screening of breast tumours, studies suggest that breast self-examination does not provide significant benefits in women at average risk; instead, it promotes unnecessary use of invasive diagnostic procedures, emotional distress, and higher rate of diagnostic mammographies [19][20]. The Canadian Task Force on Preventive Health Care issued recommendations against selfexaminations in asymptomatic women in its 2011 guideline. Mammography Mammography is the use of x-rays for breast imaging. The breast is placed between two plates that flatten the tissue for easier imaging. In mammography, radiologists look for symptoms such as calcification and mass. Bright spots on the mammogram indicate calcification and are classified into two types, macrocalcification and microcalcification. Macrocalcifications are coarse, larger depositions of calcium that are often seen among women over 50. They are associated with more benign causes such as age, inflammation, and injuries that are generally not associated with cancer [21]. Microcalcifications are much smaller deposits of calcium that are of greater concern, but do not guarantee the presence of cancer. Depending on the shape and pattern of the deposit, a biopsy may be ordered. The presence of abnormal mass can also be detected with mammography. Masses can be cysts (fluid-filled sacs), benign tumour, or malignant tumour. In cases of complex cysts (cysts that are partially solid) and tumours, a biopsy may be performed in addition to further imaging with mammography, ultrasound, or MRI. 6

14 Mammography would also be able to evaluate breast density. High breast density is both more difficult to image with mammography and linked with higher rates of breast cancer. Women with high breast density and suspicious regions may be referred for MRI. Ultrasound Ultrasound, or sonography, uses sound waves to image inside the body. In breast examinations, this is an inexpensive and widely-available tool that serves to complement mammography and physical examination, as it can help locate lymph nodes as well as distinguish between cysts and fat lobules from tumours or abnormalities that would require biopsy. Ultrasound is also useful in guiding needles for biopsies of breast lesions or lymph nodes. However, ultrasound does not always detect early signs of cancer such as microcalcifications and is not recommended as a replacement for mammography or MRI [21]. MRI Magnetic resonance imaging uses a specialized scanner to image the human body. The patient lies inside a large cylindrical scanner and remains motionless throughout the scan. MRI offers high soft-tissue contrast and looks for characteristic disordered angiogenesis that is closely associated with tumours. As MRI is more expensive than the other modalities mentioned, it is not as widely available as the other modalities. Breast MRI is primarily used for two populations. One is women with diagnosed cancer - MRI helps in the following: to improve the measurement of the tumour s size and location; to detect the existence of other tumours; preoperative staging and treatment planning; and assessing the efficacy of neoadjuvant chemotherapy [22]. The other is for screening women at high risk of developing breast cancer. For women at high-risk, MRI, with its high sensitivity, has been shown to improve cancer detection [23]. This work deals with a specific technique used in breast MRI and requires an understanding of MRI physics, its relation to breast anatomy, and breast MRI techniques. A fundamental overview of MRI physics will be given in Section

15 Positron-Emission Tomography (PET) PET requires the injection of sugar analogues labeled with a radioactive nucleus into the body. Due to the metabolic hyperactivity of cancers, there will be a preferential uptake of the radioactive sugar analogues/tracers at the cancer sites, if they are present. An image is then acquired to examine any localizations of radioactivity. PET has not found a role in early breast cancer imaging, but is useful for checking for metastases. Biopsy A biopsy is the extraction and analysis of a tissue sample in a pathology laboratory. It is performed and examined in a pathology laboratory whenever an imaging modality detects suspicious abnormalities in the breast that may be indicative of cancer. Various types of biopsies can be performed, with the three main types being fine needle aspiration, core biopsy, and surgical biopsy. Fine needle aspiration involves the use of a thin needle to extract a sample but in some cases may not give a clear diagnosis. Core needle biopsy uses a larger needle to extract a larger sample a variant of core needle biopsy is vacuum assisted core biopsies where the tissue is collected inside a localized vacuum created by a probe. Surgical biopsy may also be performed. It usually follows the removal of the entire suspected tissue and a safe margin in the surrounding tissue [3]. This is to check for the complete removal of the cancerous tissue. An important biopsy is the lymph node biopsy. If lymph nodes are enlarged, needle biopsy is performed on the node. Its significance lies in the fact that affected lymph nodes are highly indicate of cancer spread and can alter treatment plans. Some specific lymph node testing methods include axillary lymph node dissection and sentinel lymph node dissection. Procedures involving needles can be guided by different modalities such as palpation, ultrasound, mammography (used for core biopsies), and MRI. 8

16 1.2.4 Breast Cancer Diagnosis and Staging In cases where the results of the biopsy indicate benign tumour, no further treatment is necessary. However, if the results indicate a malignant tumour, the physician may request additional imaging tests. Based on these findings, the tumour is staged where the extent of its spread in the body is determined [3]. The standard for staging is the American Joint Committee on Cancer TNM system. The TNM system describes the size of the primary tumour (T), the involvement of lymph nodes (N), and the spread or distant metastases (M). A simplified description of the TNM system is provided in Table 1. Primary Tumour (T) TX Primary tumour cannot be assessed T0 No evidence of primary tumour Tis Carcinoma in situ (can be DCIS or LCIS) or Paget Disease T1 Tumour 2 cm; can be further classified in to T1a, T1b, T1c T2 5 cm >Tumour> 2 cm T3 Tumour >5 cm T4 Tumour with direct extension into the chest wall and/or skin, regardless of size; can be further classified as T4a,, T4d Lymph Nodes (N) NX Lymph nodes cannot be assessed i.e. removed previously 9

17 N0 No nearby lymph node metastasis N1 Cancer spread to 1-3 nearby axillary lymph nodes N2 Cancer spread to 4-9 axillary lymph nodes or enlarged internal mammary lymph nodes Distant Metastases (M) MX Metastasis cannot be evaluated M0 No distant metastasis detected; Further classification cm0(i +) means small amounts of cancer cells detected in blood or bone marrow M1 Metastasis found in distant organs e.g. bone, lung, brain, liver, etc. Table 1 Simplified description of TNM system for breast cancer staging Treatment Treatments may include one or more of the following: surgery (i.e. lumpectomy for partial breast tissue removal or mastectomy for full removal), chemotherapy, radiation therapy, and hormone therapy [3]. Oftentimes, treatment types may be combined to ensure maximal effectiveness in both removing and preventing the recurrence of cancer. For example, radiation therapy is often used together with lumpectomy and occasionally with mastectomy or chemotherapy. The chronological order of multiple treatment options may also be important. For example, to minimize the invasiveness and extent of surgery, patients may undergo chemotherapy or hormone therapy prior to the operation in an attempt to shrink the size of the tumour. Now that an overview of breast cancer and the clinical process is given, a more in-depth look into breast MRI will be given to provide more focused context for this work. 10

18 1.3 Breast MRI MRI Fundamentals Introductory Physics When placed in an external magnetic field, hydrogen nuclei have a net magnetic dipole moment (a vector known as spin or bulk magnetization). At clinical field strengths, a small but detectable fraction of hydrogen nuclei aligns to the magnetic field. When the bulk magnetization is not aligned with the direction of the magnetic field, it will precess about the direction of the field at a resonant frequency called the Larmor frequency. Conventional MRI places a target object in a magnetic field created inside the MRI scanner, with the direction of the magnetic field conventionally denoted by z (also called the longitudinal direction) and the strength of the magnetic field denoted by B0 (throughout this work, B0 is used interchangeably to refer to the strength of the main magnetic field and the main magnetic field itself - including inhomogeneous effects). A radiofrequency (RF) pulse, provided at the Larmor frequency of the hydrogen nuclei in the object, excites the hydrogen nuclei so that the spin rotates away from the axis of the effective field by an angle (known as the flip angle) determined by the strength and duration of the RF. For example, a 90 flip angle places the spin in the plane perpendicular to the longitudinal direction (known as the transverse plane, commonly denoted with xy). This is shown in Figure 1. z 90 Figure 1.Illustrative example of 90 excitation of a spin. Z-axis represents x longitudinal direction. Transverse plane is the xy plane. Gold arrow y B 1 Transverse Plane xy represents the RF or B1 field; 11

19 Once the bulk magnetization is out of alignment with B0, it will precess at the Larmor frequency around the direction of B0; that is, an axis that is parallel to B0 and coincident at the spatial location of the spin isochromat or microscopic group of spins. The precession of the spin causes a changing magnetic field, which exhibits Faraday s Induction Law (where a changing magnetic field induces a voltage in neighboring loops of wire, which can be measured). It is possible to detect the precessing spin, as the spin will generate alternating currents at the Larmor frequency in nearby coils. MRI uses the information from these currents to generate images. Larmor Frequency and Chemical Shift The Larmor frequency (f) is linearly proportional to the magnetic field experienced by the spin. The constant of proportionality is called the gyromagnetic ratio, γ, which is unique to each type of nuclei; for hydrogen nuclei, γ =42.58 MHz/T. When the magnetic field is solely from B0, the Larmor frequency is given by: 2π f = γ 2π B o. (1) For example, the frequency of hydrogen nuclei in water is 63.9 MHz in a magnetic field of 1.5 T whereas its frequency is MHz when B0 is 3 T. Due to the molecular environment s ability to alter the local magnetic field, spins may have different frequencies depending on the material they are in. Specifically, electron shielding affects the Larmor frequency as the electrons surrounding the hydrogen nucleus affect the local magnetic field. In water and fat, the shielding effects differ such that hydrogen nuclei in fat exhibits a range of resonant frequencies, with the dominant frequency having a chemical shift difference of 3.5 parts-per-million (ppm) relative to water[24]. Figure 2 shows a representative spectrum of subcutaneous fat with the water hydrogen frequency (63.9 MHz) set as the reference frequency (i.e. 0 Hz). In a magnetic field of 1.5 T, this translates to a frequency difference or shift of 210 Hz (i.e. the dominant frequency of hydrogen in fat precesses at 210 Hz slower than water). 12

20 Figure 2. Illustrative spectrum of subcutaneous fat at 1.5 T, adapted from data by Yu et al [24]. Water hydrogen frequency (63.9 MHz) set as reference frequency 0 Hz. While subcutaneous fat is composed of multiple frequencies, the predominant is centered approximately around -210 Hz. For this work, the focus is on suppressing the fat peak at -210 Hz. Relaxation Times T1 describes the exponential regrowth of the longitudinal component of the magnetization after excitation. Following a 90 excitation, the equation describing the longitudinal magnetization is: M z (t) = M o (1 e t T1 ) (2) Where Mz(t) is the longitudinal component of the magnetization as a function of time t (after excitation), T1 is the relaxation value, and M0 is the amount of longitudinal magnetization at static equilibrium. The physical basis for T1 relaxation is the interactions between the tipped or excited hydrogen spins and other neighboring atoms or molecules. Through these interactions, the hydrogen spins lose the energy gained from the RF pulse and relax towards their equilibrium state. Materials or 13

21 tissues whose molecular environment enable these interactions would have a shorter (smaller) T1, allowing for a faster longitudinal relaxation. As different types of tissue generally have different T1 values, it is possible to differentiate tissues by using T1-weighted (T1w) MRI sequences. Generally, in T1w images, the shorter the T1 is, the stronger the signal is. In the breast at a field strength of 1.5 T, fat has a short T1 of approximately 250 ms, fibroglandular tissues are longer at approximately 700 ms, and water-filled tissues such as certain types of cancers and cysts have much longer T1 values (800 ms - 1 s and 3 s respectively) [25]. Due to the short T1 value of fat relative to other tissues, particularly water, T1w sequences would see bright signals where there is fatty tissue in the breast. T1 can also be changed with the use of contrast agents such as the commonly used Gd-DTPA (a gadolinium chelate). The gadolinium-based contrast agents shorten T1 and enhance the signal in T1w images. T2 describes the decay of the magnitude of the spin in the transverse plane. Immediately following a 90 tip, the equation describing the transverse magnetization is: M xy (t) = M xy (0)e t T2 (3) where Mxy(t) is the magnitude of the magnetization in the transverse plane, t is time after excitation, and T2 is the tissue s specific T2 relaxation value. T2 relaxation arises from the loss of quantum coherence caused by the internal field effect of the sample itself. The individual hydrogen spins (or dipoles) create slightly different local magnetic fields that fluctuate over time. They cause the local spins to precess at frequencies that change over time and are different from each other, causing destructive interference over time. This destructive interference is also known as true T2 dephasing as the reduced signal cannot be reversed by gradients or RF pulses. The reduction in signal is described as an exponential decay in (3). Another property that can be measured is T2*. Whereas T2 is due to inherent material property, T2* is a result of all non-uniform magnetic field effects across the material, such as magnetic field susceptibility differences and non-uniform B0. T2* is shorter than T2 because the non-uniform magnetic field effects all serve to dephase the spins faster. In MRI, to acquire T2 instead of T2*, a spin-echo is used where a 180 RF pulse is applied between the 90 excitation pulse and data 14

22 acquisition. The 180 RF pulse serves to reverse the direction of dephasing caused by non-uniform magnetic field effects, leaving only true T2 effects. Just as different types of tissue have different T1 values, different types of tissue generally have different T2 values and it is possible to differentiate tissues by using T2-weighted (T2w) MRI sequences. In the breast, water and fluid-filled cysts have a long T2 (several hundred ms to 2s) compared to other normal tissues such as fibroglandular tissues and fat (60 80 ms). Tumours have T2 values slightly longer than normal tissue at ms [25]. Bloch Equation The Bloch Equation, given in matrix form, can describe both the precession and relaxation dynamics (described in the previous sections) as: 1 T 2 γb z γb y d dt (M x M y M z ) = γb z 1 T 2 γb x γb ( y γb x 1 T 1 ) ( M x M y ) + ( 0 0 ). (4) Mo M z T1 In Eq. 4, M0 is the equilibrium magnetization arising from the main external magnetic field pointed in the z direction (i.e. the longitudinal direction) and Bx, By, Bz are the magnetic fields (i.e. RF pulses) applied, γ is the gyromagnetic ratio, and T1 and T2 are the relaxation times Breast MRI Protocol Historically, breast MRI first generated significant interest in the medical community with T1w contrast-enhanced images as it was discovered that malignant tumours take up contrast agents much faster and more intensely than normal tissue[26]. By looking for early enhancements as an indication of a malignant tumour, sensitivity and specificity were reported to be at 95% and 53% respectively. With the advancement of faster sequences, subsequent dynamic studies found that time intensity curves (taken from multiple images acquired within a minute of each other or less) yielded important and more discerning information that improved the high false-positive rate. By determining whether an enhancement steadily increased over time (known as type I - indicative of 15

23 benign lesion), increased sharply followed by a plateau (type II - suggestive of malignant tumour), or increased sharply followed by a drop in intensity (type III - indicative of malignant tumour), the specificity was vastly improved (sensitivity: 91% specificity: 83%) [27]. Morphological features have also been found to aid in differentiating benign and malignant tumours. Orel et al. reported in a 1994 study that carcinomas (malignant tumours) presented with irregular borders and rim enhancement while fibroadenomas (typically benign tumours) presented with lobulated borders with non-enhancing septations [28]. Currently, it is standard practice to observe both dynamic and morphological information to help detect tumours. A typical minimal protocol will have several features [25]: 1. Localizer; 2. Pre-contrast non-fat-suppressed T1 weighted (T1w) pulse sequence; 3. T2 weighted (T2w) fat-suppressed pulse sequence; 4. Pre-contrast fat-suppressed T1 weighted (T1w) pulse sequence; and 5. Multiple post-contrast fat-suppressed T1w pulse sequences. The localizer locates the position and spatial extent of the volume of interest within the patient body. The non-fat-suppressed pre-contrast T1w pulse sequence is used to acquire information about fat and glandular morphology. In these pulse sequences, the acquired images show brighter fat signals than surrounding tissues due to the relatively short T1 value of fat. T2w imaging reveals features such as cysts and vessel structures [25]. As cysts are fluid filled with higher T2 values and higher hydrogen densities, T2w imaging is particularly helpful for separating benign cysts from solid masses and tumours, a feature that is enhanced by fat suppression. T2w imaging can also reveal lymph nodes. Pre- and post-contrast enhanced fat suppressed T1w images are referred to as dynamic contrastenhanced (DCE) imaging. Due to their characteristic disordered blood vessel development, breast tumours are particularly good at accumulating gadolinium-based contrast agents and would be enhanced in a T1w sequence with contrast agent [25]. DCE typically works by injecting a gadolinium based contrast agent into the blood stream, which enhances tumours due to the 16

24 tumours increased vascularity and capillary fenestrations. The enhanced images are subtracted from the pre-contrast image in order to enhance lesions. Multiple post-injection enhanced images provide dynamic information about the retention of the contrast agent. Tumours usually exhibit rapid intake; malignant tumours typically exhibit a drop in enhancement after the initial rapid intake. DCE imaging requires the use of identical parameters for all pre- and post-contrast enhanced pulse sequences in order to allow for subtraction Role of Fat Suppression In breast MRI, the abundance of fatty tissue creates strong fat signals that may be isointense with the tumour signals in the acquired MR image, which may make tumour detection difficult for the radiologist [25].Fat suppression is important in many sequences found in a breast MRI protocol such as T1w and T2w images. Although DCE can remove some fat signals due to the subtraction, motion artifacts can lead to imperfect subtraction, creating bright and dark edges that may cause misregistration [10]. In T2w imaging, the suppression of fat signals in the breast allows for stronger contrast of the bright cyst signals against the surrounding tissues [25]. While a skilled radiologist may still be able to elicit the same information without fat suppression, fat suppression makes it easier to read images by reducing the effects of motion in DCE images and makes it easier to identify cysts. Fat suppression improves the radiologist s efficiency and is a standard part of nearly all breast MRI protocols. The different fat suppression techniques available will now be presented Fat Suppression Techniques There are several fat suppression methods. They fall generally in the following categories [29], [30]: 1. Chemical Shift Encoding (CSE) 2. Water excitation 3. Inversion recovery (IR) 4. Spectral fat saturation (SFS) (See Table 2 for a summary of the different fat suppression methods advantages and disadvantages.) 17

25 The CSE technique takes advantage of the chemical shift difference between protons in water and lipid/fat (approximately 3.5 ppm or a frequency shift of 210 Hz at 1.5 T). The chemical shift leads to a difference in phase between fat and water signal during image acquisition. In one example of the CSE technique, an in-phase image (i.e. fat and water spins are in phase) and an opposed-phase image (i.e. fat and water spins are out of phase by 180 ) are acquired which can then be used to calculate separate fat and water images. Examples of CSE include Dixon, Flex, and IDEAL (a technique that is used in the methods of this work, as will be seen in Chapter 2). CSE methods are fairly tolerant to magnetic field B0 inhomogeneity; however, the acquisition of multiple datasets for in-phase and opposed-phase results in much longer scan times. Water excitation techniques excite water frequencies only for imaging purposes without exciting fat frequencies. This technique uses composite pulses; the water spins are flipped closer to the transverse plane with subpulses played at specific intervals in time, based on the chemical shift difference or frequency difference of fat and water. In between the subpulses, the interval of time would allow fat spins (which precess at a different frequency to water) to precess such that the following subpulse would tip the fat spin back towards the longitudinal axis while tipping the water spin towards the transverse plane. This ultimately leads to a 90 flip of water spins and 0 flip for fat. This method has also been applied to spectral-spatial pulses where the selection occurs in the spectral and spatial dimensions [31]. However, this method is sensitive to B0 inhomogeneity: the reliance of the timing of pulses on the resonance frequency difference between water and fat means that B0inhomogeneity would render subsequent flips inaccurate. For excitation with spectralspatial pulses, its relatively coarse spatial resolution (~1 cm [31]) is also impractical for the fine resolution required in breast MRI (<= 3 mm for through-plane resolution [10][25]). IR acquires a water-only image, as it is a method based on the different T1 relaxation times of fat and water. Both water and fat spins are inverted or flipped by 180 (i.e. there is no transverse component) followed by relaxation. When the longitudinal magnetization of fat is zero (also known as the null point), the excitation pulse is applied which excites the water spins into the transverse plane for imaging. It is insensitive to B0 inhomogeneity and is relatively short but due to relaxation of water spins following the 180 flip, there is less water signal and the SNR of the image is reduced. 18

26 SFS (also known as FATSAT when used for fat suppression) takes advantage of the chemical shift difference between protons in water and fat. It applies a radiofrequency (RF) pulse with a narrow bandwidth centered at the specific resonance frequency of fat, excites the spins in the fat, and dephases the associated magnetization with strong crusher or spoiler gradients. Advantages include preserving the magnetization of water and relatively little increase in scan time, particularly if the ratio of preparatory pulses to slice excitation pulses is less than one. It is commonly used in both T1w and T2-weighted (T2w) imaging of the breast. However, spectral fat saturation is sensitive to B0inhomogeneity. Method Name CSE Water Excitation Inversion Recovery SFS Duration Long i.e. ~10mins for breasts Short i.e. adds ~2.5s for T2w sequence Short i.e. adds ~2.5s for T2w sequence Short i.e. adds ~2.5s for T2w sequence Robustness to B0 Inhomogeneity SNR Efficiency Robust High yes Sensitive High no Robust Poor yes Sensitive High yes Suitability for breast slice selection Table 2. Comparison of practical aspects of various fat suppression techniques The Effect of Field Inhomogeneity on Spectral Fat Saturation SFS works by selecting the range of fat frequencies to be suppressed. The problem of spectrally selective fat saturation can be posed as a filtering problem, where a pass band of the filter is placed over the fat frequencies (exciting and saturating these frequencies) and a stop band of the filter is placed over the water frequencies (no excitation/saturation). As fat is separated from 19

27 water by 210 Hz, the filter can be designed with up to a 210 Hz transition band (or distance) between the pass and stop bands. The size of this transition band is important because it sets a minimum on the excitation pulse duration. Specifically, a pulse of duration D seconds cannot achieve a transition band of less than 1/D Hz in the associated filter. This 1/D minimal spectral transition of a pulse is called the spectral resolution of the pulse. In an ideal homogeneous 1.5 T environment, water and fat frequencies differ by 210 Hz, regardless of spatial locations. In the presence of magnetic field inhomogeneity, the spectral separation becomes smaller as it is the difference between the lowest water frequency and the highest fat frequency. Field inhomogeneity makes it more difficult for SFS to target fat frequencies while avoiding water frequencies, which can result in incomplete fat suppression. In cases where the inhomogeneity is less than the frequency shift between fat and water, the spectral separation is reduced between fat and water, requiring a longer spectrally selective pulse to create a sufficiently narrow transition band to achieve fat saturation. When the inhomogeneity is greater than the chemical shift, incomplete fat saturation is unavoidable. See Figure 3 for a visual illustration. Figure 3. Illustrative example of fat-water spectral separation. At 1.5T, fat and water have a spectral separation of 210 Hz. Left: Homogeneous magnetic field means that the fat and water frequencies do not vary across the imaging region (x). As the pulse duration is the inverse of the spatial resolution, which is less or equal to the spectral separation, the pulse duration needed is 4.76 ms or more. Center: In this example of an inhomogeneous field, the spectral separation is 160 Hz, which would require a pulse duration of 6.25 ms or more. Right: In this 20

28 example of a very inhomogeneous field, the inhomogeneity means SFS will not achieve complete fat saturation Patient Effects on Magnetic Field Inhomogeneity While modern MRI scanners can typically achieve < 0.2 ppm B0 variation over a 30-cm diameter spherical volume, one of the challenges in creating a homogeneous magnetic field in the clinical setting is overcoming the effect the patient has on the field. Magnetic susceptibility differences at air-tissue interfaces and the unique geometry of each patient gives rise to magnetic field inhomogeneity, which creates shifts in the resonance frequency of fat and water. A review of magnetic susceptibility and its effects on field inhomogeneity will now be given Magnetic Susceptibility The magnetic susceptibility of a material is the quantitative measure of the material s ability to interact with and distort an external magnetic field. When an object of non-zero susceptibility is introduced into a magnetic field, it becomes magnetized and creates a magnetic field of its own that perturbs the original field. (Please refer to [32] for a more in-depth discussion.) The integration of all non-zero susceptibility materials effects on the magnetic field over space yields the field inhomogeneity. The calculation of the magnetization and total field perturbation from irregularly shaped objects requires a numerical computation. See Figure 4 for an example of the simulated field inhomogeneity map of the breast and chest wall at different field strengths; in the simulation, the range in frequency is approximately 18 ppm (1.154 khz in the 1.5 T and khz in the 3.0 T). 21

29 Figure 4. Simulated field maps of virtual breast showing different inhomogeneities at different field strengths (left: 1.5 T; right: 3.0 T) using a method described in Section Note that B0 points out of the plane Techniques for Reducing Magnetic Field Inhomogeneity Techniques to reduce magnetic field inhomogeneity commonly fall under two categories: susceptibility matched pads and shimming. Susceptibility matched pads involve the use of pads whose susceptibility value closely matches human tissue. As a major source of field inhomogeneity arises from the air-tissue interface, placing a susceptibility matched pad next to the body removes this interface and thus reduces the inhomogeneity. [33] These pads offer significant field inhomogeneity reduction but are limited by their bulkiness, patient discomfort, and inability to correct for air-tissue interfaces within the body (e.g. lung cavity, sinuses, etc.). Shimming corrects field inhomogeneity and is categorized as active or passive shimming. Passive shimming involves the strategic placement of metal in the scanner bore to improve homogeneity. However, it is not suitable for quick, individual customization. Active shimming involves the use of magnetic coils to change the field. The standard x, y, z gradient coils in MRI scanners are used for first-order shimming they produce linear offsets to correct for the field inhomogeneity. In some scanners, additional coils may be included to create higher-order shims but higher order shims may not be available in all systems. 22

30 Furthermore, higher order shims may still not adequately correct field inhomogeneity issues caused by the unique geometry of patients. Thus, even with shimming, inhomogeneity issues may still lead to incomplete SFS. The authors approach the issue of SFS s sensitivity to B0 inhomogeneity through the incorporation of spatial variance in spectral excitation. Spatial variance in spectral selection would allow the bending of the saturation band according to the field inhomogeneity over space Spectral Spatial Selection Spatial variation in spectral selection requires the interplay of the RF pulse with magnetic gradients [31]. A Fourier Transform describes the relationship between the magnetization of spins at a particular spectral-spatial location, the RF pulse, and magnetic gradients for a small tip angle: T M xy (x ) = γ B 1 (t)e i2πk x x dt 0 (5) where x = (r, f), r is the spatial location and f is the frequency and k x = (k r (t), t), k r (t) is the position in k-space as a function of time, t is time (i.e. the Fourier pair to frequency). The dot product can then be expanded as k x x = k r (t) r + t f. The position in k-space can be controlled by applying the gradients during the RF pulse and is given by: k r (t) = T γ 2π G(s)ds t (6) where γis the gyromagnetic ratio, T is time of end of the gradient, and G(s)is the gradient amplitude as a function of time. A gradient waveform played over time creates a continuous k- space trajectory. Discretizing (5)into matrix form yields: m x 1 [ m x n ] = γdt [ e i2πk x,1 x 1 e i2πk x,p x 1 B 1,t1 ] [ ] x n e i2πk B x,p 1, tp e i2πk x,1 x n (7) where x 1,, x n is a series of spectral-spatial locations, t 1,, t p is the series of time points. 23

31 The significance of equation (7) is that on the right hand side (RHS), there is the matrix containing the k-space trajectory (as illustrated in Figure 5), which is related to the gradient waveform via (6), and the RF (B1) waveform while on the left hand side (LHS), there is the magnetization of various spectral-spatial locations. For a given set of waveforms (e.g. gradient and RF), equation (7) would predict the resulting magnetization. Figure 5. A visual representation of the Fourier encoding matrix. The top is the gradient vs time plot, which is related to the excitation k-space trajectory by the Fourier relationship. The encoding portions of the trajectory are implemented into the Fourier encoding matrix as indicated by the arrows: each encoded point on the trajectory represents a coordinate k x,i in the matrix. Progressing through a single row in the matrix is equivalent to traversing temporally through the encoding portions of the trajectory for a given spectral-spatial location and seeing its effect on a single point in spectral-spatial space. Progressing down a 24

32 single column is equivalent to considering the contribution of a particular point in the excitation trajectory to the magnetization map in spectral-spatial space, in which a coordinate is denoted by x i. With the basics of breast MRI, the importance of fat saturation, the effects of field inhomogeneity on SFS, and spectral spatial selectivity covered, the design, methods, and experimental results of spatially-varying saturation pulse will be presented. 25

33 Chapter 2 Spatially Varying Saturation Pulse (SVSP) for Fat Suppression 2.1 Design of SVSP Prior to discussing the methods for the experiments, the process for designing the SVSP will be presented. In essence, the RHS of equation (7) (e.g. gradient and RF waveforms) was solved via least-squares given a target magnetization (i.e. LHS of equation (7)) over spectral-spatial space. For this work, a 1-spatial-dimensional unipolar Flyback trajectory in excitation k-space (i.e. kx-t) was used, as illustrated in Figure 5. The Flyback trajectory used was divided into two parts: an encoding phase and a non-encoding phase. The trajectory was designed to traverse the necessary distance in excitation k-space as slowly as possible within one cycle or period of the trajectory during the encoding phase at a constant gradient, before traversing back to the start of a new cycle at maximum slew during the non-encoding phase. Its uniploarity and the fact that the RF was played only during the constant-gradient portion (i.e. the encoding portion) of the Flyback trajectory minimized sensitivity to eddy current induced artifacts. A more in depth discussion is provided in Chapter 3. Only the constant-gradient portion was encoded into the matrix on the RHS of equation (7). The design of Flyback SVSP involves two major steps: 1. The design of the gradient waveforms to play the desired trajectory 2. The production of optimized RF waveforms using a Fourier Model and least-squares optimization, given the desired trajectory For step 1, the gradient parameters include the total pulse duration (D), Flyback period (T), and spatial resolution of voxel size R. It should be noted that there is an ambiguity in language regarding spatial resolution: higher resolution generally means finer and better resolution with smaller voxel sizes i.e. smaller R in this work, finer resolution and smaller R will be used in lieu of higher resolution. The gradient parameters have to take into account the following constraints: frequency difference between fat and water (Δf = 210 Hz at 1.5 T), the 3D B0 field map, hardware limits (e.g. maximum gradient amplitude Gmax, maximum slew amplitude Smax, RF peak output B1max), and SAR limit. 26

34 T is set to be less than or equal to the inverse of the sum of Δf (i.e. ~200 Hz) and the range in B0 (including susceptibility effects). This ensures that there is no aliasing within the frequency range of the spins in the image. From literature [34], the B0 range expected for breast MRI is 300 Hz, which means T should be Hz+300 Hz to give a factor of safety of approximately two. = 2 ms or less. For our experiments T = 1 ms was chosen R is determined by the relationship 2 kx,max * R = 1, where 2 kx,max is the extent in k-space that is sampled. The extent in k-space that is sampled is determined by the gradient strength. R is limited by T and the hardware limits Gmax, Smax, and B1max. Smax is proportional the maximum acceleration in k-space; Gmax is proportional the maximum speed that k-space can be traversed. In the scanner (MR450w) available at Sunnybrook Health Sciences Center, the Gmax is 3.4 G/cm and the Smax is 15 G/cm/ms. This yields a maximum kx,max of 8.15 cm -1 or minimum R of 1.22 mm(see Appendix for calculation) for T= 1 ms. However, a farther extent in k-space in the same period means that k-space is sampled at a faster rate, which would require a stronger B1 input to deposit the same amount of energy as sampling k-space at a slower rate. In addition, a stronger B1 leads to a squared increase in the specific absorption rate (SAR), the power absorbed per unit mass, which runs the risk of exceeding SAR safety limits. Should they be exceeded, the voxel size should be increased (i.e. increasing R) which would allow better energy and RF distribution over a smaller extent in kx. Although this work used a coarse resolution with a fixed R value of 2.5 cm and 3.0 cm as described in Section 2.2 (which was not close to reaching the limits, see Section 2.3 of this chapter) for the purpose of demonstrating feasibility, an iterative approach may be used with the calculation of B1 (see step 2) to ensure that the B1max and SAR limits are not exceeded to give an optimal design. It should also be noted that for a fixed R value of 3.0 cm, the non-encoding portion of the trajectory that is played at maximum slew required only 0.14 ms, meaning for a period of 1 ms, 86% of the pulse duration was able to be used for encoding. D is set as 1 Δf+ Δf B0 (R), where Δf B0 (R) is the most negative of values calculated from the highest frequency subtracted from the lowest frequency within spatial bins of width R (the spatial bins are created by dividing the MRI s field-of-view into bins of width R).For example, if B0is homogeneous, D would be the inverse of 210 Hz. If among the spatial bins, the largest spectral difference in B0 is 200 Hz, D would be the inverse of 10 Hz. However, if Δf + Δf B0 (R) 27

35 is less than 0 (i.e. the largest spectral difference in B0 is greater than 210 Hz at 1.5 T) or is longer than a maximum allowable amount (i.e. a time comparable to the T1 value of fat), then incomplete fat suppression would result. Step 1 can thus be summarized as the following steps: 1.1. Set T <= 1 = 1 Δf+(B o,max B o,min ) 210 Hz +(B o,max B o,min ) 1.2. Set R within hardware and SAR limits 1.3. Set D >= 1 = 1. Δf+Δf Bo (R) 210 Hz+Δf Bo (R) See Figure 6 for a trajectory diagram with its relationship to T, D, and R labeled. 28

36 Figure 6. Illustration of desired trajectory with gradient parameters pulse duration (D), Flyback period (T), and spatial resolution (R) labeled. 29

37 Step 2 is relatively straightforward. The RF pulse is designed by rearranging (7)to compute the following least squares solution with Tikhonov regularization: b 1 = (E H E + δi) 1 E H m target (8) where the b 1 is the RF pulse, I is the identity matrix, m target is the desired or target magnetization, E is the discrete Fourier transform operator for the encoding portions of the (kx, t) trajectory (as determined by the gradient waveform), and δ is the Tikhonov regularization value, which applies a cost to the RF amplitude and prevents over-fitting which runs the risk of increasing B1 amplitude and SAR. For this work, δ was not optimized and was chosen at a value of 200 (for matrix size of 128x128) which was found to be able to apply a cost to the RF amplitude during the solving of least squares while maintaining good magnetization targeting. The target magnetization is calculated from the fat-water distribution map and the frequency-shift map. Specifically, voxels at specific spectral-spatial locations that are designated as water have 0 magnetization assigned while voxels at specific spectral-spatial locations designated as fat have magnetization assigned as 1 (i.e. 90 flip angle). Please see Figure 7. Potential methods for generating the fat-water distribution map may include using a fast, low resolution CSE method or distribution estimations based on previously acquired data. The spatial variation of the SVSP used in this work varied only in the x direction. For a single plane or slice in xy, all spectral-spatial locations in the y direction were projected along the x direction. Thus, a map of the desired magnetization in spectral-spatial space yielded a range of frequencies per x coordinate. In Figure 7, this is reflected in the subscript of the elements in the target magnetization vector. 30

38 m target = m water, x 1 m water, x n m fat, x 1 m fat, x n ] [ 0 0 = 1 [ 1] Figure 7. A visual representation of the designation of individual target magnetization points as elements in the vector m target as used in the least squares problem. The red and blue areas are composed of individual dots representing targets to be saturated (blue) or not saturated (red) areas that appear continuous are due to the high density of dots. Red dots are water spins in spectral-spatial space that are not to be saturated (i.e. target magnetization = 0, or 0 flip angle), while blue dots are fat spins that are to be saturated (i.e. target magnetization = 1, or 90 flip into transverse plane). The particular target magnetization map used in this figure is from the virtual experiment, as described in Section Methods Three distinct sets of experiments were performed: virtual experiment on a numerical breast phantom, verification in scanner, and physical experiments. 31

39 2.2.1 Virtual Experiment The virtual experiment compared the effects of SFS (i.e. sinc pulse) and SVSP on a virtual breast phantom. Virtual Phantom Design The virtual breast phantom was composed of a chest wall (rectangular prism with filleted edges that was hollow to simulate the cavity of the lungs, measuring approximately 30 cm x 20 cm x 15 cm) and two breasts (modeled as two parabolic extrusions from the chest wall with height of 7.5 cm and radius of 5 cm). The breast was modeled to have three distinct layers: an outer layer composed solely of fat, a middle layer composed of fat and water, and an inner layer composed solely of water. This manner of layer organization in the virtual phantom served as a very rough approximation of the human breast, with the ducts and lobules on the inside (i.e. higher water signal) surrounded by fatty tissue on the outside. The susceptibility value was set at x 10-6 throughout the breast, which is the value for water and lies within the range for human tissue [32]. The calculation of the magnetic field inhomogeneity was based on an existing method as described by Karimi et al [35]. The method makes the approximation of the phantom as a collection of a finite number of spheres. The equation of a sphere s (of susceptibility χ, where χ << 1 ) effect on the magnetic field is: B z = χb o 3 (a r ) 3 (3cos 2 θ 1) (9) where B z is the disturbance in magnetic field at a particular location, χ is the susceptibility value of the sphere, B0 is the environment magnetic field strength, a is the radius of the sphere, r is the distance from the sphere to the specified location, and theta is the angle between the sphere and the specified location [32]. Using this equation for the magnetic field contribution for a sphere of a certain susceptibility value χ, the summation of the different voxel-spheres susceptibilities over space yields an approximation of the phantom s resulting magnetic perturbations or inhomogeneity as a function of space [35]: 32

40 B z (r χ(r) B o a ) = ( 3 r r ) all spheres 3 (3cos 2 θ 1) (10) where r is the position for which the magnetic inhomogeneity was calculated, r is the position in space that was integrated over, and θ is the corresponding angle. The sphere radius a was chosen to be the radius of a sphere of equal volume to an individual element making up the virtual phantom. In the virtual phantom, a was mm, B0 was 1.5T, and χ was -11 x 10-6 for human tissue [32]. As the Larmor frequency is linearly proportional to the magnetic field strength by the gyromagnetic ratio γ or khz/g, the magnetic field map was used to calculate the frequency 2π shift map. The layout of the phantom, the desired image after fat suppression, and the frequency map are shown in Figure 8. Figure 8. Virtual experiment setup. Left: Magnitude Image of Virtual Breast. Region 1 contains fat, 2 contains fat and water, 3 contains water. Middle: Desired Magnitude Image of Virtual Breast after Saturation - a water image. Right: frequency-shift map based on susceptibility value of human tissue [32]. Blue dotted box represents the linear shim volume. Note that the magnetic field B0 points out of the plane. 33

41 Figure 9. Frequency map at z = 12 cm of virtual breast from Figure 8. Note that despite being shimmed, there still exhibits approximately 150 Hz range in frequency differences over x. The distribution map of materials in the phantom (i.e. the spatial location of the fat and water) and the frequency-shift map were used to simulate the effects of standard FATSAT and SVSP. In the virtual breast phantom, areas of water were assigned frequencies at +210 Hz above the spatiallycorresponding frequencies in the frequency-shift map while areas of fat were assigned spatiallycorresponding frequencies in the frequency-shift map. With the spatial and spectral information known, the magnetization of every voxel was calculated based on the magnetization profile of the saturation pulse used. Specifically, a saturation magnetization map in spectral-spatial space was calculated for both SVSP and FATSAT (i.e. msaturation(x,f) where msaturation is the transverse magnetization due to the saturation pulse as a function of space (x) and frequency (f)). The intensity of a voxel, I(x), at spatial location x post-saturation (i.e. magnetization after saturation and a 90 flip) is: I(x) = i (1 m saturation (x, f o (x) + f i ))ρ i (x) (11) where i is the species (i.e. fat or water), x is the spatial location, f o (x) is the frequency shift due to the magnetic field value at location x, f i is the frequency shift of the i th species, and ρ i (x) is the density of protons in the i th species at location x. The power deposition of the RF pulse was calculated according to the following equation [36] that assumed the shape of the target as a sphere for ease of implementation: P = 4 15 πσω2 B 1 2 r 5 (12) 34

42 where r is the radius set at 20 cm, σ is the conductivity set at 0.1 S/m (within the conductivity range for human tissue [37]), and f is the resonant frequency at 64 MHz. The energy deposition was divided by a time of 200ms, roughly the T1 of fat and potential repetition time of SVSP (see Chapter 3 for exploration in SVSP repetition time). Mass was calculated with density of water at 1000 kg/m 3. It should be noted that the SAR limit is 2W/kg, as set by the International Electrotechnical Commission. FATSAT Pulse A sinc pulse with duration of 16 ms and time-bandwidth product of 4 was used for the FATSAT pulse. The full-width-half-max of the magnetization profile of the sinc pulse was 4 / 16 ms or 250 Hz. These parameters reflected the typical parameters found in a FATSAT module in a MRI scanner [38] and was one of the stock FATSAT pulses available on the 1.5 T scanner (MR450w, GE Healthcare, Waukesha, WI) at Sunnybrook Health Sciences Centre. Figure 10. RF vs Time of Windowed Sinc Pulse used in FATSAT SVSP 35

43 To generate the SVSP, the frequency-shift map along with the map of fat and water distribution were inputted into the SVSP generating algorithm. Using a preset excitation k-space Flyback trajectory as shown in Figure 11 for ease of implementation, the gradient waveform and optimized RF pulse were generated, from which the spectral-spatial magnetization map was calculated and used to determine the degree of excitation experienced by the different materials in the virtual phantom. Figure 11. Excitation k-space trajectory and gradient waveform. Top: X-gradient waveform of SVSP as function of time. Bottom: Corresponding excitation k-space Flyback trajectory used for spectralspatial encoding. The RF pulse was designed to saturate a spectral band that varied in one spatial dimension with the field map (i.e. aims to saturate the fat frequencies) while not saturating spins +210 Hz away (i.e. water frequencies at 1.5 T). See Figure 12 for the target magnetizations (i.e. the pass and stop bands for the fat and water frequencies respectively) and see Section for comparison of target magnetizations with saturation results (see Figure 18 and Figure 24 for frequency profiles at specific x locations and spatial magnetization profiles at specific spectral location respectively). 36

44 Figure 12. Spectral-spatial target magnetizations, as determined from virtual breast phantom s frequency-shift map in a single slice. The blue and red areas are composed of individual dots representing targets to be saturated and not saturated respectively areas that appear continuous are due to the high density of dots. Red dots denote water spins specified to have no magnetization. Blue dots are fat spins specified to be saturated. The target fat frequencies that appear higher than the water frequencies at around x = 9 13cm and cm is a modeling inaccuracy that is discussed in Section 2.4. Most parameters for the pulse were not optimized. They were chosen to show feasibility and were enough to demonstrate the effectiveness of SVSP. The duration of the pulse was chosen to be ms (the duration of the FATSAT sinc pulse was 16 ms) which gave a spectral resolution of ~60 Hz, enough for fat-water separation. The time step or discretization of time was set at ms, yielding 2012 points. The Flyback period was set to 1 ms, giving a spectral bandwidth of 1 khz and a safety factor of two as discussed in Section 2.1. For the virtual experiment, the extent in excitation k-space achieved by the trajectory was 0.4 cm -1, chosen simply to show feasibility, which gave a 2.5 cm spatial resolution that allowed bending of the saturation band with the field inhomogeneity (Figure 24 in Section demonstrates this well). The magnetization map of the solved pulse b 1 was calculated using both forward Fourier: m calculated = Eb 1 (13) 37

45 and with Bloch simulation, using the Bloch Equation (equation (4) ) Verification of Simulated Magnetization Map in Spectral-Spatial Space in Scanner The magnetization map of the generated RF pulse generated from the scanner was evaluated on a 1.5 T scanner (MR450w, GE Healthcare, Waukesha, WI).A constant y-gradient was applied while the pulse excited a homogeneous water phantom to create a spectral-spatial linear dependence in the y direction. In other words, the spectral dimension was mapped to the y-direction, which would create an image that would show the excited locations in the phantom that correspond to an (x, frequency) magnetization or saturation map Physical Phantom Experiment The physical phantom experiment consisted of two experiments one with a metal paper clip placed in a holder approximately 20 cm away from the physical phantom in the scanner, the other with the paper clip placed approximately 15 cm away and compared a standard FATSAT to SVSP in saturating a physical phantom for each. The physical phantom used in both phantom experiments was a hollow plastic model of a breast with a wider base than top. The phantom base measured approximately 12 cm x 10 cm. At a height of about 18 cm, the top measured 12cm x 7 cm. The phantom was filled with water. Inside the phantom, a test tube filled with mineral oil was attached at an oblique angle to the interior wall of the phantom such that the tip of the tube was at approximately an interior wall s midpoint and the tube s head was at the center of the bottom. The metal paper clip was secured with tape inside a plastic container and placed approximately 20 cm and 15 cm away from the phantom for the first and second part of the experiment respectively. See Figure 13 for an illustration and Figure 14 for a picture of the physical phantom. 38

46 Figure 13. Illustration of physical phantom filled with water (enclosed blue space) with oil-filled tube (yellow tube) attached to the side. Paper clip held in a holder placed at a distance d = 20 cm or 15 cm. Figure 14. Physical phantom filled with water with oil-filled tube attached to the side. FATSAT used a stock sinc pulse for saturation (16 ms duration, time-bandwidth product was 4). FATSAT results without and with explicitly placed shim volumes were acquired. The SVSP portion consisted of acquiring a fast, low resolution frequency shift map from the phantom via a variant of IDEAL (Iterative Decomposition of water and fat with Echo Asymmetry and Least-Squares) - a CSE least-squares based field-map estimation method that was able to generate both water and fat distribution maps with a region growing algorithm [39][40]. For IDEAL, three separate images were acquired of the phantom via gradient echo at lowest available 39

47 resolution (128 x 128 x 30), with TE = 4, 5, 6 ms respectively and TR of 50 ms. The frequency estimated for the fat was -220 Hz less than that of water. The low resolution of the IDEAL images minimize the time required to generate the frequency and distribution maps; please see Section 2.4 and Chapter 3 for more discussion on IDEAL, frequency shift map, and fat-water distribution map generation. After acquisition of the field map and fat-water distribution maps, they were inputted into the SVSP generator. The extent used by the excitation k-space trajectory was 0.33 cm -1, which gave a 3.0 cm spatial resolution that allowed the bending of the saturation band with the field inhomogeneity. The gradient, RF amplitude (rho), and RF phase (theta) waveforms were then uploaded into the scanner to allow for the execution of SVSP onto the phantom as part of a 3D GRASS sequence. See Figure 15 for an illustration of the MRI sequence. Saturation Module Figure 15. Illustration of the 3D GRASS sequence used for physical experiments. Note the saturation module played before the excitation pulse. Although this sequence is not the sequence used in actual breast image acquisition, it is capable of showing the effects of fat saturation including SVSP. 40

48 The resulting images for SVSP and FATSAT were compared against a non-fat-suppressed image and the suppression levels were compared within both the fat and water region using a 20 log ratio decibel scale. 2.3 Results Virtual Phantom Figure 16 shows the waveforms produced by the proposed SVSP design methodology for the virtual phantom experiment. The SVSP that was generated had a maximum amplitude of 9.6 ut and a power per unit mass of mw/kg. As displayed in Figure 17, magnetization maps as calculated from the Fourier model and Bloch simulation showed good agreement with each other. Furthermore, the design was effective in saturating the fat spins without significantly exciting the water spins. The mean-squared error for the encoded fat regions was 0.13 [unit of normalized magnetization] and for the encoded water regions. Figure 18 shows the magnetization profile as a function of frequency at x = 9.5 cm. The encoded fat frequencies at this spatial location are represented by the blue vertical lines with target transverse magnetization = 1 (i.e. 90 degree tip) in the bottommost subplot. The translucent blue shade that spans from the lowest target frequency to the highest target frequency represents the range of target fat frequencies or the pass band. It should be noted that it is the individual target frequencies that is encoded, not the pass band as the pass band is drawn for visual purposes. In the middle subplot, the red vertical lines represent target transverse magnetization = 0 (i.e. no tip) for target water frequencies at x = 9.5 cm. A translucent red shade spans the lowest to highest target water frequencies, representing the stop band. The topmost subplot shows the magnetization profile as a function of frequency. Note that the encoded target fat frequencies correspond well to areas of strong magnetization and the encoded water frequencies correspond well to areas of weak or zero magnetization. Figure 19 shows result of applying the waveform in Figure 16 to the virtual breast phantom. The magnitude image of the virtual breast phantom after FATSAT showed incomplete fat suppression near the apex of the breast, the lateral sides of the breast, and the base. It also 41

49 showed significant water suppression near the lateral edges of the chest wall. The post-svsp magnitude image of the virtual breast phantom showed significantly better fat suppression near the apex of the breast and the lateral sides of the breast, as indicated on both images by thick arrows. There was still incomplete fat suppression near the lateral edges at the base of the breast but still showed significant improvement over FATSAT. At label 1 in Figure 19, the suppression level for SVSP was db, the suppression level for FATSAT was db. At label 2, SVSP resulted in suppression level of db and FATSAT resulted in suppression level of db. There was also significantly less water suppression near the edges of the chest wall as shown by the thin arrows. At label 3 in Figure 19 at pixel location, the suppression level db for SVSP and db for FATSAT. 42

50 Figure 16. Plots of waveforms for virtual experiment. Top left: SVSP RF amplitude. Top right: SVSP RF phase. Bottom left: x gradient waveform as function of time. Bottom right: k-space trajectory in kx and t, calculated from x gradient. 43

51 Figure 17. Simulations of magnetization map of SVSP in virtual experiment. Top: Fourier simulation with target magnetizations overlaid. Red dots are water spins specified to have no magnetization, blue dots are fat spins specified to be saturated. Bottom: Bloch simulation of magnetization map 44

52 Figure 18. Frequency profile of magnetization map at x = 9.5 cm of SVSP for virtual phantom (i.e. cross-section at x = 9.5 cm of Figure 17). The bottommost subplot shows the pass band, where blue vertical lines represent desired transverse magnetization = 1 for target fat frequencies at x = 9.5 cm (i.e. 90 degree tip). A semi-transparent blue range (i.e. rectangular prism) is drawn from the lowest target frequency to the highest target frequency, representing the conventional idea of a pass band or range of target fat frequencies. Similarly, in the middle subplot, the red vertical lines represent the desired transverse magnetization = 0 for target water frequencies at x = 9.5 cm (i.e. no tip). A semi-transparent red range is drawn from the lowest to the highest target water frequencies, representing the conventional idea of a stop band. The topmost subplot shows the magnetization profile as a function of frequency. Note that while the pass band in this figure overlaps with the stop band due to the existence of some outliers (the discussion of which is in Section 2.4), the encoded target fat frequencies correspond well to areas of strong magnetization from the SVSP and the encoded water frequencies correspond well to areas of weak or zero magnetization. 45

53 Figure 19. Virtual experiments of fat suppression on virtual breast phantom. Top: post- FATSAT magnitude image. Bottom: post-svsp magnitude image. 46

54 2.3.2 Verification of Simulated Magnetization Map In Figure 20, the magnetization map was verified in the scanner and showed good agreement to the Fourier simulation. The mean-squared error for the encoded fat regions was and [unit of normalized magnetization] for the encoded water regions between the scannergenerated map and the Fourier simulation. Figure 20. Verification of simulated magnetization map in scanner. Left: Fourier simulation with target magnetizations (red dots representing water target frequencies that are not to be saturated; blue dots representing fat target frequencies that are to be saturated) overlaid for comparison. Right: Scanner-acquired magnetization map. The aliased copies were not present in the scan as they were outside the dimensions of the imaged water block Physical Phantom Experiment Figure 21 and Figure 22 shows the physical experiment performed on the breast phantom with the paper clip placed ~20 cm away. In the field map displayed in Figure 21B, the range in field inhomogeneity (within 3 standard deviations) was 328 Hz with a relatively symmetrical distribution of the inhomogeneity. The SVSP generated had a maximum amplitude of µt and a power per unit mass of mw/kg. It offered good fat suppression with minimal water suppression (Figure 22D) while the FATSAT performed for complete fat suppression showed 47

55 significant water suppression (Figure 22B) and the FATSAT performed for reduced water suppression (Figure 22C) showed significantly less water suppression at the cost of fat suppression. At the tip of the oil tube in the region enclosed by a blue circle with radius cm centered at spatial coordinate (14.06 cm, cm), the suppression levels for SVSP, FATSAT with reduced water suppression, and FATSAT for complete fat suppression were db, db, and db respectively (Figure 22E). Near the bottom of the phantom where there is only water (region enclosed by a red circle, radius cm centered at spatial coordinate (10.78 cm, 2.03 cm)), the suppression levels for SVSP, FATSAT with reduced water suppression, and FATSAT for complete fat suppression were db, db, and db respectively (Figure 22F). Figure 23 and Figure 24 shows the results for the physical experiment performed on the breast phantom with the paper clip placed ~15 cm away. In the frequency shift map displayed in Figure 23B, although the range in field inhomogeneity (within 3 standard deviations) was 339 Hz, which was similar in value to the previous experiment, the distribution is much more asymmetric, with higher frequencies on the right side of the figure near the paper clip. The frequency shift map revealed a significant increase in frequency at the edge of the phantom, increasing the range of frequencies spanned by the oil tube inside the phantom. The SVSP generated had a maximum amplitude of µt and power per unit mass of 0.146mW/kg. It offered good fat suppression with some water suppression, as shown in Figure 24C. For comparison, FATSAT showed both greater water suppression and less fat suppression (Figure 24B).At the tip of the oil tube in the region enclosed by a blue circle (radius cm centered at spatial location (14.06 cm, cm)), the average suppression levels in Figure 24C (post SVSP) and Figure 24B (post FATSAT) were db and db respectively. At the top of the phantom and bottom of the phantom, FATSAT shows water suppression over a larger volume than SVSP. 48

56 Figure 21. Physical experiment 1 - phantom experiment with paper clip ~20 cm away. A: pre suppression magnitude image of phantom. B: low resolution field map estimate of phantom using IDEAL with Region Growing algorithm. C: fat-water distribution maps of phantom. D: waveforms for solved SVSP. E: simulated magnetization map with target magnetization overlaid. Red dots represent water spins and blue dots represent fat spins. 49

57 A B C D E F Figure 22. Comparisons of ROIs in pre-saturation (A), post FATSAT (B, C), and post SVSP (D) images in physical phantom with paper clip ~20 cm away. The ROIs are circled in blue centered at (14.06 cm, cm) and in red centered at (10.78 cm, 2.03 cm). Signal profile comparisons were made at x = cm (E) and x = cm (F). 50

58 Figure 23. Physical experiment 2 - phantom experiment with paper clip ~15 cm away. A: pre suppression image of phantom. B: low resolution field map estimate of phantom using IDEAL with Region Growing algorithm. C: low resolution fat-water distribution maps of phantom. D: waveforms for solved SVSP. E: simulated magnetization map with target magnetization overlaid. Red dots represent water spins and blue dots represent fat spins. 51

59 A B C D Figure 24. Comparisons of a region of interest in pre-saturation (A), post FATSAT (B), and post SVSP (C) images in physical phantom with paper clip ~15 cm away. The region of interest is circled in blue with centre at (14.06 cm, cm).a signal profile comparison is made at x = cm (D). 52

60 Three objectives were demonstrated with these results: 1. The SVSP design methodology can produce a spatially varying saturation pulse that more precisely targets fat for signal suppression. 2. SVSP can be played out on existing scanner hardware with results that agree very closely with theory and simulation. 3. Noticeably improved fat suppression can be achieved in a fat/water phantom with field inhomogeneity similar to that experienced in breast imaging. 2.4 Discussion The experiments highlighted SVSP s ability to overcome limitations to conventional spectral saturation. In the virtual phantom, the susceptibility effects (i.e. field inhomogeneity) were particularly strong near the corners and vertices, which resulted in incomplete fat suppression via conventional FATSAT. In the physical phantom experiments, the field was greater on the sides and lower on the top and bottom of the phantom. This meant that fat placed near the sides would have higher frequencies and water at the top would have lower frequencies, resulting in frequency overlap. This overlap can be seen in Figure 21E, where a horizontal line cannot be drawn to separate the red (encoded water frequencies) and blue (encoded fat frequencies) target frequencies. It was therefore not a surprise that when applying FATSAT to get complete fat saturation as in Figure 22B, the water frequencies at the top and bottom were suppressed. Conversely, when applying FATSAT to avoid suppressing water, there was incomplete fat suppression as seen in Figure 22C. In contrast, SVSP was able to offer better fat suppression with less water suppression. This was because SVSP offered the advantage of shaping the saturation frequency according to the field inhomogeneity, giving flexibility beyond conventional SFS methods. It encoded fat and water isochromats spectral-spatial locations so that the pulse while not exciting the water would selectively excite the fat. Both simulated and experimental results suggest that SVSP can improve fat suppression in breast imaging. However, some potential issues exist and they will be discussed here and in Chapter 3. In the virtual phantom experiment, the interfaces between tissue and air created drastic jumps in frequencies that led to incomplete saturation. These jumps in frequencies can be seen in Figure 9 (at x < 2.8 cm and x > 27.2 cm) and Figure 12 at x = 3 cm to 5 cm and at x = 25 cm to 27 cm where a few blue targets (encoded fat frequencies) jump much higher than the red targets (encoded water frequencies). In Figure 12, the range and jumps in dots (i.e. target 53

61 magnetizations) for a given spatial location is a result of the projection and accumulation of target frequencies from two spatial dimensions onto one spatial dimension for our SVSP. They affect the encoding process as well, adding outlying targets that resulted in a passband that overlapped with the stopband as seen in Figure 18. Specifically, the target fat frequencies that appear higher than the water frequencies at around x = 9 13cm and cm are a result of jumps in frequencies at the air-tissue interface. Poorer modeling resolution (i.e. number of discrete balls/elements making up the virtual phantom) of the phantom worsened this feature, suggesting that it is a modeling inaccuracy. This is a limitation of the current virtual field map generator that can be minimized by increasing resolution or using a more accurate modeling algorithm. Improvements to the encoding process may also involve the exclusion of outliers as seen in Figure 18 that may allow SVSP to be more optimized towards saturating and not saturating the relevant regions of fat and water respectively. Nonetheless, the modeling inaccuracy does not hinder the demonstration of SVSP s advantages. One potential area of concern is SVSP s reliance on good field estimation. Currently, the field estimation is based on the author s implementation of IDEAL with region growing. Throughout experimentation, the algorithm was susceptible to incorrectly labeling parts of the sample as fat or water and required occasional manual intervention such as specifying water-only areas in the sample. Incorrect estimation of the field and distribution of water-fat content would lead to incorrect encoding of the isochromats, which in turn would lead to incorrect saturation. Thus, the success of SVSP is highly dependent on having access to a robust field estimation routine. Indepth discussion of potential improvements and future work will be made in the next chapter. 54

62 Chapter 3 Future Work and Conclusion There remain many aspects worth investigating such as field estimation methods, multi-slice saturation, additional dimensions, SAR and peak RF at different field strengths, and in-vivo experimentation. Robust Field Estimation As mentioned in the previous section, robust field estimation is very important for the effective usage of SVSP. In addition, the field estimation routine would need to be fast in order for it to be clinically relevant. For example, it may be possible to perform voxel-by-voxel spectroscopy, which would be able to track the frequency shifts and the water-fat distribution, but would not be practical due to the extremely long duration required. Some current, more robust field estimation algorithms include variants of the multipoint Dixon techniques that involve applying different region labeling methods [41]and fat-water likelihood analysis [42] to an iterative fitting process. Another new method uses a non-iterative phase correction approach called B0-NICE, which was successful in estimating large inhomogeneities [43]. A caveat is that the computational time required (1423 s) may not be practical, but there may be hope that the computational time may decrease in the future with better implementation and faster computers. The field map required for SVSP can be fairly low resolution. The 128x128 matrix used for the field map in this work was the minimum matrix size allowed by the stock sequence used; it is expected that smaller matrix sizes (e.g. 64x64 and maybe even 32x32) would work well with SVSP, potentially making it easier to rapidly create a high quality but low resolution field map. SVSP vs IDEAL s Estimated Fat-Water Maps Another aspect worth exploring is the comparison of SVSP with the production of water images from IDEAL s fat-water separation. As part of the field-estimation algorithm, IDEAL provides estimates of fat and water distribution in the sample, which means it could create a water-image, with the accuracy of the estimate depending on the accuracy of the field estimation algorithm. A constraint is that IDEAL requires the acquisition of multiple data sets at different TEs that are relatively close together. As in-plane clinical images are required to have 1 mm resolution or 55

63 less, this could translate to a relatively long acquisition time. This may be a particular issue when applied in DCE T1w images, where it is important to keep the acquisition of complete images within 1-2 minutes in order to track the dynamics of the contrast agent. SVSP requires the use of a field estimation routine but has the freedom of playing the saturation pulse at any subsequent point. Although not explored rigorously, the results of this work suggest that the field variation across samples would be at a larger spatial scale than the clinically required resolution. A coarse-resolution field estimation routine that has a much reduced duration could be used that would still allow SVSP to saturate fat. Moreover, the aim of SVSP is the removal of fat signal without the saturation of water. Even in the case of incomplete fat saturation, a SVSP-saturated image would still retain the true water image, unlike an estimated water image based on fat-water separation from software. However, motion artifacts may be a problem such that field estimations may not reflect the actual patient s position after a period of time. Exploration into the robustness of field-estimation-with-svsp and motion should be performed in future work. Different Excitation K-Space Trajectories A potential technical investigation is the use of different excitation k-space trajectories. In this work, a unipolar Flyback trajectory was used. Future work may include the use of the bipolar echo-planar trajectory. The benefits of having a bipolar trajectory includes the ability to deposit energy twice in one cycle halving the energy distribution load per cycle. However, potential problems may include n/2 ghosting artifacts, which is a result of eddy currents that cause opposing shifts in excitation k-space, depending on the direction the trajectory is traveling in. Encoding Multiple Spatial Directions In the experiments, the target frequencies that SVSP tries to saturate are a result of the projection of multiple spatial dimensions, as the SVSP only had 1 spatial selectivity dimension (i.e. SVSP varied only in the x direction). Future work may include the sampling of multiple directions in excitation k-space to enable spatial variation in the SVSP in more than one direction e.g. future SVSP may have 1 spectral 2 spatial selectivity. Additional spatial dimensions would allow for the ability to calculate the optimal direction in which to apply the pulse. Based on the information 56

64 provided by the field map, it may be possible to select a direction that is a linear combination of x, y, and/or z that would allow for the greatest amount of saturation. A possible sampling method is to perform an EPI that samples kx very quickly (to an extent of kxmax) while simultaneously traversing ky more slowly (to kymax). The quick sampling of kx ensures that for every minimal sampling distance in ky that is traversed (i.e. ky sampling distance that needs to match the field of view in y), there is approximately a full line in kx that is sampled. In other words, there is a periodicity associated with the sampling of ky that needs to be met when simultaneously sampling kx. As an example: the sampling distance in ky should be 1 30 cm 1 to have a field of view in y of 30 cm. The trajectory would still have to meet the periodicity requirement to have sufficient bandwidth i.e. the trajectory needs to come back to the same (kx, ky) coordinate at the beginning of every period at ~2 ms at 1.5 T. The use of a spiral sampling pattern in excitation k-space (kx and ky) may also be explored here. Issues to look out for include the fact that adding an additional dimension to the spatial variation would put a tighter constraint on the resolution of the spatial variation. For example, in our experiments, we achieved 3 cm spatial resolution along x and a theoretical potential of up to 1.22 mm. To add spatial variation along y, the resolution along x may have to be coarsened (i.e. kxmax may have to be smaller) in order to achieve the ky-sampling periodicity and this tradeoff will need to be explored. Another consideration would be the speed that is needed to traverse a multidimensional k-space. Multiple spatial dimensions would require traversing through k-space quickly, which would mean a smaller time interval spent traversing near the centre of k-space. This means a higher B1 and SAR would be needed in order to deposit the required amount of energy. Integration into Imaging SVSP could apply to both T2w and T1w imaging sequences. In breast T2w sequences, the TR is usually a few seconds (i.e. 2 s) and the TE is usually around ms, with data acquisition for the excited slice completing ms after the slice excitation. With the use of an interleaved multi-slice sequences, multiple slices may be acquired within one TR (e.g. n = ~10 slices, n being the number of slices per TR). With SVSP, it is possible to combine the spectral-spatial locations of fat spin isochromats in multiple target slices into the target magnetization in order to 57

65 saturate the fat in multiple target slices simultaneously. In effect, the third dimension (i.e. slice direction, z) is projected onto the 1-spectral 1-spatial space. Given that fat in breast generally has a T1 value of 250 ms, the fat magnetization would recover to ~63 % by 250 ms and to ~84% by 500 ms. It may be reasonable to acquire up to two slices per SVSP resulting in n/2 or more number of SVSPs per TR which means each SVSP should suppress the fat in the two slices. This could provide a more efficient and less restrained way to saturate fat isochromats throughout the scan, especially when performing interleaved acquisition in an order that would most benefit from the overlapping of encoded fat isochromat selection-saturation. For example, in one TR, a target slice s isochromats may be grouped together with some of the next target slice s isochromats during the encoding phase of the SVSP such that they would be saturated prior to slice acquisition. When selecting the next slice, the encoding process of the next SVSP would either not need to consider the previously targeted isochromats or only need to provide a weaker target magnetization value onto the previously targeted isochromats, depending on how much the longitudinal magnetization has recovered. This method may lead to both relaxation of the design which may lead to better overall saturation as there are fewer targets to hit and reduced energy deposition, leading to less SAR. However, it is also important to ensure that the SVSP does not suppress water spin isochromats in the other slices, especially given that water has a long T1 value (~2 s). The water spatial-spectral locations of all slices would need to be encoded into the stop band. Naturally, this may also work well with multiband multi-slice techniques. The multiple slices that would be imaged simultaneously in multiband multi-slice could have their fat signals suppressed simultaneously via a single SVSP played prior to excitation. Using the frequency shift map from the virtual breast phantom, the frequency variation in the slice direction (i.e. superior-inferior direction) shows relatively little change (up to 20 Hz change within tissue - see Figure 25) with symmetry present due to the fact that the phantom was created from a revolved parabola, as is evident in Figure 25. In this model, it would be easy to simultaneously encode imaging planes that correspond to each other due to this symmetry. In the clinical setting, breasts are not likely to exhibit this symmetry, but uneven spatial distribution of tissue may perhaps be modeled as a skewing of tissue which may be reflected in the field map as skewing as well. It is 58

66 conceivable that with adjustment of the simultaneously encoded planes' spatial locations to account for the skewing, this method would work well. Figure 25. Left: Frequency map of sagittal view of virtual breast phantom. Right: Cross section of above frequency map at z = 12 cm. Notice the relatively small changes in the frequency (20 Hz) in the actual tissue between ~12 cm and 18 cm. This figure shows the expected field variation in Y, the slice direction in axial images, suggesting that simultaneously encoding multiple axial planes for fat suppression would be feasible. Aside from T2w imaging, SVSP could apply equally well to T1w imaging where SVSP is played once every ~ ms. Use for Other Inhomogeneous Regions of the Body Clinically, SVSP can find potential uses in regions of the body with severe, irregular field inhomogeneities. These areas may include regions with large amounts of air-tissue interfaces such as the sinuses, areas of the torso near the lungs, and the gastrointestinal tract. Similarly, body parts with implants or prosthetics may also benefit. For example, SVSP can be used for fat suppression in women with breast implants, which can be a major source of field inhomogeneity [44]. Exploration into Applicability at Different Field Strengths 59