由於其優越之信噪比特性，平衡穩定態磁振造影序列逐漸成為一種廣為使用之掃描序列。非平衡穩定態造影序列亦逐漸受到重視，尤其在於此種掃描序列在臨床上的應用。舉例而言，雙重迴訊穩定態造影序列能同時接收到兩種截然不同特性之信號，並可藉由分析這兩種不同來源之信號而擷取出組織特性。

此份論文旨在利用雙重迴訊穩定態造影序列，藉以研究、分析其所收集之信號特性。我們提出了一種雙重迴訊穩定態之變體造影序列，並應用於腦部磁振造影。利用我們的方法，可以從該序列所收取到之兩種特性迥異的信號中，同時解析出兩種橫向磁緩速率以及組織內部磁場擾動。而解析出之組織特性在腦部鐵質含量定量上有相當大的助益。

此外，為了能獲得最佳的掃瞄參數，我們運用了數值分析模擬了解該此兩種信號的演進，以及掃描序列之特性。在此篇論文的最末一章，我們針對可能影響組織參數特性解析之因素加以討論；同時，我們也提出了兩種可能適用此改良序列的應用。我們期待此篇論文能貢獻于非平衡穩定態掃描序列的發展；同時，也希望我們的改良序列亦能在其他應用上發揮貢獻。

As balanced steady-state sequence becomes a popular MR imaging modality for its terrific efficiency in terms of SNR per TR, unbalanced steady-state sequences draw more and more attention for their clinical applicability. In particular, dual-echo in the steady-state (DESS) sequence acquires diverse signals of two different signal pathways, so that tissue properties may be revealed.

In this thesis, we aim to exploit the sampling ability of unbalanced steady-state sequence to investigate signal evolutions of different pathways. A variant of DESS sequence is designed and applied to brain imaging. To be specific, transverse relaxation rates and the internal field perturbation are simultaneously extracted from signals acquired by our proposed compact method, and the extracted information could be valuable in estimating brain iron concentration.

To obtain a proper set of scanning parameters, numerical simulations are employed to evaluate sequence performance. In addition, potential image artifacts are discussed, and two possible applications are proposed in a later chapter in this thesis. We expect this work may advance the current development of unbalanced steady-state sequences, and the proposed sequence would be a handy imaging sequence for other applications as well.

Table of Contents
中文摘要 ...................................................................................................................................... I
Abstract ........................................................................................................................................ II
Table of contents ...................................................................................................................... III
Table of figures and table ..................................................................................................... V

Chapter 1 Introduction ............................................................................................................ 1

Chapter 2 Unspoiled steady-state sequences ............................................................. 3
2.1 Extended phase graph, signal pathways, and echo formation ..................... 4
2.2 Balanced steady-state free-precession (bSSFP) ................................................. 11
2.3 Break the balance: unbalanced steady-state free-precession (ubSSFP).. 16

Chapter 3. Simultaneous relaxometry and internal field perturbation in the brain
3.1 Introduction: brain iron accumulation and parametric mapping in the brain ...................................................................................................................................... 25
3.2 Theory .................................................................................................................................. 27
3.3 Sequence optimization .................................................................................................. 36
3.4 Experimental design and data processing ............................................................ 43
3.5 Results .................................................................................................................................. 53
3.6 Discussions and conclusions ...................................................................................... 57

Chapter 4. Discussions and conclusions ........................................................................ 61
4.1 Potential problems .......................................................................................................... 62
4.2 Possible applications ...................................................................................................... 73
4.3 Conclusions ........................................................................................................................ 78

References ....................................................................................................................................... 79

Table of figures and table
Figure 2.1 Extended phase diagram ............................................................................. 2-5
Figure 2.2 Four different gradient configurations for signal acquisition .... 2-8
Figure 2.3 Sequence diagram of standard bSSFP sequence .............................. 2-11
Figure 2.4 Signal variations of bSSFP with different flip angles ...................... 2-13
Figure 2.5 Simplified sequence sketches of FISP and PSIF sequences .......... 2-18
Figure 2.6 Sequence diagram of DESS sequence .................................................... 2-21

Figure 3.1 Dual pathway steady-state sequence with multiple acquisition and echo formations ..................................................................................... 3-5
Figure 3.2 Comparison of two spectral distributions of isocromats .............. 3-11
Figure 3.3 Simulations of FISP and PSIF signals, and the SNR performance in the fitted frequency ...................................................... 3-16
Figure 3.4 Simulated SNR in fitted R2 and R2′ .......................................................... 3-18
Figure 3.5 Coil combination workflow ........................................................................ 3-22
Figure 3.6 Comparisons of two different approaches to estimate relaxation rates ............................................................................................... 3-26
Figure 3.7 Workflow of both phase and magnitude processing ...................... 3-28
Figure 3.8 Comparisons of the internal field perturbations with two different TRs ..................................................................................................... 3-30
Figure 3.9 Comparisons of R2 and R2* mappings with two different TRs ... 3-31
Table 3.1 Results of R2 and R2* values in brain regions ................................... 3-32

Figure 4.1 Simulations of b-factor using designed gradient scheme ............. 4-5
Figure 4.2 Signal void artifact in images acquired with different sequences .......................................................................................................... 4-8
Figure 4.3 Illustration of flow displacement artifact ............................................ 4-9
Figure 4.4 Flow-related displacement artifact in images ................................... 4-10

1.Bruder H, Fischer H, Graumann R, Deimling M. A new steady-state imaging sequence for simultaneous acquisition of two MR images with clearly different contrasts. Magn Reson Med. 1988;7(1):35-42.
2.Welsch GH, Scheffler K, Mamisch TC, Hughes T, Millington S, Deimling M, Trattnig S. Rapid estimation of cartilage T2 based on double echo at steady state (DESS) with 3 Tesla. Magn Reson Med. 2009;62(2):544-9.
3.Madore B, Panych LP, Mei CS, Yuan J, Chu R. Multipathway sequences for MR thermometry. Magn Reson Med. 2011;66(3):658-68.
4.Hennig J. Echoes—How to generate, recognize, use or avoid them in MR-imaging sequences. Part I: fundamental and not so fundamental properties of spin echoes. Concepts in Magnetic Resonance. 1991;3:125-43.
5.Mizumoto CT, Yoshitome E. Multiple echo SSFP sequences. Magn Reson Med. 1991;18(1):244-50.
6.Hanicke W, Vogel HU. An analytical solution for the SSFP signal in MRI. Magn Reson Med. 2003;49(4):771-5.
7.Scheffler K, Hennig J. Is TrueFISP a gradient-echo or a spin-echo sequence? Magn Reson Med. 2003;49(2):395-7.
8.Hargreaves BA, Vasanawala SS, Pauly JM, Nishimura DG. Characterization and reduction of the transient response in steady-state MR imaging. Magn Reson Med. 2001;46(1):149-58.
9.Dharmakumar R, Wright GA. Understanding Steady-State Free Precession: A Geometric Perspective. Concepts in Magnetic Resonance. 2005;26A(1):1-10.
10.Baur A, Stabler A, Bruning R, Bartl R, Krodel A, Reiser M, Deimling M. Diffusion-weighted MR imaging of bone marrow: differentiation of benign versus pathologic compression fractures. Radiology. 1998;207(2):349-56.
11.Chung YC, Merkle EM, Lewin JS, Shonk JR, Duerk JL. Fast T(2)-weighted imaging by PSIF at 0.2 T for interventional MRI. Magn Reson Med. 1999;42(2):335-44.
12.Naganawa S, Ishihara S, Satake H, Kawai H, Sone M, Nakashima T. Simultaneous three-dimensional visualization of the intra-parotid facial nerve and parotid duct using a three-dimensional reversed FISP sequence with diffusion weighting. Magn Reson Med Sci. 2010;9(3):153-8.
13.Chhabra A, Soldatos T, Subhawong TK, Machado AJ, Thawait SK, Wang KC, Padua A, Jr., Flammang AJ, Williams EH, Carrino JA. The application of three-dimensional diffusion-weighted PSIF technique in peripheral nerve imaging of the distal extremities. J Magn Reson Imaging. 2011;34(4):962-7.
14.Chhabra A, Subhawong TK, Bizzell C, Flammang A, Soldatos T. 3T MR neurography using three-dimensional diffusion-weighted PSIF: technical issues and advantages. Skeletal Radiol. 2011;40(10):1355-60.
15.Redpath TW, Jones RA. FADE--a new fast imaging sequence. Magn Reson Med. 1988;6(2):224-34.
16.Hardy PA, Recht MP, Piraino D, Thomasson D. Optimization of a dual echo in the steady state (DESS) free-precession sequence for imaging cartilage. J Magn Reson Imaging. 1996;6(2):329-35.
17.Welsch GH, Mamisch TC, Zak L, Mauerer A, Apprich S, Stelzeneder D, Marlovits S, Trattnig S. Morphological and biochemical T2 evaluation of cartilage repair tissue based on a hybrid double echo at steady state (DESS-T2d) approach. J Magn Reson Imaging. 2011;34(4):895-903.
18.Heule R, Ganter C, Bieri O. Triple echo steady-state (TESS) relaxometry. Magn Reson Med. 2013.
19.Cheng CC, Chao, TC, Chung, HW, Panych, LP, Madore, B. Simultaneous relaxometry and susceptibility imaging in the brain. The 21st Annual Meeting of International Society of Magnetic Resonance in Medicine. Salt Lake City, UT, USA: ISMRM, 2013; p. 4126.
20.Staroswiecki E, Granlund KL, Alley MT, Gold GE, Hargreaves BA. Simultaneous estimation of T2 and apparent diffusion coefficient in human articular cartilage in vivo with a modified three-dimensional double echo steady state (DESS) sequence at 3 T. Magn Reson Med. 2012;67(4):1086-96.
21.Haacke EM, Cheng NY, House MJ, Liu Q, Neelavalli J, Ogg RJ, Khan A, Ayaz M, Kirsch W, Obenaus A. Imaging iron stores in the brain using magnetic resonance imaging. Magn Reson Imaging. 2005;23(1):1-25.
22.Ordidge RJ, Gorell JM, Deniau JC, Knight RA, Helpern JA. Assessment of relative brain iron concentrations using T2-weighted and T2*-weighted MRI at 3 Tesla. Magn Reson Med. 1994;32(3):335-41.
23.Gelman N, Gorell JM, Barker PB, Savage RM, Spickler EM, Windham JP, Knight RA. MR imaging of human brain at 3.0 T: preliminary report on transverse relaxation rates and relation to estimated iron content. Radiology. 1999;210(3):759-67.
24.Schweser F, Deistung A, Lehr BW, Reichenbach JR. Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: an approach to in vivo brain iron metabolism? Neuroimage. 2011;54(4):2789-807.
25.Langkammer C, Krebs N, Goessler W, Scheurer E, Ebner F, Yen K, Fazekas F, Ropele S. Quantitative MR imaging of brain iron: a postmortem validation study. Radiology. 2010;257(2):455-62.
26.Langkammer C, Schweser F, Krebs N, Deistung A, Goessler W, Scheurer E, Sommer K, Reishofer G, Yen K, Fazekas F, Ropele S, Reichenbach JR. Quantitative susceptibility mapping (QSM) as a means to measure brain iron? A post mortem validation study. Neuroimage. 2012;62(3):1593-9.
27.Ma J, Wehrli FW. Method for image-based measurement of the reversible and irreversible contribution to the transverse-relaxation rate. J Magn Reson B. 1996;111(1):61-9.
28.Slichter CP. Principles of magnetic resonance. Berlin: Springer-Verlag, 1989.
29.Kennan RP, Zhong J, Gore JC. Intravascular susceptibility contrast mechanisms in tissues. Magn Reson Med. 1994;31(1):9-21.
30.Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn Reson Med. 1995;34(6):910-4.
31.Haacke EM, Brown, RW, Thompson, MR, Venkatesan, R. Magnetic resonance imaging: physical principles and sequence design. New York: Wiley-Liss, 1999: 375.
32.Jenkinson M, Beckmann CF, Behrens TE, Woolrich MW, Smith SM. Fsl. Neuroimage. 2012;62(2):782-90.
33.Li L, Leigh JS. High-precision mapping of the magnetic field utilizing the harmonic function mean value property. J Magn Reson. 2001;148(2):442-8.
34.Haacke EM, Ayaz M, Khan A, Manova ES, Krishnamurthy B, Gollapalli L, Ciulla C, Kim I, Petersen F, Kirsch W. Establishing a baseline phase behavior in magnetic resonance imaging to determine normal vs. abnormal iron content in the brain. J Magn Reson Imaging. 2007;26(2):256-64.
35.Hammond KE, Lupo JM, Xu D, Metcalf M, Kelley DA, Pelletier D, Chang SM, Mukherjee P, Vigneron DB, Nelson SJ. Development of a robust method for generating 7.0 T multichannel phase images of the brain with application to normal volunteers and patients with neurological diseases. Neuroimage. 2008;39(4):1682-92.
36.Walsh AJ, Wilman AH. Susceptibility phase imaging with comparison to R2 mapping of iron-rich deep grey matter. Neuroimage. 2011;57(2):452-61.
37.Kyriakos WE, Panych LP, Kacher DF, Westin CF, Bao SM, Mulkern RV, Jolesz FA. Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP). Magn Reson Med. 2000;44(2):301-8.
38.Le Bihan D. Diffusion and perfusion magneitc resonance imaging: Applications to functional MRI. New York: Raven Press, 1995.
39.Mills R. Self-Diffusion in Normal and Heavy-Water in Range 1-45 Degrees. J Phys Chem-Us. 1973;77(5):685-8.
40.An H, Lin W. Quantitative measurements of cerebral blood oxygen saturation using magnetic resonance imaging. J Cereb Blood Flow Metab. 2000;20(8):1225-36.
41.He X, Yablonskiy DA. Quantitative BOLD: mapping of human cerebral deoxygenated blood volume and oxygen extraction fraction: default state. Magn Reson Med. 2007;57(1):115-26.
42.Yablonskiy DA. Quantitation of intrinsic magnetic susceptibility-related effects in a tissue matrix. Phantom study. Magn Reson Med. 1998;39(3):417-28.
43.Hindman JC. Proton Resonance Shift of Water in the Gas and Liquid States. Journal of Chemical Physics. 1966;44(12):4582-92.
44.Ishihara Y, Calderon A, Watanabe H, Okamoto K, Suzuki Y, Kuroda K. A precise and fast temperature mapping using water proton chemical shift. Magn Reson Med. 1995;34(6):814-23.
45.De Poorter J. Noninvasive MRI thermometry with the proton resonance frequency method: study of susceptibility effects. Magn Reson Med. 1995;34(3):359-67.
46.Rieke V, Butts Pauly K. MR thermometry. J Magn Reson Imaging. 2008;27(2):376-90.