隨著醫療技術的日新月異，諸多疾病例如缺血性心臟病與中風，其致病率與死亡率都獲得了極大的改善；然而，與精神疾病相關的失能與自殺率，和過去相比卻無明顯的下降；因此，我們對於人腦必須有更深入而徹底的瞭解。對活體人腦進行評估一直是一件非常困難而富有挑戰性的工作，為了解開人腦的謎團，核磁共振是最常使用的影像工具之一。
擴散頻譜磁振造影(Diffusion Spectrum Imaging, DSI)是一種評估人腦細微結構的先進技術，它能用來評估腦中的神經纖維走向與不等向性分率。除此之外，它在q空間中的信號可能還傳達了其他重要的生物參數，例如神經纖維的水分子分率(Axonal Water Fraction, AWF)。目前已經有很多的生物模型涵蓋了AWF的測量，例如雙指數模型(Bi-Exponential model)、擴散峰度磁振造影(Diffusional Kurtosis Imaging, DKI)、ActiveAx模型與NODDI模型。因為胼胝體的神經纖維走向相當一致，為了證實生物模型的可靠性，我們將針對人腦的胼胝體進行評估。
在我們的第一個實驗中，我們收集了一個相當特別的DSI數據，它在q空間與影像空間中都是二維的數據。將改良過後的ActiveAx模型應用到我們的二維DSI數據之後，我們可以估計人腦胼胝體不同部位的AWF。實驗結果與Aboitiz的組織學觀察相當一致，證實了實驗設計的可行性。在第二個實驗中，我們藉由事先建構好的NTU-DSI-122模板，另外建構了一個DKI模板。我們選擇了限制性線性最小平方法(Constrained Linear Least Square)來計算峰度張量(kurtosis tensor)的元素；另外，藉由DKI 的組織模型，我們能夠在較低的電腦計算負擔下，畫出全腦的AWF圖譜。總結來說，我們的研究能夠增進後續研究者對於人腦細微結構的探索，並在未來應用於精神或神經疾病的診斷，例如多發性硬化症(Multiple Sclerosis)的早期發現。

Although morbidity and mortality rate of some diseases, such as ischemic cardiac attack or stroke, decrease prominently with improvement in medical technology, disability and suicide rate related to mental diseases remain as before. Therefore, it is crucial for us to achieve a better comprehension of human brains. However, in vivo evaluation of human brains is always difficult and challenging. Magnetic Resonance Imaging (MRI) is the most commonly used method to tackle the mystery of human brains.

Diffusion Spectrum Imaging (DSI), a kind of diffusion MRI, is an advanced technique for evaluating microstructure of the human brain, such as axonal direction and general fractional anisotropy (GFA). Its signal in the q space may convey other important biological parameters such as axonal water fraction (AWF). There are lots of researchers who integrate AWF measurement into their models, including Bi-Exponential model, Diffusional Kurtosis Imaging (DKI), CHARMED model, ActiveAx model, and NODDI model. To confirm the reliability of various models, we focus on AWF of the human corpus callosum (CC), in which axonal directions are very coherent.

In our first experiment, we acquire a special DSI data, which is 2D in q space as well as in image space. Applying a modified ActiveAx model to our 2D DSI data, we can estimate AWF over the human CC. Our result is consistent to Aboitiz’s observation in histology, demonstrating the feasibility of our experimental setup. In the second experiment, we construct a DKI template from NTU-DSI-122 template, which is a DSI template. Constrained Linear Least Square (CLLS) is chosen for calculating kurtosis tensor elements. In addition, using a tissue model for DKI, we are able to obtain AWF map of whole brain with low computational loads. In conclusion, the proposed methods can facilitate further researches in probing microstructure of the human brain, and hence contribute to early diagnosis of mental or neurological diseases such as multiple sclerosis.

誌謝 ii
中文摘要 iii
英文摘要 iv
目錄 vi
圖目錄 viii
第一章 Introduction 1
1.1 Principles of Diffusion Magnetic Resonance Imaging 1
1.1.1 Diffusion and Magnetic Resonance Imaging 2
1.1.2 Free Diffusion 6
1.1.3 Restricted Diffusion 7
1.1.4 Diffusion Tensor Imaging (DTI) 9
1.1.5 Diffusion Spectrum Imaging (DSI) 11
1.1.6 Diffusional Kurtosis Imaging (DKI) 12
1.2 Tissue Models for Evaluating Microstructure of the Human Brain 19
1.2.1 Bi-Exponential Model 19
1.2.2 CHARMED and AxCaliber Model 20
1.2.3 ActiveAx and NODDI Model 21
1.2.4 Tissue Model for Diffusional Kurtosis Imaging 22
1.2.5 Relationship of Axonal Water Fraction and Fractional Anisotropy 24
1.3 Motivation 25
第二章 Materials and Methods 27
2.1 Experiment 1: Evaluating Microstructure of the Corpus Callosum 27
2.1.1 Modified ActiveAx Model for DSI 27
2.1.2 Experimental Setup: Q Plane Imaging (QPI) 29
2.2 Experiment 2: Evaluating Microstructure of the Whole Brain 30
2.2.1 Modified CLLS-H Algorithm and Tissue Model for DKI 30
2.2.2 DSI Template: NTU-DSI-122 31
第三章 Results 33
3.1 Experiment 1 33
3.1.1 Axonal Water Fraction (AWF) 33
3.1.2 Intra-axonal and Extra-axonal Diffusivities 37
3.2 Experiment 2 38
3.2.1 Colored Fractional Anisotropy (FA) Map 38
3.2.2 Mean Kurtosis, Axial Kurtosis and Radial Kurtosis Map 39
3.2.3 Axonal Water Fraction Map 42
3.2.4 Correlation between AWF and FA 44
第四章 Discussion and Conclusion 47
4.1 Strategies of Probing Microstructures of the Human Brain 47
4.1.1 What is the Difference between Strategies? 47
4.1.2 Which Strategy is Better? 48
4.2 Applications 49
4.2.1 Axonal Loss or Demyelination? 49
4.2.2 Early Diagnosis of Mental or Neurological Diseases 50
參考文獻 52

[1]Basser, P. J., Mattiello, J., &; LeBihan, D. (1994). MR diffusion tensor spectroscopy and imaging. Biophysical journal, 66(1), 259-267.
[2]Wedeen, V. J., Hagmann, P., Tseng, W. Y. I., Reese, T. G., &; Weisskoff, R. M. (2005). Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magnetic Resonance in Medicine, 54(6), 1377-1386.
[3]Jensen, J. H., Helpern, J. A., Ramani, A., Lu, H., &; Kaczynski, K. (2005). Diffusional kurtosis imaging: The quantification of non&;#8208;gaussian water diffusion by means of magnetic resonance imaging. Magnetic Resonance in Medicine, 53(6), 1432-1440.
[4]Crank, J. (1975). The mathematics of diffusion. Oxford University Press.
[5]Callaghan, P. T. (1991). Principles of nuclear magnetic resonance microscopy. Oxford University Press.
[6]Torrey, H. C. (1956). Bloch equations with diffusion terms. Physical Review, 104(3), 563.
[7]Karger, J., &; Heink, W. (1983). The propagator representation of molecular transport in microporous crystallites. Journal of Magnetic Resonance, 51(1), 1-7.
[8]Stejskal, E. O., &; Tanner, J. E. (1965). Spin diffusion measurements: Spin echoes in the presence of a time&;#8208;dependent field gradient. The journal of chemical physics, 42(1), 288-292.
[9]Tanner, J. E., &; Stejskal, E. O. (1968). Restricted self&;#8208;diffusion of protons in colloidal systems by the pulsed&;#8208;gradient, spin&;#8208;echo method. The Journal of Chemical Physics, 49(4), 1768-1777.
[10]Carslaw, H. S., &; Jaeger, J. C. (1959). Conduction of heat in solids. Oxford: Clarendon Press
[11]Douglass, D. C., &; McCall, D. W. (1958). Diffusion in paraffin hydrocarbons. The Journal of Physical Chemistry, 62(9), 1102-1107.
[12]Neuman, C. H. (1974). Spin echo of spins diffusing in a bounded medium. The Journal of Chemical Physics, 60(11), 4508-4511.
[13]Basser, P. J., &; Pierpaoli, C. (1996). Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. Journal of Magnetic Resonance, Series B, 111(3), 209-219.
[14]Tuch, D. S. (2004). Q&;#8208;ball imaging. Magnetic Resonance in Medicine, 52(6), 1358-1372.
[15]Jensen, J. H., &; Helpern, J. A. (2010). MRI quantification of non&;#8208;Gaussian water diffusion by kurtosis analysis. NMR in Biomedicine, 23(7), 698-710.
[16]Liu, C., Bammer, R., Acar, B., &; Moseley, M. E. (2004). Characterizing non&;#8208;gaussian diffusion by using generalized diffusion tensors. Magnetic Resonance in Medicine, 51(5), 924-937.
[17]Tabesh, A., Jensen, J. H., Ardekani, B. A., &; Helpern, J. A. (2011). Estimation of tensors and tensor&;#8208;derived measures in diffusional kurtosis imaging. Magnetic Resonance in Medicine, 65(3), 823-836.
[18]Clark, C. A., &; Le Bihan, D. (2000). Water diffusion compartmentation and anisotropy at high b values in the human brain. Magnetic Resonance in Medicine, 44(6), 852-859.
[19]Maier, S. E., Vajapeyam, S., Mamata, H., Westin, C. F., Jolesz, F. A., &; Mulkern, R. V. (2004). Biexponential diffusion tensor analysis of human brain diffusion data. Magnetic resonance in medicine, 51(2), 321-330.
[20]Assaf, Y., Freidlin, R. Z., Rohde, G. K., &; Basser, P. J. (2004). New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magnetic Resonance in Medicine, 52(5), 965-978.
[21]Assaf, Y., &; Basser, P. J. (2005). Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain. Neuroimage, 27(1), 48-58.
[22]Assaf, Y., Blumenfeld&;#8208;Katzir, T., Yovel, Y., &; Basser, P. J. (2008). AxCaliber: a method for measuring axon diameter distribution from diffusion MRI. Magnetic Resonance in Medicine, 59(6), 1347-1354.
[23]Barazany, D., Basser, P. J., &; Assaf, Y. (2009). In vivo measurement of axon diameter distribution in the corpus callosum of rat brain. Brain, 132(5), 1210-1220.
[24]Alexander, D. C., Hubbard, P. L., Hall, M. G., Moore, E. A., Ptito, M., Parker, G. J., &; Dyrby, T. B. (2010). Orientationally invariant indices of axon diameter and density from diffusion MRI. Neuroimage, 52(4), 1374-1389.
[25]Zhang, H., Hubbard, P. L., Parker, G. J., &; Alexander, D. C. (2011). Axon diameter mapping in the presence of orientation dispersion with diffusion MRI. Neuroimage, 56(3), 1301-1315.
[26]Zhang, H., Schneider, T., Wheeler-Kingshott, C. A., &; Alexander, D. C. (2012). NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage, 61(4), 1000-1016.
[27]Szafer, A., Zhong, J., &; Gore, J. C. (1995). Theoretical model for water diffusion in tissues. Magnetic Resonance in Medicine, 33(5), 697-712.
[28]Fieremans, E., Jensen, J. H., &; Helpern, J. A. (2011). White matter characterization with diffusional kurtosis imaging. Neuroimage, 58(1), 177-188.
[29]Weng, J. C., &; Lin, S. Y. (2013). Bi-Gaussian Q-planar MR Measurement of Axonal Diameter and Density of Human Corpus Callosum In Vivo. Retrieved from embc.embs.org database
[30]Hsu, Y. C., Lo, Y. C., Chen, Y. J., Wedeen, V., &; Tseng, W. Y. (2014). NTU-DSI-122: A Diffusion Spectrum Imaging Template Constructed from 122 Healthy Adults in a Standard Space. Manuscript submitted for publication.
[31]Hsu, Y. C., Hsu, C. H., &; Tseng, W. Y. I. (2012). A large deformation diffeomorphic metric mapping solution for diffusion spectrum imaging datasets. NeuroImage, 63(2), 818-834.
[32]Aboitiz, F., Scheibel, A. B., Fisher, R. S., &; Zaidel, E. (1992). Fiber composition of the human corpus callosum. Brain research, 598(1), 143-153.
[33]Douek, P., Turner, R., Pekar, J., Patronas, N., &; Le Bihan, D. (1991). MR color mapping of myelin fiber orientation. Journal of computer assisted tomography, 15(6), 923-929.
[34]Jones, D. K. (2010). Diffusion MRI: Theory, Methods, and Applications. Oxford University Press.
[35]Longo D. L., Harrison T. R. Harrison’s principles of internal medicine, 18th edition. (2012). New York: McGraw-Hill.
[36]Song, S. K., Sun, S. W., Ramsbottom, M. J., Chang, C., Russell, J., &; Cross, A. H. (2002). Dysmyelination revealed through MRI as increased radial (but unchanged axial) diffusion of water. Neuroimage, 17(3), 1429-1436.
[37]Campbell, J. S. W., Stikov, N., Dougherty, R. F., Pike, G. B. (2014, May 10-16). Combined NODDI and qMT for full-brain g-ratio mapping with complex subvoxel microstructure. Paper presented at the 22nd International Society for Magnetic Resonance in Medicine Annual Meeting, Milan. Retrieved from
http://www.ismrm.org/14/.