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In order to accurately investigate the directionally anisotropic diffusion information of water molecule in tissue, the diffusion sensitive gradient fields need to be applied alone many directions in order to obtain corresponding diffusion coefficients in diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI) experiments. The problems facing to current diffusion sensitive gradient magnetic fields encoding schemes include the spatial uniformity of directions needs to be improved, there is no general direction design for arbitrary number of directions, flaw in any directions will cause failure or defect of the whole dataset. In this paper, we provide a generalized Fibonacci number based direction encoding scheme. This scheme can generate nearly uniform distribution for arbitrary number of directions and satisfy the spatial uniformity using partial directions from one raw data set. Besides, the diffusion sensitive gradients of neighboring directions are nearly opposite, which will reduce eddy current induced by rapid varying gradient magnetic fields.
[1] Wedeen V J, Rosene D L, Wang R, Dai G, Mortazavi F, Hagmann P, Kaas J H, Tseng W Y 2012 Science 335 1628
[2] Gao S, Wang X Y, Bao S L 2006 Prog. Nat. Sci. 16 706
[3] Zhang S Y, Bao S L, Kang X J 2013 Acta Phys. Sin. 62 208703 (in Chinese) [张首誉, 包尚联, 亢孝俭 2013 物理学报 62 208703]
[4] Hasan K M, Parker D L, Alexander A L 2001 J. Magn. Reson. Imaging 13 769
[5] Alderman D, Sherwood M H, Grant D M 1990 J. Magn. Reson. 86 60
[6] Basser P J, Pierpaoli C 1998 Magn. Reson. Med. 39 928
[7] Skare S, Nordell B 1999 Proceedings of the 7th Annual Meeting of ISMRM Philadelphia, United States of America, May 22-28, 1999 p322
[8] Jones D K, Horsfield M A, Simmons A 1999 Magn. Reson. Med. 42 515
[9] Conturo T E, McKinstry R C, Akbudak E, Robinson B H 1996 Magn. Reson. Med. 35 399
[10] Wong S T, Roos M S 1994 Magn. Reson. Med. 32 778
[11] Anderson P G 1993 Applications of Fibonacci numbers (Berlin: Springer-Verlag) p1
[12] Chan R W, Ramsay E A, Cunningham C H, Plewes D B 2009 Magn. Reson. Med. 61 354
[13] Chan R W, Ramsay E A, Cheung E Y, Plewes D B 2012 Magn. Reson. Med. 67 363
[14] Gao S, Zu Z L, Bao S L 2008 Chin. Phys. Lett. 25 325
[15] Winkelmann S, Schaeffter T, Koehler T, Eggers H, Doessel O 2007 IEEE Trans. Med. Imag. 26 68
[16] Qin L, Li Q 2013 Chin. Phys. B 22 038701
[17] Bao S L, Du J, Gao S 2013 Acta Phys. Sin. 62 088701 (in Chinese) [包尚联, 杜江, 高嵩 2013 物理学报 62 088701]
[18] Du J, Diaz E, Carl M, Bae W, Chung C B, Bydder G M 2012 Magn. Reson. Med. 67 645
[19] Fang S, Wu W C, Ying K, Guo H 2013 Acta Phys. Sin. 62 048702 (in Chinese) [方晟, 吴文川, 应葵, 郭华 2013 物理学报 62 048702]
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[1] Wedeen V J, Rosene D L, Wang R, Dai G, Mortazavi F, Hagmann P, Kaas J H, Tseng W Y 2012 Science 335 1628
[2] Gao S, Wang X Y, Bao S L 2006 Prog. Nat. Sci. 16 706
[3] Zhang S Y, Bao S L, Kang X J 2013 Acta Phys. Sin. 62 208703 (in Chinese) [张首誉, 包尚联, 亢孝俭 2013 物理学报 62 208703]
[4] Hasan K M, Parker D L, Alexander A L 2001 J. Magn. Reson. Imaging 13 769
[5] Alderman D, Sherwood M H, Grant D M 1990 J. Magn. Reson. 86 60
[6] Basser P J, Pierpaoli C 1998 Magn. Reson. Med. 39 928
[7] Skare S, Nordell B 1999 Proceedings of the 7th Annual Meeting of ISMRM Philadelphia, United States of America, May 22-28, 1999 p322
[8] Jones D K, Horsfield M A, Simmons A 1999 Magn. Reson. Med. 42 515
[9] Conturo T E, McKinstry R C, Akbudak E, Robinson B H 1996 Magn. Reson. Med. 35 399
[10] Wong S T, Roos M S 1994 Magn. Reson. Med. 32 778
[11] Anderson P G 1993 Applications of Fibonacci numbers (Berlin: Springer-Verlag) p1
[12] Chan R W, Ramsay E A, Cunningham C H, Plewes D B 2009 Magn. Reson. Med. 61 354
[13] Chan R W, Ramsay E A, Cheung E Y, Plewes D B 2012 Magn. Reson. Med. 67 363
[14] Gao S, Zu Z L, Bao S L 2008 Chin. Phys. Lett. 25 325
[15] Winkelmann S, Schaeffter T, Koehler T, Eggers H, Doessel O 2007 IEEE Trans. Med. Imag. 26 68
[16] Qin L, Li Q 2013 Chin. Phys. B 22 038701
[17] Bao S L, Du J, Gao S 2013 Acta Phys. Sin. 62 088701 (in Chinese) [包尚联, 杜江, 高嵩 2013 物理学报 62 088701]
[18] Du J, Diaz E, Carl M, Bae W, Chung C B, Bydder G M 2012 Magn. Reson. Med. 67 645
[19] Fang S, Wu W C, Ying K, Guo H 2013 Acta Phys. Sin. 62 048702 (in Chinese) [方晟, 吴文川, 应葵, 郭华 2013 物理学报 62 048702]
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