Hsu E W, Mori S
Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, USA.
Magn Reson Med. 1995 Aug;34(2):194-200. doi: 10.1002/mrm.1910340210.
NMR measurements of anisotropic diffusion were studied using a three-dimensional random-walk model. It was found that the apparent diffusion coefficient can be expressed in a canonical form as the product of a diagonal matrix, an orthonormal rotation matrix, and a vector representing the encoding magnetic field gradient. The diffusion coefficient can be interpreted as the sum of the corresponding coefficients measured along the principal diffusion axes, weighted by the squares of the directional cosines of the encoding direction with respect to the principal axes. The analysis revealed that determining the orientation of anisotropy, in a cylindrically symmetric system, requires a minimum of four diffusion measurements. A special pulse sequence which minimized gradient cross-terms and possible restricted diffusion effects was used to characterize diffusion anisotropy in cut chicken gizzards. Diffusion coefficients parallel to the muscle fibers were found to be approximately two to three times larger than those in the transverse direction. Furthermore, the method was successful in detecting the angular change when the sample was rotated by 30 degrees. Results indicate that the proposed approach to measure fiber orientation is valid and may be used to improve the time efficiency of diffusion anisotropy measurements.
使用三维随机游走模型研究了各向异性扩散的核磁共振测量。结果发现，表观扩散系数可以表示为一个对角矩阵、一个正交旋转矩阵和一个表示编码磁场梯度的向量的乘积的标准形式。扩散系数可以解释为沿主扩散轴测量的相应系数之和，由编码方向相对于主轴的方向余弦的平方加权。分析表明，在圆柱对称系统中确定各向异性的方向至少需要进行四次扩散测量。使用一种特殊的脉冲序列来表征切好的鸡胗中的扩散各向异性，该序列可使梯度交叉项和可能的受限扩散效应最小化。发现平行于肌纤维的扩散系数大约是横向扩散系数的两到三倍。此外，当样品旋转30度时，该方法成功检测到了角度变化。结果表明，所提出的测量纤维方向的方法是有效的，可用于提高扩散各向异性测量的时间效率。
