Zhan Wang, Stein Elliot A, Yang Yihong
Neuroimaging Research Branch, Intramural Research Program, National Institute on Drug Abuse, National Institutes of Health, Nathan Shock Dr. Room 383, Baltimore, MD 21224, USA.
Neuroimage. 2006 Feb 15;29(4):1212-23. doi: 10.1016/j.neuroimage.2005.08.045. Epub 2005 Oct 12.
A new rotation-invariant spherical harmonic decomposition (SHD) method is proposed in this paper for analyzing high angular resolution diffusion (HARD) imaging. Regular SHD methods have been used to characterize the features of the apparent diffusion coefficient (ADC) profile measured by the HARD technique. However, these regular SHD methods are rotation-variant, i.e., the magnitude and/or the phase of the harmonic components changes with the rotation of the ADC profile. We propose a new rotation-invariant SHD (RI-SHD) method based on the rotation-invariant property of a diffusion tensor model. The basic idea of the proposed method is to reorient the measured ADC profile into a local coordinate system determined by the three eigenvectors of the diffusion tensor in each imaging voxel, and then apply a SHD to the ADC profile. Both simulations and in vivo experiments were carried out to validate the method. Comparisons were made between the component maps from a regular SHD method, diffusion circular spectrum mapping (DCSM) method and the proposed RI-SHD method. The results indicate that the regular SHD maps vary significantly with the rotation of the diffusion-encoding scheme, whereas the maps of the DCSM and the proposed method remain unchanged. In particular, the (0,0)-th, (2,2)-th and (4,4)-th component maps from the RI-SHD method exhibited good consistency with the 0th, 2nd and 4th order maps of the DCSM method, respectively. Compared with the regular SHD methods used in HARD imaging, the proposed RI-SHD method is superior in characterizing the diffusion patterns of multiple fiber structures between different brain regions or across subjects.
本文提出了一种新的旋转不变球谐分解（SHD）方法，用于分析高角分辨率扩散（HARD）成像。常规的SHD方法已被用于表征通过HARD技术测量的表观扩散系数（ADC）轮廓的特征。然而，这些常规的SHD方法是旋转可变的，即谐波分量的幅度和/或相位会随着ADC轮廓的旋转而变化。我们基于扩散张量模型的旋转不变特性，提出了一种新的旋转不变SHD（RI-SHD）方法。该方法的基本思想是将测量的ADC轮廓重新定向到由每个成像体素中的扩散张量的三个特征向量确定的局部坐标系中，然后对ADC轮廓应用SHD。进行了模拟和体内实验以验证该方法。对常规SHD方法、扩散圆谱映射（DCSM）方法和所提出的RI-SHD方法得到的分量图进行了比较。结果表明，常规SHD图随扩散编码方案的旋转而显著变化，而DCSM和所提出方法的图保持不变。特别是，RI-SHD方法的（0,0）阶、（2,2）阶和（4,4）阶分量图分别与DCSM方法的0阶、2阶和4阶图表现出良好的一致性。与HARD成像中使用的常规SHD方法相比，所提出的RI-SHD方法在表征不同脑区之间或不同受试者之间多个纤维结构的扩散模式方面更具优势。
