中文摘要：

为研究非正定矩阵对水分子扩散张量导出量的影响，提出了一种计算扩散张量导出量的优化算法。采集5位健康志愿者脑部磁共振扩散张量图像，沿25个方向施加强度为40mT／m的扩散敏感梯度磁场，扩散权重值为1000s／mm^2，求解超定方程，得到了各体素的二阶扩散张量。在灰质区域非正定矩阵较少，在胼胝体的膝部和压部发现大量非正定矩阵。由于这些非正定矩阵的影响，使用常规算法得到的平均扩散率和各向异性分数分别被低估和高估。为此修正了常规算法，使用矩阵特征值的绝对值计算扩散张量导出量。结果表明，由修正算法得到的扩散张量导出量图像的鲁棒性及可靠性均得到提高。

英文摘要：

To evaluate the effect of the positive-indefinite matrix on the diffusion tensor-derived parameters, a modified algorithm is proposed for calculating these parameters. Magnetic resonance （MR） diffusion tensor images of five healthy volunteers are collected. The diffusion sensitive gradient magnetic fields are applied along 25 directions and the diffusion weighting value is 1 000 s/mm^2. Many positive-indefinite diffusion tensors can be found in the white matter area, such as the genu and the splenium of corpus callosum. Due to the positive-indefinite matrix, the mean diffusivity （MD） and the fractional anisotropy （FA） are under-estimated and over-estimated by using the conventional algorithm. Thus, the conventional algorithm is modified by using the absolute values of all eigenvalues. Results show that both the robustness and the reliability for deriving these parameters are improved by the modified algorithm.