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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40 mT/m的扩散敏感梯度磁场,扩散权重值为1 000s/mm2,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。
In order to study the influence of non-positive definite matrix on the derivation of diffusion tensor of water molecules, an optimization algorithm for calculating the derivation of diffusion tensor is proposed. Brain magnetic resonance diffusion tensor images of 5 healthy volunteers were collected, and diffusion-sensitive gradient magnetic fields of intensity 40 mT / m were applied in 25 directions with a diffusion weight of 1 000 s / mm2. The second order diffusion tensor. In the gray matter region less positive definite matrix, the corpus callosum knee and pressure found in a large number of non-positive definite matrix. Due to the influence of these non-positive definite matrices, the average diffusivity and anisotropy fraction obtained using conventional algorithms are underestimated and overestimated, respectively. To this end, the conventional algorithm is modified, and the diffusion tensor derived quantity is calculated using the absolute value of the matrix eigenvalue. The results show that the robustness and reliability of the diffusion tensor derived image obtained by the modified algorithm are improved.