Ziener C H, Glutsch S, Jakob P M, Bauer W R
Julius-Maximilians-Universität Würzburg, Lehrstuhl für Experimentelle Physik 5, Würzburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046701. doi: 10.1103/PhysRevE.80.046701. Epub 2009 Oct 9.
We numerically solve the Bloch-Torrey equation by discretizing the differential operators in real space using finite differences. The differential equation is either solved directly in time domain as initial-value problem or in frequency domain as boundary-value problem. Especially the solution in time domain is highly efficient and suitable for arbitrary domains and dimensions. As examples, we calculate the average magnetization and the frequency distribution for capillaries and cells which are idealized as cylinders and spheres, respectively. The solution is compared with the commonly used Gaussian approximation and the strong-collision approximation. While these approximations become exact in limiting cases (small or large diffusion coefficient), they strongly deviate from the numerical solution for intermediate values of the diffusion coefficient.
我们通过使用有限差分在实空间中离散微分算子来数值求解布洛赫 - 托里方程。该微分方程既可以作为初值问题在时域中直接求解，也可以作为边值问题在频域中求解。特别是时域中的解效率很高，适用于任意域和维度。作为示例，我们分别计算了理想化为圆柱体和球体的毛细血管和细胞的平均磁化强度和频率分布。将该解与常用的高斯近似和强碰撞近似进行了比较。虽然这些近似在极限情况（小或大扩散系数）下变得精确，但对于扩散系数的中间值，它们与数值解有很大偏差。
