Calculation of the NMR signal behaviour inside physiological muscle tissue models is of high interest for human and biological studies. Both diffusion and susceptibility effects have to be considered to characterize the time evolution of the transverse magnetization. Herein, we demonstrate a novel discretization scheme which allows to semi-analytically solve the Bloch-Torrey equation efficiently using a Heisenberg-style Hamiltonian matrix. Angular eigenfunctions are calculated as Chebyshev polynomials which can be implemented without needing special functions. The method allows a correct calculation of both, the gradient echo free induction decay and the inhomogeneous relaxation rate $R_2^{\text{’}}$, over the whole diffusion range. We further provide an efficient implementation and demonstrate its use.

生理肌肉组织模型内部的NMR信号行为的计算对于人类和生物学研究非常重要。必须考虑扩散效应和磁化率效应来表征横向磁化的时间演化。在这里，我们展示了一种新颖的离散化方案，该方案可以使用海森堡式哈密顿矩阵有效地半解析布洛赫-托里方程。角本征函数计算为Chebyshev多项式，无需特殊函数即可实现。该方法可以正确计算梯度回波自由感应衰减和不均匀弛豫率${\mathrm{[R}}_2^{\text{'}}$在整个扩散范围内。我们进一步提供了有效的实施方式，并演示了其用法。