We discuss some challenges and recent advances in understanding the macroscopic signal formation at high non-narrow magnetic field gradients at which both the narrow pulse and the Gaussian phase approximations fail. The transverse magnetization and the resulting signal are fully determined by the spectral properties of the non-selfadjoint Bloch-Torrey operator which incorporates the microstructure of a sample through boundary conditions. Since the spectrum of this operator is known to be discrete for isolated pores, the signal can be decomposed onto the eigenmodes of the operator that yields the stretched-exponential decay at high gradients and long times. Moreover, the eigenmodes are localized near specific boundary points that makes the signal more sensitive to the boundaries and thus opens new ways of probing the microstructure. We argue that this behavior is much more general than earlier believed, and should also be valid for unbounded and multi-compartmental domains. In particular, the signal from the extracellular space is not Gaussian at high gradients, in contrast to the common assumption of standard fitting models.

我们讨论了一些挑战和最新进展，以了解在高非窄磁场梯度下窄脉冲和高斯相位近似均失效时的宏观信号形成。横向磁化强度和产生的信号完全由非自伴​​Bloch-Torrey算子的光谱特性确定，该算子通过边界条件合并了样品的微观结构。由于已知该算子的频谱对于孤立的孔是离散的，因此可以将信号分解到算子的本征模上，从而在高梯度和长时间下产生拉伸指数衰减。此外，本征模位于特定的边界点附近，这使信号对边界更加敏感，从而开辟了探测微观结构的新方法。我们认为，这种行为比以前认为的要普遍得多，并且对于无边界和多隔室域也应有效。特别是，与标准拟合模型的常见假设相反，来自细胞外空间的信号在高梯度下不是高斯分布。