Sukstanskii A L, Yablonskiy D A, Ackerman J J H
Department of Radiology, Biomedical MR Laboratory, Washington University, One Brookings Drive, St. Louis, MO 63130, USA.
J Magn Reson. 2004 Sep;170(1):56-66. doi: 10.1016/j.jmr.2004.05.020.
The local magnetization distribution M(x,t) and the net MR signal S arising from a one-dimensional periodic structure with permeable barriers in a Tanner-Stejskal pulsed-field gradient experiment are considered. In the framework of the narrow pulse approximation, the general expressions for M(x,t) and S as functions of diffusion time and the bipolar field gradient strength are obtained and analyzed. In contrast to a system with impermeable boundaries, the signal S as a function of the b-value is modeled well as a bi-exponential decay not only in the short-time regime but also in the long-time regime. At short diffusion times, the local magnetization M(x,t) is strongly spatially inhomogeneous and the two exponential components describing S have a clear physical interpretation as two "population fractions" of the slow- and fast-diffusing quasi-compartments (pools). In the long-diffusion time regime, the two exponential components do not have clear physical meaning but rather serve to approximate a more complex functional signal form. The average diffusion propagator, obtained by means of standard q-space analysis procedures in the long-diffusion time regime is explored; its structure creates the deceiving appearance of a system with multiple compartments of different sizes, while in reality, it reflects the permeable nature of boundaries in a system with multiple compartments all of the same size.
考虑在Tanner-Stejskal脉冲场梯度实验中，具有可渗透屏障的一维周期性结构产生的局部磁化分布M(x,t)和净磁共振信号S。在窄脉冲近似框架下，得到并分析了M(x,t)和S作为扩散时间和双极场梯度强度函数的一般表达式。与具有不可渗透边界的系统不同，信号S作为b值的函数，不仅在短时间范围内，而且在长时间范围内，都能很好地模拟为双指数衰减。在短扩散时间下，局部磁化M(x,t)在空间上强烈不均匀，描述S的两个指数分量具有明确的物理解释，即慢扩散和快扩散准隔室（池）的两个“总体分数”。在长扩散时间范围内，这两个指数分量没有明确的物理意义，而是用于近似更复杂的函数信号形式。探索了在长扩散时间范围内通过标准q空间分析程序获得的平均扩散传播子；其结构造成了一个具有不同大小多个隔室的系统的假象，而实际上它反映了一个具有相同大小多个隔室的系统中边界的可渗透性质。
