Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02215, USA.
Lund University, Lund, Sweden.
J Chem Phys. 2018 Feb 21;148(7):074109. doi: 10.1063/1.5014044.
The rate of water exchange across cell membranes is a parameter of biological interest and can be measured by diffusion magnetic resonance imaging (dMRI). In this work, we investigate a stochastic model for the diffusion-and-exchange of water molecules. This model provides a general solution for the temporal evolution of dMRI signal using any type of gradient waveform, thereby generalizing the signal expressions for the Kärger model. Moreover, we also derive a general nth order cumulant expansion of the dMRI signal accounting for water exchange, which has not been explored in earlier studies. Based on this analytical expression, we compute the cumulant expansion for dMRI signals for the special case of single diffusion encoding (SDE) and double diffusion encoding (DDE) sequences. Our results provide a theoretical guideline on optimizing experimental parameters for SDE and DDE sequences, respectively. Moreover, we show that DDE signals are more sensitive to water exchange at short-time scale but provide less attenuation at long-time scale than SDE signals. Our theoretical analysis is also validated using Monte Carlo simulations on synthetic structures.
细胞膜上水交换的速率是一个生物学上的重要参数，可以通过扩散磁共振成像（dMRI）来测量。在这项工作中，我们研究了水分子扩散和交换的随机模型。该模型使用任何类型的梯度波形为 dMRI 信号的时间演化提供了一个通用的解决方案，从而推广了 Kärger 模型的信号表达式。此外，我们还推导出了一种通用的 n 阶累积展开式，用于考虑水交换的 dMRI 信号，这在早期研究中尚未得到探索。基于这个解析表达式，我们为单扩散编码（SDE）和双扩散编码（DDE）序列的特殊情况计算了 dMRI 信号的累积展开式。我们的结果分别为 SDE 和 DDE 序列的实验参数优化提供了理论指导。此外，我们还表明，与 SDE 信号相比，DDE 信号在短时间尺度上对水交换更敏感，但在长时间尺度上衰减更少。我们的理论分析也通过对合成结构的蒙特卡罗模拟得到了验证。
