Zielinski Lukasz J, Sen Pabitra N
Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877-4108, USA.
J Magn Reson. 2003 Nov;165(1):153-61. doi: 10.1016/s1090-7807(03)00248-9.
We analytically compute the apparent diffusion coefficient D(app) for an open restricted geometry, such as an extended porous medium, for the case of a pulsed-field gradient (PFG) experiment with finite-width pulses. In the short- and long-time limits, we give explicit, model-independent expressions that correct for the finite duration of the pulses and can be used to extract the pore surface-to-volume (S/V) ratio as well as the tortuosity. For all times, we compute D(app) using a well-established model form of the actual time-dependent diffusion coefficient D(t) that can be obtained from an ideal narrow-pulse PFG. We compare D(app) and D(t) and find that, regardless of pulse widths and geometry-dependent parameters, the two quantities deviate by less than 20%. These results are in sharp contrast with the studies on closed geometries [J. Magn. Reson. A 117 (1995) 209], where the effects of finite gradient-pulse widths are large. The analytical results presented here can be easily adapted for different pulse protocols and time sequences.
我们通过解析计算，针对开放式受限几何结构（如扩展多孔介质），在有限宽度脉冲的脉冲场梯度（PFG）实验情况下的表观扩散系数(D_{app})。在短时间和长时间极限情况下，我们给出了明确的、与模型无关的表达式，这些表达式校正了脉冲的有限持续时间，可用于提取孔隙表面积与体积比（(S/V)）以及曲折度。对于所有时间，我们使用一种已确立的实际随时间变化的扩散系数(D(t))的模型形式来计算(D_{app})，该(D(t))可从理想窄脉冲PFG获得。我们比较了(D_{app})和(D(t))，发现无论脉冲宽度和几何相关参数如何，这两个量的偏差小于20%。这些结果与关于封闭几何结构的研究[《磁共振杂志A》117(1995)209]形成鲜明对比，在封闭几何结构的研究中，有限梯度脉冲宽度的影响很大。这里给出的解析结果可以很容易地适用于不同的脉冲协议和时间序列。
