DECAY OF NUCLEAR MAGNETIZATION BY BOUNDED DIFFUSION IN A CONSTANT FIELD GRADIENT
DECAY OF NUCLEAR MAGNETIZATION BY BOUNDED DIFFUSION IN A CONSTANT FIELD GRADIENT
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DOI：
10.1063/1.467127
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发表时间：
1994-04-15
影响因子：
4.4
通讯作者：
SEN, PN
中科院分区：
文献类型：
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作者：
DESWIET, TM;SEN, PN
研究了在存在恒定场梯度的情况下在有界区域中扩散的自旋的横向磁化强度。我们研究了无界空间中恒定梯度中常用的哈恩回波振幅公式在短时间内的崩溃：M(2tau)/M(0) = exp(-2D0g2tau3/3)。这里 D0 是无界空间中的扩散常数，g 是场梯度乘以旋磁比。 我们发现这个公式被 M(2tau)/M(0) = exp[-2D(eff)g2tau3/3 + O(D0(5/2)g4tau13/2S/V)] 替换，有效扩散系数为 D(eff)(2tau) = D0[1-alpha 平方根 D0tau(S/V) + ...]，其中 alpha 是常数，S/V 是有界区域的表面积与体积之比。分解很复杂，但我们发现自然长度尺度 l(c) = (g/D0)-1/3 和区域几何形状之间的相互作用决定了问题。然后在预期纯 exp[-const t] 衰减的情况下考虑自由感应衰减和回波幅度的长期行为。我们考虑一些简单的几何形状，除了众所周知的结果之外，发现 In\M(z,t)\ 大约为 -D0g2R(p)4t，对于远小于 l(c) 的 R(p) 有效（其中 R(p) 是限制空间的大小），在 R(p) 远大于 l(c) 的区域中，衰减变为 ln\M(z,t)\ 大约为 -g2/3D0(1/3) t。然后我们认为后一个结果应该适用于更一般的几何形状。我们讨论了对实际实验回波测量的影响，并得出结论：g2/3D(0)1/3 衰减范围很难测量。还讨论了核磁共振显微镜中边缘增强效果的影响。
Transverse magnetization of spins diffusing in a bounded region in the presence of a constant field gradient is studied. We investigate the breakdown at short times of the much used formula for the Hahn echo amplitude in a constant gradient in unbounded space: M(2tau)/M(0) = exp(-2D0g2tau3/3). Here D0 is the diffusion constant in unbounded space and g is the field gradient multiplied by the gyromagnetic ratio. We find that this formula is replaced by M(2tau)/M(0) = exp[-2D(eff)g2tau3/3 + O(D0(5/2)g4tau13/2S/V)] with an effective diffusion coefficient D(eff)(2tau) = D0[1-alpha square-root D0tau(S/V) + ...], where alpha is a constant and S/V is the surface to volume ratio of the bounded region. Breakdown is complex but we find that the interplay between a natural length scale l(c) = (g/D0)-1/3 and the geometry of the region governs the problem. The long-time behavior of the free induction decay and echo amplitude are then considered where pure exp[-const t] decay is expected. We consider some simple geometries and find in addition to the well-known result, In\M(z,t)\ approximately -D0g2R(p)4t, valid for R(p) much less than l(c) (where R(p) is the size of the confining space) that in the regime R(p) much greater than l(c) the decay becomes ln\M(z,t)\ approximately -g2/3D0(1/3) t. We then argue that this latter result should apply to more general geometries. We discuss implications for realistic experimental echo measurements and conclude that the g2/3D(0)1/3 decay regime is hard to measure. Implications for the effect of edge enhancement in NMR microscopy are also discussed.