Hrabe Jan, Hrabetová Sabina, Segeth Karel
Center for Advanced Brain Imaging, Nathan S. Kline Institute, Orangeburg, New York 10962, USA.
Biophys J. 2004 Sep;87(3):1606-17. doi: 10.1529/biophysj.103.039495.
Tortuosity of the extracellular space describes hindrance posed to the diffusion process by a geometrically complex medium in comparison to an environment free of any obstacles. Calculating tortuosity in biologically relevant geometries is difficult. Yet this parameter has proved very important for many processes in the brain, ranging from ischemia and osmotic stress to delivery of nutrients and drugs. It is also significant for interpretation of the diffusion-weighted magnetic resonance data. We use a volume-averaging procedure to obtain a general expression for tortuosity in a complex environment. A simple approximation then leads to tortuosity estimates in a number of two-dimensional (2D) and three-dimensional (3D) geometries characterized by narrow pathways between the cellular elements. It also explains the counterintuitive fact of lower diffusion hindrance in a 3D environment. Comparison with Monte Carlo numerical simulations shows that the model gives reasonable tortuosity estimates for a number of regular and randomized 2D and 3D geometries. Importantly, it is shown that addition of dead-end pores increases tortuosity in proportion to the square root of enlarged total extracellular volume fraction. This conclusion is further supported by the previously described tortuosity decrease in ischemic brain slices where dead-end pores were partially occluded by large macromolecules introduced into the extracellular space.
细胞外空间的曲折度描述了与无任何障碍物的环境相比，几何结构复杂的介质对扩散过程造成的阻碍。在生物学相关的几何结构中计算曲折度很困难。然而，这个参数已被证明对大脑中的许多过程非常重要，从缺血和渗透压应激到营养物质和药物的输送。它对于扩散加权磁共振数据的解释也很重要。我们使用体积平均程序来获得复杂环境中曲折度的一般表达式。然后，一个简单的近似方法可以得出在许多二维（2D）和三维（3D）几何结构中的曲折度估计值，这些几何结构的特点是细胞成分之间存在狭窄通道。它还解释了在三维环境中扩散阻碍较低这一违反直觉的事实。与蒙特卡罗数值模拟的比较表明，该模型对许多规则和随机的二维和三维几何结构给出了合理的曲折度估计值。重要的是，研究表明，死胡同状孔隙的增加会使曲折度与扩大的总细胞外体积分数的平方根成比例增加。先前描述的缺血性脑切片中曲折度降低的情况进一步支持了这一结论，在缺血性脑切片中，死胡同状孔隙被引入细胞外空间的大分子部分堵塞。
