Department of Neuroscience and Physiology, New York University School of Medicine, 550 First Avenue, New York, NY, 10016, USA.
Darmiyan Inc, 1 Sansome Street, Suite 3500, San Francisco, CA, 94104, USA.
Neurochem Res. 2020 Jan;45(1):42-52. doi: 10.1007/s11064-019-02793-6. Epub 2019 Apr 16.
The real-time iontophoretic method has measured volume fraction and tortuosity of the interstitial component of extracellular space in many regions and under different conditions. To interpret these data computer models of the interstitial space (ISS) of the brain are constructed by representing cells as Basic Cellular Structures (BCS) surrounded by a layer of ISS and replicating this combination to make a 3D ensemble that approximates brain tissue with a specified volume fraction. Tortuosity in such models is measured by releasing molecules of zero size into the ISS and allowing them to execute random walks in the ISS of the ensemble using a Monte Carlo algorithm. The required computational resources for such simulations may be high and here we show that in many situations the 3D problem may be reduced to a quasi-1D problem with consequent reduction in resources. We take the simplest BCS in the form of cubes and use MCell software to perform the Monte Carlo simulations but the analysis described here may be extended in principle to more complex BCS and an ISS that has a defined viscosity and an extracellular matrix that interacts with diffusing molecules. In the course of this study we found that the original analytical description of the relation between volume fraction and tortuosity for an ensemble of cubes may require a small correction.
实时离子电渗法已经测量了许多区域和不同条件下细胞外空间间质成分的体积分数和迂曲度。为了解释这些数据，构建了脑间质空间（ISS）的计算机模型，通过将细胞表示为基本细胞结构（BCS），并在其周围复制一层 ISS，从而构建一个 3D 组合体，该组合体以指定的体积分数近似脑组织。在这种模型中，迂曲度是通过将零尺寸的分子释放到 ISS 中，并使用蒙特卡罗算法允许它们在组合体的 ISS 中执行随机漫步来测量的。这种模拟所需的计算资源可能很高，在这里我们表明，在许多情况下，3D 问题可以简化为准 1D 问题，从而减少资源。我们采用最简单的 BCS 形式，即立方体，并使用 MCell 软件执行蒙特卡罗模拟，但这里描述的分析原则上可以扩展到更复杂的 BCS 和具有定义粘度和与扩散分子相互作用的细胞外基质的 ISS。在这项研究中，我们发现，对于立方体组合体，体积分数和迂曲度之间关系的原始解析描述可能需要进行微小的修正。
