Sen Pabitra N, Basser Peter J
Schlumberger-Doll Research, Ridgefield, CT 06877, USA.
Biophys J. 2005 Nov;89(5):2927-38. doi: 10.1529/biophysj.105.063016. Epub 2005 Aug 12.
Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.
分子在大脑和其他组织中的扩散在广泛的生物过程和测量中都很重要，从药物递送扩散加权磁共振成像。扩散张量成像（DTI）是一种强大的非侵入性方法，用于在体内表征人类大脑中的神经元组织。作为理解测量的宏观表观扩散张量与潜在微观隔室几何形状和物理性质之间关系的第一步，我们将白质纤维束视为由相同的厚壁圆柱管组成的阵列，这些圆柱管以规则的晶格周期性排列，并浸没在外部介质中。我们考虑了正方形和六边形阵列。扩散分子在不同区域（即管的内核、膜、髓鞘以及外部介质内）可能具有不同的扩散系数和浓度（或密度）。分析结果用于探索一系列微观结构和成分参数对表观扩散张量和扩散各向异性程度的影响，从而能够表征正常生理条件下的扩散以及发育、疾病和衰老过程中发生的变化。在此建模框架的背景下，讨论了扩散张量成像以及从扩散加权磁共振数据原位估计微观结构参数的可能性。
