中文摘要：

目的：采用磁共振示踪法模拟药物在脑细胞外间隙中的扩散、分布与清除过程,将获得的数据建立数学模型,对其分布相关参数进行拟合求解。方法：将示踪剂钆喷酸葡胺（gadolinium-diethylene triamine pentaaceticacidm,Gd-DTPA）作为外源药物注入大鼠脑细胞外间隙内,采用磁共振示踪法动态监测示踪剂在大鼠脑内的扩散、分布与清除,采用获得数据对药物在脑细胞外间隙中的各向同性分布建立包括扩散、清除及自分泌过程的生物数学模型,用Laplace变换法得到问题的解,并对实验观测数据进行数值微分处理后,在球坐标系中用线性回归的方法,给出包括药物在脑细胞外间隙中的扩散系数、清除率等参数估计方法。结果：将该方法用于动物实验数据,求得了实验动物的扩散系数D为（2.73±0.364）×10-4mm2/s,清除速率常数k为（1.40±0.206）×10-5/s。结论：本方法可较准确地反映药物在脑细胞外间隙中各向同性分布的规律,并可作为进一步解决药物在脑细胞外间隙中各向异性分布问题的基础。

英文摘要：

Objective： To build a mathematical model to simulate the drug distribution accompanying with diffusion, distribution and clearance in the brain extraeellular space （ECS）. Methods： Magnetic resonance imaging （MRI） technology was used to monitor changes in the signal-intensity-related tracer gadolinium-diethylene triamine pentaacetic acidm （Gd-DTPA） , as an external drug which was injected into the rat brain, and then the mathematical model was built by using the data to establish the diffusion, distribution and clearance process of Gd-DTPA in the brain ECS. The model equation was resolved by Laplace transform. In the sphere coordinates, the linear regressive model was adopted to obtain the esti- mation method of diffusion coefficient, clearance rate of drugs distribution in the brain ECS. Results： The diffusion coefficient D and the clearance rate k were obtained as （2.73 ±0. 364） × 10^（-4） mmE/s and （1.40±0. 206） × 10^（-5）/s, respectively. Conclusion： The proposed method can accurately reflect the isotropic drug distribution in the brain ECS, and can serve as the foundation to further solve problems about the orthotropic distribution in the brain ECS.