A Novel Parameter Estimation Method for Drug Diffusion, Distribution and Clearance in the Rat Brain Extracellular Space

Abstract

Purposes to estimate parameters for gadolium-diethylenetriaminepentaacetic acid (Gd-DTPA) diffusion and distribution after drug delivery in the rat brain extracellular space (ECS). Methods An isotropic diffusion pattern in the homogeneous media was presumed for Gd-DTPA diffusion in the rat brain ECS, and a mathematical model was established to describe the pharmacokinetics of Gd-DTPA. Results the analytical solution of the diffusion equation was obtained by Laplace transform, and the least square method was utilized to calculate the diffusion coefficient (D) and the clearance rate (k) of drugs in the sphere coordinates. Animal experimental data of Gd-DTPA-related intensity was acquired by magnetic resonance imaging (MRI). D and k were computed as 0.0129 mm2/h and 0.0957 /h, respectively. Conclusions By the proposed method, drug diffusion, distribution, and clearance in the rat brain can be quantitatively analyzed, which will enhance our understanding of drug delivery in the central nervous system.

Homogeneous orthogonal diffusion of drugs in the rat brain

“…In this study, the diffusion coefficients calculated along the three orthogonal axes were approximate to the coefficient (0.0129 mm 2 /h) of drugs isotropic diffusion in a homogeneous medium . The diffusion coefficient along the rostrocaudal direction was larger than the coefficient along the x ‐axes.…”

“…The diffusion coefficients of Gd‐DTPA molecules acquired in the rat brain were much lower than its diffusion coefficient (3.816 mm 2 /h) in the gel phantom (0.3% (w/v), 37°C), which demonstrated that the movements of Gd‐DTPA molecules were hindered severely. This is related to the characteristics of ECS in the rat brain.…”