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Purpose:  To build a mathematical model based magnetic resonance (MR) method to simulate drug anisotropic distribution  in vivo  in the interstitial space (ISS) of the brain.   Materials and Methods:  An injection of signal intensity-related gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA), which is an exogenous drug, was administered, and its diffusion was traced in the ISS of the brain using MRI. Dynamic MRI scans were performed to monitor and record the changes in signal intensity in each pixel of the region of interest. The transport parameters were calculated using the modified equation to simulate three-dimensional anisotropic diffusion, which was resolved using a Laplace transform and a linear regressive model.   Results:  After Gd-DTPA was introduced into the caudate nucleus, its distribution was demonstrated in real time. As the Gd-DTPA gradually cleared, the associated hyperintensity attenuated over time. The average diffusion coefficient (D) and the clearance rate constant (k) were (1.305 ± 0.364) × 10 −4  mm 2 /s and (1.40 ± 0.206) × 10 −5  s −1 , respectively.   Discussion:  The combination of trace-based MRI and modified diffusion mathematical models can visualize and measure the three-dimensional anisotropic distribution of drugs in the ISS of the brain.

Stimulation Modeling on Three-Dimensional Anisotropic Diffusion of MRI Tracer in the Brain Interstitial Space