  The brain extracellular space (ECS), an irregular, extremely tortuous
nanoscale space located between cells or between cells and blood vessels, is
crucial for nerve cell survival. It plays a pivotal role in high-level brain
functions such as memory, emotion, and sensation. However, the specific form of
molecular transport within the ECS remain elusive. To address this challenge,
this paper proposes a novel approach to quantitatively analyze the molecular
transport within the ECS by solving an inverse problem derived from the
advection-diffusion equation (ADE) using a physics-informed neural network
(PINN). PINN provides a streamlined solution to the ADE without the need for
intricate mathematical formulations or grid settings. Additionally, the
optimization of PINN facilitates the automatic computation of the diffusion
coefficient governing long-term molecule transport and the velocity of
molecules driven by advection. Consequently, the proposed method allows for the
quantitative analysis and identification of the specific pattern of molecular
transport within the ECS through the calculation of the Peclet number.
Experimental validation on two datasets of magnetic resonance images (MRIs)
captured at different time points showcases the effectiveness of the proposed
method. Notably, our simulations reveal identical molecular transport patterns
between datasets representing rats with tracer injected into the same brain
region. These findings highlight the potential of PINN as a promising tool for
comprehensively exploring molecular transport within the ECS.
