# Quantitative Analysis of Molecular Transport in the Extracellular Space Using Physics-Informed Neural Network

arXiv: https://arxiv.org/abs/2401.12435 · HTML: https://mlsanity.com/paper/2401.12435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Learning with Known Operators reduces Maximum Training Error Bounds](https://mlsanity.com/paper/1907.01992/) (2019)
- [Investigating molecular transport in the human brain from MRI with physics-informed neural networks](https://mlsanity.com/paper/2205.02592/) (2022)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Physics-driven Synthetic Data Learning for Biomedical Magnetic Resonance](https://mlsanity.com/paper/2203.11178/) (2022)
- [Physics-informed neural networks for myocardial perfusion MRI quantification](https://mlsanity.com/paper/2011.12844/) (2020)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [GlymphVIS: Visualizing Glymphatic Transport Pathways Using Regularized Optimal Transport](https://mlsanity.com/paper/1808.08304/) (2018)
- [Bloch Equation Enables Physics-informed Neural Network in Parametric Magnetic Resonance Imaging](https://mlsanity.com/paper/2309.11763/) (2023)

## Abstract (arXiv)

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.