GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transport

Neurons exhibit intricate geometries within their neurite networks, which play a crucial role in processes such as signaling and nutrient transport. Accurate simulation of material transport in the networks is essential for understanding these biological phenomena but poses significant computational challenges because of the complex tree-like structures involved. Traditional approaches are time-intensive and resource-demanding, yet the inherent properties of neuron trees, which consists primarily of pipes with steady-state parabolic velocity profiles and bifurcations, provide opportunities for computational optimization. To address these challenges, we propose a Graph-Autoencoder-based Latent Dynamics Surrogate (GALDS) model, which is specifically designed to streamline the simulation of material transport in neural trees. GALDS employs a graph autoencoder to encode latent representations of the network's geometry, velocity fields, and concentration profiles. These latent space representations are then assembled into a global graph, which is subsequently used to predict system dynamics in the latent space via a trained graph latent space system dynamic model, inspired by the Neural Ordinary Differential Equations (Neural ODEs) concept. The integration of an autoencoder allows for the use of smaller graph neural network models with reduced training data requirements. Furthermore, the Neural ODE component effectively mitigates the issue of error accumulation commonly encountered in recurrent neural networks. The effectiveness of the GALDS model is demonstrated through results on eight unseen geometries and four abnormal transport examples, where our approach achieves mean relative error of 3% with maximum relative error <8% and demonstrates a 10-fold speed improvement compared to previous surrogate model approaches.