  Neurons exhibit complex geometry in their branched networks of neurites which
is essential to the function of individual neuron but also brings challenges to
transport a wide variety of essential materials throughout their neurite
networks for their survival and function. While numerical methods like
isogeometric analysis (IGA) have been used for modeling the material transport
process via solving partial differential equations (PDEs), they require long
computation time and huge computation resources to ensure accurate geometry
representation and solution, thus limit their biomedical application. Here we
present a graph neural network (GNN)-based deep learning model to learn the
IGA-based material transport simulation and provide fast material concentration
prediction within neurite networks of any topology. Given input boundary
conditions and geometry configurations, the well-trained model can predict the
dynamical concentration change during the transport process with an average
error less than 10% and 120~330 times faster compared to IGA simulations. The
effectiveness of the proposed model is demonstrated within several complex
neurite networks.
