Neurons exhibit remarkably complex geometry in their neurite networks. So far, how materials are transported in the complex geometry for survival and function of neurons remains an unanswered question. Answering this question is fundamental to understanding the physiology and disease of neurons. Here, we develop an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We model the transport process by reaction-diffusion-transport equations and represent geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solve the Navier-Stokes equations to obtain the velocity field of material transport in the networks. We then solve the transport equations using the streamline upwind/Petrov-Galerkin (SU/PG) method. Using our IGA solver, we simulate material transport in three basic models of the network geometry: a single neurite, a neurite bifurcation, and a neurite tree with three bifurcations. In addition, the robustness of our solver is illustrated by simulating material transport in three representative and complex neurite networks. From the simulation we discover several spatial patterns of the transport process. Together, our simulation provides key insights into how material transport in neurite networks is mediated by their complex geometry.

To enable fast prediction of the transport process within the complex geometry of neurite networks, we develop a Graph Neural Networks (GNN) based model to learn the material transport mechanism from simulation data. In this study, we build the graph representation of the neuron by decomposing the neuron geometry into two basic structures: pipe and bifurcation. Different GNN simulators are designed for these two basic structures to predict the spatiotemporal concentration distribution given input simulation parameters and boundary conditions. In particular, we add the residual term from PDEs to instruct the model to learn the physics behind the simulation data. To recover the neurite network, a GNN-based assembly model is used to combine all the pipes and bifurcations following the graph representation. The loss function of the assembly model is designed to impose consistent concentration results on the interface between pipe and bifurcation. Through machine learning, we can quickly provide a prediction of material transport given a new complex neuron tree.

References:

\[1\] A. Li, X. Chai, G. Yang, Y.J. Zhang. An Isogeometric Analysis Computational Platform for Material Transport Simulations in Complex Neurite Networks. Molecular & Cellular Biomechanics, 16(2):123-140, 2019. 

\[2\] A. Li, R. Chen, A.B. Farimani, Y.J. Zhang. Reaction Diffusion System Prediction Based on Convolutional Neural Network. Scientific Reports, 10:3894, 2020.

\[3\] A. Li, A.B. Farimani, Y.J. Zhang. Deep Learning on the Material Transport in Complex Neurite Networks. In Preparation, 2020.


Material Transport Simulation in Complex Neurite Networks Using Isogeometric Analysis and Machine Learning Techniques - Part 2

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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