Neuron geometry exhibits complex morphology, which is essential for neuronal functions and biochemical material transport. Many neurodegenerative diseases have been associated with the disruption of the material transport. Therefore, it is essential to study how the neurons control the transport process to deliver materials to the right destination without oversupply or shortage. In previous study, we developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations coupled with the Navier-Stokes equations, and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). To enable fast prediction of the transport process within complex neurite networks, we also developed a Graph Neural Networks (GNN) based model to learn the material transport mechanism from simulation data.&nbsp;&nbsp;In this talk, we will present our latest research on developing an IGA solver using partial differential equations (PDEs) constrained optimization (PDE-CO) model to study traffic jam during the material transport in neurites. The&nbsp;model is designed in particular to simulate the material transport process in healthy neurons and predict the formation of a traffic jam in abnormal neurons. The transport is controlled to avoid traffic jam of the material by minimizing a designed objective function. The optimization of the function subjects to a set of PDEs that describe the material transport process based on a macroscopic molecular motor assisted transport model of intracellular particles. Different simulation parameters are used to introduce traffic jam and study how neurons handle the transport issue. Note that the PDE-CO can be computationally challenging since the associated PDE needs to be solved at every iteration of the optimization. Here, we also propose to accelerate the optimization by integrating machine learning (ML) framework into the IGA solver. The ML framework learns the underlying physics from IGA simulation results and outputs essential gradient information used for the optimization. Given the input geometry and simulation parameters, the proposed ML-enhanced approach can perform and accelerate the optimization bypassing the time-consuming simulation.&nbsp;Reference:[1] A. Li, Y. J. Zhang.&nbsp;A PDE-constrained optimization model for the material transport control in neurons. In preparation, 2021.[2] A. Li, X. Chai, G. Yang, Y. J. Zhang.&nbsp;An Isogeometric Analysis Computational Platform for Material Transport Simulations in Complex Neurite Networks.&nbsp;Molecular &amp; Cellular Biomechanics, 16(2):123-140, 2019.[3] A. Li, R. Chen, A. B. Farimani, Y. J. Zhang.&nbsp;Reaction Diffusion System Prediction Based on Convolutional Neural Network.&nbsp;Scientific Reports, 10:3894, 2020.

Machine Learning Enhanced PDE-Constrained Optimization for Material Transport Control Simulation in Neurons

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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