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Modeling traffic jam and growth process of neurons using isogeometric analysis and physics-informed neural network

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USMW02 - Mathematical mechanical biology: old school and new school, methods and applications

The motor-driven intracellular transport plays a crucial role in supporting a neuron cell’s survival and function, with motor proteins and microtubule (MT) structures collaborating to promptly deliver the essential materials to the right location in neuron. The disruption of transport may lead to the onset of various neurodegenerative diseases. To study how neurons regulate the material transport process and have a better understanding of the traffic jam formation, we develop a PDE -constrained optimization model and an isogeometric analysis (IGA) solver to simulate traffic jams induced by MT reduction and swirl. We also develop a novel IGA -based physics-informed graph neural network (PGNN) to quickly predict normal and abnormal transport phenomena in different neuron geometries. The IGA -based PGNN model contains simulators to handle local prediction of both normal and two MT-induced traffic jams in pipes, as well as another simulator to predict normal transport in bifurcations. Bézier extraction is adopted to incorporate the geometry information into the simulators to accurately compute the physics informed loss function with PDE residuals. Moreover, a GNN assembly model is adopted to tackle different neuron morphologies by assembling local prediction into the entire geometry. The well-trained model effectively predicts the distribution of transport velocity and material concentration during traffic jam and normal transport with an average error less than 10% compared to IGA simulations.   To model neuron growth, we develop a new computational framework and an open-source software package “NeuronGrowth_IGAcollocation” based on the phase field method. Neurons consist of a cell body, dendrites, and axons. Axons and dendrites are long processes extending from the cell body and enabling information transfer to and from other neurons. There is high variation in neuron morphology based on their location and function, thus increasing the complexity in mathematical modeling of neuron growth. We propose a novel phase field model with isogeometric collocation to simulate different stages of neuron growth by considering the effect of tubulin. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation, and dendrite formation considering the effect of intracellular transport of tubulin on neurite outgrowth. By incorporating neurite features from experiments, we can demonstrate similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks. Based on the IGA simulation data, a CNN model is also built to efficiently predict the growth process.   REFERENCES

Li, Y. J. Zhang. Isogeometric Analysis-Based Physics-Informed Graph Neural Network for Studying Traffic Jam in Neurons. Computer Methods in Applied Mechanics and Engineering, 403:115757, 2023. Li, Y. J. Zhang. Modeling Intracellular Transport and Traffic Jam in 3D Neurons Using PDE -Constrained Optimization.  Journal of Mechanics, 38:44-59, 2022. Li, Y. J. Zhang. Modeling Material Transport Regulation and Traffic Jam in Neurons Using PDE -Constrained Optimization. Scientific Reports, 12:3902, 2022. Qian, A. Pawar, A. Liao, C. Anitescu, V. Webster-Wood, A. Feinberg, T. Rabczuk, Y. J. Zhang. Modeling Neuron Growth Using Isogeometric Collocation Based Phase Field Method. Scientific Reports, 12:8120, 2022. Qian, A. S. Liao, S. Gu, V. Webster-Wood, Y. J. Zhang. Biomimetic IGA neuron growth modeling with neurite morphometric features and CNN -based prediction. Computer Methods in Applied Mechanics and Engineering, 2023.

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