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1. Modeling intracellular transport and traffic jam in 3D neurons using PDE-constrained optimization

   https://doi.org/10.1093/jom/ufac007  

   Li, Angran; Zhang, Yongjie Jessica (March 2022, Journal of Mechanics)

   Abstract The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in three-dimensional complex geometries of neurons. The transport is controlled to avoid traffic jams of materials by minimizing a predefined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using the isogeometric analysis. Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by the reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neurons. 

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2. Deep Learning of Material Transport in Complex Neurite Networks

   Li, A; Farimani, A.B.; Zhang, Y.J. (January 2021, Scientific reports)

   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. 

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3. Deep learning of material transport in complex neurite networks

   https://doi.org/10.1038/s41598-021-90724-3  

   Li, Angran; Barati Farimani, Amir; Zhang, Yongjie Jessica (December 2021, Scientific Reports)

   null (Ed.)

   Abstract 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 $$120 \sim 330$$ 120 ∼ 330 times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks. 

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4. An Isogeometric Analysis Computational Platform for Material Transport Simulations in Complex Neurite Networks

   https://doi.org/10.32604/mcb.2019.06479  

   Angran Li, Xiaoqi Chai (January 2019, Molecular & cellular biomechanics)

   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 have developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solved the Navier-Stokes equations to obtain the velocity field of material transport in the networks. We then solved the transport equations using the streamline upwind/Petrov-Galerkin (SU/PG) method. Using our IGA solver, we simulated 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 discovered 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. 

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5. Generative Design of Multi-Material Hierarchical Structures via Concurrent Topology Optimization and Conformal Geometry Method

   https://doi.org/10.1115/DETC2019-97617  

   Jiang, Long; Chen, Shikui; Gu, Xianfeng David (August 2019, ASME IDETC/CIE 2019)

   Abstract Topology optimization has been proved to be an automatic, efficient and powerful tool for structural designs. In recent years, the focus of structural topology optimization has evolved from mono-scale, single material structural designs to hierarchical multimaterial structural designs. In this research, the multi-material structural design is carried out in a concurrent parametric level set framework so that the structural topologies in the macroscale and the corresponding material properties in mesoscale can be optimized simultaneously. The constructed cardinal basis function (CBF) is utilized to parameterize the level set function. With CBF, the upper and lower bounds of the design variables can be identified explicitly, compared with the trial and error approach when the radial basis function (RBF) is used. In the macroscale, the ‘color’ level set is employed to model the multiple material phases, where different materials are represented using combined level set functions like mixing colors from primary colors. At the end of this optimization, the optimal material properties for different constructing materials will be identified. By using those optimal values as targets, a second structural topology optimization is carried out to determine the exact mesoscale metamaterial structural layout. In both the macroscale and the mesoscale structural topology optimization, an energy functional is utilized to regularize the level set function to be a distance-regularized level set function, where the level set function is maintained as a signed distance function along the design boundary and kept flat elsewhere. The signed distance slopes can ensure a steady and accurate material property interpolation from the level set model to the physical model. The flat surfaces can make it easier for the level set function to penetrate its zero level to create new holes. After obtaining both the macroscale structural layouts and the mesoscale metamaterial layouts, the hierarchical multimaterial structure is finalized via a local-shape-preserving conformal mapping to preserve the designed material properties. Unlike the conventional conformal mapping using the Ricci flow method where only four control points are utilized, in this research, a multi-control-point conformal mapping is utilized to be more flexible and adaptive in handling complex geometries. The conformally mapped multi-material hierarchical structure models can be directly used for additive manufacturing, concluding the entire process of designing, mapping, and manufacturing. 

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