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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)

   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

   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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3. 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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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. Reduced Model for Properties of Multiscale Porous Media with Changing Geometry

   https://doi.org/10.3390/computation9030028  

   Peszynska, Malgorzata ; Umhoefer, Joseph ; Shin, Choah ( March 2021 , Computation)

   null (Ed.)

   In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities. 

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