Modeling neuron growth using isogeometric collocation based phase field method

Abstract

We present a new computational framework of neuron growth based on the phase field method and develop an open-source software package called “NeuronGrowth_IGAcollocation”. 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. In this paper, 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. Through comparison with experimental observations, we can demonstrate qualitatively and quantitatively similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks.

NeuM: A Neuron‐Selective Probe Incorporates into Live Neuronal Membranes via Enhanced Clathrin‐Mediated Endocytosis in Primary Neurons

“…In summary, NeuM consistently stained healthy neurons across all stages of primary neuron development (Figure 5E). The representative NeuM‐stained neuron images vividly showcase characteristics specific to the five distinct stages of neurogenesis [43] are visible. NeuM effectively visualizes lamellipodia in stage 1, minor neurite projections in stage 2, axonal outgrowth in stage 3, dendritic outgrowth, and axonal growth cone development in stage 4, progressing up to full maturation in stage 5.…”

Quantitative evaluation of neuron developmental morphology in vitro using the change-point test

“…The novel application of the Change-Point Test, which was initially developed for studying animal walking paths, could also provide additional insight on factors that alter the neurite trajectories in future studies. In addition, quantifying the development of neuron morphology can inform parameters needed for computational simulations of neuron growth (Qian et al (2022)), materials transport (Li, Barati Farimani, and Zhang (2021); Li, Chai, Yang, and Zhang (2019)), and molecular traffic jams Zhang (2022a, 2022b)). More accurate computational models could help guide future in vitro studies by exploring experimental parameters in silico prior to costly and time intensive experimentation.…”

“…Nevertheless, these stages are still used as expected growth events when assessing cultures (Kaech and Banker (2006)). Neurite growth quantification is needed for consistent stage identification to monitor culture health, test intra-and extracellular sensory cues, and compare experiments and computational models (Liao, Webster-Wood, and Zhang (2021); Qian et al (2022)).…”

Survey of Optimization Algorithms in Modern Neural Networks

“…This optimization method is still used in approximation theory and machine learning. Various back propagation methods ( [23], [24], [25], [26]) are based on calculating of local partial derivatives, which rectify the value of weights of neural networks using (2). But such approach can be modified to others more effective versions, which converge to minimum faster.…”

“…The question of rising the accuracy of neural networks remains actual. There are many approaches applied for solving this problem: data augmentation [1], improving the mathematical model of neurons [2], adding complement neural network [3] and so on. Indeed, all this approaches resolve the problem of increasing the accuracy of neural networks particularly.…”