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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. [ABSTRACT FROM AUTHOR]

Neuron growth is a complex, multi-stage process that neurons undergo to develop sophisticated morphologies and interwoven neurite networks. Recent experimental research advances have enabled us to examine the effects of various neuron growth factors and seek potential causes for neurodegenerative diseases, such as Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis. A computational tool that studies the neuron growth process could shed crucial insights on the effects of various factors and potentially help find a cure for neurodegeneration. However, there is a lack of computational tools to accurately and realistically simulate the neuron growth process within reasonable time frames. Bio-phenomenon-based models ignore potential neuron growth factors and cannot generate realistic results, and bio-physics-based models require extensive, high-order governing equations that are computationally expensive. In this paper, we incorporate experimental neurite features into a phase field method-based neuron growth model using an isogeometric analysis collocation (IGA-C) approach. Based on a semi-automated quantitative analysis of neurite morphology, we obtain relative turning angle, average tortuosity, neurite endpoints, average segment length, and the total length of neurites. We use the total neurite length to determine the evolving days in vitro (DIV) and select corresponding neurite features to drive and constrain the neuron growth. This approach archives biomimetic neuron growth patterns with automatic growth stage transitions by incorporating corresponding DIV neurite morphometric data based on the total neurite length of the evolving neurite morphology. Furthermore, we built a convolutional neural network (CNN) to significantly reduce associated computational costs for predicting complex neurite growth patterns. Our CNN model adopts a customized convolutional autoencoder as the backbone that takes neuron growth simulation initializations and target iteration as the input and predicts the corresponding neurite patterns. This approach achieves high prediction accuracy (97.77%) while taking 7 orders of magnitude less computational times when compared with our IGA-C neuron growth solver. [ABSTRACT FROM AUTHOR]