Multi-physics modeling and finite-element formulation of neuronal dendrite growth with electrical polarization

Abstract

The neuron serves as the basic computational unit for the brain. Altered neuronal morphologies are usually found in various neurological diseases, such as Down syndrome, Williams syndrome, and idiopathic autism. Compelling biological evidence demonstrates that neuronal morphology can be dynamically regulated by neuronal activity through the mediation of calcium signaling pathways. Moreover, studies have revealed that exposure to an applied electric field can induce directional migration of neurites toward the cathode. In this study, we developed a coupled system that combines an advective Gray–Scott model with Gauss’s law to gain a better understanding of dendrite growth and response to electrical polarization. Our simulation results successfully capture key features such as dendrite branching, space-filling, self-avoidance, and electrical polarization. With the help of the convolutional neural network, we inversely identified model parameters of real dendrite morphologies from an online open source. Finally, we calibrated our model using experimental data on growing neurons under applied electric fields.

Statement of Significance: The work sheds light on the underlying mechanisms that govern the growth of neuronal dendrites under electrical polarization via mathematical modeling and numerical simulations. We also use a machine-learning technique to calibrate the model against real neuron images. Our numerical implementations and machine-learning pipeline provided online would benefit researchers in understanding the development of various abnormal neuronal morphologies and related neurological diseases.