3D neuron growth and neurodevelopmental disorder modeling based on truncated hierarchical B-splines with multi-level local refinements

TL;DR

This work addresses the inadequacy of 2D models for capturing 3D neurite morphologies and neurodevelopmental disorder dynamics by developing a 3D isogeometric analysis–phase-field framework built on truncated hierarchical B-splines (THB-splines). The approach integrates multi-level local refinements, adaptive domain expansion, and KD-tree transfer to simulate healthy neurite outgrowth and NDD-associated deterioration with high accuracy and efficiency. Key contributions include a 3D THB-spline–based discretization for phase-field neurite growth, specialized algorithms for 3D neuron identification and tip detection, and a dynamic domain expansion strategy enabling scalable simulations on HPC. The framework advances understanding of 3D neuron development and provides a computational platform for exploring therapeutic strategies by simulating complex morphologies and disorder-driven remodeling in 3D.

Abstract

3D neuron growth and neurodevelopmental disorders (NDDs) deterioration exhibit complex morphological transformations as neurites differentiate into axons and dendrites, forming intricate networks driven by tubulin concentrations and neurotrophin signals. Conventional 2D models fall short of capturing such morphological complexity, prompting the need and development of advanced 3D computational approaches. In this paper, we present a complex 3D neuron growth model based on isogeometric analysis (IGA) and the phase field method, utilizing locally refined truncated hierarchical B-splines (THB-splines). IGA offers isoparametric representation and higher-order continuity, which are essential for simulating the smooth, evolving interfaces of phase field neurites. In contrast, the phase field method can automatically handle diffuse interfaces and complex topological changes without explicit boundary tracking. This IGA-based phase field method enables accurate and efficient simulation of neurite extensions, branching, and retraction in a fully 3D setting. The THB-spline implementation supports multi-level local refinement, focusing computational resources on regions of active growth, while dynamic domain expansion adapts the simulation domain to extend with growing neurites. KD-tree-based interpolation ensures that phase field variables are accurately transferred onto newly refined meshes. NDDs associated neurite deterioration is simulated by modulating the driving force term within the phase field model to induce interface retraction. This comprehensive 3D framework enhances the accuracy of neurite morphology simulations, advancing the study of complex neuron development, network formation and NDDs.

Figures (8)

• Figure 1: Overview of 3D neuron growth computational model. (Orange Module) 3D model preprocessing and parallelization pipeline that handles local refinements and mesh preparations. (Green Module) 3D mesh domain expansion module that expands the domain as the neurites approach the boundary. (Red) 3D phase field solver that solves the phase field model to simulate neurite morphological transformations.
• Figure 2: 3D nested domains for constructing the THB-splines hierarchy based on $\Omega_l \supset \Omega_{l+1}$ for $l = 0, 1, ...$. Gray elements are selected for local refinements. In the context of $\phi$ interface-based local refinements for neuron growth, we use $\phi$ value to select refinement region.
• Figure 3: 3D phase field-based local refinements on THB-splines. (A) THB-splines with local refinements. (B) Cross-section view of three levels of refinement. (C) 3D phase field neuron growth variable $\phi$ on locally refined THB-splines.
• Figure 4: 3D tip detection visualizations. (A) Clipped view of $\phi$ on locally refined THB-splines with a zoomed-in view of the locally refined mesh. (B) Corresponding $\phi$ isocontour surface. (C) Detected 3D tips (purple isocontours) on the 3D neurites $\phi$ (grey isocontours).
• Figure 5: 3D neuron growth domain expansion. (A) Initial control mesh. (B) Domain expands directionally in positive $z$ axis as neurite grows towards the boundary. (C) Neurite continues to grow in positive $z$ direction and the domain expands again. (D) Neurite turns towards positive $x$ direction and domain expands in positive $x$ direction to accommodate growth.